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DOI: 10.1036/0071429069

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Contents

ACKNOWLEDGMENTS
INTRODUCTION

vii

ix

PART ON E

Assessing Your Current Wealth
FINANCIAL CALCULATOR:#1 How to Determine Your Net Worth3#2 How to Determine a Cash Inﬂows andOutﬂows Statement8#3 How to Formulate a Budget

12#4 Time Value of Money and What It Can Do for You

20#5 Simple Interest and How to Calculate It 22#6 Compound Interest and How to Determine Future Value

23#7 What You Need to Know About Nominal Versus Effective
Interest Rates and How to Calculate the Effective Rate
#8 Present Value and How to Calculate It

33#9 Annuities and How to Calculate Them

37

30

#10 How to Determine the Amounts
Needed to Fund Your Objectives

52#11 How to Reconcile Your Checking Account61#12 How to Prepare Your Records for Your Tax Accountantiii
Copyright 2003 by Esme Faerber. Click Here for Terms of Use.

68

iv

Contents

PART T WO

Managing Your Personal Wealth—Debt
FINANCIAL CALCULATOR:#13 Determine Your Debt Capacity75#14 How to Determine the Best Source of Credit

77#15 How to Determine the Annual
Percentage Rate Costs of Using Credit Loans

81#16 How to Determine the Rate ofInterest on Your Credit Cards#17 How to Manage Your Debt

90
94

#18 How Much of a Mortgage Can You Afford?

99#19 How to Calculate Your Monthly Mortgage Payment#20 How to Determine Your Mortgage Balance

103

107

#21 Determine Your Mortgage Balance
When Additional Principal Payments Are Made

111

#22 Adjustable Rate Mortgages and How They Work114

#23 Which Type of Mortgage Should You Choose?

121#24 When Should You Reﬁnance Your Mortgage?

125#25 Should You Rent or Buy a House?

127#26 What You Should Know
About Leasing a Car and How a Lease Works

131#27 Should You Buy, Lease, or Finance Your Car?

136

#28 How to Create a Simple Interest Loan Schedule

142

Contentsv

PART TH R EE

Managing Your Personal Wealth—Investments
FINANCIAL CALCULATOR:#29 Determine Your Investment Objectives#30 Determine Your Risk Tolerance

149

152

#31 How to Allocate Your Investments

158#32 How to Determine Your Equity Style in
the Selection of Individual Stocks

165#33 How to Determine Which Types ofBonds to Buy for a Portfolio

171#34 How to Rebalance Your Portfolio

175#35 The Rule of 72 and How to Use It to Determine
How Long It Will Take to Double Your Money

179#36 How to Assess and Balance Risk andReturn in the Choice of Different Investments

180#37 How to Calculate a Simple Rate of Return for
Stocks and Bonds

186#38 How to Determine a Rate of Return for a Mutual Fund
#39 How to Determine the Yield on Treasury Bills#40 How to Determine the Purchase andSelling Price of Treasury Bills197#41 How to Buy and Sell Treasury Securities
Directly from the Federal Reserve

201#42 How to Convert Municipal Bond Yields to
Before-Tax Yields

207

193

190

vi

Contents#43 Duration and How It Can Help You in
the Choice of Bonds for Your Portfolio#44 How to Value Bonds

211

217

#45 How to Value Common Stock220#46 How to Determine the Growth Rate of a Stock226#47 How to Analyze and Evaluate Your Common Stocks#48 How to Choose a Mutual Fund

246

#49 How to Determine the Tax Consequences of
Buying and Selling Shares in a Mutual Fund

254

#50 How to Determine the Average Cost in
Dollar Cost Averaging

259

PART FOU R

Planning for Your Future
FINANCIAL CALCULATOR:#51 How to Determine Your Future
Financial Needs and How to Fund Them

265

#52 How to Determine How Long Your Money
Will Last in Retirement and the Amount of the
Payment in a Systematic Withdrawal Plan
APPENDICES
INDEX

287

277

272

229

AcknowledgmentsT

he preparation of this book was greatly facilitated by many people atthe McGraw-Hill Publishing Company. Most notably, I am grateful for the
support of Stephen Isaacs and Kelli Christiansen. Rena J. Copperman and Linda
Gorman provided superb editorial assistance and were a pleasure to work with.
I am especially appreciative of their help.
My husband Eric and our children Jennifer and Michael were patient andsupportive, for which I am especially grateful.

vii
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IntroductionI

have always wanted to write a book that would be different from every
other book on the market. There are no basic money management books
that provide the tools and resources to determine and quantify answers topersonal financial situations and most people’s pressing financial problems. There are countless personal ﬁnance books on the market, but many
do not address how to quantify the speciﬁcs of each situation to make thedecisions that will help you achieve your ﬁnancial objectives and attain ﬁnancial freedom. To get answers about a speciﬁc issue, you would have to consult a textbook on the subject, which might not be tailored to the problem
facing you. Most people have never had any formal money management education, and this holds true for many of the current business graduates fromfour-year college and university programs. The Personal Finance Calculator
was written to bridge this gap and provide you with a practical set of tools
you can use not only to solve your ﬁnancial problems but also to better manage your ﬁnancial affairs.
Financial decisions form the basis of much of what we do in our lives.
Poorly thought out personal ﬁnance decisions can at best cause great anxiety and at worst lead to bankruptcy, whereas well thought out, sound ﬁnancial decisions can lead to a prosperous lifestyle. Now more than ever, we needto understand the complexities of our ﬁnancial circumstances to make sounddecisions. We are confronted by countless ﬁnancial decisions in our daily lives,
and this book provides a format to assist you in most, if not all, of yourdecision-making. Fifty-two different ﬁnancial calculators provide you withthe opportunity to take charge of your own ﬁnancial affairs. Each ﬁnancial
calculator has one or more worksheets with step-by-step instructions to assist
you in determining your answers to each of the ﬁnancial questions.

ix
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xIntroduction

The ﬁnancial tools in this book are arranged into four parts:
1. Assessing your current wealth
2. Managing your debt
3. Managing your investments
4. Planning for your future
Using the ﬁnancial calculators in each section, you will be able to:• Determine how much money you have, how much you owe, andhow to better control your ﬁnances• Use the time value of money calculations to make better ﬁnancial
and investment decisions• Formulate a plan to manage your debt by using credit wisely• Figure out how much your debt is costing you and how to choose
the least costly form of ﬁnancing• Determine whether you should buy or rent a house• Determine whether to buy, ﬁnance, or lease a car.
• Set investment objectives, make asset allocation plans, and measure
the returns on different investments• Determine your needs in retirement
The ﬁnancial tools presented in this book allow you to work through theseand other personal ﬁnancial problems that you are likely to encounter in managing your personal ﬁnances. Most personal ﬁnance decisions involve choices,and making the right choice most of the time involves more than intuition
and guesswork. By working through the different calculations, you will be able
to make informed decisions, which in many cases may save considerable
amounts of money over time. Keep in mind, however, that decision-making
is an ongoing process that will affect your current and future choices.
Each of the ﬁnancial tools in the four parts can be read and used individually, except for those calculations involving the time value of money. Readthe sections on the time value of money, simple interest, compound interest

Introductionxi

and future value, present values and annuities (sections 4, 5, 6, 8, and 9) ﬁrst
for an understanding of the subject matter before attempting to use any of
the calculations. Understanding the basis of present and future values is helpful in determining the price of a bond. Similarly, understanding annuities can
assist you in the calculation of a monthly mortgage payment and the determination of a mortgage schedule. There are many software programs andﬁnancial calculators that can assist you in your calculations, obviating the needto crunch numbers with pen and paper. Reading the text can help you determine what ﬁgures to punch into these programs.
By successfully managing your personal ﬁnance decisions, you will manage and increase your wealth.

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P A R T

O N E

ASSESSING YOUR
CURRENT WEALTH

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F I N A N C I A L C A LC U L ATO R # 1

How to DetermineYour Net WorthN

et worth is synonymous with your wealth at a single point in time.
It is the starting point for ﬁnancial planning and indicates your capacity to achieve your ﬁnancial goals. Your net worth can be ascertained by drawing up a personal balance sheet, as shown in Worksheet 1.1. The process
consists of three steps:
1. List your assets (items of value that you own).
2. List your liabilities (amounts that you owe to others).
3. Subtract your liabilities from your assets; the difference is yournet worth.
This relationship is shown below:
Items of Value − Amounts Owed = Net WorthIn other words, if you sell all your assets and use the money to pay off
all your debts, what is left over is your net worth.

AssetsAssets are arranged in order of liquidity; that is, the ability to convert theminto cash without losing much in the conversion. The most liquid are at the
top of the list and include cash, checking accounts, money market securities, and money market mutual funds.

3

WORKSHEET 1.1 How to determine your net worth
AssetsCash
Checking account balance
Savings accounts/money market funds
Certiﬁcates of deposit
Current value of savings bonds
Cash surrender value of life insurance
Cash surrender value of annuities
Market value of investments
Mutual funds
StocksBonds
Other
Market value of IRA/Keoghpension/proﬁt sharing/401K
Market value of house/real estate
Investment property
Other
Automobile(s)Household furniture/appliances
Jewelry/precious metals
Collectibles
Loan receivables
Other
Total assets
Liabilities
Credit card balances
Bills outstanding
Auto loan balances
Taxes dueMortgage loans
Total liabilities
Net worth (assets minus liabilities)$ __________________________________________________________________________________________________________________________________________________________$ _______$ ___________________________________$ _______$ _______

Step 1 List all items of value starting with cash, investment assets, the current value of
your house, and possessions.
Step 2 List and total all liabilities.
Step 3 Subtract total liabilities from total assets.

Assessing Your Current Wealth5

Determining the value of your stocks, bonds, and mutual funds is easy.
The prices can be found in the ﬁnancial pages of a newspaper or obtained
from brokerage and mutual fund statements.
Determining the current value of pension funds may be more difﬁcult
if the pension fund provides amounts of future income to be received. Thismeans that for this type of plan, you would need to determine the present
value of the plan. The human resources or beneﬁts department of your company can provide this information.
If the cash surrender values of your whole life insurance policies andannuities are not shown on the latest statements you receive, call your insurance agent for this information.
Your home is likely to be your largest asset, so its value should not be overinﬂated or underinﬂated. The ﬁgure that you are looking for is the current
market value; that is, what someone would be willing to pay for your house.
Generally, the cost of the property is not particularly relevant if you haveowned your house for a long period of time. The most recent selling prices ofhouses similar to yours in your area are a good indicator of the likely market value of your house. Real estate brokers can also provide you with an estimate of the value of your house.
The value of cars can be obtained from used car price guides such as the
N.A.D.A. Ofﬁcial Used Car Guide and the Kelley Blue Book (www.kbb.com).
These guides can be found in most public libraries, or you can obtain the priceof your car from your bank, which should have copies of these guides.
Household furniture, clothing, and personal effects should be more conservatively valued so as not to overstate their value. In an actual sale of these
items, you might get far less than the estimated values.
Add the estimates of the value of all the items that you own and you
will have the total of your assets.

Liabilities

Begin by listing your most current debts, such as utility bills, telephone bills, andothers. Next, list the balances outstanding on your credit card debts and loans.

6

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

For most people, a home mortgage is their largest single debt outstanding. The amount to include is not the original amount of the loan but the current outstanding balance. The reason is because a part of the monthly payments
made to the lender over the duration of the mortgage reduce the outstanding balance of the loan. The current outstanding balance of the loan may beobtained directly from the lender or from mortgage statements from the lender.
You can also determine the balance yourself. See the ﬁnancial calculator in section 20, which explains how to determine your mortgage balance.
Add up all the amounts owed to others and you have the total of yourliabilities.

Net WorthYour net worth is the difference between the totals of your assets and liabilities. In other words, if you sold all your assets for the values stated and paid
off all your debts, the amount left over would be your net worth. Your net
worth should not be thought of as cash to be spent. Rather, it is a measureof a person’s ﬁnancial position as of the date of the personal balance sheet.
Can your net worth be a negative number? Yes, this is possible. If you havemore debt than total assets, you are technically insolvent. A continuation ofthis position may make it difﬁcult for you to pay off all your debts on a timely
basis, which could necessitate a declaration of bankruptcy.

Why Is Determining Net Worth Important?
Determining your net worth is the ﬁrst step in ﬁnancial planning and assessing your ﬁnancial wealth. Net worth changes on a daily basis, so it is not agood idea to focus on these changes, as net worth is not cash available for use.
Rather, net worth is a yardstick for comparing the changes in your ﬁnancial
position over a period of time. An increase in net worth over a period of time
is a favorable trend, and a decrease in net worth is a reduction in wealth.

Assessing Your Current Wealth

7

There are a number of ways to increase net worth:• Appreciation of assets (for example, a rise in the value of stocks,
bonds, mutual funds, and real estate).
• Reducing liabilities. This also reduces the amount of interest payments made to service the debt.
• Increasing your income, such as through salary and wage increases
and increases in investment income.
• Reducing the amount spent on living expenses.
The importance of increasing net worth is obvious, but the addition ofassets may not always increase your net worth. This is especially true for depreciating assets, such as automobiles, computers, stereo equipment, and the like.
Investment assets could also lose some of their value, as in the stock market
decline of 2000–2002. Paying off liabilities will also increase net worth if assets
remain the same.
Creating a personal balance sheet will assist you in tracking your personal
wealth over time and enable you to see relationships among the balance sheet
items. The relationship between liquid current assets and current liabilities
indicates the relative ease or difﬁculty in paying upcoming debts. This evaluation ratio is the current ratio and is determined as follows:
Current Ratio = Current Assets ÷ Current Liabilities

For example, if a person has $10,000 in liquid current assets and $5,000
in current liabilities, the current ratio is 2. This means that for every $1 in current debts, there is $2 in liquid assets. Generally, most current debts are repaid
from liquid current assets such as cash, savings accounts, and money market funds. In the event of unemployment or insufﬁcient liquid current assets
to cover current debt, longer-term investment assets would need to be liquidated to pay off the debt.
The other signiﬁcant relationship between balance sheet items is the debt
ratio, which is total liabilities divided by net worth:8

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

Debt Ratio = Total Liabilities ÷ Net WorthFor example, if a person has $100,000 in total liabilities and a net worthof $200,000, the debt ratio is 0.5.
By setting aside more money for savings and investment assets eachmonth, you will increase your worth. In general, if total current liabilities andtotal liabilities are reduced over time, your net worth will also improve andthis will be indicated by a lower debt ratio.

F I N A N C I A L C A LC U L ATO R # 2

How to Determine a
Cash Inflows andOutflows StatementOne good reason to draw up a cash inﬂows and outﬂows statement
is to see where your hard-earned money has gone. Many people complain that they earn large sums of money, but they never have anything left
over. Recording their expenditures is a ﬁrst step to taking control of their ﬁnancial affairs. Because earnings and living expenses also inﬂuence net worth, thisstatement, also known as an income statement, shows that change. The income
statement shows actual income and expenditures over a period of time,
whereas a balance sheet shows ﬁnancial position at a single point in time.
There are three easy steps to creating an income statement, as shown in Worksheet 2.1.
1. List income received during the time period.
2. List expenditures made during the time period.
3. Determine the surplus/deﬁcit of income over expenditures.

WORKSHEET 2.1 Determine your statement of cash inﬂows and cash outﬂows forthe period ____________, ended ____________
Income (cash inﬂows)
Gross salary/wages
Payroll taxes
Federal income taxes
State income taxes
FICA tax
Minus total payroll taxes
Net salary/wages
Interest/dividend income
Gain on the sale of stocks/
bonds/investment bonds
Tax refund
Receipts from pension/
retirement plans
Gifts/grants
Alimony/child support receipts
Other
Total income
Expenditures (cash outﬂows)
Auto expenses
Food
Telephone & utilities
Medical & dental expenses
Entertainment/recreation
Donations
Gifts
Other
Rent/mortgage payments
Credit card payments
Loan payments
Insurance premiums
House maintenance/repairs
Total expenditures
Cash surplus/deﬁcit__________________________________________________________________________________________________$ __________________________________________________________________________________________________$ _______$ _______

Step 1 List all sources of income for the period.
Step 2 List all the cash payments made during the period.
Step 3 Subtract expenditures from income. Cash surplus is positive and a deﬁcit negative.

10

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

Step 1: List All Sources of Income
List all sources of income for the period of the income statement (one month,three months, six months, or one year). Income from wages and salaries isgenerally received net of payroll tax withholdings. In other words, taxes aretaken out of your gross income, leaving you with income after taxes. Someforms of income are paid gross of taxes (in other words, no payroll taxes
are withheld). If these sources of income are large, you would need to estimate the quarterly federal and state tax payments that you need to make.
Quarterly tax payments are made to avoid the possibility of being assessed
penalties for underestimating your federal and state taxes at the end of thetax year.
The main source of income for most people comes from what is earned fromtheir occupations in the form of salaries, wages, self-employment income, andcommissions. Other sources of income include bonuses, interest, dividends, rent,
alimony and child support payments, income from Social Security, gains on
the sale of assets, and gifts and inheritances. All sources of income should be
included in order to make the income statement complete and accurate.

Step 2. List All Expenditures
Expenditures show where cash ﬂows have been spent. The types of expenditures to include in the income statement will depend on the complexity ofyour ﬁnancial affairs. Major categories of expenditures should be listed, but
it is not necessary to account for every penny spent. By reviewing checkbook records and credit card statements and performing the more difﬁculttask of tracing cash payments, you can easily develop categories of expenditures. By adding the payments made in each category, you will have a fairly
accurate account of where your money has gone.
Certain expenditures are ﬁxed; that is, they remain the same each monthor year. Examples are rent, mortgage payments, life insurance premiums, andchild care payments.

Assessing Your Current Wealth

11

Variable expenditures are payments and expenses that change frommonth to month, such as food, clothing, medical, dental, gas, and auto
expenses; telephone and utility payments; household operating expenses; contributions; and recreational expenses.

Step 3: Determine Whether There Is a Surplus or
Deﬁcit of Net Cash Flow
When income exceeds expenditures, there is a surplus. When expenditures
exceed income, there is a deﬁcit. Funds to cover a deﬁcit can come from savings or a loan, both of which decrease net worth. A surplus represents anincrease to net worth if the amount is used to increase savings, acquire additional assets, and/or pay off debt.

What an Income Statement Can Tell You
The income statement shows whether you have been successful in living
within your income. If the amount saved is negligible or there is a deﬁcit, you
should review where you can make changes to your income and expenditures.
Income is difficult to increase in the short term, although it can be done;for example, by taking a part-time job. Longer-term income can be increased
by establishing yourself in your profession, ﬁnding a better-paying job, orchanging careers. The latter alternative should be deliberated carefully before
any moves are made.
Expenditures are also difﬁcult to reduce, but variable expenditures areeasier to cut than ﬁxed expenditures. For example, it may be easier to reduce
recreation, summer vacation, and/or entertainment expenses than necessary living expenses, such as food, mortgage, auto, and utility expenses.
By going through the process of compiling an income statement, you cansee where money has been spent and where you need to reduce expenditures,
if necessary. The income statement is not only an important tool in helping
to understand current spending patterns, it also assists in formulating a budget.

12

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

F I N A N C I A L C A LC U L ATO R # 3

How to Formulate a Budget“Cheshire Puss,” Alice began . . . “would you please tell me which way
I ought to go from here?”“That depends,” said the cat, “on where you want to get to.”Lewis Carroll, Alice in WonderlandAbudget is a plan for how you intend to spend your money during
the coming month, months, or year. It is an integrated statement basedon details of your income statement and balance sheet for the past month,
months, or year and a reﬂection of your ﬁnancial goals. It expresses what you
would like to achieve in terms of spending and savings in the future.
A budget can assist you in determining whether:• You are living within your income limits• Your current spending patterns are satisfactory• You are saving and investing sufﬁcient amounts to satisfy your ﬁnancial goals• You need to make changes in order to satisfy your ﬁnancial goals
A suggested budget format is shown in Worksheet 3.1. You can use thisas a model for your own budget sheets, or you can make several copies to allow
you to project your budget for several months into the future. There are many
personal ﬁnance software programs, such as Quicken and Microsoft Money,
that make it easy to compile a budget using your personal computer.
A budget can be drawn up in six easy steps:
1. Estimate your future net income for the period of the budget.
2. Determine your expected expenditures during the period of thebudget.

WORKSHEET 3.1 How to develop a budget
IncomeBudgeted

ActualVariance

Step 1
List expected
income from all
sources forthe period.

Net salaryBusiness proﬁt(Net)
Dividends/interest
Capital gains
Gifts received
Total income______________________________________________________________________________________________________________________________

Step 2
List all expected
expenditures forthe period.

Expenditures
Food
Clothing
Utilities
Mortgage/rentHome maintenance/
repairs
Medical/Dental
Auto loan
Auto expenses
Insurance payments
Real estate taxes
Recreation/entertainment
Vacation
Donations/gifts
Child care payment
Other
Total

___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Step 3
List all expectedamounts to fundgoals.

Goals
Emergency fundNew car
Savings–investment
Retirement fund
Total

Step 4
Determinewhether there is adeﬁcit or surplus.

Surplus/deﬁcit
Income lessexpenditures
Cash deposit/
withdrawal

Step 5
Record actual income and expenditures todetermine variances.

Step 6
Evaluate whether changes in spending
and savings are necessary.

14

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

3. Determine what you expect to spend to fund your personal goals.
4. Determine whether there is a surplus or a deﬁcit.
5. Record your actual income and expenditures.
6. Evaluate whether changes in spending and saving are necessary.

Step 1: Estimate Your Future Income
Estimated income includes all anticipated receipts of money, such as futuresalary, estimated proﬁts (or losses, which are deductions from income) froma business, bonuses, commissions, interest, dividends, rent, gains, tax refunds,
loans, and other sources of income.
Wages, salary, and/or partnership/corporate income should be included netof payroll taxes. Payroll tax deductions can be shown in the income section or
the expenditure section. An example of these deductions is shown in Figure
3.1. Mr. X is expecting a 5 percent increase in salary for the coming year and Mrs.
X expects her business income to be $36,000 for the coming year. The expected
gross income for Mr. X is shown, along with the deductions withheld to givehis net monthly income. Payroll tax withholdings are the amounts deductedby an employer from employees’ paychecks to pay their taxes. The amount ofincome earned and the number of exemptions ﬁled by the employee on Form
W-4 determines how much is withheld for federal income taxes.
Self-employed workers receive income that is not subjected to payroll tax
withholdings. This does not mean that they do not have to pay taxes on thisincome. The tax laws require such taxpayers to estimate their tax liability andpay it in quarterly installments by April 15, June 15, September 15, and January 15 for the tax year. The amount of these payments depends on a person’s
total income from all sources, deductions, exemptions, and credits, which
determine taxable income.
Mrs. X estimates that her monthly gross budgeted income will be $3,000.
Mrs. X would have to make quarterly estimated tax payments to the U.S. Treasury on this business income and, depending on the requirements of the statein which she lives, to the state as well.

Assessing Your Current Wealth

15

FIGURE 3.1 Budgeted monthly income for Mr. and Mrs. X

Salary Mr. X
Less withholdings
Federal income tax
Social security tax
Medicare tax
State tax
Net salaryBusiness proﬁt Mrs. X
Less estimated taxes
Federal tax
State tax
Net business proﬁt

Budgeted
annualActualannualBudgetedmonthly

Actualmonthly$54,000________$4,500________(4,800)(3,348)(783)(1,512)$43,557________________________________________

(400)
(279)
(65)
(126)
$3,630________________________________________$36,000________$3,000________(3,000)(1,008)$31,992________________________

(250)
(84)
$2,666________________________

Income from sales commissions may be difﬁcult to estimate, as they may
be irregular or seasonal. Being conservative by underestimating budgetedincome may be prudent in order to avoid overspending and, consequently,
having to dip into cash accounts.

Step 2: Determine Your Expected Expenditures
The second step is to estimate all expenditures during the period of the budget.
Certain expenditures such as rent, mortgage, and auto loan payments are ﬁxed
in amount and do not vary from month to month, whereas other expenditures such as food, clothing, and utilities do vary in amount from month tomonth. Anticipating these variable expenditures with accuracy may be difﬁcult. The purpose of budgeting is not to put you in a straitjacket in which you

16

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

cannot maneuver. On the contrary, its purpose is to provide you with ﬂexibility in your ﬁnancial planning so you can achieve your ﬁnancial goals.

Step 3: Determine Your Financial Goals
In order to set aside money for your ﬁnancial future, you need to estimate theexpenditures that go toward your savings and investments. Financial goals
vary from person to person over time. Some ﬁnancial goals are:• Saving for an emergency fund
• Increasing savings and investments• Buying a new car• Paying off a loan
• Buying a house• Buying a larger house• Saving to fund children’s education• Providing retirement income• Saving for annual vacations
Some of these are short-term goals while others are longer term. It is
often easier to concentrate on the short-term goals and neglect longerterm goals. By assigning priorities to each of the goals and quantifying
their cost, you can determine the amount of savings needed to fund them.
Figure 3.2 contains an example of Mr. and Mrs. X’s goals and the amounts
needed to achieve them.
Column 1 shows the estimated amount of money needed to fund eachgoal, while column 2 lists each goal’s priority. Buying new furniture is the lowest of Mr. and Mrs. X’s priorities. Column 3 shows when the expenditures will
be needed. For example, they hope to buy a new car in 12 months; be able
to fund their children’s education in 15 years (180 months); retire in 30
years (360 months); and buy new furniture in two years (24 months).

Assessing Your Current Wealth

17

FIGURE 3.2 Mr. and Mrs. X’s personal ﬁnancial goals

Goals
New carChildren’s
college fundRetirement
fund
New furniture

(1)

(2)

Estimated
cost

Priority(3)
Time
needed(mos.)(4)(5)
Monthly amountMonthly using time value
amountof money$24,000

1

12$2,000.00$1,972.65

100,0002

180

555.56343.46600,000
5,000

3
4

360
24

1,666.67
208.33$4,430.56

597.30202.41$3,115.82

Column 4 shows the monthly amount needed to ﬁnance each goal, calculated as follows:
Monthly Amount = Estimated Cost ÷ Time Needed

In order to have funds to buy a new car for $24,000 in a year’s time, Mr.
and Mrs. X will need to save $2,000 a month for the next year. If they were
to fund all their goals, they would need to save $4,430.56 per month.
The astute reader is apt to disagree on that amount and argue that the Xs
will need to save less per month due to the fact that the monthly amounts will
be invested, which will earn a return. That is correct. Assuming a conservative rate of interest of 3 percent for short-term goals and 6 percent for longerterm goals, Mr. and Mrs. X would need to save $3,115.82 per month to fund
all four goals (column 5). See the time value of money calculator (section 4)
to determine how to calculate these amounts.
Realistically, however, Mr. and Mrs. X would have to save more than theamount in column 5 to fund all their goals because of two factors: income
taxes and inﬂation. Mr. and Mrs. X will have to pay taxes on their interest
income and inﬂation will push up future prices.

18

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

Step 4: Determine Whether There Is a
Surplus or a Deﬁcit
If budgeted amounts for income exceed expenditures, there is a surplus.
Expenditures and the amounts needed to fund personal goals added together
equal the total expected expenditures. It is a good idea to incorporate goals
into a budget so that monthly or periodic income is set aside to address them.
When projected income exceeds projected expenditures, there will be additional amounts of cash, which can then be added to savings/investment plansor used to pay down liabilities.
When projected expenditures exceed projected income, there is a deﬁcit.
This means additional amounts will have to be withdrawn from savings/
investment plans to pay for these additional expenditures. In such a case, it
may be necessary to review projected expenditures and reduce some of them,or look for ways to increase projected income.

Step 5: Record Actual Income andExpenditures for the Period Budgeted
Actual amounts earned and spent are not always the same as those projected.
By recording the actual amounts and comparing them with the budgetedamounts, you can immediately see the differences, called variances. Spending
more than a budgeted amount for one item can be offset by spending less thanthe budgeted amount for another item.
Similarly, if actual income exceeds actual expenditures, there is a surplus,
which means additional cash. The opposite is a deﬁcit, which means that cash
will have to be withdrawn from cash savings or other assets in order to pay
for the deﬁcit spending.

Assessing Your Current Wealth19

Step 6: Evaluate Whether Changes in the
Budget Are Necessary
If there are large variances, or your surplus/deﬁcit is not what you would like,you need to analyze your budget. Examine the variances and study where theamounts spent are greater than the budgeted amounts. For example, if your actual
utility bills are consistently greater than the amounts budgeted, then you need toeither reduce your utility usage, if possible, or increase the amount budgeted
for this item. When you increase planned spending, you will need to ﬁnd items
where you can make corresponding cuts to compensate for the increases. If
you don’t, the amounts set aside for personal goals or savings will be reduced.
There are certain expenditures over which you have some degree of control. These are your variable expenditures, such as entertainment and miscellaneous expenses. Entertainment and food are the most common areasof overspending, particularly when they involve eating out at restaurants.
By contrast, ﬁxed expenditures such as rent, mortgage payments, taxes, andinsurance premiums cannot be easily trimmed without undue consequences.
Deﬁcit spending may be more difﬁcult to remedy when you have already
reduced many of your unnecessary and variable expenditures. It then becomes
more difﬁcult to cut essential spending items. If spending still exceeds income
after revising spending amounts, you need to reevaluate your entire budget.
Perhaps you have created too tight a straitjacket for yourself. Revise your goals
and set aside amounts to attain them before allocating the rest of your income
to your expenditures. You may need to prioritize your expenditures to see
which are necessary and which can wait.
The purpose of a budget is to help you plan the use of your resources
so that you can fund your goals and set aside more of your money to savings.
Following your budget will help you achieve what you want most from yourresources.

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

F I N A N C I A L C A LC U L ATO R # 4

Time Value of Money andWhat It Can Do for YouT

he time value of money is one of the most important concepts in personal ﬁnance decision-making. Money does not have the same value overtime due to the fact that it earns interest. Consequently, a dollar today is not
the same as a dollar in the future even if it is the same physical dollar bill notethat is presented. Investing that dollar today yields an amount greater thanthe dollar in the future. Put another way, the rate of interest is the bridgethat links present and future values. Similarly, a dollar expected in the future
can be discounted at the rate of interest to yield a present value, which isless than a dollar.
The time value of money is equally important in decision-making withregard to annuities, which are a series of payments as opposed to a single payment. Suppose you win the lottery and you are given the option of receiving$50,000 a year for 20 years or taking a lump sum now of $623,110.52. Whatshould you do? If you can earn more than 5 percent on your investment,
you should take the lump sum of $623,110.52. If you are not able to earn asmuch as 5 percent, you are better off taking the $50,000 per year for 20
years. Bear in mind that this decision is based solely on the time value ofmoney and that taxes have not been considered. In real life, this would be
the first step; then you would look at the differential taxes involved witheach alternative to come to a decision as to whether to take a lump sum
now or receive a series of payments into the future.
The impact of the time value of money is dependent on the following
three factors:
1. The amount of money
2. The annual rate of interest
3. The length of timeAssessing Your Current Wealth21

No doubt you are familiar with these factors from your school days when
you used them to determine the simple interest on an amount of money. Thesesame factors are also used in the determination of future values and present
values, using compound interest and discount rates, respectively. The ﬁnancial calculators that follow this section show you how easily these amounts
can be determined.
Another way to look at the time value of money is to view it as an opportunity cost. Spending rather than saving means lost interest. What you could
have earned on that money has been lost. It therefore becomes important toknow the interest rate on all your savings and investments to determine whether
you should be saving or spending your money. Worksheet 4.1 is helpful in

WORKSHEET 4.1 Determine the interest rates on your savings

Accounts
Checking account
Savings account
Savings account 2
Certiﬁcate of deposit
Certiﬁcate of deposit 2
Money market fundMoney market fund 2
Treasury bills
Treasury bills
Bonds
Bonds
Bonds
StocksStocksBond mutual funds
Stock mutual funds
Other
Other
Total

Amounts

Annual Rates
of Interest________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

determining the trade-off between savings and spending. Determining the rateof interest that you can earn on different investments makes it easier to compare your alternatives—to save or to spend. The ﬁnancial calculators that follow will help you determine the future values of these investments using thetime value of money.

F I N A N C I A L C A LC U L ATO R # 5

Simple Interest andHow to Calculate ItT

he most basic method of calculating interest is the simple interest method. The other, more common method of calculating interest is
the compound interest method (described in section 6).
Interest is the cost charged or payment made for the use of money. The
simple interest method calculates interest on the principal only without any
compounding. In other words, the interest earned is not used to earn further interest.
The elements used to determine simple interest are the principal, the rateof interest, and the length of time that the principal is invested or borrowed.
The formula for simple interest is as follows:
Interest = Principal Amount × Annual Interest Rate × Time Period

or
I=P×R×T

For example, $2,000 deposited for two years at 5 percent per annum
would earn $200 in simple interest ($2,000 × 2 × 0.05). The total amountreceived at the end of two years would be $2,200, the principal amount plus
the interest.

Assessing Your Current Wealth23

WORKSHEET 5.1 How to calculate simple interest
Principal amountP____________
Annual interest rateR____________
Time period of deposit or loan
T____________
Simple interest = P × R × T= ___________ × ___________ × ___________= $ ___________

The following example illustrates simple interest earned when the amountis deposited for less than a year. A principal amount of $2,000 is depositedin a certiﬁcate of deposit at an annual rate of 6 percent for six months. Theinterest is $60 ($2,000 × 0.06 × 6 ÷ 12).
The rate can be expressed in decimal form or as a fraction (0.06 or
6 ÷ 100, respectively). The time is shown in months (6 ÷ 12). It can also be
expressed in days (360 per year, used by banks, or 365 days). Worksheet 5.1 provides the framework for you to calculate simple interest on a deposit or loan.

F I N A N C I A L C A LC U L ATO R # 6

Compound Interest and How to
Determine Future ValueCompound interest differs from simple interest in that interest is paid
not only on the principal but also on the accumulated interest, assuming that the interest is left to accumulate. The greater the number of periods
for which interest is calculated, the greater the accumulation of interest earned
on interest plus interest earned on the principal.

24

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

The formula for compound interest is expressed as follows:
Future Value = Principal (1 + Interest Rate)n
FV = P (1 + i)nwhere
FV = Total future value (principal plus total compound interest)
P = Principal (amount invested)i = Interest rate per year or annual percentage raten = The number of periods at the interest rate
To illustrate the difference between simple and compound interest, assume
that $100 is invested at 5 percent per year for three years and the interest is notwithdrawn. If compounded annually, the compound interest earned would be$15.76, while the simple interest earned would be $15, as shown in Figure 6.1.
The principal amount of $100 is used to determine the interest in the simple interest method, whereas compound interest uses the principal plus theaccumulated interest from the previous year to calculate the interest for the
next year. Thus, when given a choice between investing in a simple interest orcompound interest account, you would choose compound interest, assuming
risk and all other factors are the same.
FIGURE 6.1 Simple interest versus compound interest
Simple interest
Year 1
Year 2
Year 3$100 × 5%; FV = $105.00$100 × 5%; FV = $110.00$100 × 5%; FV = $115.00

Total interest = $15.00
FV = Future value

Compound interest$100.00 × 5% = $5.00; FV $105.00$105.00 × 5% = $5.25; FV $110.25$110.25 × 5% = $5.51; FV $115.76
Total interest = $15.76

Assessing Your Current Wealth

25

There are easier ways of determining the compound interest than by going
through this tedious calculation: for example, by using a formula and pen,
paper, and a calculator; using ﬁnancial tables; using a ﬁnancial calculator withtime value of money keys; or using a personal ﬁnance software program. Mostof these methods for calculating future values are described in the following
pages. First, however, an important aspect of the compounding process needs
to be noted, and that is that compounding is not always done on an annual
basis. Banks and savings and loan associations may compound their accounts
on a semiannual, quarterly, daily, or continuous basis.
For example, if $10,000 is invested in a certiﬁcate of deposit (CD) for ﬁve
years at 6 percent compounded semiannually, there are 10 six-month periods
earning 3 percent each period. Similarly, if this same CD is compounded quarterly, then there are 20 three-month periods earning 1.5 percent each period.
The formula below includes modiﬁcations to take into account nonannual compounding periods:
FV = P(1 + i ÷ m)mn

where
FV = Total future value at the end of n periods
P = Principal or original amount invested
I = Annual compound interest rate
m = The number of times compounding occurs during the year
n = The number of years of compounding

Using Financial Tables to
Determine the Future Value
Future values can be determined by using the compound sum of $1 tablefound in Appendix A. You may ﬁnd it helpful to know how the values in thetable are computed.

26

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

TABLE 6.1 Determining the future value of $1
Year

FormulaFuture value

12
3(1 + 0.02)
1.02 (1 + 0.02)
1.04 (1 + 0.02)

$1.02
1.04
1.061

Assume that $1 is invested at 2 percent compounded annually for three
years. Table 6.1 shows the accumulated values.
The future value amounts in the right column in Table 6.1 are found in
the compound sum of $1 table in Appendix A under the 2 percent column,
the ﬁrst three rows indicating the ﬁrst, second, and third investment periods. Worksheet 6.1 illustrates how to determine the future value using ﬁnancial tables.
An example on page 27 illustrates the ease of using ﬁnancial tables todetermine the future value.

WORKSHEET 6.1 How to determine the future value using ﬁnancial tables
FV = P (1 + i ÷ m)mn
FV = _____ ( _____ ) ___FV = _____ ( _____ )FV = ____________
Step 1 Insert values into the formula.
Step 2 Find the row with the number of periods (mn) that the principal will be
invested in Appendix A.
Step 3 Find the column with the interest rate for the period (i ÷ m) that the principal
will be invested in Appendix A.
Step 4 The intersection of the row and the column locates the factor.
Step 5 Multiply the factor by the principal. The product is the future value.

Assessing Your Current Wealth27

How much money will you have if you deposit $2,000 in an account yielding 8 percent interest compounded quarterly for 10 years?
FV = P(1 + i ÷ m)mn
FV = 2,000(1 + 0.08 ÷ 4)(4 × 10)
FV = 2,000(1 + 0.02)40
FV = 2,000(2.208)
FV = $4,416

Using a Financial Calculator to
Determine the Future Value
Future value calculations can also be made using a ﬁnancial calculator. Witha ﬁnancial calculator it is easy to solve time value of money calculations if you
have any three of the four variables. The exact steps depend on the type of calculator. Most ﬁnancial calculators use the following format, but if there are
deviations consult your calculator’s manual.
Worksheet 6.2 shows the step-by-step use of a ﬁnancial calculator to determine the future value.
The previous problem can be solved using a ﬁnancial calculator. Whatis the future value of $2,000 invested at 8 percent compounded quarterlyfor 10 years?
Step 1 Key in quarterly payments instead of the default mode ofannual or monthly.
Step 2 Key in 40 as the number of payments into N.
Step 3 Key the interest rate of 8 percent into I.
Step 4 Enter the principal, $2,000, into the PV button.
Step 5 Press the FV button to calculate the future value, which isdisplayed as $4,416.08.

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

WORKSHEET 6.2 How to determine the future value using a ﬁnancial calculator
Most ﬁnancial calculators have the following keys:
N = Total number of compounding periods or payments
I = Interest
PV = Present value
FV = Future value
PMT = Annuity payment or receipt
Step 1 Key the number of compounding periods per year (annual,semiannual, etc.) into the calculator program.
Step 2 Key the number of payment periods for the investment into the
N button on the calculator.
Step 3 Key the interest rate into the I button.
Step 4 Key the principal into the PV button.
Step 5 Press the FV button to calculate the future value.

Using a Computer to
Determine the Future Value
With the popularity of personal computers, there are several programs thatcan be used to determine the future value. Worksheet 6.3 illustrates the use of
Microsoft’s Excel program and Quicken’s software.
Using Quicken software, click on the ﬁnancial planner.

WORKSHEET 6.3 Using a computer to determine the future value
Using Microsoft’s Excel spreadsheet, click on f *, which is on the top row of thetoolbar. A list of functions pops up. Highlight FV in the right-hand box and click
OK. A box comes up with ﬁve rows, as shown below.

Rate
Nper
Pmt
PV
Type
Using the previous example,
key in the numbers:
Rate
Nper
Pmt
PV
Type

Step 1 Enter the interest rate per period.
Step 2 Enter the total number of periods.
Step 3 Enter the payments made each period.
Step 4 Enter the principal or present value.
Step 5 Enter the value representing timingof the payment: 1 for payment at the
beginning of the period; 0 for payment at the end of the period.

.02
40
0
−$2,000
0

Formula result = $4416.079
Using Quicken software, click on the ﬁnancial planner.
Step 1 Select savings account.
Step 2 Enter information as shown in the boxes:
Opening savings balance$2,000

Annual yield

8%

Number of quarters

40

Contribution each quarter0

Ending savings balance$4,416.08

Inﬂation0%

Calculate
Step 3 Click on the calculate button.
Step 4 Ending savings balance is calculated and appears in the box ($4,416.08).

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

F I N A N C I A L C A LC U L ATO R # 7

What You Need to Know
About Nominal Versus
Effective Interest Rates and
How to Calculate the Effective RateW

hen given a choice between investing in a simple interest accountor a compound interest account, you would obviously choose compound interest. With simple interest only the principal is used to calculate interest, whereas compound interest uses the principal plus accumulated interest
to earn interest.
The difference between simple interest and compound interest is magniﬁed further when the rate of interest and/or the number of compounding
periods are increased. When the interest rate is doubled using compoundinterest, interest earned is more than doubled.
For example, if $1,000 is invested at 6 percent compounded annuallyfor 10 years, the interest earned is $791. A doubling of the interest rate to
12 percent compounded annually results in interest of $2,106, almost triple
the growth.
Carrying this example further, if the $1,000 is invested for 20 years(instead of 10) at 6 percent and 12 percent, the accumulated interest would
be $1,397 and $4,474, respectively. Thus, higher interest rates and a greater
length of time result in accelerated growth of interest.
In order to make the right decision with regard to investing or borrowing money, you need to make sense of the stated interest rates so that they arecomparable. Generally, banks do not quote their rates the same way. Somequote their rates for deposit accounts as compounded annually, while others quote their rates as compounded semiannually, quarterly, monthly, or daily.
You cannot compare accounts with different compounding periods unless
you convert them to a common compounding period, also known as anannual percentage rate (APR) or effective yield.

Assessing Your Current Wealth31

For example, consider one bank’s certiﬁcate of deposit offered at 7 percent compounded annually versus another offered at a second bank at 6.95
percent compounded monthly. These are nominal or stated rates and are
not comparable.
The more frequent the compounding, the greater the future value and theamount of interest that accrues. Thus, the effective rate is always greater than
the nominal rate when the compounding of interest is done more than once ayear. Table 7.1 provides a comparison of some nominal and effective rates.
As Table 7.1 shows, the nominal rate of interest is not the true rate if there
is frequent compounding within the year. Also important to note is that theeffective annual rate increases at a decreasing rate. For instance, the nominal
rate of 7 percent increases by 0.12 percent with semiannual compounding,then by a further 0.07 percent with quarterly compounding, and then by only
0.04 percent with monthly compounding.
Investors should choose savings and deposit accounts that offer the highest effective rates. In order to compare different rates, effective rates should becompared with other effective rates.

TABLE 7.1 A comparison of nominal and effective rates compounded annuallyand semiannually
Nominal ratecompoundedannually
Semiannually
5%
6%
7%
8%
9%

5.06%
6.09%
7.12%
8.16%
9.20%

Quarterly

Effective rates
Monthly

Daily

5.09%
6.13%
7.19%
8.24%
9.31%

5.12%
6.16%
7.23%
8.30%
9.38%

5.13%
6.18%
7.25%
8.33%
9.42%

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

How to Calculate the Effective Rate
The formula for calculating the effective rate is as follows:
Effective rate = (1 + I)f − 1

where
I = Interest rate per periodf = Compounding frequency
For example, if the nominal rate is 10 percent compounded quarterly, theeffective rate is 10.381 percent:Effective rate = (1 + I)f − 1= (1 + 0.025)4 –1= (1.10381) –1= 10.381%

Worksheet 7.1 provides the format for calculating the effective rate.

WORKSHEET 7.1 How to calculate the effective rate
Effective rate = (1 + I)f −1= (1 + ___) ___ −1= (_____) −1= _____
Step 1 Insert values into the formula.
Step 2 Add 1 to the interest per period and multiply to the power f. Subtract 1 to obtain
the answer.

Assessing Your Current Wealth

33

F I N A N C I A L C A LC U L ATO R # 8

Present Value andHow to Calculate ItInterest rates and time relate present and future values mathematically.
Future values focus on the movement of money forward in time. How much
will money grow in the future when compounded at a particular interest rate?
Present value is the opposite of future value. It is the movement of money
back in time to the present. How much is money to be received in the future
worth today? In other words, a future amount of money is discounted for aperiod of time to give an amount in today’s dollars.
The example in the future value ﬁnancial calculator (section 6) showedthat $100 invested at 5 percent compounded annually for three years grows
to $115.76. The reverse also applies: $115.76 to be received in three years
discounted at 5 percent compounded annually has a present value of $100.
The equation for determining the future value can be manipulated
algebraically to calculate the present value as follows:
FV = P(1 + i)nwhere
FV = Future value
P = Present value or principal
I = Interest per periodn = Number of periods that the principal earns interest
Divide both sides of the equation by (1 + i)n and you arrive at the formula for calculating the present value (P or PV):

PV =

FV
(1 + i)n34

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

Using Financial Tables to
Determine the Present Value
The present value of $1 table shown in Appendix B simpliﬁes the computation of the present value. The table eliminates the need to compute the present value interest factor (1 ÷ 1 + the interest rate to the power n) because
the computation is included in the table. Table 8.1 shows how the interest factors are computed in the ﬁnancial tables for 5 percent.
The present value amounts shown in the fourth column in Table 8.1
are found in the present value of $1 table in Appendix B under the 5 percent column, the ﬁrst three rows indicating the ﬁrst, second, and third discount periods. Worksheet 8.1 illustrates how to determine the present value
using ﬁnancial tables.
To illustrate the use of ﬁnancial tables, consider the following problem.
What is the present value of $10,000 to be received in 10 years discounted at
8 percent?
PV = FV(present value of 1 discounted at 8% for 10 years)
PV = $10,000(0.463)
PV = $4,630

Present value calculations can also be made using a ﬁnancial calculator.
As long as you have three of the four variables, you can solve for the fourth.
The exact steps for the calculation depend on the type of calculator.

TABLE 8.1 Determining the present value of $1
Discount period
123

Future value

FormulaPresent value$1111 ÷ (1 + 0 .05)
1 ÷ (1 + 0 .05)2
1 ÷ (1 + 0 .05)3
1

0.952
0.907
0.864

Assessing Your Current Wealth35

WORKSHEET 8.1 How to determine the present value using ﬁnancial tables
PV = FV (present value of 1 discounted at i% per period for n periods.)
PV = _____ ( _____ )PV = _____
Step 1 Insert values into the formula.
Step 2 Find the row for the number of discounting periods n in Appendix B.
Step 3 Find the column for the discount rate i.
Step 4 The intersection of the row and column locates the factor.
Step 5 Multiply the factor by the future value. The product is the present value.

Using a Financial Calculator to
Determine the Present Value
Worksheet 8.2 outlines the steps to determine the present value using a ﬁnancial calculator.
The following example illustrates these steps using a ﬁnancial calculator. What is the present value of $5,000 to be received in ﬁve years discounted
at 6 percent per annum?
Step 1 Key annual payments into the default mode of your calculator.
Step 2 Key in 5 as the number of discounting periods into N.
Step 3 Key the discount rate of 6 percent into I.
Step 4 Enter $5,000 into FV.
Step 5 Press the PV button, which calculates the answer: $3,736.29.

Using a Computer to Determine the Present Value
Microsoft’s Excel spreadsheet is used here to illustrate the ease of calculating
the present value on a computer, but there are other software programs that
can also be used. Worksheet 8.3 on page 37 illustrates the determination of
the present value with an example.

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

WORKSHEET 8.2 How to determine the present value using a ﬁnancial calculator
Most ﬁnancial calculators have the following keys:
N = Total number of discounting periods
I = Interest rate per period
PV = Present value
FV = Future value
PMT = Annuity payment or receipt
Step 1 Key the number of discounting periods per year (annual, semiannual, monthly)
into the default mode of the calculator.
Step 2 Key the number of discounting periods into the N button.
Step 3 Key the discount/interest rate into the I button.
Step 4 Key the future value into the FV button.
Step 5 Press the PV button to calculate the present value.

The present value of an amount is always less than the future value
because the future value is always discounted back to the present. The relationships in the discounting process are:
• The higher the discount rate, the lower the present value.
• The later the future payment or receipt is extended into the future,
the smaller the present value becomes.
• If the frequency of discounting is increased; for example, from annually to quarterly, the present value of an amount will decrease.

Assessing Your Current Wealth37

WORKSHEET 8.3 Using a personal computer to determine the present value
Using Microsoft’s Excel spreadsheet, click on f *, which is on the top row of thetoolbar. A list of functions pops up. Highlight ﬁnancial in the left-hand box and
PV in the right-hand box and click OK. A box comes up with ﬁve rows, as
shown below.
Step 1 Enter the interest rate per period.
Step 2 Enter the total number of periods.
Step 3 Enter the payments made eachperiod.
Step 4 Enter the future value.
Step 5 Enter the value representing timingof the payment: 1 for payment
What is the present value of $2,000 toat beginning of the period; 0 for
be paid in 4 years discounted at 8%?
payment at the end of the period.
Rate
Nper
Pmt
FV
Type

Rate
Nper
Pmt
FV
Type

.08
4
0
−$2,000
0

Formula result = $1,470.059

F I N A N C I A L C A LC U L ATO R # 9

Annuities and How to Calculate ThemT

here are many ﬁnancial situations that involve a series of payments orreceipts, such as loans, installment contracts, leases, pension and retirement
plans, and life insurance contracts. (For discussions of the future value andpresent value of a single principal amount, see sections 6 and 8, respectively.)An annuity is a series of equal payments or receipts made or received atregular intervals. These payments (receipts) can be made (received) at the
beginning or the end of a period. When payments are made at the end of a

38

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

FIGURE 9.1 Difference between an ordinary annuity and an annuity due
Ordinary annuity
An annuity of four payments of $1,000 made at the end of each year.
Payment
Year$1,000$1,000$1,000$1,000————————————————————————————
0
1
2
3
4

Annuity due
An annuity due of four payments of $1,000 made at the beginning of the year.
Payment
Year$1,000———————
0$1,000———————
1$1,000———————
2$1,000———————
3

4

period, it is called an ordinary annuity. When payments are made at the beginning of a period, it is called an annuity due. Figure 9.1 illustrates the difference between the two types of annuities.
As you might well infer from the time value of money, it is important torecognize the difference between an ordinary annuity and an annuity due. Withan annuity due, the payments (receipts) are made (received) earlier, and therefore have a greater present value and future value than an ordinary annuity.

Future Value of an Ordinary Annuity and Annuity Due
Future Value of an Ordinary Annuity

The future value of an ordinary annuity involves payments (receipts) of an
equal sum of money at the end of each period for a certain number of periods and allows the interest to accumulate over the total period of time. For
example, a deposit of $1,000 made at the end of every year for ﬁve years earning 6 percent will grow to $5,637.10, as shown in Table 9.1.

Assessing Your Current Wealth

39

TABLE 9.1 Future value of ordinary annuity of $1,000 compounded at 6% for 5 years
Year 1$1,0002$1,0003$1,0004$1,0005
FV end of 5 years$1,000$1,000.00
1,060.00
1,123.60
1,191.02
1,262.48$5,637.10

In Table 9.1 the future value of an ordinary annuity is found by compounding each deposit and summing the interest earned on the deposits. Thisannuity can also be expressed in equation form as follows:
FV = 1,000(1+ 0.06)4 + 1,000(1+ 0.06)3 + 1,000(1+ 0.06)2+ 1,000(1 + 0.06) +1,000= 1,262.48 + 1,191.02 + 1,123.60 + 1,060.00 + 1,000= $5,637.10
This calculation can be cumbersome if you don’t have a calculator or if thetime period is long. Financial tables can simplify the calculation, as shown
in Worksheet 9.1 using the same example. The future value of an ordinary
annuity table is shown in Appendix C.

40

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

WORKSHEET 9.1 How to determine the future value of an ordinary annuity usingﬁnancial tables
FV = PMT (FVIFA i, n)
Where
PMT = Annuity or regular payment/receipt
FVIFA = Future value interest factor of an annuity
i = Interest rate per periodn = Number of periods
FV = _____ (FVIFA _____)FV = _____ (_____)FV = _____
Example:PMT = $1,000
i = 6%n=5
FV = PMT (FVIFA i, n)
FV = 1,000 (FVIFA 6%, 5)
FV = 1,000 (5.637)
FV = $5,637
Step 1 Fill in the values.
Step 2 Fill in the FVIFA factor from Appendix C at intersection of i row and n column.
Step 3 Multiply the annuity by the interest factor to obtain the future value.

Future Value of an Annuity Due

The difference between an ordinary annuity and an annuity due is the timing of the payments/receipts. For an annuity due, the payments are made at
the beginning of the period.

Assessing Your Current Wealth

41

TABLE 9.2 Future value of annuity due of $1,000 compounded at 6% for 5 years
Year 0$1,0001$1,0002$1,0003$1,0004
FV end of 5 years$1,000$1,060.00
1,123.60
1,191.02
1,262.48
1,338.23$5,975.33

Using the same example as the one used for the ordinary annuity, thefuture value of an annuity due of $1,000 invested for ﬁve years at 6 percent
is $5,975.33, as calculated in Table 9.2.
With the future value of an annuity due, each deposit earns interest in
the period deposited, whereas with an ordinary annuity the last deposit
does not earn interest in the period deposited. In other words, the future valueof an ordinary annuity has one less interest earning period than the number of deposits.
Although it is possible to calculate the future value of an annuity due
by summing the interest calculations, as shown in Table 9.2, it is easier to
use the future value of an ordinary annuity table in Appendix C and convert the factor as shown in Worksheet 9.2.
The use of ﬁnancial calculators and computers can easily simplify the taskof calculating the future value of both an ordinary annuity and an annuity due.
Worksheets 9.3, on page 43, and 9.4, on page 44, illustrate the use of these tools.

42

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

WORKSHEET 9.2 How to determine the future value of an annuity due usingﬁnancial tables
Analysis of Tables 9.1 and 9.2 shows that there is one less interest payment
for an ordinary annuity. Thus, if the last deposit or payment is deducted, theamount will equal an annuity due for one less period.
Determine the future value of an annuity due of $1,000 deposited at the
beginning of each year for ﬁve years compounded at 6%.
FVIFA 6%, 6 = 6.975
6.975 − 1 = 5.975
1,000 × 5.975 = $5,975
Step 1 Look up the factor for an ordinary annuity in Appendix C for one more period.
Step 2 Deduct 1 from the factor, which is the same as reducing the number of deposits
by one.
Step 3 Multiply the converted factor by the amount of the deposits.

Using a Financial Calculator to Determine the
Future Value of an Annuity (Ordinary and Annuity Due)Worksheet 9.3 outlines the steps to determine the future value of both an ordinary annuity and an annuity due using a ﬁnancial calculator. The following
example illustrates these steps to determine the future value of an ordinary
annuity ﬁrst, and then an annuity due.
Example 1 What is the future value of an ordinary annuity of $1,000 to bedeposited at the end of every year for ﬁve years invested at 6 percent per year?
Example 2 What is the future value of an annuity due of $1,000 to bedeposited at the beginning of each year for ﬁve years invested at 6 percent per year?

WORKSHEET 9.3 How to determine the future value of an annuity (both ordinary
and annuity due) using a ﬁnancial calculator
Most ﬁnancial calculators have the following keys:
N = Total number of discounting periods
I = Interest rate per period
PV = Present value
FV = Future value
PMT = Annuity payment or receipt
Step 1 Key the number of discounting periods per year (annual,semiannual, monthly) into the mode of your calculator.
Step 2 Set the mode at the end of the period or beginning of the period.
Step 3 Key the number of discounting periods for the investment into the N button.
Step 4 Key the discount/interest rate into the I button.
Step 5 Key the amount of the annuity into the PMT button.
Step 6 Press the FV button to calculate the future value.
Example 1 Future Value of an Ordinary Annuity
Step 1 Key the annual mode into your calculator and set the end mode for an
ordinary annuity.
Step 2 Key the number of payments as 5 into the N button.
Step 3 Key 6% into the I button.
Step 4 Key the deposit of $1,000 into the PMT button.
Step 5 Press the FV button to calculate the future value, which is $5,637.09.
Example 2 Future Value of an Annuity Due
Step 1 Key the annual mode into your calculator and set the beginning mode for anannuity due.
Step 2 Key the number of payments as 5 into the N button.
Step 3 Key 6% into the I button.
Step 4 Key the deposit of $1,000 into the PMT button.
Step 5 Press the FV button to calculate the future value, which is $5,975.32.

WORKSHEET 9.4 How to determine the future value of an annuity (both ordinary
and annuity due) using a computer
Using Microsoft’s Excel spreadsheet, click on f *, which is on the top row of thetoolbar. A list of functions pops up. Highlight ﬁnancial in the left box and FV in
the right box. Click OK. A box comes up with ﬁve rows, as shown below:
Rate is the interest per period.
Nper is the total number of periods.
Pmt is the payment amount made.
PV is the present value; in this case, 0.
Type represents the timing of the payment: 1 forpayment made at the beginning of the period,
0 for payment made at the end of the period.

Enter this information and the future value is calculated.
Using the same example as used previously, key in the numbers to determine:
Future value of an
ordinary annuity

Future value of anannuity due

Rate

6%

Rate

6%

Nper

5

Nper

5

Pmt

$1,000Pmt$1,000

PV

0

PV

0

Type

0

Type

1

Formula result = $5,637.0929

Formula result = $5,975.316

Future value of an ordinary annuity is $5,637.09
Future value of an annuity due is $5,975.32

Assessing Your Current Wealth45

Using a Computer to Determine the
Future Value of an Annuity (Ordinary and Annuity Due)

Microsoft’s Excel spreadsheet is used here to illustrate the ease of calculating
the future value of an annuity on a computer. There are any number of othersoftware programs that can also be used. Worksheet 9.4 illustrates thedetermination of the future value of both an ordinary annuity and an annuity due using the same example used in the ﬁnancial calculator worksheet.
Not only does the timing of the payments/receipts have an impact on the
future value, but the rate of interest also has an enormous impact on the accumulation of the future value.
Table 9.3 illustrates these two factors using the example of an ordinary
annuity and an annuity due of $1,000 deposited each year for a 10-year anda 20-year period invested at 6 percent and 12 percent per annum.

TABLE 9.3 Future value of an ordinary annuity and an annuity due invested at
6% and 12% for 10-year and 20-year periods
Investment Rate

6%

12%

Difference

Ordinary annuity of $1,000
invested for 10 years$13,180.79$17,548.74$4,367.95

Annuity due of $1,000
invested for 10 years$13,971.64$19,654.58$5,682.94

Difference$790.85$2,105.84

Investment Rate

6%

12%

Difference

Ordinary annuity of $1,000
invested for 20 years$36,785.59$72,052.44$35,266.85

Annuity due of $1,000
invested for 20 years$38,992.73$80,698.74$41,706.01

Difference$2,207.14$8,646.30

46

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

Changing the timing of deposits from the end of the period to the beginning of the period increases the future value (note the differences of $790.85
and $2,105.84 for a 10-year period, and $2,207.14 and $8,646.30 for a 20-year
period). The differences are due to the ﬁrst deposit earning additional interest for the annuity due.
Similarly, when the interest rate per period is doubled from 6 percent
to 12 percent, the differences in the future values grow (from $4,367.95 to$5,682.94 for a 10-year period). When the investment period is doubled from
10 years to 20 years, the difference between the two rates accelerates.
The conclusions to be drawn from this table are:• Save earlier as opposed to later in the year.
• Look for investments with a higher rate of return where you are
comfortable with the level of risk.

Present Value of an Ordinary Annuity and Annuity Due
The present value of an annuity is the present value of a series of equal payments
to be received (or paid) in the future discounted at a rate of interest. There aremany uses for determining the present value of an annuity. In retirement planning, if you project that you will need $50,000 a year for 20 years, you can calculate how much you need to invest now to support those payments.

Present Value of an Ordinary Annuity

As with the future value of an annuity, the timing of the payments will havean impact on the amount of the present value. For an ordinary annuity,
payments (deposits) are made at the end of a period, and for an annuity due,payments (deposits) are made at the beginning of a period. As an example,
the present value of an ordinary annuity of $1,000 discounted at 6 percent for
ﬁve years is shown in Table 9.4.

Assessing Your Current Wealth

47

TABLE 9.4 Present value of an ordinary annuity of $1,000 discounted at 6%
for 5 years
YearPV$943.00
890.00840.00792.00747.001$1,0002$1,0003$1,0004$1,0005$1,000___________________________________________________________________________________________________________________________________________________________$4,212.00

Financial tables can simplify the calculation of the present value of an
ordinary annuity. Worksheet 9.5 illustrates the use of ﬁnancial tables in determining the present value of an ordinary annuity. The present value of an annuity table can be found in Appendix D.

Present Value of an Annuity Due

In Table 9.4, which shows the determination of the present value of an ordinary
annuity, each payment/receipt is discounted for the same number of periods.
Table 9.5 shows the computation of the present value of an annuity due
where there is one less discount period than in Table 9.4. The first payment/receipt is not discounted. Therefore, the present value of an ordinary
annuity tables can be converted to determine the present value of an annuity due. The present value of an annuity due factor is equal to the present valueof an ordinary annuity factor multiplied by one plus the interest rate perperiod. Refer to Worksheet 9.6, which shows the steps for using ﬁnancial tables
to determine the present value of an annuity due.

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

TABLE 9.5 Present value of an annuity due of $1,000 discounted at 6% for 5 years
YearPV$1,000.00
943.40890.00839.62792.09$4,465.11

0$1,0001$1,0002$1,0003$1,0004$1,000___________________________________________________________________________________________________________________________________________________________

Using a Financial Calculator to Determine thePresent Value of an Annuity (Ordinary and Annuity Due)

A ﬁnancial calculator takes out all the number crunching in the determination of the present value of an annuity. The only difference in determining anannuity due from an ordinary annuity is the setting of the mode of payments(for an annuity due the mode is set to the beginning of the period, and for an
ordinary annuity the mode is set to the end of the period). All the otherkeys are punched in the same way with the same information. Worksheet
9.7 outlines the steps in calculating the present value of an ordinary annuity
in example 1 and the present value of an annuity due in example 2.
Using a Computer to Determine thePresent Value of an Annuity (Ordinary and Annuity Due)Worksheet 9.8 illustrates the use of Microsoft Excel’s spreadsheet software
to determine the present value of both an ordinary annuity and an annuity
due using the same examples as in the previous section.
As seen from the totals in Worksheet 9.8, the present value of an annuity due is always greater than the present value of an ordinary annuity because
the payments are received sooner and the ﬁrst payment is not discounted. The
following conclusions can be drawn for the present value of an annuity:

Assessing Your Current Wealth49

WORKSHEET 9.5 How to determine the present value of an ordinary annuity usingﬁnancial tables
PV = PMT (PVIFA i, n )Where
PMT = Annuity or equal payments/receipts
PVIFA = Present value interest factor of an annuity
i = Interest/discount rate per periodn = Number of periods
PV = __________ (PVIFA ___ , ___ )PV = __________ ( __________ )PV = __________
Example:PMT = $1,000
i = 6%
n=5
PV = PMT (PVIFA i, n )PV = $1,000 (PVIFA 6%, 5 )PV = $1,000 (4.212)
PV = $4,464.72
Step 1 Fill in the values.
Step 2 Fill in the PVIFA factor from Appendix D at the intersection of the i row and then column.
Step 3 Multiply the annuity by the interest factor to obain the present value.

• The greater the rate of interest used to discount the annuity
payments, the smaller the present value of the annuity.
• The sooner the annuity payments are received, the greater thepresent value.

WORKSHEET 9.6 How to determine the present value of an annuity due usingﬁnancial tables
PV = PMT (PVIFA i, n ) × (1 + i )Where
PMT = Annuity or equal payments/receipts
PVIFA = Present value interest factor of an annuity
i = Interest/discount rate per periodn = Number of periods
PV = __________ (PVIFA ___ , ___ ) × (1 + ___ )PV = __________ ( __________ ) × (1 + ___ )PV = __________
Example:PMT = $1,000
i = 6%
n=5
PV = PMT (PVIFA i, n ) × (1 + i )PV = $1,000 (PVIFA 6%, 5 ) × (1 + .06 )PV = $1,000 (4.212) × (1.06 )PV = $4,464.72
Step 1 Fill in the values.
Step 2 Fill in the PVIFA factor from Appendix D at the intersection of the i row and then column. Multiply this factor by 1 plus the interest rate.
Step 3 Multiply the annuity by the interest factor to obain the present value.

WORKSHEET 9.7 How to determine the present value of an annuity (bothordinary and annuity due) using a ﬁnancial calculator
Most ﬁnancial calculators have the following keys:
N = Total number of discounting periods
I = Interest rate per period
PV = Present value
FV = Future value
PMT = Annuity payment or receipt
Step 1 Key in the number of discounting periods per year (annual,semiannual, monthly) into the mode of your calculator.
Step 2 Set the mode at the end of the period or beginning of the period for payments.
Step 3 Key the number of payment periods for the investment into the N button.
Step 4 Key the discount/interest rate into the I button.
Step 5 Key the amount of the annuity into the PMT button.
Step 6 Press the PV button to calculate the present value.
Example 1 Present value of an ordinary annuity
Step 1 Key the annual mode into your calculator.
Step 2 Set the end mode for an ordinary annuity.
Step 3 Key the number of payments as 5 into the N button.
Step 4 Key 6% into the I button.
Step 5 Key the deposit of $1,000 into the PMT button.
Step 6 Press the PV button to calculate the present value, which is $4,212.36.
Example 2 Present value of an annuity due
Step 1 Key the annual mode into your calculator.
Step 2 Set the beginning mode for an annuity due.
Step 3 Key the number of payments as 5 into the N button.
Step 4 Key 6% into the I button.
Step 5 Key the deposit of $1,000 into the PMT button.
Step 6 Press the PV button to calculate the present value, which is $4,465.11.

52

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

WORKSHEET 9.8 How to determine the present value of an annuity (ordinary andannuity due) using a computer
Using Microsoft’s Excel spreadsheet, click on f *, which is on the top row of thetoolbar. A list of functions pops up. Highlight ﬁnancial in the left-hand box and
PV in the right-hand box and click OK. A box comes up with ﬁve rows, as
shown below.
Step 1 Enter interest rate per period.
Step 2 Enter the total number of periods.
Step 3 Enter the payments made each period.
Step 4 Enter the future value.
Step 5 Enter the value representing timing of
the payment: 1 for payment
at beginning of the period; 0 for
payment at the end of the period.

Rate
Nper
Pmt
FV
Type

Using the same examples as in theprevious section using a ﬁnancial
calculator, key in the numbers:

Rate
Nper
Pmt
FV
Type

Present value ofan ordinary annuity= .06=5= $1,000=0=0Result: $4,212

Present value ofan annuity due= .06=5= $1,000=0=1
Result: $4,465

F I N A N C I A L C A LC U L ATO R # 10

How to Determine the Amounts
Needed to Fund Your Objectives

S

aving to fund ﬁnancial objectives is important, particularly for people who are concerned about the future. Everyone has different goals andpriorities, and irrespective of what they are, something should be done toAssessing Your Current Wealth53

address them before it becomes too late. Worksheet 10.1 on page 56 illustrates
the process of determining the amounts needed to fund objectives. The stepby-step process is elaborated on in the discussion that follows.

Step 1: List Your Objectives
Some of the most common objectives are:• Establishing an emergency fund
• Saving to buy and own a house• Saving to pay for children’s educations• Saving to start a business• Saving for retirement
Emergency Fund This is the fund that is used for unexpected events. Thereis always the possibility of losing a job, getting sick, or having some other
unfortunate situation occur, which could cause ﬁnancial chaos. Having an
emergency fund can help in such situations. The question is: How muchshould be kept in an emergency fund?
The rule of thumb is to have three to six months of living expenses in an
emergency fund. The exact amount depends on your circumstances. If you
have a stable employment situation and other accounts or sources that you cantap into for your short-term needs, then three months of living expenses would
probably be adequate. However, if your income ﬂuctuates, there is a greaterrisk of losing your job, and you have no relatives or friends who could assist
you, then you should keep at least six months of living expenses in this account.
There may be circumstances in which you need to keep more than six monthsof living expenses. If you have a high probability of losing your job and might
not be able to ﬁnd another job within a reasonable period of time, and you
have no relatives or friends who could assist you, then you should keep ninemonths’ to one year’s worth of living expenses in an emergency fund.
Saving to Buy a House Owning a house is a high priority for most people.
Not only are there the tax breaks of being able to deduct the mortgage inter-

54

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

est and real estate taxes from personal taxes, but there is also the buildup in
equity that comes from paying down a mortgage.
Funding Children’s Education Expenses This is not as straightforward an
objective as it seems because the current ﬁnancial aid system works againstparents with substantial assets and includes similar penalties for savings
invested in children’s names. As of this writing, parents are responsible for an
amount worth roughly 6 percent of their assets for their children’s college costs
annually, and children are responsible for an amount worth 35 percent of thesavings in their names. People with substantial savings and assets may not
qualify for ﬁnancial aid, and children with assets of $100,000 in their names
would also disqualify themselves for aid, assuming private education costs are$35,000. Thus, funding this objective over retirement savings may be a mistake under certain circumstances. Parents should look into all aspects of theirﬁnancial situations before funding this objective over other objectives.
Saving for Retirement The rule of thumb is that most people will need about
75 to 80 percent of their preretirement income in retirement to maintain theirstandard of living.
Some people may be able to get by on less and others may need moremoney to live on. Determining your needs for retirement is important because
you can fund most of them through tax-deferred retirement accounts such asa 401(k), a 403(b), SEP-IRAs, Keoghs, Roth IRAs, and IRAs. Contributions tothese accounts are generally tax deductible below threshold amounts and theearnings in these accounts accumulate free of taxes until they are withdrawn.
If the amounts saved in these tax-deferred retirement accounts are not
sufﬁcient to meet your expected retirement needs, you may want to save additional amounts outside of your tax-deferred retirement accounts.
The future cannot be predicted, but by setting aside amounts for an emergency fund, big ticket purchases (car, home), educational needs, and retirement, you are preparing to cope for any ﬁnancial changes in the future.
Now list the objectives that are most important to you.

Assessing Your Current Wealth55

Step 2: Prioritize Your Objectives
There are many factors that will determine your objectives, such as your age
or stage in life, your income level, the size of your family, and your perspective on the future. People in their twenties will have decidedly different objectives from people in their forties. Achieving objectives requires regular,
disciplined deposits to savings and investment accounts. The longer the investment period, the greater the accumulation of interest, as shown in the timevalue of money ﬁnancial calculator (section 4).
Most people do not have the ﬁnancial resources to fund all of their objectives, and the difﬁculty comes in deciding which ones to fund. Should you
save for retirement or a down payment on a house, or should you use thefunds to start a business? Some objectives are short term while others are
longer term. It is often easier to concentrate on the short-term objectives andneglect the long-term objectives. Assigning priorities to your objectives canhelp you determine which ones to fund.

Step 3: Assess the Cost andTime Frame for Each Objective
By quantifying the cost for each objective and the time frame for when you
will need this amount, you make it easier to determine how much to savefor each objective. The example in Worksheet 10.1 shows two objectives withcosts of $15,000 and $1,000,000 and time frames of six months and 30 years,
respectively. A simple way to determine the monthly amount needed to ﬁnanceeach objective is to divide the cost by the number of months until needed,
as shown below:

Monthly amount for emergency fund ==$15,000
6$2,500

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

Monthly amount for retirement=$1,000,000
360= $2,777.78

The astute reader is bound to observe that the amounts computed are
not accurate determinations of what to save because they do not take into

WORKSHEET 10.1 Steps to determine the amounts needed to fund objectives

Rate ofreturnMonthlysavings
required_________________________________________________________________________________

Objectives

Priority

Cost

Time
needed___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Examples:Emergency fund1

$15,000

6 months

1%$2,494.80
per annum

Retirement2$1,000,000

30 years8%
per annum

Step 1 List your objectives.
Step 2 Attach priorities.
Step 3 Assess cost and time needed.
Step 4 List rates of return.
Step 5 Compute monthly savings required.

$670.98

Assessing Your Current Wealth57

account the time value of money. This is correct, because the deposits madeinto various investments will earn a rate of return, which will result in having
to make smaller monthly deposits.

Step 4: List the Rates of Return for Each Objective
The investment choice for the deposits for each of your objectives depends
on several factors, such as the time frame, the level of risk, and the expected
rate of return. Generally, with a short-term time horizon of one year or less,money market securities offer low rates of return but almost no risk of lossof principal. Money market securities consist of Treasury bills, certiﬁcates ofdeposit, commercial paper, bankers’ acceptances, money market funds, andbank and savings accounts. For intermediate-term time horizons (one to ﬁve
years), notes and bonds offer higher returns, but they also carry greater risk.
Common stocks offer the highest returns of most ﬁnancial investments, butthey carry much greater risk of loss of principal. Consequently, you need along time horizon (greater than ﬁve years) to ride out the loss of having to sell
stocks at less than their purchase prices.
Current rates of return used in the examples in Worksheet 10.1 are 1 percent per annum for a savings account and 8 percent per annum for an investment in stocks. In the event of inﬂation, you would have to save more thanthe cost listed, as inﬂation erodes future purchasing power. If inﬂation is estimated to be 2 percent per year, the real rate of return for stocks in this example would be 6 percent (8 percent minus 2 percent).

Step 5: Compute the Monthly Amounts
Needed to Fund Objectives
The easiest methods for determining the monthly amounts needed to fundobjectives into the future are to use either a ﬁnancial calculator or a computer.
Using ﬁnancial tables becomes cumbersome if the monthly interest rate is not

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

a whole number. However, there are ﬁnancial tables printed with fractional
interest rates that can be used.

Using a Financial Calculator to Determine theMonthly Amounts Needed to Fund Objectives

Example 1 in Worksheet 10.1
Determine the monthly amount to save for an emergency fund of $15,000
in six months’ time.
Step 1 Key in the number of interest periods
as monthly.
Step 2 Key in the end mode for an ordinary
annuity.
Step 3 Key the number of payments into the
N button.
Step 4 Key the interest rate per annum into
the I button.
Step 5 Key the future value into the FV button.
Step 6 Press the PMT button to determine themonthly amount.

12 per year
end mode6
1%$15,000$2,494.80

Example 2 in Worksheet 10.1
Determine the monthly amount needed to save for a retirement fund of$1,000,000 in 30 years’ time.
Step 1 Key in the number of interest periods
as monthly.
Step 2 Key in the end mode for an ordinary
annuity.
Step 3 Key the number of payments into
the N button.

12 per year
end mode360

Assessing Your Current Wealth

Step 4 Key the interest rate per annum into
the I button.
Step 5 Key the future value into the FV button.
Step 6 Press the PMT button to determine themonthly amount.

59

8%$1,000,000$670.98

Using a Computer to Determine the Monthly Amounts
Needed to Fund Objectives

Microsoft’s Excel spreadsheet is used here to illustrate the computation of theannuity amounts needed to fund the two example objectives in Worksheet
10.1, as shown in Worksheet 10.2. There are a few differences from the Excel
examples in section 9. Instead of calculating the future value, in these examples you are looking for the payment amount/annuity amount (PMT) that
equals the future value at a particular interest rate per period for a speciﬁednumber of periods. Instead of clicking FV in the right-hand box, you would
highlight PMT. Thereafter, you would enter the variables as described in Worksheet 10.2.
What becomes tricky is the determination of the interest rates per period.
In example 1, the interest rate is 1 percent per year, which means that interest per month is 0.01 ÷ 12. The same applies for example 2, where the interest rate per month is 0.08 ÷ 12.

WORKSHEET 10.2 How to determine the monthly amounts needed to ﬁnanceyour objectives using a computer
Using Microsoft’s Excel spreadsheet, click on f *, which is on the top row of thetoolbar. A list of functions pops up. Highlight ﬁnancial in the left-hand box
and PMT in the right-hand box and click OK. A box comes up with ﬁve rows,
as shown below.
Rate
Nper
PV
FV
Type

Step 1 Enter the rate, which is the interest
rate per period.
Step 2 Enter the total number of periods.
Step 3 Enter the present value, which is 0.
Step 4 Enter the future value.
Step 5 Enter the value representing timingof the payment: 1 for payment
at beginning of the period; 0 for
payment at the end of the period.

Formula result =Using the same examples as in
Worksheet 10.1, key in the numbers:
Payment of a future value, example #1:
Rate
Nper
PV
FV
Type

0.01 ÷ 12
6
0$15,000
0= .0008333= 6= 0= $15,000= 0

Formula result = $2,494.80
Payment of a future value, example #2:
Rate
Nper
PV
FV
Type

.08 ÷ 12360
0$1,000,000
0Formula result = $670.98= .0066667
= 360
= 0
= $1,000,000= 0Assessing Your Current Wealth61

F I N A N C I A L C A LC U L ATO R # 11

How to Reconcile
Your Checking Account*Failure to reconcile your checking account can cost you moneyover time. If either you or the bank make any errors, they might not be
discovered in a timely fashion unless you reconcile your account on a monthly
basis. If the bank deducts more for a check than the amount written or does
not credit your account for a deposit made, you need to let it know about theseerrors in a timely manner or it will not do anything about them. Similarly,
you could have made a mistake and assumed that your balance was higher
than it really was, which could result in an overdrawn check, which in turnwould result in additional bank fees.
The starting point in reconciling your checking account is to examine yourmonthly checking account statement. The bank statement shows the deposits
that have been credited and the checks that have cleared the account for themonthly period. Figure 11.1 shows a typical bank statement for John Y.

Step 1: Mark Off Canceled Checks inYour Check Register
Canceled checks or copies of them are included with your monthly bank statement. In addition to marking off canceled checks, you should also check theamounts that the bank has debited for each check. Figure 11.2 shows an example of a check that was written for $1,200.00 but for which the bank charged
the account $1,201.00. The amount charged by the bank is shown in the bottom right-hand corner of the check. The ﬁgure in the bottom right-hand corner of each canceled check should be checked against the amount written for*Portions of this section have been previously published by Esmé Faerber in Managing
Your Investments, Savings and Credit, (McGraw-Hill: New York, 2001).

62

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

FIGURE 11.1 Example of a monthly bank statement

Everlasting Bank
Account Title: John Y.

Account #: 000-00000

Previous Balance: $2,140.57
4 Deposits/Credits: 3,082.87
15 Checks/Debits:
2,379.10
Ending Balance:
2,844.34
Date
2/1
2/2
2/5
2/6
2/9
2/12
2/14
2/16
2/20
2/21
2/23
2/24
2/28

Check #
343
356
357
359
361
362
363
365
366
367
368
369
370
373

Debits$20.001,201.00
56.14
91.12
150.00221.5087.20
200.00
26.00
15.36
76.12
150.0056.06
23.50
5.10 SC

Credits$2,906.37

25.00

150.001.50 IN

Balance$ 2,140.57
5,026.94
3,825.94
3,769.80
3,703.68
3,553.68
3,332.18
3,244.98
3,044.98
3,018.98
3,153.62
3,077.50
2,927.50
2,871.44
2,847.94
2,844.34

DM = Debit Memo SC = Service Charge FC = Finance Charge IN = Interest

that check. This way bank errors can be spotted promptly and then corrected
when brought to the bank’s attention.
Arrange checks you have written that have cleared the bank in numerical order of check numbers and then mark them off in your check registeras shown in Figure 11.3. Checks not marked with a (√) are outstanding andhave not cleared Mr. Y’s account as of the bank statement date. Similarly,

Assessing Your Current Wealth63

FIGURE 11.2 A canceled check

John Y
1 Upbeat Place
Somewhere, U.S.A.

Feb. 1

20

02

356
310

Complete Financial Services, Inc. $ 1,200.00
Tweleve Hundred and 00/100
DOLLARSPAY TO THE
ORDER OFEVERLASTING BANK
1 Sparkle Place
Somewhere, U.S.A.
MEMO

000000002

you should check off all the ATM withdrawals that are listed on the bank statement against your checkbook register.

Step 2: Determine Your Adjusted Checkbook Balance
Begin with your checkbook balance at the closing date of the monthly statement, add interest income, and then deduct bank charges and fees.
Balance per checkbook at end of month
Deduct: service charge
Add: interest income
Adjusted checkbook balance$4,877.90(5.10)
1.50$4,874.30

Step 3: Compare the Deposits Listed on Your Bank
Statement with the Deposits in Your Register
Determine whether there are any deposits that you have recorded in yourcheckbook that are not on your bank statement. Looking at the checkbook
register in Figure 11.3, we see that the deposit of $2,906.37 on 2/28 is in

FIGURE 11.3 Mr. Y’s checkbook register
Mr. Y’s Checkbook Register
NUMBER DATE
2002

356

DESCRIPTION OF TRANSACTIONPAYMENT/DEBIT(–)$ 1200√T

FEE
IF ANY(–)

00 ✓ $

2-1

Complete Financial Service

2-2

Deposit357

2-3

Bell Telephone

56

14 ✓

358

2-4

Electric Company

124

16

359

2-5

EZ Food Market

91

12 ✓

2-9

Deposit–Forever S&L Dividend

360

2-10

Ace Insurance Company

650

00

361

2-11

Cash

150

00 ✓

362

2-12

Leak Free Roofers

221

50 ✓

363

2-15

EZ Food Market

87

20 ✓

364

2-16

Animal Hospital

35

00

365

2-17

Last County Bank

200

00 ✓

366

2-18

Kraft Pharmacy

26

00 ✓

367

2-19

First Bookstore

15

36 ✓ $

2-20

Deposit–Seave Brokerage Dividend

368

2-21

Gas Company

76

12 ✓

369

2-21

Cash

150

00 ✓

370

2-22

EZ Food Market

56

06 ✓

371

2-23

Playful Toy Store

23

25

372

2-24

Numero Uno Department Store

45

00

373

2-27

EZ Food Market

23

50 ✓

2-28

DepositDEPOSIT/CREDIT
(+)
$

✓

2906

✓

$

✓

25

$

150

2906

BALANCE$2120$ 1200920
37 2906
3826
56
3770
124
3646
91
3555
00
25
3580

57
37
94
14
80
16
64
12
52
00
52

650
2930
150
2780
221
2559
87
2471
35
2436
200
2236
26
2210
$
15
2195
150
00
2345
76
2269
150
2119
56
2063
23
2040

00
52
00
52
50
02
20
82
00
82
00
82
00
82
36
46
00
46
12
34
00
34
06
28
25
03

45
1995
23
1971
2906
4877

00
03
50
53
37
90

37

57

Assessing Your Current Wealth65

transit. In other words, the funds have not been credited to John Y’s bankaccount as of the bank statement date. All deposits in transit need to be added
to the bank balance.
Similarly, if your bank has received electronic fund transfers into youraccount that you have not recorded in your checkbook register, you will needto add these to the balance.

Step 4: List All Outstanding Checks
List the outstanding checks from the checkbook register. These are the checks
that have not been presented to the bank for payment as of the bank statement date.
Checks outstanding:
#
358
360
364
371
372

Amount$ 124.16
650.00
35.00
23.25
45.00
$ 877.41

Step 5: Determine Your Adjusted Bank BalanceStart with the ending balance shown on your bank statement, add all deposits
in transit (step 3), and deduct any checks outstanding (step 4). The resulting balance should equal the adjusted balance in your checkbook (step 2). If
there are any errors, they need to be adjusted, as shown below with the example in John Y’s account.

66

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

Balance per bank
Add: deposits in transit
Deduct: outstanding checks$ 2,844.34
2,906.37(877.41)
4,873.30

Add: bank error (check #356 written for$1,200.00, bank charged $1,201.00)
Adjusted bank balance

1.00$ 4,874.30

See Worksheet 11.1 for a summary of this process. If the adjusted bankbalance and the adjusted checkbook balance are not the same, you have madean error. Proceed to step 6.

WORKSHEET 11.1 Reconciling your checking accountYour checkbook
Ending balanceBank statement
Ending Balance$__________

Deduct fees/charges
shown onbank statement _________

Add deposits in transit__________

Add interest
earnedDeductoutstanding checks__________

Adjusted bankbalance___________

Add direct
deposits$___________________________

Adjusted checkbook
balance_________

Assessing Your Current Wealth67

Step 6: Looking for Errors
1. Conﬁrm that you have included all the outstanding checks and thatthey are correctly added.
2. Check that you have included all the deposits in transit.
3. Check your bank statement to see that you have included all bankcharges and interest earned.
4. Recheck the addition and subtraction in your checkbook register.
5. Recheck the amounts written on the canceled checks with theamounts written in your checkbook register.
6. Recheck the amounts written on the canceled checks with the coded
digits in the bottom right-hand corner of the checks.
If you still have not found the error, it is more than likely that you areoverlooking something obvious. Leave it for a while and come back to it later.

Using a Computer to Reconcile Your Checking AccountComputers can be used to reconcile a checking account, which eliminates thearithmetic errors that can so easily be made when determining checkbook
register balances. There are many different software programs available. Worksheet 11.2 outlines the steps to reconcile your checking account using Quicken
software. For other software programs, consult the software guide for the speciﬁc steps to reconcile your account.
There is a basic similarity between manually reconciling your accountand doing it on a computer. The advantage of using a computer is that reconciling your account is much easier because arithmetic errors are eliminated.
The disadvantage is that it is time consuming to enter the transactions fromyour paper checkbook register into the computer checkbook register.
By reconciling your checking account monthly, you conﬁrm that yourchecking account balance is what it should be, and you safeguard an important asset—your cash.

68

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

WORKSHEET 11.2 Using Quicken software to reconcile a checking accountStep 1Enter transactions into the Quicken checkbook register.
The Quicken checkbook register looks the same as the one shown in
Figure 11.3. Enter all the transactions from your checkbook register into
your computer checkbook register.

Step 2

Click on the reconcile box.
When you have ﬁnished entering all the transactions from your checkbook
register into your computer checkbook register, you are ready to begin thereconciliation process. On the top row above the register, there is the word
reconcile. Click on the reconcile box and you will get a larger box on the nextscreen. In number 1, there is an opening balance ﬁgure; ﬁll in the endingbalance as it is stated on your bank statement. In number 2, ﬁll in any service
charges and interest earned also from your bank statement. When you haveﬁnished, click on the OK box.

Step 2Check off checks, withdrawals, and deposits that have cleared the bank.
As you did in your manual reconciliation, you want to check off all thetransactions that have cleared the bank. A large box appears with transactions
sorted into two categories. One includes all withdrawals and checks written
and the other includes all deposits. Click on each transaction that has cleared
the bank, as indicated on your bank statement. When you have completed
marking these off, you will see a balance differential in the lower right-handcorner below the box. If you have not made any mistakes, the differential will
equal 0, indicating that you have successfully reconciled your checkbook
register balance to your bank balance.

F I N A N C I A L C A LC U L ATO R # 12

How to Prepare Your Records forYour Tax Accountant*There are many reasons why you should keep orderly and complete tax
records. When you keep inclusive records of your income and deduc-*Portions of this section have been previously published by Esmé Faerber in Managing
Your Investments, Savings and Credit (McGraw-Hill: New York, 1992).

Assessing Your Current Wealth69

tions, you are able to prepare an accurate tax return. If the Internal Revenue Service (IRS) audits your return, the orderly records you’ve kept can easily verify
your deductions with a minimum of effort. (This won’t prevail for any nondeductible items or highly questionable deductions you may have taken.) By keeping all-inclusive records of your expenses, you may be able to reduce the amountof income taxes you pay. If you can’t prove your deductions because of sloppy
record keeping, you may have to pay more income tax than necessary.
Copies of your tax returns should be kept in your home ﬁle as part ofyour tax records, with all records and receipts pertaining to income, deductions, and credits that appear on your tax return. Worksheet 12.1 lists all thetax records you should keep, not only to present to your accountant but also
for the reasons listed above. All the 1099 series of forms should be retained tosupport receipts of different types of income. Other such records, such as brokerage statements and mutual fund statements that can prove the amounts ofincome shown on your tax return, should be kept in your tax folder.
Your checkbook and credit card statements provide basic records of yourdeductible expenditures. However, canceled checks alone may not be sufﬁcient evidence for the IRS, so you should keep records of receipts and sales
invoices. Dated and signed sales receipts are important if you paid cash.
Many people meet with an accountant at least once a year to prepare theirincome tax returns. By organizing and summarizing your tax informationahead of the appointment, you can save your accountant considerable time,
which should reduce the cost of preparing your tax return.
By organizing and summarizing your information, you can do the “legwork” rather than have your accountant plow through your receipts, canceled
checks, and other documentation. Many accountants require photocopies
of supporting documentation along with a summary sheet of information or
a completed questionnaire requesting similar information. Also, most accountants require a copy of your prior year’s tax return if prepared by anotheraccountant. Worksheet 12.2 lists the categories of information required toprocess a basic 1040 tax form.
Your summary sheet should show your name, name of spouse (if applicable), address, telephone number, Social Security number(s), marital status,

WORKSHEET 12.1 What tax records to keep
IncomeRecords

Wages and salary
Independent contractor

W-2 issued by employer
1099-Misc issued by the entity
you have provided services for
Business books, K-1 issued by partnership

Business income: proprietorship,partnership, estates, trusts,
S-corporations, rents, royalties
Interest and dividends

Capital gains and losses

State and local tax refunds
Payments/distributions fromretirement plans and annuities
Social Security beneﬁts
Unemployment compensation
Barter income

Expenditures
Medical and dental expenses
Taxes

Interest

Charitable contributions
Miscellaneous deductions
Business use of auto, home
Alimony1099-Int and 1099-Div issued by theﬁnancial institutions paying the interestand dividends
1099-B issued by broker who sold theassets; 1099-S issued by broker reporting
proceeds on the sale of real estate1099-G issued by state or local government that provided the refund1099-R or W-2P issued by the trustee ofthe plan making the payment
SSA-1099 issued by the federal
government1099-G issued by government agency
paying unemployment compensation
1099-B issued when services orproperties are exchanged
Records
Canceled checks and receipts
Canceled checks and receipts for realestate taxes, personal property taxes,
and state and local taxes
1098 issued by mortgage company,
canceled checks, and receipts fordeductible interest
Canceled checks and receipts from donees
Canceled checks and receipts
Canceled checks, receipts, anddocumentation
Canceled checks, copy of divorce
decree or separation agreement

Assessing Your Current Wealth71

WORKSHEET 12.2 Income tax summary
Name:

Date of birth:

Social Security #:Name of spouse:

Date of birth:

Social Security #:Name:

Date of birth:

Social Security #:Name:

Date of birth:

Social Security #:Federal withholding

Social Security

Marital status:
Children:

IncomeSalary W-2
GrossState tax

Local tax

Business income
Refund of state tax
Interest income

Dividend income

Capital gains
Description

Date of purchase

Date of sale

Proceeds

Cost

Adjustments
IRA/Keogh deposit
Deductions
Mortgage interest expense

Real estate taxes

names of dependents (if applicable), their Social Security number(s), and theirdates of birth. List all sources of income. If your ﬁnancial activities have notchanged very much since last year, your prior year’s tax return is a good source
to check to see if you have omitted any sources of income.
List your adjustments, such as deposits to IRA accounts, and alimony andchild support payments.
If your deductions exceed the amount of the standard allowable deduction, you may choose to itemize your deductible expenses. By organizing andsummarizing your deductible expenses, you will save your accountant time

72

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

FIGURE 12.1 Check analysis of deductible expenses

Check 1990
# DatePayee

215 1/5 F.A.S. Bee, CPA
2 216 1/15 State-Personal Prop Tax
3 230 2/10 Dr. B. Well
4 231 2/10 Ds. P.D. Rad
5 256 3/15 Church-Temple Donation
6 270 4/20 Super Quick Motors-Auto
Personal
7 291 5/08 Fail Safe Bank- InterestChild
8 296 5/30 Central School- Care
9 315 6/15 IRS 1040 ES
10 316 6/15 State Estimated Payment
Safe Deposit
11 325 7/20 State Bank-Box
12 380 8/29 Go Moving Company
13 399 9/15 IRS 1040 ES
14 400 9/15 State Estimated Payment
15 450 10/30 SPCA-Donation
16 490 11/16 Best Auto Insurance
1

1

2

3

4

5

6

AmountTaxes

MedicalInterest

Contributions

Other

200 00
39 00
80 00
90 00
200 00
187 00150 00500 00750 00150 0040 00
2 000 00
750 00150 0050 00
500 00200 00
39 00
80 00
90 00
200 00
187 00150 00500 00750 00150 0040 00
2 000 00
750 00150 0050 00
500 00

17
18
19
20
21

Subtotals
From W2
State Tax
City Tax

5 836 00

1 839 00

1 050 00
2 156 00

1 050 00
2 156 00

From 1098
Real Estate Tax
Mortgage Interest

2 100 00
5 001 00

2 100 00

Totals16 143 00

7 145 00

170 00150 00200 003 477 00

200 003 477 00

22
23
24
25

5 001 00

26
27

170 005 15 1 00

28______________________________________________________________________and yourself money. Figure 12.1 shows a worksheet on which checks of
deductible expenses are sorted and summarized. If you are not sure which
expenses are deductible, check with your accountant. You should give youraccountant your W-2 forms, which are then attached to your federal, state,
and local tax returns.
Your accountant may ask you to ﬁll out a checklist or questionnaire sothat all relevant information is obained. The aim of working closely with youraccountant is to prepare an accurate tax return and not overpay your taxes.

P A R T

T W O

MANAGING YOURPERSONAL WEALTH—DEBT

Copyright 2003 by Esme Faerber. Click Here for Terms of Use.

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F I N A N C I A L C A LC U L ATO R # 13

Determine Your
Debt Capacity

S

ince credit card companies set debt limits on the amount of credit
that they will issue to credit card holders, it would be prudent for people
to set their own limits on their total debt capacities. Before immersing yourself in debt, you should determine how much debt you can comfortably afford.
In other words, you should set your own debt limit, which is the maximum
amount that you can comfortably afford to service the interest payments.
One method of determining your debt limit is to draw up a monthly
budget with your cash receipts of income and your cash disbursements for
expenses. Worksheet 13.1 provides the framework for this approach.
The amount left over when monthly cash disbursements are subtracted
from monthly receipts is the amount available for debt payments. If disbursements are greater than receipts, you cannot afford to take on any new
debt, as you will not be able to pay the interest and principal payments without drawing down on your assets.
Not everything is as simple or clear-cut as this ﬁrst approach suggests,
which leads to a second approach for determining whether you can afford to
take on debt. This approach involves analyzing your budget to determine where
potential trade-offs may lie. By forgoing spending in some areas, you canincrease the amount available to ﬁnance debt payments. Cutting vacation andentertainment expenses, for example, can free up funds for servicing debt, but
it becomes progressively harder to cut down on necessary types of expenses.
The rule of thumb of a 20 percent ceiling on the amount of debt payments to monthly disposable income is a useful guideline. This means that
if your monthly disposable income is $2,000, your debt payments should notexceed $400. This does not include your mortgage.

75

WORKSHEET 13.1 Budgetary approach to determining your debt capacity
Monthly cash receipts
Net monthly income
Other income
Total monthly receipts__________________________
A _____________

Monthly cash disbursements
Mortgage/rent
FoodHousehold expenses
Transportation/auto expenses
Child care expenses
Savings and investments
Other expenses
Total monthly disbursements___________________________________________________________________________________________
B _____________

Annual expenses
Taxes
Real estate taxes
Other taxes
Insurance
Medical and dental expenses
Other______________________________________________________________________________

Total annual expenses
Divide total by 12
Equals monthly expenses (C ÷ 12)_____________ ÷ 12

C _____________

Total monthly disbursements (B + D)
Cash receipts minus disbursements (A − E)
(If F is positive, this is the amount available for debt payments.)

D _____________
E _____________
F _____________

Managing Your Personal Wealth—Debt

77

The greater the level of income, the easier it becomes to support this levelof debt. For example, it may be difﬁcult for someone with take-home pay of$1,000 per month to support debt payments of $200 per month, whereas
someone with disposable income of $3,000 per month may have an easiertime supporting debt payments of $600.
The following are the warning signs of taking on too much debt:• You are unable to save any money.
• You have to cut back on necessary expenses just to make ends meet.
• You only pay the minimum amounts on your credit card bills.
• You are juggling certain payments in order to pay other obligations,which are all due at the same time.
• You are unable to meet payments in emergency situations.
Fill in Worksheet 13.1, which shows the amount that you can afford for
debt, and set your debt limit at a comfortable level.

F I N A N C I A L C A LC U L ATO R # 14

How to Determine theBest Source of Credit

C

redit is costly, and if you can get by without using expensive sourcesof credit you will be better off ﬁnancially. If you do have to use credit,
use it sparingly. There are many different sources of credit, and you should
investigate them carefully as their costs can differ signiﬁcantly. Commercial
banks, credit unions, savings and loan associations, consumer ﬁnance companies, and life insurance companies are all sources of credit. Not only will
the types of credit and the terms vary from source to source but so too will
the costs. Using credit cards as a source for credit purchases can be the most
costly if you do not repay the full amount of the credit balance within thegrace period offered by the credit card issuer. Rates can range as high as

78

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

12 to 30 percent per annum, which puts things into perspective when compared with the puny returns of 1 to 3 percent currently received from savingsand money market accounts. This situation points to the importance of comparing the rates charged by the different sources of credit. The yardstick ofcomparison is the annual percentage rate (APR). Lenders are required by
the Federal Truth in Lending Act to use the APR when quoting interest rates
on sources of credit.
Worksheet 14.1 outlines the different sources of credit with the different types of loans and typical lending policies. As interest rates ﬂuctuate withmarket conditions in the economy, you will need to check with each individual source of credit as to the APR for the different types of credit inwhich you are interested.
The sources of credit that are least expensive are family members and friends.
You should always check these sources ﬁrst before going to institutional lenders,which will generally charge much more for credit. Family members may be willing to lend to you at rates that are only slightly in excess of what they can earnfrom their savings accounts and money market securities, which are currently
quite low at 1 to 3 percent. If such an arrangement is made, the loan agreement, interest rate, maturity date, and/or repayment schedule should be in writing. The downside to borrowing from friends and family is that if there are any
deviations from the terms of the agreement it could strain the relationship.
Some generalizations that you should keep in mind in determining thebest sources of credit are as follows:• The most expensive sources of credit are from consumer ﬁnancecompanies. The reason is because they lend to people who cannot
obtain ﬁnancing from other sources, such as banks, savings and loan
associations, and credit unions.
• Cash advances through credit card charge accounts are also
extremely expensive. Fees are levied in addition to having to pay
interest on a daily basis. The interest rate is usually at the high end of
the range, and there is no grace period for cash advances like there isfor charge purchases.

WORKSHEET 14.1 Determine your best sources of credit
Sources ofcreditTypes ofloans

Lending
policies

Commercial
banksSingle-payment
loan
Installment loan
Credit cardloan
Passbook loan
Check-credit plan
Second mortgage

Customers withestablishedcredit history
May require
collateral

Credit cardloan
Installment loan
Share draft-credit
plan
Second mortgage

Available tomembers only ____________________________

Installment loan
Savings accountloan
Education loan

Need anestablishedcredit history
May require
collateral

Credit unions

Savings & loan
associations

Home improvement
loan
Second mortgage
Consumer ﬁnancecompanies

Life insurancecompanies

Installment loan

Cost and terms(APR)______________________________________________________________________________________________________________________________________________________________________________________

Second mortgage

Do not need______________
an establishedcredit history ______________

Loans up to 95% of
the insurer’s
cash value

Need to have a ______________
life insurance
policy in force

80

T H E P E R SO N A L F I N A N C E C A LC U L ATO R• Before going to a bank for a car loan, check with the car dealer toﬁnd out if there are any special ﬁnancing deals available from theauto manufacturer. During tough economic times, many auto manufacturers provide 0 percent loans to potential buyers as an incentive
to increase sales of new cars.
• Credit unions may charge lower rates than banks, but you have to bea credit union member.
• Unsecured loans have higher rates than secured loans.
• Expanding the term of an installment loan results in smaller
monthly payments, but the total interest paid will be greater thana shorter-term loan.
Using Worksheet 14.1, fill in the APRs and the terms charged by thedifferent sources of credit to determine your best sources of credit.
Should you decide to make a sizable purchase and know that you will
be in a position to pay for it in full within a few weeks, use a credit card andpay off the entire amount within the grace period. Credit card companies normally provide a grace period, which is a period of time between the recording of the transaction and the due date during which interest is not charged
if the balance is paid in full. If there is a balance due after the grace period,
interest is charged on the daily balance.
The use of credit is costly, and if you can pay cash instead of using credit
you will save more in the long run, as shown in Worksheet 14.2. In this worksheet, you can compare the cost of using credit versus paying cash.
When ﬁnancing costs and fees related to the use of credit are added, thetotal cost of credit is much greater than the use of cash.

Managing Your Personal Wealth—Debt

81

WORKSHEET 14.2 Cost of using credit versus paying cash for a purchaseCashCreditNet cost of item________
Sales tax
+ ________
Delivery, service costs+ ________
Interest revenue forgone
by purchasing for cash + ________

Down payment
Credit-related fees
Financing costs*________+ ________+ ________

Total cash cost

Total credit cost__________________*To determine the ﬁnancing costs, multiply the monthly cost by the number of months
payments are to be made.

F I N A N C I A L C A LC U L ATO R # 15

How to Determine theAnnual Percentage Rate Costsof Using Credit LoansW

hen comparing the credit costs of different borrowing situations,
it is helpful to know how the costs are determined. Since 1969, lenders
have been required to disclose the annual percentage rate (APR) and the total
dollar amount paid in ﬁnance charges. The APR is the true cost of the debt
and is determined by dividing the total ﬁnance charges by the loan balance.
By comparing the APRs of competing sources of credit, you can choose thesource with the lowest cost.

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

How to Determine the APR forSingle-Payment Loans
Single-payment loans can charge interest using the simple interest method or
the discount interest method.

Simple Interest Method

Using simple interest, the ﬁnance charge is calculated by multiplying thestated annual rate by the amount of the loan. For example, if you borrow $2,000
from the Friendly Bank for two years at 10 percent simple interest, the interest
expense is $200 per year and the APR is 10 percent, as shown in Worksheet 15.1.
When simple interest is used, the annual percentage rate is equal to thestated rate.

Discount Interest Method

With the discount interest method, the lender deducts the interest payments at the inception of the loan. For example, with a single-payment discount loan of $2,000 at 10 percent for two years from the Friendly Bank, theloan will have the same total interest expense of $400 ($200 per year) as a simple interest loan.
The difference with this method is that the borrower will receive only
$1,600, as the ﬁnance charge of $400 is deducted from the loan. The true costor APR of this loan is 12.5 percent. This is shown in Worksheet 15.2, which
outlines the steps for determining the APR for a single-payment loan using
the discount interest method. The discount interest method results in a higher
APR than the simple interest method.

WORKSHEET 15.1 How to determine the APR using simple interest=I×P×T

Total interest expense

I = Interest rate
= 10% × $2,000 × 2
P = Amount of the loan
= $400T = Length of time for the loan
Total interest expense=I×P×T= ____ × ____ × ____
= ____APR ==Average annual ﬁnance charge
Average annual loan balance$400 ÷ 2$2,000

= 10%
APR =

Average annual ﬁnance charge
Average annual loan balance= ____= ____ %Step 1 Fill in the interest rate, amount of the loan, and time to determine the totalinterest expense.
Step 2 Determine the average annual ﬁnance charge and divide this by the averageannual loan balance.

WORKSHEET 15.2 How to determine the APR using discount interest
Total interest expense
I = Interest rate
P = Amount of the loan
T = Length of time for the loan

=I×P×T= 10% × $2,000 × 2= $400Total interest expense=I×P×T= ____ × ____ × ____
= ____

Discounted loan balance = loan balance − total interest expense= $2,000 − $400
= $1,600
Discounted loan balance = loan balance − total interest expense= $_____ − $_____= $_____
APR =

APR =

Average annual ﬁnance charge
Average annual loan balance$400 ÷ 2$1,600= 12.5%APR =Average annual ﬁnance charge
Average annual loan balance= _____= _____ %Step 1 Fill in the interest rate, amount of the loan, and time to determine the totalinterest expense.
Step 2 Subtract the total interest from the total amount of the loan.
Step 3 Determine the average annual ﬁnance charge and divide this by the averageannual loan balance.

Managing Your Personal Wealth—Debt

85

How to Determine the APR for Installment Loans
Installment loans are used mainly to buy consumer goods such as cars, furniture, and appliances. The amounts range widely, from under $100 up to$40,000 and more, as do the ﬁnance rates, which range from 10 to 30 percent
per annum. These rates change with market changes in interest rates.
There are different methods for determining the APRs for installment
loans. There is the precomputed interest method (also know as the effective
interest rate method), the simple interest method (a variant of the precomputed interest method), the add-on method, and the discount method (rarely
used). These methods are used by different ﬁnancial institutions. Understanding how the interest is calculated can assist you in the choice of thelowest-cost provider of installment loans.

Precomputed Interest or Effective Interest Rate Method

An installment loan requires you to make regular payments of interest andprincipal. Under this method, the total interest is computed at the outset ofthe loan. Table 15.1 gives an example of a $1,000, 12 percent, one-year installment loan, with payments on a monthly basis.
The total precomputed interest is $66.20 and the monthly payments
are $88.85, due on the last day of the month. Table 15.1 shows how the payments are divided into principal and interest. The interest remains the sameeven if payments are made before the due date. If payments are made signiﬁcantly after the due date (usually two weeks after), a late penalty is assessed.
The outstanding loan balance declines every month by the amount of theprincipal reduction, which is the greater part of the monthly payment inthis loan schedule.
With the precomputed interest method, the APR is always the same as
the stated rate unless there are additional fees that are charged on the installment loan.

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

TABLE 15.1 Installment loan—precomputed interest method
Monthly payment $88.85; interest rate 12%; term in months: 12MonthPayment

Interest

Principal
reduction

January
February
March
April
May
June
July
AugustSeptember
OctoberNovember
December$88.85
88.85
88.85
88.85
88.85
88.85
88.85
88.85
88.85
88.85
88.85
88.85

$10.00
9.21
8.42
7.61
6.80
5.98
5.15
4.31
3.47
2.61
1.75
0.89

$78.85
79.64
80.43
81.24
82.05
82.87
83.70
84.54
85.38
86.24
87.10
87.96

$1,066.20$66.20$1,000.00

TotalsLoanbalance$1,000.00
921.15841.51761.08679.84597.79514.92431.22346.68261.30175.0687.96
0.00

The following formula can be used to determine the APR of precomputed
interest loans:
APR =

2×M×I
P(n + 1)

where
M = number of payment periods in the year
I = total interest charge
P = initial amount of the loann = total number of payments

Managing Your Personal Wealth—Debt

87

The APR for the precomputed interest loan example is:
APR =

=

2 × 12 × $66.20$1,000(12 + 1)
$1,588.80$13,000

APR = 12.2%

The simple interest method is a variant of the precomputed interest
method. With the simple interest method, you pay simple interest on the outstanding balance only for the time that the money is used. For example, using
the same loan of $1,000 with a 12 percent simple interest calculation and aterm of 12 months, the monthly interest expense is determined by when payments are received. Monthly payments of $88.85 will be the same, but theinterest expense will be determined by the number of days before the payment is received.
Assume that the ﬁrst payment is made after 20 days, the second after 36
days, and the third after 21 days. Table 15.2 shows the amortization schedule for the ﬁrst three months.

TABLE 15.2 Installment loan—simple interest method
Monthly payment $88.85; interest rate 12%; term in months: 12

MonthDays between
payment

Interest

Principal
reduction

January
February
March

20
36
21

$6.58
10.86
5.80

$82.27
77.99
83.05

Loan
balance$1,000.00
917.73839.74756.69

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

The interest expense of $6.58 for January is calculated as follows: $1,000
× 20 days × 12 percent ÷ 365. The principal reduction of $82.27 is the monthly
payment of $88.85 minus the interest expense of $6.58. For February, the interest expense is $10.86 ($917.73 × 36 days × 12 percent ÷ 365). The Februaryinterest expense of $10.86 is greater than the interest expense using the precomputed interest method because there is a 36-day lapse since the firstpayment date. In March, the interest expense is less than the precomputed
interest method because the interest period is 21 days as opposed to the regular 30- or 31-day cycle used for the precomputed interest method.
The advantage of the simple interest loan is that if you make your payments before the due dates, especially at the beginning of the loan when theprincipal balance is the highest, your interest charges will be lower than theywould be using the precomputed interest method. However, with both of thesetypes of installment loans, you should check to see that there are no restrictions or penalties to making early payments of additional principal.

Add-On Method

The add-on method of computing interest on an installment loan results ina higher APR than the stated rate. Suppose you get an installment loan of$1,000 with a 12 percent add-on rate for one year with payments on a monthly
basis. The total interest is calculated as follows:
Interest expense = $1,000 × 12%= $120
The total interest is added to the loan amount and then divided by 12
to get the monthly payment of $93.33 [(1,000 + 120) ÷ 12]. With this method,
the monthly interest expense is $10 even though the loan balance declines
with each payment. Simply stated, the true interest rate is higher than the 12
percent stated rate because the borrower is still paying $10 per month in interest even after the loan balance has declined.

Managing Your Personal Wealth—Debt

89

Table 15.3 shows the ﬁrst four months of the amortization schedule forthe add-on method.
There are actuarial tables to determine the APR of the add-on method,
but the use of the formula stated previously will approximate the APR:
APR =

2×M×I
P(n + 1)

where
M = number of payment periods in the year
I = total interest charge
P = initial amount of the loann = total number of payments
The APR for the 12 percent add-on loan is:APR =2 × 12 × 120
1,000(12 + 1)

APR = 22.2%

TABLE 15.3 Installment loan—add-on method
Monthly payment $93.33; interest rate 12%; term: 12 months

Month

Payment

Interest

Principal
reduction

January
February
March
April

$93.33
93.33
93.33
93.33

$10
10
10
10

$83.33
83.33
83.33
83.33

Loan
balance$1,000.00
916.67833.34750.01
666.68

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

The lender is required by federal law to disclose the APR. If you see that
the APR is signiﬁcantly higher than the stated rate, you know that the loan
is an add-on method installment loan. Of the three methods (precomputed,
simple interest, and add-on) used to calculate interest charges, the add-on
method results in the highest interest charges and the greatest APR.

F I N A N C I A L C A LC U L ATO R # 16

How to Determine theRate of Interest on Your Credit Cards

B

anks and ﬁnancial institutions, retail and oil companies offer credit
cards. These companies are obliged to tell consumers the annual percentage rate (APR) charged as well as the method used to calculate the ﬁnancecharges. In addition, they are obliged to disclose the periodic rate, which is the
APR divided by the number of billing cycles per year (12 per year). For example, if the APR is 15 percent, then the periodic rate is 1.25 percent per month.
However, if you are not in the habit of paying off your credit card balances infull, then the effective rate is much higher than 15 percent.
Credit card issuers are very creative with their enhancements to entice
you to choose their cards. For example, most gold cards offer buyer protection packages and extended warranties on goods purchased with the cards.
Besides the waiving of the annual fee, there are other factors to consider inchoosing a credit card: the range of acceptance, the interest rates charged, thelength of the grace period (the time between the billing date and the paymentdate), and other enhancement features.
If you are in the habit of paying your credit card bills in full every month,then choosing a credit card that has no annual fee and a grace period becomes
important. However, if you are not in the habit of paying your credit card balances off in full, the interest rates charged become important. Interest rates
charged by credit card issuers can vary signiﬁcantly. Some issuers charge morethan 20 percent. By shopping around, it is possible to ﬁnd interest rates in theManaging Your Personal Wealth—Debt

91

9 to 15 percent range, possibly even lower. Bear in mind that even a 12 percent per annum rate works out to a monthly rate of 1 percent on the unpaidbalance. This is still a substantial rate when you consider that savings accounts
are only paying between 1 to 2.5 percent per annum. Be aware that someissuers of low-interest credit cards may not include a grace period.
If you sometimes pay your balances in full and other times run up abalance, you should carry two types of cards: a no-annual-fee card and asecond, low–interest rate card. Credit card issuers can use several different
methods to determine the average daily balance, which can make the effective
interest rate much greater than the stated APR.
Outlined below are four different methods of determining financecharges: the ﬁrst determines the average daily balance excluding new purchases, the second computes the average daily balance including new purchases, the third is the adjusted balance method, and the fourth is the previous
balance method.
To illustrate the calculations, the same example is used for all methods.
Assume the following:
APR

= 18%

Periodic rate

= 1.5%

New purchases on the 20th day of themonth = $200
Payments on the 15th day of themonth = $250

Unpaid balance = $500

Average Daily Balance Excluding New Purchases
Step 1: Determine the Average Daily Balance
Average daily balance ==($500 × 15 days) + ($250 × 15 days)
30 days$7,500 + $3,750
30= $375

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

Step 2: Determine the Finance Charge to Be Added to the Next
Month’s Balance
Interest/ﬁnance charge = Average daily balance × Periodic rate

= $375 × 0.015= $5.63

Average Daily Balance Including New Purchases
Step 1: Determine the Average Daily Balance
Average daily balance ==($500 × 15 days) + ($250 × 5 days) + ($450 × 10)
30 days$7,500 + $1,250 + $4,500
30= $441.67

Step 2: Determine the Finance Charge to Be Added to the Next
Month’s Balance

Interest/ﬁnance charge = Average daily balance × Periodic rate
= $441.67 × 0.015= $6.63
Of these two methods, the ﬁnance charge will always be higher when the
average daily balance includes new purchases.

The Adjusted Balance Method
This method determines the adjusted balance, which is the previous balanceminus any payments made.

Managing Your Personal Wealth—Debt

93

Step 1: Determine the Adjusted Balance
Adjusted balance = Previous balance − payments= $500 − $250
= $250

Step 2: Determine the Interest/Finance Charge
Interest/ﬁnance charge = Adjusted balance × Periodic rate

= $250 × 0.015= $3.75

The Previous Balance Method
This method gives you no credit for payments made during the period. The
previous balance is the same as the adjusted balance even if a substantial payment is made against the balance during the billing period.

Determine the Interest/Finance Charge
Interest/ﬁnance charge = Adjusted balance × Periodic rate

= $500 × 0.015= $7.50
The previous balance method results in the highest interest/ﬁnance chargeof all the methods. With the Truth in Lending law, the credit card issuer musttell you which method it uses. Worksheet 16.1 outlines the steps for determining
the ﬁnance charges for the different methods.

94

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

WORKSHEET 16.1 Steps to determine the interest/ﬁnance charge on credit cards
Average daily balance =Weighted average account balanceDays in the billing cycle= ______________= ______________
Adjusted balance = Previous balance − payments= ______________ − ______________= ______________
Interest/ﬁnance charge = Average daily balance × periodic rate
or = Adjusted balance × periodic rate
or = Previous balance × periodic rate
Step 1 Determine the average daily balance for methods including and excluding
new purchases.
Step 2 Determine the adjusted balance.
Step 3 Determine the interest/ﬁnance charge for all four methods.

F I N A N C I A L C A LC U L ATO R # 17

How to Manage Your Debt

I

f you ﬁnd that you are not saving any money because most of yourincome is tied up in debt, or you are having to juggle your payments to service
your debt payments on time, you have a problem.You should address your debt
problem before it progresses to the point of your having to declare bankruptcy.
If you have too much debt, you need to reduce it. However, before determining a strategy, you need to examine your total debt—the individual components that make up the total—the costs, and the uses for this debt toManaging Your Personal Wealth—Debt

95

determine your alternatives. Filling in Worksheet 17.1 is a starting point. By
listing all your sources of debt, the uses for this debt, and the APR costs of eachsource of credit, you will have a better understanding of your situation andhow to address any problems that might occur.

WORKSHEET 17.1 Sources of credit, uses, and costs
Sourcesof credit

Uses

Credit cards

Costs

Total
liability

Interest andprincipal

APR%_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Bank loans

Education loans

Home equity loans

Mortgage loan_______________96

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

The worksheet shows not only the monthly payments that you need tomake to service your debt, but also the APR costs and uses for this debt. You
can see your total indebtedness and evaluate whether you need to rein in yourspending. For example, being indebted because of education loans is far preferable to being indebted because of frivolous spending on short-term consumption items such as restaurants and entertainment, and living it up.
Investing in education improves your long-term earning power.
Based on the analysis of your debt and the costs, there are a number ofalternatives that you could pursue. While you are pursuing these alternatives,
you should stop making additional purchases using your credit cards. If yourdebt is more than you can handle, you should cut up all your credit cards andcall the issuers to cancel your accounts.

Pay Down Your Debt from Savings
Paying down your debt from savings may seem like a senseless option in thatyou are urged to take money out of savings/investment plans to pay down debt.
In the long-term, this approach can increase your net worth, however, particularly if the debt that you are paying down consists of high-interest credit cards.
Borrowing at 12 to 18 percent per annum means that your investments need toearn in excess of these rates in order to justify not paying down debt fromsavings/investment accounts. Start paying down your highest APR cost debt
ﬁrst. While you are paying down this debt, do not charge any more purchases.

Roll Higher-Interest Credit Card
Debt into a Lower-Rate Loan
If you have a good credit record, you can consolidate your high-interest credit
card debt into a lower-rate bank loan, or home equity loan if you are a home-Managing Your Personal Wealth—Debt

97

owner. This will reduce the amount of your monthly interest and principal
payments. The downside to this strategy is that if you are unable to pay
the monthly payments on your home equity loan, you could eventually lose
your house.

Apply for Lower-Rate Credit Cards
If you have a good credit record, you can ask your credit card issuers to rollover your accounts into lower-rate credit card accounts. If this is not possible, look for other lower-rate credit card issuers and arrange for your balance
to be transferred into these new accounts. Beware of low introductory ratecredit cards that revert to high interest rates after a few months.

Contact Your Creditors or
Get Credit AssistanceIf you are having difficulty making your payments to your creditors ontime, you should contact them. Tell them of your difﬁculties, but stress yourintentions to pay them in full at a later date when you get your ﬁnancial affairs
back in order. Ask if they can stretch out your payments and waive interest
and penalty fees until you can get on your feet again. If they agree, put it in
writing so that it is more difﬁcult for them to change their minds.
If they will not agree, seek credit counseling from a nonproﬁt credit counseling service. The toll-free number of a national nonproﬁt credit counseling ofﬁce is 800-388-2227. This ofﬁce will refer you to a local ofﬁce. You willmeet with a counselor who will, for a small fee, devise a repayment plan. Counselors will also call or meet with your creditors to get their agreement on theplan. For the plan to work, all of your creditors must agree to it and you
may be precluded from taking on any new debt. If the credit counseling ofﬁcemanages your payments to creditors, you will be charged a monthly fee.

98

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

Declare Bankruptcy
If you are so swamped with debt that you are unable to take corrective action
or if the amounts that you are able to repay are so small that it will takeyears to pay off your debt, there is a last resort—personal bankruptcy.
If you choose bankruptcy, you need to decide whether to seek legal
help. Bankruptcy lawyers may charge a ﬂat fee, which would depend on thenature and difﬁculty of the case. Legal help is expensive, but if you have a signiﬁcant amount of assets that you want to retain after ﬁling it may be advisable to seek such help.
You have two options to choose from in the Bankruptcy Code: Chapter
7, which accounts for the bulk of personal bankruptcy ﬁlings, or Chapter
13. Under Chapter 7, a court-appointed trustee takes title to your assets andsells them to raise money to repay creditors. Generally, the proceeds will notcover all the debts, which means that lenders must settle for less than theamounts that they were owed. The unpaid amounts are canceled. Certain debts
are not exempt and must be fully repaid. You must pay student loans, alimony,child support, unpaid taxes, and certain other debts. You may keep certain
assets. Some states are more generous than others with regard to assets you
may retain.
Chapter 13 of the Bankruptcy Code allows you, under a court-approved
plan, to repay debts in part or in full over an extended period of time. Thisis also known as the wage earner’s plan because it protects the ﬁler’s wages andessential property from being surrendered. Filers pay their debts over an
extended period of time and are protected from being sued by creditors.
Filing for bankruptcy may offer some relief from creditors, but there
are some major disadvantages. Personal credit records are tainted for a periodof 10 years, and many people (employers, landlords) may view you with
disfavor. Finally, bankruptcy is an expensive way to correct the excessive useof credit.
The best way to manage your debt is to use credit with care and only whennecessary.

Managing Your Personal Wealth—Debt

99

F I N A N C I A L C A LC U L ATO R # 18

How Much of a Mortgage
Can You Afford?

W

hen you are ready to buy a house or move into a larger house, thequestion to consider is: How much can you afford to spend on a house?
Two rough guidelines apply to the affordability of a house:• The house price can equal up to roughly 21⁄4 to 21⁄2 times your annual
income.
• All housing expenditures, which include mortgage payments, realestate taxes, and home owner’s insurance, should be less than 28 percent of your gross income. If you have other debt payments, the total
amount of your housing expenditures plus debt should fall below 35
to 38 percent of your monthly income. With this monthly payment,
you can then determine the amount of the loan that you would qualify for and then back into the price of the house that you can afford.
These quick and easy formulas can be inaccurate for a large percentage
of cases because everyone’s ﬁnancial circumstances are different. You needto consider many other factors, such as if you have enough cash for a down
payment on a house and closing costs at settlement, and enough income to
be able to maintain a house.
If you ﬁnance the purchase of a house with a mortgage, lenders requirethat you put some equity into the purchase, which is a down payment. Minimum down payments can vary from 5 to 20 percent of the purchase price.
For example, a $150,000 house may be unaffordable if the lender requires a
20 percent down payment ($30,000), as opposed to a 5 percent down payment ($7,500), from someone whose income will qualify for a $142,500 mortgage but who does not have $30,000 in cash for a down payment.

100

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

You will also need to have enough cash to cover mortgage points and closing costs. Mortgage points are up-front fees that lenders charge for borrowing.
These vary from 0 to 3 percent of the mortgage loan. Hence, two points on
a $95,000 mortgage would cost the buyer $1,900 (2% × $95,000). Closing costs
are the costs of settlement, which can average 3 to 6 percent of the cost of
the house. They include the costs for a title search, title insurance, attorney’s
fees, and recording fees.
Even if you have enough cash to cover the down payment, mortgage
points, and closing costs, you need to be able to cover the costs of owning thehouse. These costs include your monthly mortgage payment, real estate taxes,
home insurance premiums, utility costs, maintenance, and repairs. You alsoneed to consider whether you can cover future increases in these costs.
Worksheet 18.1 presents a sequence of steps to determine the amountthat you can afford for a house. It uses the general rule of thumb that lenders
require that payments for housing not exceed 28 percent of gross income. If
there are other outstanding debt payments, the combined housing and debt
payments should not exceed 36 percent.
By working out how much you can afford for your mortgage payments,
you can then determine the maximum amount of your mortgage as outlinedin Worksheet 18.2. From this you can determine the range of house prices thatyou can afford. The actual purchase price that you can afford depends on
the amount of your assets, which are not included in this computation. If there
are no other assets, this ﬁgure may be on the high end of the acceptable rangeof purchase prices.

________ (4)________ (5)

− 300
− 200
$1,930$290,093.61$290,093.61 ÷ 0.8

4. Deduct monthly property taxes and home insurance

5. Deduct estimated maintenance and repairs

6. Determine the monthly payment for a mortgage.

7. Use Excel or a ﬁnancial calculator to determine thetotal amount of the mortgage. See Worksheet 18.2:
interest rate 7%; 30-year term mortgage.

8. Purchase price range of house:
Divide mortgage amount in (6) by 0.9 with a 10%
down payment, or by 0.8 with a 20% down payment________ (9)________ (8) = (7) ÷ 0.9 or 0.8________ (7)________ (6) = (2) – [(3) + (4) + 5]________ (3)= $362,617.01

Worksheet________ (2) × 0.28 or 0.36 = (2)________ (1)− 450

8,000 × 0.36 = $2,880$8,000

Example3. Deduct other monthly debt payments.

2. If you have no other debt payments, multiply yourmonthly income by 28%; if you do have other debt,
multiply your income by 36%.

1. Fill in your total monthly income.

WORKSHEET 18.1 How to determine an affordable amount for a house

WORKSHEET 18.2 How to determine the total amount of a mortgage
1. Click on the f * key in the toolbar of Microsoft’s Excel spreadsheet program.
2. Highlight ﬁnancial in the left box and PV in the right box and click OK.
3. The following box comes up:
Rate
Nper
Pmt
FV
Type
Formula result =4. Enter your data.
Interest rate per period
Number of payments for the termMonthly payment
FV
Type

7% ÷ 12360$1,93000_______________________________________________________$290,093.61___________

The formula result is the amountof the mortgage loanRate

.07 ÷ 12

Nper

360

Pmt

$1,930

FV

0

Type

0

Formula result = − $290,093.61

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103

F I N A N C I A L C A LC U L ATO R # 19

How to Calculate Your
Monthly Mortgage Payment

Amortgage is a long-term loan taken out on a home/property or apiece of land. A conventional, ﬁxed-rate mortgage has equal payments
over the term of the mortgage. These equal payments are composed of twoparts: an amount derived from interest on the loan balance, and an amountthat goes toward the reduction of the loan balance.
A 30-year mortgage has 360 monthly payments (30 × 12); a 25-year mortgage has 300 monthly payments; and a 15-year mortgage has 180 payments.
The amount of the equal monthly payments is highest for the 15-year mortgage as compared with the longer-term mortgages with the same rate of interest. Conversely, the total interest expense for the 15-year mortgage will be thelowest when compared with the longer-term mortgages. Table 19.1 illustrates
these points by showing a comparison of the monthly payments, total interest, and total payments made on a $100,000 mortgage with an interest rate of
8 percent for different maturities.
The ﬂexibility provided by the different maturities of the mortgages isimportant, especially for home owners whose incomes cannot support thehigher payments of the shorter-duration mortgages. Many mortgage lenders
require that the amount of the monthly payment not be greater than 28 to 36
percent of the home owner’s income.

TABLE 19.1 Comparison of a $100,000, 8% mortgage for different maturities
MaturityMonthly payment

Total interest

Total payments

15 years
25 years
30 years$955.65
771.82733.76$72,017.00
131,546.00
164,153.60$172,017.00
231,546.00
264,153.60

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

TABLE 19.2 The effect of different interest
rates on a $100,000, 30-year mortgage
Interest rate

Monthly payment

6%
7%
8%
9%
10%

$599.55
665.30733.76804.62877.57

A change in the interest rate has a great impact on the amount of themonthly payment. Table 19.2 illustrates the effect of different interest rates on
the monthly payment for a $100,000, 30-year mortgage.

How to Lower Your Monthly Mortgage Payments• Look for the lowest interest rate when shopping for a mortgage.
• Choose a shorter-term mortgage, which will increase your monthly
payments over a longer-term mortgage with the same interest rate.
However, the total interest and total amount paid will be lowest witha shorter-term mortgage.

How to Calculate the Monthly Payment
The monthly payment that is paid to the lender is an even annuity, and theamount lent by the lender is the present value of the annuity. Since payments
are made on a monthly basis, divide the yearly interest rate by 12 to determine
the monthly rate. The formula to determine the monthly payment is:
Present value = Monthly annuity (Present value of an ordinary annuity
factor at i% for n periods)

Managing Your Personal Wealth—Debt

105

Substituting the mortgage amount for the present value and the PV of anannuity factor from annuity tables, the monthly annuity can be determined.
The tables in this book do not include 180, 300, and 360 periods. However,speciﬁcally designed mortgage tables can be purchased in most bookstores.
With these tables, the monthly annuity payments can be easily determined.
Worksheet 19.1 outlines the steps to determine the monthly payment on amortgage loan using Microsoft’s Excel spreadsheet software. The use of a ﬁnancial calculator can also assist in the determination of the monthly payment.

WORKSHEET 19.1 How to determine the monthly mortgage payment using Excel
1. Click on the f * key in the toolbar of Microsoft’s Excel spreadsheet program.
2. Highlight ﬁnancial in the left box and PMT in the right box and click OK.
3. The following box comes up:
Rate
Nper
PV
FV
Type
Formula result =4. Enter your data.
ExampleYour worksheet data

Determine the monthly payment fora $200,000, 30-year, 7% mortgage.
0.07 ÷ 12360$200,0000____________________________________________

Using Excel, the formula result is $1,330.60.

___________

Rate
Nper
PV
Type

Rate

.07 ÷ 12

Nper

360

PV

$200,000

FV

0

Type

0

Formula result = $1,330.60

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107

F I N A N C I A L C A LC U L ATO R # 20

How to DetermineYour Mortgage BalanceMortgages and installment loans encompass the same ﬁnancial principles and are essentially the same except for the length of their terms.
Mortgages have terms of 15 to 30 years, whereas installment loans have shorter
maturities. The maturities differ because the amount borrowed to ﬁnance thepurchase of a house is invariably so large that it requires a long period of time
to pay it back. The equal payments are made on a monthly basis, with a portionof the payment going toward principal reduction and the balance going toward
covering the interest expense charged by the lender. In the early years of themortgage a large proportion of the payment goes toward interest expense, as
shown in the amortization schedule in Table 20.1. As the loan balance declines,
the portion of the payment applied to interest expense declines and the portion
applied to the principal reduction increases. Toward the end of the term of
the mortgage, most of the payment is applied to reducing the loan balance.
There are many software programs that can print an amortization schedule such as the one in Table 20.1, which shows the ﬁrst 20 payments on a$200,000, 7 percent, 30-year mortgage. Some ﬁnancial calculators can also
determine mortgage balances. However, if you have neither a computer nor
a ﬁnancial calculator, you can quite easily compute an amortization scheduleusing pen and paper.

How to Calculate an Amortization Schedule
Using Pen and Paper
Using the same example as above, a $200,000, 7 percent, 30-year mortgage
with equal monthly payments of $1,330.60, the ﬁrst step is to determine howmuch of each payment is applied to interest and how much goes toward reducing the loan balance. Assume that in this example the mortgage for $200,000

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

TABLE 20.1 Amortization schedule for a $200,000, 7%, 30-year mortgage
Payment
number

Payment
amountPrincipal
reduction

Interest

Loanbalance

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

$1,330.60
1,330.60
1,330.60
1,330.60
1,330.60
1,330.60
1,330.60
1,330.60
1,330.60
1,330.60
1,330.60
1,330.60
1,330.60
1,330.60
1,330.60
1,330.60
1,330.60
1,330.60
1,330.60
1,330.60$163.93164.89165.85166.82167.79168.77
169.76
170.75171.74172.74173.75174.76
175.78176.81
177.84178.88179.92180.97182.03183.09$1,166.67
1,165.71
1,164.75
1,163.78
1,162.81
1,161.83
1,160.84
1,159.85
1,158.86
1,157.86
1,156.85
1,155.84
1,154.82
1,153.79
1,152.76
1,151.72
1,150.68
1,149.63
1,148.57
1,147.51$200,000.00
199,836.07
199,671.18
199,505.33
199,338.51
199,170.72
199,001.95
198,832.19
198,661.44
198,489.70
198,316.96
198,143.21
197,968.45
197,792.67
197,615.86
197,438.02
197,259.14
197,079.22
196,898.25
196,716.22
196,533.13

is taken out on January 1. The ﬁrst payment of $1,330.60 is made on January 31. The interest expense is the interest rate per month, which is 0.00583333(0.07÷12). Multiply the loan balance outstanding at the beginning of themonth by this monthly rate to get the interest expense for the month (200,000
× 0.00583333 = 1,166.67). Thus, from the payment of $1,330.60, $1,166.67
is applied to interest and the balance (1,330.60 − 1,166.67) of $163.93 goes
toward repaying the loan. The new loan balance becomes the old balanceminus the principal reduction, which is 199,836.07 ($200,000.00 − 163.93).
Repeating this procedure gives February’s figures, and by continuing theManaging Your Personal Wealth—Debt

109

procedure the entire amortization schedule can be determined. Table 20.2
shows the ﬁrst few months of the schedule.
Worksheet 20.1 outlines the steps for you to determine your own amortization schedule.

TABLE 20.2 Determination of an amortization schedule

Date
Jan 1
Jan 31
Feb 28

Payment(a)Interest(b)

Principal
reduction(c)

Loanbalance(d)$1,330.60
1,330.60$1,166.67
1,165.71$163.93164.89$200,000.00
199,836.07
199,671.18

Interest = rate per month multiplied by the loan balance at the beginning of
the month= 0.00583333 × 200,000= $1,166.67
Principal reduction = payment minus interest expense (a ) − (b)= 1,330.60 − 1,166.67= 163.93
New loan balance = old balance minus principal reduction (d) − (c)= 200,000 − 163.93= 199,836.07
February Interest = 0.00583333 × 199,836.07= 1,165.71
Principal reduction = 1,330.60 − 1,165.71 (a) − (b)= 164.89
New loan balance = 199,836.07 − 164.89 (d) − (c)= 199,671.18

WORKSHEET 20.1 How to determine your own mortgage amortization schedule

Date__________________________________________________________________________________________________________________________________

Payment(a)Interest(b)

Principal
reduction(c)

Loanbalance(d)__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Step 1 Fill in the loan balance at the beginning of the period.
Step 2 Fill in the monthly payments in column (a).
Step 3 Divide the interest rate of the loan by 12 to get the monthly rate.
Step 4 Multiply the monthly rate by the beginning loan balance to determine theinterest expense (b).
Step 5 Subtract the interest expense from the monthly payment to determine theprincipal reduction (c) = (a) − (b).
Step 6 Determine the new loan balance by subtracting the principal reduction fromthe old balance (d) − (c).
For the next month’s ﬁgures, go through steps 4–6.

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111

F I N A N C I A L C A LC U L ATO R # 21

Determine Your Mortgage Balance
When Additional
Principal Payments Are MadeThere are many trade-offs when choosing a mortgage/loan. Most
borrowers want to limit the amount that they pay for a mortgage, but thismeans that they need to put up a larger down payment or borrow less. Similarly, by extending the term of the mortgage/loan, the monthly payments are
smaller but the amount of interest paid over the life of the loan increases. This
trend is illustrated in Table 21.1.
The ﬂexibility provided by the different lengths of the mortgages is important, especially for home owners whose incomes cannot support the higher
payments of the shorter-duration mortgages. However, home owners can still
reduce the amount of total interest paid on longer-duration mortgages by making additional payments of principal. This strategy is illustrated in Table 21.2,
where the same principles apply as for an amortization schedule except that theloan balance is reduced by the additional principal payment. The table assumes
a $100,000, 7 percent, 30-year mortgage, with a monthly payment of $665.30;
with the ﬁrst payment, an additional $300 is sent to the mortgage company.
To complete the amortization schedule, you need to work through thethree steps for each month before moving on to the next month. In otherwords, you cannot work through an additional three months of interest andthen move to the principal reduction. You would need to determine the
TABLE 21.1 Comparison of a 13%, $100,000 mortgage with different maturities
MaturityMonthly payment

Total interest

Total payments

15 years
25 years
30 years$1,265.24
1,127.84
1,106.20$127,743.59
238,350.59
298,231.83$227,743.20
338,350.00
398,232.00

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

TABLE 21.2 The construction of an amortization schedule with additional payments

Date

6/01
6/30
7/01
8/31
9/30

Payment(a)Additional
payment(b)$665.30
665.30665.30665.30$300.00
350.00150.00
0.00

Interest(c)

Principal
reduction(d)Loanbalance(e)$583.33
581.11578.57577.19$381.97434.19236.7388.11$100,000.00
99,618.03
99,183.84
98,947.11
98,859.00

Interest = monthly interest rate times loan balance of the previous month:0.07 ÷ 12 × (e)6/30 = 0.00583333 × 100,000.00 = $583.33
7/31 = 0.00583333 × 99,618.03 = 581.11
8/31 = 0.00583333 × 99,183.84 = 578.57
9/30 = 0.00583333 × 98,947.11 = 577.19
Principal reduction = payment + addt’l payment – interest: (a) + (b) − (c) = (d)6/30$665.30 + 300.00 − 583.33 = 381.97
7/31
665.30 + 350.00 − 581.11 = 434.19
8/31
665.30 + 150.00 − 578.57 = 236.73
9/30
665.30 + 0.00 − 577.19 = 88.11
Loan balance = beginning loan balance − principal reduction: (e) − (d)6/30 $100,000.00 − 381.97 = 99,618.03
7/31
99,618.03 − 434.19 = 99,183.84
8/31
99,183.84 − 236.73 = 98,947.11
9/30
98,947.11 − 88.11 = 98,859.00

interest expense for the next month, and then determine the principal reduction and new loan balance before determining the interest for the next month.
Making extra payments of principal decreases the total interest paid on
the loan/mortgage. Worksheet 21.1 provides the outline and steps for the construction of your own mortgage schedule with additional payments.

WORKSHEET 21.1 How to determine an amortization schedule with additional
payments of principal

Date__________________________________________________________________________________________________

Payment(a)Additional
payment(b)______________________________________________________________________________________________________________________________________________________________________________________

Interest(c)

Principal
reduction(d)Loanbalance(e)________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Step 1 Fill in the loan balance at the beginning of the period.
Step 2 Fill in the monthly payments in column (a).
Step 3 Enter the additional payment (b).
Step 4 Divide the interest rate of the loan by 12 to get the monthly rate.
Step 5 Multiply the monthly rate by the beginning loan balance to determine theinterest expense (c).
Step 6 Subtract the interest expense from the sum of the monthly payment to determine the principal reduction (d) = (a) + (b) − (c).
Step 7 Determine the new loan balance by subtracting the principal reduction from theold balance (e) − (d)For the next month’s ﬁgures, go through steps 3–7.

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

Making extra payments on a loan not only saves you interest but also shortens the length of the loan. Beware of institutions that offer to assist you in the
additional payments of your mortgage. They are offered under the name ofbiweekly mortgages and various other names. If you do not have a prepayment
penalty clause in your mortgage, you can make additional payments by yourself without the help of these institutions. These institutions charge fees and collect your payments twice a month, but they submit a payment to your mortgage
company only at the end of the month. Thus, they have the use of your money
to your detriment, and you end up paying them for this.

F I N A N C I A L C A LC U L ATO R # 22

Adjustable Rate Mortgages
and How They WorkC

onventional mortgages have a ﬁxed interest rate over the term of
the mortgage, but with an adjustable rate mortgage (ARM) the interest rate ﬂuctuates over the life of the loan. With an ARM, the borrower bears
the risk of changing interest rates, whereas with a conventional ﬁxed-rate
mortgage, the lender bears the risk of changing interest rates in the economy.
When interest rates rise, the lender of a conventional mortgage is stuck holding a lower–interest rate mortgage. On the other hand, if interest rates fall theborrower is stuck holding a higher-rate mortgage, but the borrower has theoption of reﬁnancing the mortgage with a lower-rate loan.
With an ARM, the interest rate changes according to an index selectedby the lender. The adjustment period varies on a quarterly, semiannual, or
annual basis, or for longer periods of time. Some indices are more volatile
than others, so you should take care in selecting your ARM by investigating
the index tied to the mortgage. For example, if you anticipate a decline ininterest rates, you would want an ARM that has an index that is tied to
one-year Treasury securities versus a slower-moving index tied to ﬁve-year
Treasury securities.

Managing Your Personal Wealth—Debt

115

ARMs are offered at lower rates than conventional mortgages, usually 1
to 3 percent lower. Some ARMs are offered at very low rates, known as teaser
rates, to encourage borrowers. However, after a short period of time, generally a year, the rate reverts back to normal rates.
With an ARM, a decline in the interest rate results in a drop in the monthly
payment; conversely, an increase in the rate results in an increase in the monthly
payment. Consequently, borrowers should always work out the worst-case scenario to make sure that they can cover those larger payments.
There are a number of features of these loans that you should consider
before settling on a particular ARM. Worksheet 22.1 provides a checklist ofthese features to assist you in your choice of an adjustable rate loan. Most
ARMs have interest rate caps and/or payment caps. Interest rate caps limit theamount of the rate increase or decrease over the term of the mortgage. Commonly, there is a limit from one adjustment period to another (for example,

WORKSHEET 22.1 Comparison list for choosing an adjustable rate mortgage (ARM)
Financial institution____________________________________

Loan amount____________________________________

Points____________________________________

Down payment____________________________________

Beginning APR____________________________________

Beginning monthly payment____________________________________

Interest rate cap____________________________________

Lifetime rate cap____________________________________

Payment cap____________________________________

Maximum monthly payment____________________________________

Negative amortization yes/no ____________________________________

Type of index____________________________________

Prepayment penalty____________________________________

Convertible ARM____________________________________

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

no more than 2 percent a year) and a lifetime interest rate cap (no morethan 6 percentage points, for example, over the life of the loan).
Payment caps limit the amount of the payment increases or decreases atadjustment periods and over the life of the loan. If an ARM has a payment cap
without an equivalent interest rate cap, when interest rates rise signiﬁcantly,
there is the possibility of the payment not covering the interest expense, whichcauses negative amortization. This means that instead of the loan balance declining with the monthly payment, it will increase. For example, an ARM with apayment cap of $700 per month has an interest rate increase to 10 percent,which results in a monthly payment of $720. The additional $20 of the payment is not covered and will be added to the mortgage balance, thereby increasing the amount to be paid back. Avoid an ARM with a payment cap.
In evaluating the different ARMs, the most important factors are the interest rate caps and the frequency of rate changes, the upper and lower limits on
the monthly payments, the type of index to which the mortgage is tied, andwhether there is negative amortization. Other factors to consider are a prepayment penalty and a conversion privilege. The former refers to the ability
to pay down additional principal without being penalized, and with the latter, the borrower has the option to convert to a ﬁxed-rate mortgage within acertain period of time. Avoid loans with prepayment penalties.

How to Calculate an ARM Schedule
Assume an ARM of $100,000 with an initial rate of 4 percent, an adjustment period of a year, and an annual interest rate cap of 1 percent with a lifetime cap of 5 percentage points, for a term of 30 years.

Step 1: Determine the Monthly Payment

The monthly payment can be determined using Microsoft’s Excel program,as shown here, or with a ﬁnancial calculator.

Managing Your Personal Wealth—Debt

Rate.04 ÷ 12

Nper

360

PV

$ −770.36

FV

0

Type

0

117

Formula result = $477.415

The monthly payment is $477.42. With software programs, you can printout an amortization schedule. Alternatively, you can easily prepare one byhand, as shown next.

Step 2: Determine the Amortization Schedule to the End of theFirst Adjustment Period

In Table 22.1, the interest is determined by multiplying the monthly rate
(0.04 ÷ 12) by the beginning loan balance. The interest is deducted from thepayment to determine the principal reduction, which is then deducted fromthe beginning loan balance to determine the new loan balance.

TABLE 22.1 Amortization schedule to the end of the ﬁrst adjustment period

Date

Payment

Interest

Principal
reduction

Loanbalance

1
2
3
4
5
—
12

$477.42477.42477.42477.42477.42—477.42$333.33
332.85332.37331.89331.40—327.96$144.09144.57145.05145.53146.02—149.46$100,000.00
99,855.91
99,711.34
99,566.29
99,420.76
99,274.74—
98,238.91

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

Step 3: If the Interest Rate Changes, Determine the New Monthly
Payment

There are two changes involved in the determination of the new monthly payment. There is a rate change (the rate could go up or down by 1 percent fromthe beginning rate of 4 percent) and the new term for the mortgage is 29 years(348 monthly payments). If the rate goes up to 5 percent and the principalbalance is $98,238.91, the new monthly payment will be $535.26, determined
as follows using Excel:
Rate 0.05 ÷ 12
Nper 348
PV$98,238.91
FV
0Type 0
Formula result = $535.264

Step 4: Determine the New Amortization Schedule

The following adjusted data is used to determine the new amortization schedule (Table 22.2).

TABLE 22.2 Amortization schedule for the beginning of the second adjustment
periodDate

Payment

Interest

Principal
reduction

13
14$535.26535.26$409.33
408.80$125.93
126.46

Loanbalance$98,238.91
98,112.98
97,986.52

Managing Your Personal Wealth—Debt

119Interest rate = 0.05 ÷ 12
Loan balance = $98,238.91
Payment= $535.26
Interest = 0.05 ÷ 12 × $98,238.91= $409.33
Principal reduction = $535.26 − $409.33= $125.93
New loan balance = $98,238.91 − $125.93= $98,112.98

These steps are repeated to determine the new monthly data until there
is a new rate change. If the rate goes down, the new rate will be used together
with the remaining months to term and the current loan balance to determine the new monthly payment.
Worksheet 22.2 outlines the steps for you to determine your own amortization schedule.

WORKSHEET 22.2 Steps to determine your amortization schedule
Step 1 Determine your monthly payment.
_________
Step 2 Determine the amortization schedule through the end of the ﬁrst adjustment
period.
Monthly payment
Term of loan__________________

Monthly rate _________
Loan balance _________

Date

Payment

Principal
interest

Loan
reduction

Loanbalance____________________________________________________________________________

Step 3 With a rate change, determine your new monthly payment.
Use the number of months remaining for the loan, the new monthly
interest rate, and the loan balance at the beginning of the month(end of last month).
New monthly payment _______________
Step 4 Determine your new amortization schedule.

Date

Payment

Principal
interest

Loan
reduction

Loanbalance____________________________________________________________________________

Steps 3 and 4 are repeated at the next rate change.

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121

F I N A N C I A L C A LC U L ATO R # 23

Which Type of Mortgage
Should You Choose?

Although only two major types of mortgages, ﬁxed and adjustablerate, have been discussed, there are many variants of these. No matter
what type of mortgage you consider, take the time to understand how the
mortgage works and all the intricacies of that mortgage.

Factors to Consider When Choosing a Mortgage
In weighing the choices between ﬁxed-rate and adjustable rate mortgages, you
should consider three factors:
1. Market rates of interest
2. The length of time that you plan to hold your mortgage
3. Your willingness to take on ﬁnancial risk
The trade-off is a ﬁxed monthly mortgage payment for the term of theloan with a ﬁxed-rate mortgage versus initial lower monthly payments andthe possibility of future increased monthly payments in the event of risinginterest rates with an adjustable rate mortgage.

Market Rates of Interest

If market rates are low or have been declining over the past few years, you
should consider a ﬁxed-rate mortgage. Alternatively, if market rates are highand are expected to decline, you may be swayed toward an adjustable rate
mortgage (ARM). With the latter, you need to determine the maximum
monthly ARM payment in the worst-case scenario to determine whether

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

the initial beneﬁts of lower ARM payments outweigh the risk of higher payments in the future, should interest rates rise.

Length of Time That You Plan to Hold Your Mortgage

The length of time that you plan on holding the mortgage is crucial to your decision. Savings on an ARM are guaranteed until the end of the ﬁrst adjustment
period, and with the adjustments if interest rates do go up, you may still beable to save over a ﬁxed-rate mortgage for a few years. If you plan to hold themortgage for a short time, three years or less, the total payments on an ARM may
be lower than those on a ﬁxed-rate mortgage. You would need to work throughthe calculations to determine whether you should choose an ARM over a ﬁxedrate mortgage. Worksheet 23.1 outlines the steps for these calculations.
If you plan on holding your mortgage for longer than ﬁve to seven years,
you may be better off with a ﬁxed-rate mortgage. After all, even mortgage
bankers do not know what will happen with interest rates into the future. Ifthey did, they would not issue loans where they bear the risk of changes ininterest rates. For example, if they knew that interest rates were going to decline
in the future, they would issue only ﬁxed-rate mortgages. Similarly, if they
thought that interest rates were going to increase, they would issue only ARMs.

Your Willingness to Bear Risk

With an ARM, the borrower bears the risk of higher monthly payments if
interest rates rise. You need to assess your own situation as to whether you canafford these higher monthly payments. Will these higher monthly payments
make it difﬁcult for you to make ends meet in your budget? Is your income
from your job stable? If you cannot easily afford the highest possible monthly
payments, you should go for a ﬁxed-rate mortgage.
If there are any savings in Step 7, this amount can be invested. The
invested savings will be even greater in the future when the time value ofmoney is taken into account.

Managing Your Personal Wealth—Debt

123

WORKSHEET 23.1 Adjustable rate or ﬁxed-rate mortgage
Step 1 Fill in the length of time that you plan on holding your mortgage.
______________ (1)Step 2 Determine the monthly total savings from an ARM over a ﬁxed-rate mortgage
through the end of the ﬁrst adjustment period.
ARM
Monthly payment _________ (a)Fixed-rate mortgage
Monthly payment _________ (b)Savings with an ARM (b) − (a) _________ − _________ = _________ (c )Total savings [number of months × (c )] _________ × _________ = _________ (d)Step 3 Assume the maximum rate increase until the next adjustment period.
ARM
Monthly payment _________ (a)Fixed-rate mortgage
Monthly payment _________ (b)Savings with an ARM (b) − (a) _________ − _________ = _________ (c )Total savings [number of months × (c )] _________ × _________ = _________ (d1)
Step 4 Add total savings from Steps 2 & 3 (d) + (d1) ______ + _______ = ______ (e)Step 5 Repeat Steps 3 & 4 until you reach the length of time in Step 1.
Step 6 Add the total savings, including any negative numbers (if ARM payments are
greater than ﬁxed-rate monthly payments) to determine the total savings.
Step 7 If the total is a positive amount, choose an ARM; if it is negative, go with aﬁxed-rate mortgage.

Worksheet 23.2 is an example that illustrates the use of Worksheet 23.1.
Assume a comparison of an ARM with initial monthly payments of $530.20
versus ﬁxed monthly payments of $604.30. With the maximum increase at
the end of the first adjustment period (after one year), the monthly payment for the ARM is $576.00. The next maximum increase after the second
12 months raises the monthly payment to $615.65. The holder plans on holding the mortgage for three years.

WORKSHEET 23.2 Adjustable rate or ﬁxed rate mortgage ﬁlled in
Step 1 Fill in the length of time that you plan on holding your mortgage.
36 months (1)Step 2 Determine the monthly total savings from an ARM over a ﬁxed-rate mortgage
through the end of the ﬁrst adjustment period.
ARM
Monthly payment $530.20 (a)Fixed-rate mortgage
Monthly payment $604.30 (b)Savings with an ARM (b) − (a) $604.30 − $530.20 = $74.10 (c )Total savings [number of months × (c )] 12 × $74.10 = $889.20 (d)Step 3 Assume the maximum rate increase until the next adjustment period.
ARM

Fixed-rate mortgage

Monthly payment $576.00 (a)Monthly payment $604.30 (b)Savings with an ARM (b) − (a) $604.30 − $576.00 = $28.30 (c )Total savings [number of months × (c )] 12 × $28.30 = $339.60 (d1)
Step 4 Add total savings from Steps 2 & 3 (d) + (d1) $889.20 + $339.60 = $1,228.80 (e)Step 5 Repeat Steps 3 & 4 until you reach the length of time in Step 1.
ARM
Monthly payment $615.65 (a)Fixed-rate mortgage
Monthly payment $604.30 (b)Savings with an ARM (b) − (a) $604.30 − $615.65 = − $11.35 (c )Total savings [number of months × (c)] 12 × − $11.35 = − $136.20 (d2)After 36 months the total savings for the ARM is:$889.20 + $339.60 − $136.20 = $1,092.60

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F I N A N C I A L C A LC U L ATO R # 24

When Should You
Refinance Your Mortgage?

T

here are three major reasons for reﬁnancing a mortgage:
1. To lower monthly payments because interest rates have come down
2. To switch from one type of mortgage to another; for example, froman ARM to a ﬁxed-rate mortgage or any other type of mortgage
3. To create a source of capital by reﬁnancing for a greater capitalamountWhen interest rates decline, reﬁnancing your old mortgage with a new,lower-rate mortgage can lower your monthly payments. However, there arecosts associated with reﬁnancing. The closing costs to reﬁnance a mortgage
typically range from 3 to 5 percent of the loan. In order to lower your monthly
payments from reﬁnancing, you have to pay a lump sum amount in closing
costs. Thus, there are two factors that should be considered in determining
whether you should reﬁnance: the length of time that you plan on staying
in your house and the amount of the savings from the lower mortgage payments. Taking into account the closing costs and the lower mortgage payments, you can use Worksheet 24.1 to see if you will reach the break-evenpoint to justify reﬁnancing your mortgage.
If you have an adjustable rate mortgage (ARM) and you decide thatyou are going to stay in your house for a longer period of time than originally
expected, you can reﬁnance to a ﬁxed-rate mortgage. The prospect of ﬂuctuating mortgage payments with an ARM may make you uncomfortable, causing you to reﬁnance to a ﬁxed-rate mortgage to give yourself peace of mind.
In such a case, you may not save any money by trading in an ARM for a ﬁxedrate mortgage, as rates are much higher on the latter, but you will have secured
some peace of mind with ﬁxed monthly payments.

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WORKSHEET 24.1 How much will you save from reﬁnancing?
ExampleYour worksheet50____________

Points2,000____________

Title search and insurance

1,000____________

Credit report100____________

Survey250____________

Appraisal300____________

Inspection fees300____________

Attorney fees

1,000____________

Recording fees75____________

Other fees0____________

Total reﬁnancing costs$5,075(a) ____________

Monthly savings
Current monthly payment$1,069____________New monthly payment− 919− ____________

150(b) ____________

Reﬁnancing costs
Application fee

Savings

Number of months to break even: 5,075 ÷ 150 = 34 (a) ÷ (b) ____________
Reﬁnance costs divided by monthly savings

There are other types of mortgages, such as graduated payment mortgages
and mortgages with balloon payments, that you may want to switch to aconventional ﬁxed-rate mortgage for the same reasons as cited above. With a
graduated payment mortgage, the monthly payments are lower than they would
normally be in the early years of the mortgage and then increase over a periodof time to take into account the lower earlier payments of the loan. There are
a number of disadvantages with this type of mortgage, in that the total inter-

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127

est paid will be much greater than on a conventional loan and there may also
be some negative amortization. Also, if your income does not rise as anticipated, it may be harder to meet the higher mortgage payments after the initial low-payment period. A balloon mortgage has a shorter term with equalmonthly payments, and then at the end of the mortgage there is a large payment. Even if there are no savings from trading one type of mortgage foranother, you may want to reﬁnance to give yourself greater peace of mind.
Because interest on a mortgage is still a tax-deductible item for taxpayers who itemize their deductions, many people reﬁnance their mortgages
for higher amounts in order to get the additional cash that they need forvarious purposes. The money might be used to pay off high-interest consumer
debt, which is not tax deductible, to raise funds to start a business, or to buy
a new car.
Reﬁnancing a mortgage at a lower rate will reduce your monthly payments, as well as the total interest paid on the mortgage.
In the worksheet example, in order to recoup the costs of reﬁnancing, theborrower would need to stay in the house for at least 34 months to break evenand longer to experience the beneﬁts of reﬁnancing.

F I N A N C I A L C A LC U L ATO R # 25

Should You Rent or Buy a House?

The question of whether to rent or buy is a matter of individual choice.
It is relatively easy to list the ﬁnancial factors concerning renting andbuying, but the nonﬁnancial considerations are much more difﬁcult to weigh.
Housing decisions are extremely important from many viewpoints.
The purchase of a home is probably the largest single expenditure that individuals make. For renters, rental expenses could account for up to 40 percent of their monthly budgets. However, the housing decision goes beyond
expenditures because where you choose to live determines your commuting
time to work, access to shopping, your neighborhood friends, your children’s128

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friends, the school system, and so on. A tremendous amount of time andthought are invested in making housing decisions.
In addition to financial reasons, some people rent because they may
not want to be faced with the responsibilities of home ownership or they may
expect to be in a location for only a short period of time.
There are several advantages to renting:• You have greater mobility when you rent. When your lease expires,you can leave without having to sell the property. If mobility isimportant to you, do not tie yourself down with a long-term lease
without an escape clause.
• You are not tying up your money (other than the amount of the
security deposit), which means that you can invest your money oruse it for other purposes.
• Renting may result in reduced expenses for maintenance and repairs.
Landlords are usually responsible for most, if not all, repairs.
The disadvantages of renting are:
• Your rental payments give you no ownership interest.
• You have no control over rental increases.
• If the property appreciates, you do not share in the appreciation.
• You cannot deduct your rental payments against your federal taxes(interest on a mortgage and real estate taxes are currently taxdeductible expenses).
• Your lease may restrict you from having pets or starting a family.
• You could have loud, messy neighbors or an ineffectual landlord.
Renting is much simpler and less time consuming than buying a house.
For example, if you rent a house in a neighborhood that has poor schoolsor high crime, you can easily move out. If you have bought the house, theproblem will be more time consuming to rectify, and probably more costly.
From a home owner’s point of view, there are several advantages to homeownership:

Managing Your Personal Wealth—Debt

129• Over long periods of time, most housing units appreciate in value
and prices tend to keep pace with inﬂation. Home ownership could
be considered an investment as well as a hedge against inﬂation.
• Home ownership provides some tax relief in that the interest expenseon the mortgage and the real estate taxes are deductible items fromtaxable income at the federal level. Interest expense on a mortgage is
not subject to being added back to the computation of the alternative
minimum tax (AMT).
• Over time, home owners increase their equity position in theirhomes if they had ﬁnanced their purchase. A portion of each mortgage payment goes toward the repayment of the mortgage. Thus,
over time, home owners owe less and their equity stake increases.
• Home owners who have sufﬁcient equity in their homes or who haveseen price appreciation of their homes can use the buildup as asource to provide new loans, such as home equity loans.
• Home ownership provides more freedom than renting. There are nolandlords and no restrictions concerning pets, children, and so on.
• Home ownership often brings about a greater personal commitment
to the neighborhood and community activities.
The disadvantages of home ownership are:• With home ownership, you bear the ﬁnancial risk if property values
fall. If you have to sell your house when the property market isdepressed, you could lose money.
• Home ownership decreases your mobility. It may not be that easy tosell a house and move to another location in a short period of time.
The decision of whether to rent or buy is not always clear-cut or easy. An
evaluation of both the ﬁnancial and nonﬁnancial aspects helps to resolve
the dilemma. Worksheet 25.1 compares the costs of renting versus buying
to see which is lower. The calculation in this example is used only to illustrate
the process involved and is not meant to show that it is always less costly toWORKSHEET 25.1 Comparison of the costs of renting versus buying
ExampleYour worksheet$12,000
1,800
200_________________________________

42___________$14,042___________

Mortgage payment ($967 × 12)
Real estate taxes
Maintenance & repairs (100 × 12)
Utilities (200 × 12)
Insurance
Interest foregone on the down payment
10,000 × 6% × (1 − 30%*)$11,604
2,400
1,200
2,400
500

_______________________________________________________

420___________

Gross annual cost of buying$18,524___________

×(3,383)_______________________________________________________

Less equity buildup(2,727)___________Net annual cost of buying$12,414___________

Annual cost of renting
Rent ($1,000 × 12)
Utilities (150 × 12)
Tenant’s insurance
Interest foregone on the deposit($1,000 × 6% × (1 − 30%*)
Total annual cost of renting
Annual cost of buying(with a mortgage of $90,000 at 10%)Less tax savings from deductions:Interest on mortgage
Real estate taxes
× marginal tax rate*
Tax savings$8,8772,400
11,277× 0.30

These costs could be adjusted further for any appreciation of the property.
*A 30% marginal tax rate is assumed.

Managing Your Personal Wealth—Debt

131

buy. In some areas, rental expenses may be low and interest rates on mortgages may be comparatively high, making mortgage payments very high. Consequently, it may be beneﬁcial to rent until mortgage interest rates come down.
In the worksheet example, the cost of renting ($14,042) is higher than theafter-tax cost of buying ($12,414). You need to consider, however, that manyof these figures will change over a period of a few years: rent increases,
increased home maintenance costs, decreasing mortgage interest expenses,
and possible short-term appreciation/depreciation of home prices. Homeownership provides many more ﬁnancial advantages. However, if you intend
to move in the near future, renting may be more advantageous than buying.

F I N A N C I A L C A LC U L ATO R # 26

What You Should Know
About Leasing a Car and
How a Lease WorksThe popularity of leasing cars has increased, as evidenced by the growing number of automotive advertisements in print and on radio and television containing information about speciﬁc leases. However, just because leasing
is popular does not mean that it is the right alternative for you. There are a number of things that you should know about leasing before taking the plunge.
Leasing an automobile is a contractual obligation to make monthly
payments over a predetermined period of time, usually two, three, or four
years. Depending on the type of lease, the car may be returned to the leasing
company at termination.
There are two basic types of leases: open end and closed end. An openend lease involves monthly lease payments made for the period of the lease.
At the end of the lease, a ﬁnal payment based on the resale value is made tobuy the car. With a closed-end lease, lease payments are made over the lease
period. At the end of the lease, you hand in the keys and walk away from the132

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car. Certain conditions apply, such as returning the car in reasonable condition and not exceeding the maximum mileage set by the lease agreement.
Most of the advertisements in the media are for closed-end leases, in which
there is the implication that leasing is cheaper than ﬁnancing a car. Don’t be
misled until you do your homework on the speciﬁcs of the lease. Leasing companies have to buy the cars that they lease, and after the leasing period thesecars have depreciated considerably. Consequently, leasing companies charge torecover both the interest costs that they have paid to buy the cars and theamount of the depreciation of the cars (the fall in resale value) when they are
returned to them, in addition to their overhead costs and a certain amountof proﬁt. Thus, you need to know the details of your lease, as outlined in Worksheet 26.1, because they determine the amount of the lease payments.
The ﬁrst item in the worksheet is the capitalized cost of the car, which isthe selling price of the car. To lower your lease payments, you need to negotiate the selling price of the car. The lower the capitalized cost, the lower
your lease payments. Thus, don’t fall into the trap of thinking that you do notneed to negotiate when you lease a car.
The capitalized cost reduction includes the trade-in value of your oldcar, or the amount of the down payment. This category also includes dealer
rebates and discounts.
The adjusted capitalized cost is the capitalized cost minus the cost reduction, which is the amount used to determine the monthly lease payment.
The residual value is the estimated value of the car at the end of the lease.
The percentage is supplied by the car dealer or lease company. In this case, it
is 47 percent, which is then multiplied by the manufacturer’s suggested
retail price (MSRP). Should you decide to buy the car at the end of the lease,this is the amount that you would pay. There is no reason why you cannot
negotiate an amount that is less than the residual value when you are readyto purchase the car at the end of the lease.
Depreciation is the amount charged for the decline in value of the car. The
amount for depreciation is divided by the number of months in the lease term
to determine the monthly amount for depreciation that is a major part of yourlease payment.

WORKSHEET 26.1 How to determine your lease payment
The example uses the following ﬁgures, as provided by Clews & Strawbridge,
Inc., to lease a new Saab 9-5 with a MSRP of $37,990. The negotiated priceis $36,990.
ExampleYour worksheet

1. Capitalized cost*
2. Capitalized cost reduction*$36,990.00
5,000.00______________________________

3. Adjusted capitalized cost (1 − 2)
4. Residual value*

31,990.00
17,855.40______________________________

5. Depreciation (3 − 4)
6. Number of months in lease term
7. Depreciation per month (5 ÷ 6)

14,134.60
36392.63_____________________________________________

49,845.40
0.0028139.57_____________________________________________

11. Monthly sales tax (7 + 10) × 0.09*

47.90_______________

Monthly lease payment (7 + 10 + 11)

580.10_______________

Depreciation

Finance expense
8. Adjusted cap. cost plus
residual value (3 + 4)
9. Money factor*
10. Monthly ﬁnance expense (8 × 9)
Sales Tax

*Figures provided by Clews & Strawbridge, Inc.

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The second factor that contributes toward your monthly lease payment
is the ﬁnance expense. Many lease companies use a money factor instead of aninterest rate. Multiplying the money factor by 24 will give an approximationof the interest rate charged. In this case, the money factor of 0.0028 equals
6.72 percent.
The last item that contributes toward your monthly lease payment is sales
tax. In this case it is 9 percent of the sum of the monthly ﬁnance expense
and the depreciation charge.

How to Lower Your Monthly Lease Payments
1. Negotiate the price of the car. The lower the price, the lower the capitalized cost and the lower the lease payments.
2. Do your homework to determine the resale value of the cars thatyou are interested in leasing so that you can negotiate a higher residual value.
The higher the residual value, the lower the depreciation and the lower themonthly payments.
3. Convert the money factor into an approximate interest rate and negotiate a lower interest rate.
4. Negotiate the monthly payment to see if you can reduce it.
5. If you are trading in a vehicle, do your homework to see what the resale
value is so that you get a fair price, which is used to reduce the capitalized cost.
6. Study the terms of the contract and understand them.
7. Watch for the excessive mileage charge. Negotiate additional miles
before you sign the contract. For example, if the lease agreement is for 12,000
miles per year and you generally do 15,000 miles per year, negotiate theextra mileage into the contract. This can save you additional charges at theend of the lease.
8. Do not make larger up-front payments than are required and be on
your guard for any add-on payments.

Managing Your Personal Wealth—Debt

135

9. Shop around at different dealers for their lease terms. In general, dealers—due to their backing from the car manufacturer—can offer better leasing deals than lease companies.

Advantages and Disadvantages of Leasing
The advantages of leasing a car are:
• The monthly lease payments may be lower than ﬁnancing or buying
a car.
• If you use your car for business, a lease agreement provides detailed
records for tax purposes.
• You don’t have to put out a large amount of cash at the inception of
the lease.
The disadvantages of leasing a car are:
• You are faced with a never-ending obligation of monthly lease
payments.
• If you plan on buying the car at the end of the lease, you will end
up paying more for the car than if you had originally bought or
ﬁnanced the car.
• If you turn in the car early, a termination fee is charged.
Leasing a car is good for someone who likes to exchange cars every twoor three years and who does not mind the everlasting monthly lease payments.
Understanding how the lease payment is determined will assist you in negotiating better terms for your lease agreement.

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F I N A N C I A L C A LC U L ATO R # 27

Should You Buy, Lease, orFinance Your Car?

T

he least costly method of owning a car is to buy it with cash. If you
have the money and there are no special low–interest rate loans available from the automobile manufacturing companies, pay cash. For example, currently many of the automobile manufacturers are offering 0 percent
ﬁnance deals on many of their cars. If you cannot get a further discount for
paying cash, it makes sense to use the 0 percent financing to buy the car.
This way you have the use of your money, which can be invested at current
rates of interest until it is ﬁnally used to pay for the car.
Another reason to pay cash for the purchase of a car is that a car is not an
investment. It depreciates in value, and ﬁnance costs and lease costs add signiﬁcantly to the overall cost of the car.
Since automobiles are expensive, many people do not have the cash available to buy their cars. Financing then becomes an option. Even though you
may decide at the outset to ﬁnance, you should still go through the negotiation process to obtain the best price in order to lower your monthly payments.
Car loans are available from several sources: banks, credit unions, dealer ﬁnancing, and other ﬁnancial institutions. Ask the dealer if subsidized low–interest
rate loans are available from the automobile manufacturer. However, even if
the rate of interest is lower than competitive rates, you need to make surethat the loan amount is based on your negotiated price and not the list price.
Often manufacturers will offer low-interest rates of 0 percent, 1 percent, andso on, but they will inﬂate the price to get back part of their subsidy.
Car manufacturers have also offered rebates instead of low-rate subsidized loans (often where the car price is inﬂated to the list price). In certain
cases, it may be better to take the rebates, which will lower the purchase price,and then ﬁnd your own ﬁnancing from banks, credit unions, and so on.
When comparing different sources of ﬁnancing, check the annual percentage rates (APRs), which represent the true cost of the loan. For exam-

Managing Your Personal Wealth—Debt

137

ple, the loan with the lowest monthly payments may not necessarily havethe lowest cost because you may be making the payments for a longer periodof time, and the ﬁnance charges may be greater.
When you take out ﬁnancing, do not buy life or disability insurance inconjunction with the loan. These premiums are expensive and you do notneed them. If you are underinsured, you are better off looking at your needs
independently of your purchase.
Worksheet 27.1 outlines the steps to determine whether you should pay
cash or ﬁnance the purchase of a car. In general, ﬁnancing is more costly thanpaying cash, but there are certain situations with special low-rate ﬁnancingthat would make it necessary for you to use this worksheet to see which situation is least costly.
As mentioned earlier in this section, it is almost always cheaper to pay cashthan to ﬁnance the purchase of a car. However, when special low–interest
rate loans are provided by the auto manufacturers, you need to work throughthe speciﬁcs. A shortcut to Worksheet 27.1 is to compare the APR of the special ﬁnancing with the after-tax rate of return on the use of the money.
In this case, assume the money could be invested at 3 percent for three
years. If the marginal tax rate of the investor is 39 percent, then the after-tax
rate of return on the money forgone is 1.83 percent [(1 – 0.39)0.03]. The rateof return is less than the special low-rate financing of 1.9 percent, so it
would be more costly to ﬁnance than to pay cash.
Worksheet 27.2 outlines the steps for comparing the interest rates to determine whether to ﬁnance or pay cash.
Special low–interest rate ﬁnancing and manufacturer’s rebates cloudthe issue for buyers as to which is cheaper in the acquisition of a car. Worksheet 27.3 shows the steps to determine whether you should go for the cash
rebate or the special low-rate ﬁnancing.
In the example in Worksheet 27.3, it is cheaper to accept the cash rebate
and pay cash. However, if you do not have the cash, you could take the rebate
and arrange for ﬁnancing from other sources (banks, credit unions). You
would need to work through this worksheet to compare the cost of ﬁnancing
with the rebate versus the low-rate ﬁnancing provided by the dealer.

WORKSHEET 27.1 Financing versus paying cash for the purchase of a car
Example: You can buy a car for $25,000 or ﬁnance it with a special low-rate
loan of 1.9% for three years.

ExampleYour
worksheet$25,000__________Cash cost to purchaseTotal sales priceInterest income lost on the payment of cash($25,000 invested at 3% for 3 years)
Less taxes(assume a 30% marginal tax bracket)(.30 × 2325)

2,325__________(697.50)__________

Cost to buy the car$26,627.50 __________

Cost to ﬁnance the car
Total sales price
Down payment
Interest income lost on down payment($2,000 invested at 3% for 3 years)
Less taxes (30% marginal rate)(.3 × $186)$25,000

Sales price minus down payment
Monthly payments(1.9% for 36 months)
Total payments (36 × 657.78)
Total cost to ﬁnance the car$23,000

2,000____________________

186__________(55.80)____________________$657.78
23,680.08 __________$25,810.28 __________Cash price $26,627.50

Cash price __________

Finance cost $25,810.28

Finance cost __________

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139

WORKSHEET 27.2 Comparing interest rates to determine whether to ﬁnance or
pay cash for a car
Cash

Finance

Interest rate forgone on cash payment _____________
After-tax rate of return(1 − marginal rate) × interest rate_____________

APR _____________

Compare the cash rate and the ﬁnance rate.
If the cash rate is higher, it is cheaper to ﬁnance the purchase of the car andto invest your cash.
If the ﬁnance rate is higher, it is cheaper to pay cash for the purchase of
the car.

Should you ﬁnance your car or lease it? In general, it is cheaper to ﬁnancethe purchase of a car than to lease. The reason is because a lease payment
includes an amount for the depreciation of the car plus an amount for thefinancing of the car by the dealer plus the sales tax. The finance charge builds
in a rate of interest, which is typically quite high. However, there are exceptions, particularly when the auto manufacturers are saddled with a glut of cars.
To move them, they will offer special low lease rates. By working throughWorksheet 27.4, you will be able to determine whether it is cheaper to leaseor ﬁnance.
Leasing a car often turns out to be more costly than financing a car,even though the monthly payments on a closed-end lease are less than themonthly payments to ﬁnance the car. In a closed-end lease, you have rented
the car for the lease period. If you were to buy the car and ﬁnance the purchase, you would pay the entire purchase price plus the interest expense. However, if you keep the car in relatively good condition, you can sell the car at theend of the same period, and the net outlay for ﬁnancing generally will beless than the net outlay for leasing.

WORKSHEET 27.3 How to determine whether to take a cash rebate or special
low-rate ﬁnancing
Example: Should you choose the $6,000 cash rebate or the 2.9% ﬁnancing?
ExampleYour worksheet

Vehicle priceLess manufacturer’s rebate$36,000
6,000________________________Net cash cost
Interest income forgone on cash
(3% of $30,000 for 3 years)
Less taxes on interest income(30% marginal tax bracket)

30,000____________

2,790____________(837)____________

Total cash cost of purchase$31,953____________

Vehicle priceLess down payment$36,000
3,000________________________

Amount to be ﬁnanced

33,000____________

Interest forgone on down payment(3% of $3,000 for 3 years)
Less taxes (30% marginal tax bracket)
Monthly payment $958.23 × 36279
(83.70)34,496.28____________________________________

Total cost using ﬁnancing$37,691.58____________

Cost of the car with the rebate

Cost with 2.9% ﬁnancing

WORKSHEET 27.4 Should you ﬁnance or lease a car?
Example: You can ﬁnance a car at 3.9% for 4 years or lease it for $499 permonth for 4 years.
ExampleYour worksheet

Vehicle priceLess down payment$32,000
2,000______________________________

Amount to be ﬁnanced

30,000_______________

Down payment
Finance costs ($676.03 × 48 months)
Interest income forgone on down payment(3% of $2,000 for 4 years)
less taxes (39% marginal tax bracket)
Less estimated value of car
at the end of the loan

2,000
32,449.44______________________________

252(98.28)______________________________(14,000)_______________

Total cost to ﬁnance$20,603.16_______________

2,000_______________

252(98.28)23,9521,000____________________________________________________________$27,105.72_______________

Costs to ﬁnance

Cost to Lease
Total up-front security payment
Interest income forgone on security payment(3% of $2,000 for 4 years)
Less taxes (39% marginal tax bracket)
Total payments ($499 × 48)
End-of-lease payments (mileage, etc.)
Total cost to lease

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To summarize, it is generally cheapest to buy a car by paying cash; thesecond-cheapest method is to ﬁnance, and leasing comes last. In all transactions,read through the sales contract before signing, and always check the ﬁgures.

F I N A N C I A L C A LC U L ATO R # 28

How to Create a
Simple Interest Loan ScheduleM

any automobile manufacturers choose to use simple interest loans
for the ﬁnancing of their cars. The simple interest loan is a variant of
the effective rate or precomputed interest method. Table 28.1 shows the ﬁrst
12 payments of a precomputed interest loan for the purchase of a new car.
This is the same method that is used for the majority of mortgage loans, as
illustrated in sections 19 and 20 in this book.
The difference with a simple interest loan is that you pay simple interest on the outstanding balance only for the time that the money is used. The
payment per period is determined at the beginning of the loan, in the samemanner described in earlier sections. Then the interest is determined for eachperiod based on the number of days until the payment is received. Theinterest expense for the month is deducted from the monthly payment todetermine the principal reduction. This amount is deducted from the loanbalance to determine the new loan balance. These steps are then repeated todetermine the next month’s loan balance.
Table 28.2 illustrates the steps in determining the interest expense, principal reduction, and loan balance for a simple interest loan. For comparison
purposes, the same loan details as in Table 28.1 are used in the simple interest illustration.
Assume that the loan payment is due on the first day of each monthand the loan is taken out on January 1, 2002. The ﬁrst payment is due on February 1, 2002. If the payment is received earlier than the due date, the interest expense is less than the amount shown in Table 28.1, and if the payment

Managing Your Personal Wealth—Debt

143

TABLE 28.1 Precomputed amortization schedule for the purchase of a car
Loan amount:
Annual interest rate:
Number of years:
Periods per year:
Total payments:
Payment per period:
Payment
number
1
2
3
4
5
6
7
8
9
10
11
12

$18,426.68
3.9%
3
12
36
$543.21

Payment
amount$543.21543.21
543.21
543.21
543.21
543.21
543.21
543.21
543.21
543.21
543.21
543.21

Interest$59.89
58.32
56.74
55.16
53.57
51.98
50.39
48.78
47.18
45.56
43.95
42.32

Principal
reduction

Loanbalance$483.32484.89486.47488.05489.64491.23492.82494.43496.03497.65499.26500.89$18,426.68
17,943.36
17,458.47
16,972.00
16,483.95
15,994.31
15,503.08
15,010.26
14,515.83
14,019.80
13,522.15
13,022.89
12,522.00

is made after the due date, the interest expense is greater than the amountshown in that table.

Step 1: Determine the Interest Expense
To calculate the interest expense, start by multiplying the annual interest
rate by the outstanding loan balance ($18,426.68 × 0.039). The yearly interest expense equals $718.64. To ﬁnd the daily interest expense, divide this number by 365 days ($718.64 ÷ 365); the result is $1.969. Count the days until theﬁrst payment is received and multiply the daily interest by this number of days.
For January the interest is $39.38 ($1.969 × 20).

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TABLE 28.2 Simple interest installment loan
Loan amount:
Annual interest rate:
Number of years:
Periods per year:
Total payments:
Payment per period:$18,426.68
3.9%
3
12
36
$543.21

Month

Days
betweenpayments

Payment
amountInterest

Principal
reduction

Loanbalance

1/1/02
1/20/02
2/27/02,
3/30/02
4/24/02

20
38
31
25

$543.21543.21
543.21
543.21$39.38*
72.77
57.81
45.32

$503.83**
470.44
485.40497.89$18,426.68
17,922.85
17,452.41
16,967.01
16,469.12* Interest is explainedin step 1 on page 143.
** Principal reduction is explained in step 2 on page 144.

Step 2: Determine the Principal Reduction
To determine the principal reduction, subtract the interest expense from themonthly payment ($543.21 − $39.38). The result is $503.83.
Step 3: Determine the New Loan Balance
The new loan balance as of January 20, 2002, is the old balance minus theprincipal reduction: $17,922.85 ($18,426.68 − $503.83).
These three steps are repeated to determine the ﬁgures for each successive month. The interest expense for the ﬁrst payment in the simple interest
loan is much lower than that in the precomputed method ($39.38 versus$59.89) because it involves only 20 days versus the full month in the precomputed method. Conversely, in the second month the interest expense
for the simple interest method is greater than for the precomputed method($72.77 versus $58.32) because the days between payments for the former is
38 versus the typical 30 days in the precomputed method.

Managing Your Personal Wealth—Debt

145

On balance, if you consistently pay your monthly payments earlier thanthe due date, you will save on the interest expense using the simple interest
method. Worksheet 28.1 outlines the steps to create your own simple interest
amortization schedule.

WORKSHEET 28.1 How to create a simple interest amortization schedule

Date_________________________________________________________________________________________________________

Days
betweenpayments

Payment
amount___________________________________________________________________________________________________________________________________________________________________________________________________________

Interest__________________________________________________________________________________________________

Principal
reduction

Loanbalance___________________________________________________________________________________________________________________________________________________________________________________________________________

Step 1 Fill in the date, monthly payment, and loan balance at the inception of the loan.
Step 2 Fill in the days between payments.
Step 3 Calculate the interest expense. Multiply the annual rate by the loan balance anddivide by 365. Multiply the result by the number of days between payments todetermine the interest expense.
Step 4 Subtract the interest expense from the monthly payment to determine theprincipal reduction.
Step 5 Subtract the principal reduction from the old loan balance to determine the newloan balance.

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P A R T

T H R E E

MANAGING YOURPERSONAL WEALTH—INVESTMENTS

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F I N A N C I A L C A LC U L ATO R # 29

Determine Your
Investment Objectives

I

nvestment objectives are like a rudder on a ship. The choice of whichinvestments to hold is determined by your objectives. In other words, knowing what you want to accomplish from your investments allows you to manage your portfolio more effectively. In addition, your objectives determine thepurpose and time period for the investments. For instance, you may be saving for retirement in ﬁve years, while your neighbor may be saving for retirement in 30 years. Although the objectives are the same, the time period,
level of risk tolerance, and types of investments held will be very different.
The ﬁrst step in any plan is to determine short-range, medium-range, andlong-range objectives. For example, a young family with small children may
have the following objectives:

Short Term:• Set up an emergency savings fund.
• Buy furniture.
• Save for a vacation.
• Buy a new car.
Medium Term:• Save for a down payment on a house.
• Invest in a business.
Long Term:• Save for children’s college fund.
• Save for retirement.

149

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Once you have determined your objectives, it becomes easier to see whattypes of investments to buy, the level of risk that you can withstand, and what
your expectations are from your investments.
Filling in Worksheet 29.1 is a ﬁrst step in your investment program. Noting the time frame and the dollar amounts needed to fund your objectives
gives you a better sense of how much to invest for each objective. Asking yourself the following questions can help you formulate your objectives.
• What do I intend to use my money/savings for?
• How much money do I need to fund my objectives?
• Am I committed to making sacriﬁces to fund these objectives?
• What are the consequences if I am not able to fund these objectives?
• What do I need to do to bolster my savings to fund these objectives?
Besides listing your objectives, it is equally important to quantify theamount of money needed to fund them.
By listing your objectives, you can see what you intend to save for andinvest in for the future. Included in your short-term objectives should be
the capacity to meet ﬁnancial emergency needs through the establishmentof an emergency fund.
Medium- and long-term objectives vary by individual needs. For example, some people want to save as much as possible to grow as large an estateas they can, whereas others may have more speciﬁc uses for their future funds.

WORKSHEET 29.1 List your objectives
Time horizon
in years

Dollar amountneededInvestment tofund objective________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Short term
(two years or less)________________________________________________________________________________________________________________________________________________________________
Medium term
(two to seven years)________________________________________________________________________________________________________________________________________________________________Long term(seven-plus years)________________________________________________________________________________________________________________________________________________________________

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F I N A N C I A L C A LC U L ATO R # 30

Determine Your Risk ToleranceS

etting objectives is the ﬁrst step in an investment plan, as discussed
in section 29. The next step is to determine your risk tolerance, which thenserves as a guide in the selection of the portfolio investments. An examinationof your personal characteristics is the ﬁrst step in the determination of your risk
tolerance. See Worksheet 30.1 for a survey of your personal characteristics.
An assessment of your personal characteristics determines which of thefollowing ﬁnancial stages you are in and the risk level that you can toleratewith regard to your investments:• Accumulation of wealth• Attainment of wealth• Use of wealth

WORKSHEET 30.1 An examination of your personal characteristics
Marital status: 䊐 single 䊐 married 䊐 widowed 䊐 divorced
Family: 䊐 no children 䊐 young children 䊐 teenage children 䊐 empty nest
Age: 䊐 under 25 䊐 25–39 䊐 40–60 䊐 over 60
Education: 䊐 high school graduate 䊐 college degree 䊐 graduate degree
Income: 䊐 poor growth prospects 䊐 stable/level 䊐 good growth prospects
Income level: 䊐 low 䊐 medium 䊐 highJob/profession: 䊐 low job skills 䊐 average level of skills 䊐 good job skills
Prospects for promotion: 䊐 poor 䊐 average 䊐 good
Net worth/size of portfolio:
Assets/net worth: 䊐 small asset base 䊐 medium asset base䊐 large asset base
Level of debt: 䊐 high 䊐 medium 䊐 low

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153

Generally, these three stages are coordinated with the stages in the life
cycle. Most young people starting their working careers are in the ﬁrst stage,
wealth accumulation, and as people progress to the mature stage in life they
have attained most of their objectives. In the retirement stage, people generally use the wealth that they have attained to live on. However, there are many
exceptions. In all three stages, risk tolerance varies according to the speciﬁcsof the person’s characteristics, objectives, and time frames. A young, successful trial lawyer, who has a large salary and bonuses, can withstand morerisk from the investments chosen than someone who earns a small salary andis dependent on the earnings of the investments. The latter’s investment assets
will be more conservative and geared more toward generating current income
than capital growth. The trial lawyer, however, can withstand more risk in his
or her investment portfolio, which is aimed at expanding capital (net worth)rather than generating current income.
These variables determine the types of investments and the level of riskthat can be absorbed in the development and management of the portfolio.
For example, a nonworking widow who depends entirely on income generated from her investments will not be able to tolerate the high risk of investments in junk bonds, small-company growth stocks, or newly issued public
offerings of common stocks. Her portfolio of assets would need to generate
income but not at the expense of capital preservation.
Thus, depending on an investor’s objectives, characteristics, and risk
tolerance, there is a trade-off between assets generating current income andassets seeking capital appreciation. If investors opt for capital appreciation
assets, they may sacriﬁce current income.

With What Level of Risk Do You Feel Comfortable?
On a continuum of risk, you need to determine your comfort zone with regard
to your investments (see Figure 30.1).
Classifying some of the types of investments on a continuum of risk,
we see that speculative common stocks are considered the most risky (in terms

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FIGURE 30.1 Investment continuum of risk
Speculative
stocksGrowthstocksBlue-chip stocks/
Long-term bonds

Intermediate
bonds

Short-term
bondsHigh risk

Money market
securities

Low riskof variability in share price), followed by long-term bonds, with the shorter
maturities on the low-risk end. Bear in mind that there are many othertypes of investments that are riskier than common stocks, such as commodities, futures contracts, and options. Similarly, there is a great variationof quality among common stocks. The common stocks of well-established,blue-chip companies are considered less risky than the bonds of highly leveraged companies with suspect balance sheets.
The questionnaire in Worksheet 30.2 can assist you in the determinationof your comfort level with regard to risk tolerance.

Scoring Your Questionnaire
Give yourself the following points for your answers and then total them:
1. (a) 1 point, (b) 2 points, (c) 3 points
2. (a) 1 point, (b) 2 points, (c) 3 points, (d) 4 points
3. (a) 4 points, (b) 3 points, (c) 2 points, (d) 1 point
4. (a) 1 point, (b) 2 points, (c) 3 points, (d) 4 points
5. (a) 4 points, (b) 3 points, (c) 2 points, (d) 1 point
6. (a) 4 points, (b) 3 points, (c) 2 points, (d) 1 point
7. (a) 4 points, (b) 2 points, (c) 1 point
8. (a) 2 points, (b) 1 point
9. (a) 1 point, (b) 2 points, (c) 4 points
10. (a) 1 point, (b) 2 points, (c) 3 points

WORKSHEET 30.2 Questionnaire to determine your risk tolerance for your portfolio
1. Do you have an emergency fund consisting of at least 3 month’s salary?
(a) No (b) Yes, but less than 3 months (c) Yes
Investment Planning: These investment funds should be invested in liquid assets (money market securities) so as to avoid any loss of principal
when the money is needed. The ﬁrst step is to establish an emergency
fund, after which an investment fund can be established.
2. When will you need the investment funds (over and above your emergency fund) that you have invested?
(a) Within 1 year (b) Within 5 years (c) Between 5 and 10 years(d) Longer than 10 years
Investment Planning: If you need the money within one year, you needto invest in liquid investments. Money needed within a ﬁve-year timeframe should be invested in short-term securities. Investments with a timeframe longer than ﬁve years can be invested more aggressively, dependingon your circumstances and your risk tolerance, such as in long-term bonds
and stocks.
3. What percentage of your total investment funds is in retirement accounts?
(a) Below 25% (b) Between 25 and 50% (c) Between 51 and 75%(d) Above 75%
Investment Planning: The lower the percentage in retirement funds, themore aggressively you can invest.
4. How stable is your income from employment likely to be over the next
5 years?
(a) Likely to decrease (b) Likely to stay the same (c) Likely to keep
pace with inﬂation (d) Likely to increase above inﬂation
Investment Planning: If there is uncertainty concerning future earnings,
you may have to withdraw funds from your investments, which meansthat a corresponding amount should be invested conservatively. If there isa good chance that employment earnings will increase in the future, you
can invest more aggressively.
5. How many dependents do you have?
(a) None (b) 1 (c) 2 (d) More than 2
Investment Planning: The greater the number of dependents, the greater
the responsibilities. Generally, this may require being a little more conservative in your investment approach.
(continued overleaf)

6. What percentage of your earnings goes toward paying off debts including
a mortgage?
(a) Less than 10% (b) Between 10 and 25% (c) Between 25 and 50%(d) Over 50 percent
Investment Planning: The higher the percentage of your earnings that
goes toward paying off debts, the greater the likelihood that you may needto dip into your investment accounts, which may call for a more conservative approach.
7. With regard to your investment assets, where would you feel comfortableon the scale below?
(a)

I am willing to invest
aggressively for the
maximum possible
growth even if there ispotential for losses due
to market ﬂuctuations.

(b)

I am comfortable withsome level of
ﬂuctuations in myfunds in order toachieve reasonablelevels of growth.

(c)I am uncomfortable when
my investment funds
go down in value due tomarket ﬂucuations.

Investment Planning: Your appetite for risk will determine whether you
can invest aggressively, somewhat aggressively, or conservatively.
8. If you can increase your potential returns by taking on more risk, would
you feel comfortable?
(a) Yes (b) No
Investment Planning: If yes, you can be a little more aggressive inyour investments. If no, you should invest only in those assets that you feel
comfortable with.
9. What rate of return do you expect to earn from your investments?
(a) Keep ahead of inﬂation while maintaining stability of principal.
(b) Earn returns that are greater than inﬂation even if there is some potential for loss of principal(c) Earn high returns regardless of increased potential for loss of principal.
Investment Planning: Your acceptance of risks of loss of principal will
determine whether you should invest aggressively, conservatively, or
somewhere in between.
10. What do you need from your investment assets?
(a) Investment income (b) Mix of investment income and capital growth(c) Long-term capital growth
Investment Planning: If you need investment income, the investment
assets should be allocated more toward bonds. Long-term capital growth
can be obtained from diversiﬁed investments in common stocks.

Managing Your Personal Wealth—Investments

157

If your total score is 10–15 points, you cannot tolerate risk well and you
would feel more comfortable with conservative investments. A total of 16–20
points indicates a notch above low risk, with an investment style that is stillconservative but includes more investments with higher returns. A score of
21–25 indicates a balanced approach to risk, with an equal mix of investmentsthat seek income and capital growth. A score of 26–31 points indicates greater
acceptance of risk in a portfolio, with investments geared more toward capital growth and a small percentage of funds devoted to income-producing
investments. All scores above 32 indicate an acceptance of high risk with regard
to investments.
Figure 30.2 illustrates a risk continuum. Based on your assessment of yourability to handle risk, determine where you would be comfortable on thiscontinuum.
Your tolerance for risk is an overriding factor in the selection of yourinvestment portfolio. As your personal circumstances and objectives change,
so too will there be changes in your assessment of risk. Most people strive forincreasing the returns from their investments, but this means taking on morerisk. Acceptance of a comfortable risk/return strategy is an important stepin the assessment of the different types of investment assets, as discussed in
the next section.

FIGURE 30.2 Investment continuum of risk
Aggresive
portfolio

Conservative
portfolio

Balanced
portfolioHigh risk

Moderate risk

Low risk

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F I N A N C I A L C A LC U L ATO R # 31

How to Allocate Your InvestmentsAsset allocation is a plan to invest in different types of securities sothat the capital invested is protected against adverse factors in the marketplace. This, in essence, is the opposite of putting all your eggs in one basket. Imagine an investor with $200,000 to invest who put it all into Enron stockbought at $70 per share at the beginning of 2001. The value of the portfolio
at the end of the year would have been reduced to $1,428 when Enron went
into bankruptcy and the stock traded around $0.50 per share.
Developing a portfolio is based on the idea of holding a variety of investments rather than concentrating on a single investment. The purpose is to
reduce the risk of loss and even out the returns of the different investments.
The latter point can be illustrated with the following hypothetical portfolio.
Assume the investor buys:
1,000 shares of XYZ Co. at $50 per share
100 convertible bonds of ABC Co. at $1,000 per bond
Total

Total investment:$50,000
100,000$150,000

A year later, the portfolio is valued as follows:
1,000 shares of XYZ Co. at $70 per share
100 convertible bonds of ABC Co. at $800 per bond
Total

$70,000
80,000$150,000

The investor has spread the risk of loss by owning two different types of
securities, as well as by averaging the returns of the two types of investments. Certainly the investor would have done much better had he or she
invested only in XYZ shares, but hindsight always produces the highest returns.
The fact that we are not clairvoyant points to the beneﬁts of diversifying acrossManaging Your Personal Wealth—Investments

159

a broad range of investment types. In other words, diversiﬁcation seeks a balance between the risk-return trade-off.
Diversiﬁcation is achieved by selecting a portfolio of different types of
securities in different industries. For example, investing in the stocks andbonds of General Motors, Ford, and Chrysler hardly achieves any diversiﬁcation. By carefully selecting the stocks and bonds of different companies indifferent industries and/or investing in stock and bond mutual funds, someof the risk of loss on any one security (or type of fund) will be evened out.
Asset allocation is the process of determining the right mix for the broad
asset classes that conform to your objectives, time horizons, and risk tolerance. The aim of investing in the different classes of assets is to reduce the riskof loss and even out the returns. Generally, these investment classes behave
differently.
What is the right mix of stocks, bonds, money market securities, and otherinvestment asset classes? The answer depends on the amount of risk thatthe investor is willing to tolerate, investment objectives, the time frame forthese objectives, personal characteristics, and the size of the portfolio. Generally, stocks are riskier investments than bonds. By increasing the time
horizon for stock investments, an investor can compensate for the volatility
in the stock market. Maturities on bonds can be matched to the time horizons of the investor’s needs. There are short-term bonds with maturities of
one to ﬁve years, intermediate bonds with maturities of ﬁve to 10 years, andlong-term bonds with maturities of greater than 10 years (generally 30-year
maturities, although there are 100-year maturity bonds). If an investor cannot sleep at night when the amount of his or her investments declines, thatinvestor does not tolerate risk very well and should not have a large percentage of his or her assets invested in stocks. Conversely, an investor who can tolerate risk and who has long time horizons could have a larger percentage ofassets allocated to stocks.
Investors who need to live off the interest of their investments will be
inclined to allocate more of their portfolio assets to bond investments, which
generate regular ﬁxed interest payments. Investors with a long time horizon
who do not need the income from their capital to live on can allocate a greater

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percentage of their assets toward stocks in order to generate growth for the
portfolio.
The amount of money available to be invested also has an impact on
the asset allocation. If there is a relatively small amount of money, most of it
will go toward covering the emergency fund with money market securities,
and whatever is left over will be allocated to other investment assets depending on objectives, time frames, risk tolerance, and personal characteristics.
Age is another important factor in the determination of an asset allocation mix. At a young age, an investor’s priorities are setting up an emergency fund and probably investing the rest of the funds in growth assets dueto the investor’s long time horizon. In midlife, the priorities shift toward
growth and income, and at retirement the emphasis is more on income
generation and some growth.
There is no rigid formula for asset allocation. Rather, it is a good idea tothink about the concept as a guideline for investing money. The percentage
allocated to the different types of assets can always be changed, depending on
circumstances. As individual circumstances change, so too will the investor’s
objectives. If the emphasis shifts, for example, to greater income generationand preservation of capital from capital growth, the percentage of the investments in the portfolio can be changed accordingly.
A rough rule of thumb for allocating assets is to use age as a yardstick. At
age 50, the optimal allocation is 50 percent in bonds and the rest allocatedto other asset categories. As age increases above 50, so too will the percentage allocated to bonds. This does not work for all people, as this formulaignores the speciﬁc facts pertaining to each individual, such as objectives,
amount of money, risk tolerance, and other personal characteristics. Figure31.1 illustrates some of the determinants for asset allocation models and Figures 31.2 to 31.4 break these models down into greater detail.
The most important aspect of investing is to have an asset allocation planthat reﬂects the mix of stocks and bonds appropriate for your objectives. Oncethese have been determined, the individual investments can be purchased.
Funds for emergency purposes should be liquid; in other words, they shouldbe easily convertible into cash without the loss of principal. Money market

Managing Your Personal Wealth—Investments

161

FIGURE 31.1 Determinants for asset allocation models
Years to Retirement or When the Money Is Needed

30+
Years

10+
Years

5 years

Type of investor

Aggressive

Conservative

Investment objectives
CapitalgrowthStocks
85%
Bonds
5%
Money market 10%

Incomegeneration

Stocks
50%
Bonds
40%
Money market 10%

Stocks
30%
Bonds
50%
Money market 20%______________________________________________________________________

securities are an example of liquid investments. Depending on personal circumstances, the rule of thumb is to have an emergency fund equivalent tothree to six months of living expenses invested in money market securities.
Asset allocation plans are not etched in stone, and investors should reevaluate their plans on a yearly basis or as personal needs and circumstanceschange. See Figure 31.5 for the beneﬁts of asset allocation and diversiﬁcation.
A conservative portfolio is one in which the investment goals are to preserve capital and provide for some growth. The weighting is geared toward
high-quality bonds, with a small portion toward stocks. (See Figure 31.2.)

FIGURE 31.2 Conservative portfolio
Conservative portfolio
Commonstocks10%

Moneymarket15%
Short-term
bonds
15%

Long-term
bonds
30%

Intermediate
bonds
30%
______________________________________________________________________

A balanced portfolio includes a greater percentage of common stocks,
which provide capital growth, but keeps a large percentage of assets in bonds,
which provide income. (See Figure 31.3.)
FIGURE 31.3 Balanced portfolio
Balanced portfolio
Common stocks
50%

Money
market10%Long-term
bonds
20%

Intermediate
bonds
20%

______________________________________________________________________FIGURE 31.4 Aggressive portfolio
Aggressive portfolio
Common stocks
90%

Money market
5%Intermediate bonds
5%______________________________________________________________________

An aggressive portfolio is weighted to common stocks, which provide
capital growth. (See Figure 31.4.)
Figure 31.5 lists the beneﬁts of asset allocation and diversiﬁcation andWorksheet 31.1 outlines the steps for you to determine your asset allocation.

FIGURE 31.5 Beneﬁts of asset allocation and diversiﬁcation
1. By investing in different classes of investments, the risk of loss is spreadamong the different investments rather than being concentrated in
one class.
2. A diversiﬁed portfolio of investments reduces the total risk. According toJonathan Clements,* a portfolio assembled over the past 70 years consisting of 23 percent common stock and 77 percent bonds would have thesame risk as a portfolio of 100 percent bonds.
3. Diversiﬁcation can increase overall returns. In the portfolio mentioned
above, the overall returns on a diversiﬁed portfolio of 23 percent common
stock and 77 percent bonds returned were 2 percent higher per year than a
100 percent bond portfolio.
*Jonathan Clements, “Portfolio for the Conservative and the Bold,” The Wall Street
Journal, November 10, 1998, p. C1.

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WORKSHEET 31.1 Determining your asset allocation plan
Time Horizon

Less than
12 months

1–5
years

Greater than
5 years

Risk Tolerance

Conservative
Investor

Aggressive
Investor

Investment Objectives
CapitalGrowthIncomeGeneration

Asset Allocation
Money Market ____
Bonds
____
Stocks
____
Total
100%

Money Market ____
Bonds
____
Stocks
____
Total
100%

Money Market ____
Bonds
____
Stocks
____
Total
100%

______________________________________________________________________

After determining your asset allocation plan, you are ready to select theindividual securities (stocks, bonds, and money market securities).
Money Market Securities. These include:• Treasury bills• Commercial paper• Certiﬁcates of deposit (CDs) (maturities of one year or less)• Money market mutual funds

Managing Your Personal Wealth—Investments

165

Bonds. These include the individual bonds (corporate, U.S. Treasuries,
municipal bonds, government agency bonds, foreign bonds) and/or different
bond mutual funds.
Stocks. These include individual stocks and/or equity mutual funds.
There are other assets (such as real estate, options, and futures) that canbe considered besides stocks, bonds, and money market securities. If you areconsidering them, you should include them in your asset allocation plan.

F I N A N C I A L C A LC U L ATO R # 32

How to Determine Your Equity Stylein the Selection of Individual StocksT

he question often asked by investors is,“What types of stocks should
I buy?”
Should you rush to buy the small-capitalized stocks that have been
responsible for the major moves in the Russell 200 Index? Or should you lookfor value stocks and technology stocks that have been hit in the downturnof the stock market (Dow Jones Industrial Average and the NASDAQ Composite) in the years 2001–2002? Related to this issue are the sizes of the companies. The rally has included the small-capitalization stocks while the mid-cap
and large-cap stocks have been excluded, although small-capitalization stocks
were also down in the early months of 2002.
Studies have shown that stocks can be classified into categories thathave similar patterns of performance and characteristics. In other words,
the returns of the stocks within the categories are similar, whereas the returnsof the stocks between the categories are not correlated.* James L. Farrell found
four categories for stocks; namely, growth, cyclical, stable, and energy. Other*James L. Farrell, Jr., “Homogeneous Stock Groupings: Implications for Portfolio Management,” Financial Analysts Journal, May–June 1975, pp. 50–62.

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FIGURE 32.1 Market capitalization of stocks
Small capitalization: less than $1 billion
Medium capitalization: $1–$5 billion
Large capitalization: greater than $5 billion

studies have measured stocks by their market capitalization, or size, which wasthen translated into small-cap, mid-cap, and large-cap stocks. Figure 32.1 lists
the categories based on market capitalization of the companies, which is measured by the number of shares outstanding for the company multiplied by themarket price of the stock. There are many variations in these amounts,
depending on the source. What portfolio managers have found is that theycan enhance their performance by moving their money into the different categories of stocks from time to time.
From these categories of stocks two investment styles have emerged;
namely, value and growth investing. Figure 32.2 illustrates the common stylesof equity investing. This style box originated from Morningstar Mutual Funds
for mutual fund investing, but it can also be used to determine individual
equity portfolio holdings.
Investors can use this style box to determine the bulk of the equity investments that suit their investment style, as determined by their investment objectives. Value stocks have different ﬁnancial characteristics and, as we have seen,different performance returns over the past four years compared to growth stocks.
Value stocks generally pay some dividends and have low price-earnings (P/E)
ratios. (See pages 236–239 for a discussion of P/E ratios.) Growth stocks generally have high P/E ratios and are expected to experience high sales growth fora period of time. A blend would include a mixture of growth and value stocks.
The size of the company is measured by market capitalization. Small-cap companies tend to be riskier than mid- or large-cap companies, but as many studies have shown, the returns over long periods of time from the small-caps haveexceeded those of the large-caps. This has not occurred over the past four ofﬁve years, where large-cap growth stocks have outperformed the small- and mid-Managing Your Personal Wealth—Investments

167

FIGURE 32.2 Types of equity styles
Equity styles
Value

Blend

GrowthLarge-cap
stocksMid-cap
stocksSmall-cap
stockscap stocks quite handily. However, before then small-cap stocks outperformed
the large- and mid-caps. This does not include all the large stocks on the market. In fact, over half the stocks in the S&P 500 Index had declines in shareprice or ended up with returns of 6.6 percent or less for the calendar year 1998,
while only a small number of stocks were responsible for the stellar returns.* Thismeans that stock picking becomes extremely important for individual portfolios, particularly if there is no advantage in replicating an index.
For those investors who had chosen the large nifty 50 stocks in the S&P
500 Index and most of the Dow Jones Industrial Average stocks, the returns
were very rewarding, and the implication was that it was easy to make moneyin the stock market. However, in more broad-based markets the choices are
not so overwhelmingly easy to make, and the average annual returns are generally not in the double digits, as has been the case for the past four years.
The style box in Figure 32.2 illustrates the choices in terms of these dimensions. Investors can choose the current winners, which are small-cap growthstocks, in which to invest more money. Alternatively, some investors might
not want to pay the high prices for these types of stocks and instead would look*Anne Tergesen, “Sifting for Clues,” Business Week, March 29, 1999, pp. 110–111.

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for the growth stocks that have been beaten down in the past year. These could
be small-cap, mid-cap, or large-cap stocks, or a combination of them. Some
investors might want to have a combination of growth and value stocks in the
different size stocks. This style box can also be used with international stocks.
Research has shown that value and growth stocks do not perform inthe same manner within the same time periods. This was evidenced recently
by the spectacular performance of the large-cap growth stocks while thelarge-, mid-, and small-cap value stocks underperformed the market. Some
investors will choose to invest all their funds in the stocks that are performing well and then shift to other investment styles when they perceive thatthings are about to change. This style of investing would be more conducive
to an active management style, as opposed to a passive management stylewhere investors would allocate their stocks among the different categories andthen hold them for long periods of time. Active managers are more likely to
be market timers, where they will be more inclined to be fully invested instocks when they perceive the market to be going up. When they think thatthe market is about to go down, they will exit the market. Passive investors
tend to stay fully invested in stocks irrespective of the state of the market.
Whether to be an active or a passive manager, or whether to choose growthstocks over value stocks are decisions that each investor will ultimately have to
make. There are differences in investment styles and, therefore, the ultimate
selection of stocks, but having a plan and a strategy can make the selection ofstocks much easier. The ultimate selection of individual stocks can be madeeasier if direction is provided through an asset allocation model, which breaks
down the different style categories of investments within the class asset. Table
32.1 lists a few examples of the different portfolio models. Investors could invest
in a mixture of value and growth stocks, which can be allocated among domestic stocks and international stocks. Following this, investors would then decideon the amounts to allocate to the different stock sizes (large-, mid-, and smallcap). This is illustrated in example 1 in Table 32.1.
Examples 2 and 3 show selections 100 percent weighted toward value andgrowth stocks, respectively. Diversification within the stock sector of aninvestor’s portfolio offers protection against the downside risk of being fully

Managing Your Personal Wealth—Investments

169

TABLE 32.1 Asset allocation of stocks by style
Example 1
Value/growth blend
Value stocks
Large-cap U.S. stocks 20%

Example 2
Value

Example 3
GrowthValue stocks

Growth stocks

Large-cap U.S. stocks 25%

Large-cap U.S. stocks 25%

Mid-cap U.S. stocks 20%

Mid-cap U.S. stocks 25%

Mid-cap U.S. stocks 25%

International stocks 10%

Small-cap U.S. stocks 20%

Small-cap U.S. stocks 20%

Growth stocks

International large-cap 20%

International large-cap 20%

Large-cap U.S. stocks 20%

International mid-cap 10%

International mid-cap 10%

Total portfolio 100%

Total portfolio 100%Mid-cap U.S stocks 20%
International stocks 10%

Total portfolio 100%

invested in one sector, such as large-cap value stocks, for example. If in thenear future the tide turns against these stocks, investors will be protected byparticipating in the rising prices of the other sectors should the stock market rally become more broad based.
Many may wonder why they should take the time and effort to classify theirstocks into these styles. There are a few convincing arguments. The ﬁrst is thatwithout the power of clairvoyance we have no way of knowing the future movements of the stock market. Consequently, by diversifying into different sectorsof the market, investors can reduce the risk of loss from being too heavily
invested in one sector of the market. This is amply illustrated by the sharp decline
in technology and growth stocks during the years 2000–2001.Value stocks during that period increased and the small-cap indices outperformed the large- andmid-cap indices. This means, however, that currently small-cap stocks are notas cheap as they were before the rally and may be running out of steam.
Worksheet 32.1 provides the Morningstar grid to help you to determine your investment style and then to choose individual stocks or equity
mutual funds.

WORKSHEET 32.1 Determine your equity style and choose your stocks/
mutual funds
Equity styles
Value

Blend

GrowthLarge-cap
stocksMid-cap
stocksSmall-cap
stocksAsset allocation by style
Equity styleCompany size_______________________________________________________________________________________________________________________________________

Step 1 Choose your equity style(s).
Step 2 Determine the size sectors and list the individual stocks.

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F I N A N C I A L C A LC U L ATO R # 33

How to Determine Which Types ofBonds to Buy for a Portfolio

I

nstead of investing directly in individual bond issues, investors may
choose to invest indirectly in bonds through bond mutual funds. The
mutual fund pools the money from investors and invests in different bondissues. Investors receive shares in the fund, which are proportionate to theamount of their investments.
The types of bonds an investor chooses are determined by the investor’s
objectives. Bonds may be categorized in terms of the following:• Quality. The higher the credit quality of the bond, the lower the risk
and the yields. The lower the credit quality of the bond, the higher
the risk and potential returns.
• Maturity. This is the length of time of the maturity of the bond.
Maturities are generally classiﬁed as short term, intermediate term,
and long term. The longer the maturity, the greater the risk and thegreater the potential returns (assuming a normal yield curve).
Figure 33.1 shows the types of bonds using these two dimensions. This
grid is a good planning tool to use to determine which types of bonds (orbond funds) to invest in with regard to these two dimensions.
The lower your risk tolerance, the closer you would move to the left
side of the grid, and depending on your time horizon, to the top, middle, or
bottom of the grid. If you have a long time horizon, you would choose themiddle or bottom rows (intermediate-term and long-term funds), which
are also most sensitive to changes in market rates of interest. This grid is agood tool to use to identify the types of bonds or bond funds that conformto both your time horizon and level of risk tolerance.

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Maturity

FIGURE 33.1 Grid to determine which bonds to chooseHighqualityaMediumqualityLow
qualityb

Short termc

High quality

Medium quality

Low quality

Intermediate
termdHigh quality

Medium quality

Low quality

Long termeHigh quality

Medium quality

Low quality

a. High-quality bonds have a low risk of default.
b. Low-quality bonds and junk bonds have a high risk of default.
c. Short-term bonds may be classiﬁed as having maturities ranging from
one to ﬁve years.
d. Intermediate-term bonds have maturities ranging from ﬁve to
10 years.
e. Long-term bonds have maturities of greater than 10 years.

Types of Bonds
Treasury notes and bonds are issued by the United States Treasury. There is no
credit or default risk on the interest and repayment of principal as these are
direct obligations of the federal government.
U.S. government agencies sell long-term debt issues to ﬁnance various
activities. Although they are not backed by the full credit of the U.S. government, these U.S. agency issues are considered to be of good investment qual-

Managing Your Personal Wealth—Investments

173

ity. There are many different agencies selling obligations with varying maturities, liquidity, and marketability.
Corporate bonds are debt obligations of corporations and vary considerably in their features and risk.
Municipal bonds are issues sold by states, counties, and cities. The main
advantage of municipal bonds is their special tax treatment. The interest
received from municipal bonds is exempt from federal income tax and fromstate and/or local tax if issued in that state and county.
Zero-coupon bonds are hybrid securities that pay no periodic interest
but are issued at a deep discount and are redeemed at face value ($1,000) at
maturity.
Convertible bonds are debt securities that can be exchanged for the common stock of the issuing company at the option of the bondholder.
There are independent rating services that evaluate the risk of corporate and municipal bonds. See Figure 33.2 for two rating services’ ratings,
which are similar but not identical.
Bonds with ratings of AAA, AA, A, and BBB from S&P are considered
to be investment-grade quality. Bonds with ratings below BBB are considered
to be junk bonds and are speculative. The lower ratings of junk bonds meanthat the issuers have a greater likelihood of default on their interest and principal repayments. Before buying a bond issue, you should ascertain the rating
through your broker, or if buying online, through the Internet Web site.
Use Worksheet 33.1 to determine the types of bonds or bond funds topurchase for your investment portfolio.

FIGURE 33.2 Bond ratings
Moody’sStandard & Poor’s

Interpretation of ratings

Aaa

AAA

Highest quality obligations

Aa

AA

High-quality obligations

A

A

Bonds that have a strong
capacity to repay principal
and interest but may be
impaired in the future.

Baa
Ba

BBB
BB
B

Medium grade quality.
Interest and principal isneither highly protected
nor poorly secured. Lower
ratings in this category
have some speculative
characteristics.

B
Caa
Ca

CCC
CC
C

Speculative bonds withgreat uncertainty.

C

DDD
DD
D

In default.

WORKSHEET 33.1 Determine the types of bonds to buy for your portfolio
Name and typeof bond

RatingLength of time
to maturity

Total
investment_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Managing Your Personal Wealth—Investments

175

F I N A N C I A L C A LC U L ATO R # 34

How to Rebalance Your Portfolio
1. Begin with your original asset allocation plan.
For example, assume you had started with the asset allocation plan as
illustrated in Figure 34.1.
2. Revisit the asset allocation plan after a period of time.
One year later, with the rapid expansion of the equity portfolio, the original asset allocation mix has changed to the percentages shown in Figure 34.1.
3. If necessary, rebalance the portfolio.
You need to determine whether this new asset allocation mix is consistent with your objectives, personal circumstances, and risk tolerance. With theappreciation of the equity assets, the new equity mix is now 50 percent of thetotal portfolio value and the bond mix has dropped from 50 percent to 35 percent. This may be unsuitable if you rely more on income-generating assets
than growth assets. Rebalancing requires selling off some stocks and buying
more bonds with the proceeds in order to realign the asset allocation mix withyour needs and goals.
4. The current asset allocation mix and proposed asset allocation mix after
rebalancing are shown in Figure 34.2.
Use Worksheet 34.1 on page 178 to rebalance your portfolio.

FIGURE 34.1 Original asset allocation plan and asset allocation mix—one year later
Original asset allocation plan
Money market
securities
20%

Stocks
30%

Bonds
50%
Asset allocation mix—one year later
Money market
securities
15%

Bonds
35%

Stocks50%______________________________________________________________________FIGURE 34.2 Current and proposed asset allocation mix

Current Asset Allocation Mix

Proposed Asset Allocation Mix______________________________________________________________________

WORKSHEET 34.1 Rebalance your portfolio
Step 1 Begin with your original asset allocation plan.

Money market securities
Bonds
Stocks
Other
Total

Dollar amount_______________________________________________________________________________________________

Percentage______%______%______%______%
100%

Step 2 After a period of time, ﬁll in your current asset allocation mix.

Money market securities
Bonds
Stocks
Other
Total

Dollar amount_______________________________________________________________________________________________

Percentage______%______%______%______%
100%

Step 3 Determine whether it is necessary to rebalance your portfolio. If you decide it isnecessary, go to step 4.
Step 4 Create a new asset allocation plan

Money market securities
Bonds
Stocks
Other
Total

Dollar amount_______________________________________________________________________________________________

Percentage______%______%______%______%
100%

Managing Your Personal Wealth—Investments

179

F I N A N C I A L C A LC U L ATO R # 35

The Rule of 72 and How to Use It to
Determine How Long It Will Take to
Double Your MoneyThe rule of 72 is an easy-to-use method for determining how quickly
your savings/investment will double. It can also be used in times ofhigh rates of inﬂation to determine how quickly prices will double.
The formula for the rule of 72 is:Years to double = 72 ÷ interest rate

For example, how long it will it take for $10,000 invested at 6 percent todouble using the formula?
Years to double = 72 ÷ 6 = 12 years

In the late 1970s and early 1980s, inﬂation in the United States was a problem. With an inﬂation rate of 9 percent, for example, prices would double
every eight years (72 ÷ 9).
Use Worksheet 35.1 to determine the length of time it will take for yourinvestment to double.
The rule of 72 gives an approximation of the years needed for an investment to double. The exact length of time is more accurately determined usingﬁnancial tables, a ﬁnancial calculator, or a computer. The rule of 72 is lessaccurate because it does not take into account the time value of money. However, the rule gives an excellent approximation of the doubling time and issimple and easy to use.

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

WORKSHEET 35.1 Rule of 72 and how long it will take to double your investment
Years to double =72
Interest rate

Fill in the interest rate: =72

Years to double = ________F I N A N C I A L C A LC U L ATO R # 36

How to Assess and Balance
Risk and Return in the
Choice of Different Investments

I

nvestors have different reasons or objectives for investing that areimportant in determining the choice of investments. Objectives also determine the level of risk tolerance, which then impacts on the choice of thedifferent types of investments. The most common objectives are:
• Capital preservation• Income generation• Income and growth• Growth
Figure 36.1 illustrates a continuum of these objectives as well as thecorresponding levels of risk. The level of risk increases as the objectives change
from capital preservation at one end to growth at the other.

Managing Your Personal Wealth—Investments

181

FIGURE 36.1 Objectives and level of risk
Incomeand growth

GrowthIncomegeneration

Capitalpreservation

High risk

Low risk

Use Figure 36.1 to determine your objectives and level of risk tolerance.
The next step is to determine the levels of risk of the different types of investments, as shown in Figure 36.2.
Classifying some of the types of investments on a continuum of risk,
we see that speculative common stocks are considered the most risky (in termsof variability in share price), followed by long-term bonds, with shorter maturities on the low-risk end. There is a great variation of quality among common stocks. The common stocks of the well-established, blue-chip companies
are considered less risky than junk bonds.
Speculative common stocks are considered the most risky due to the volatility of their stock prices. Blue-chip, large-capitalized stocks with established dividend records tend to be less volatile and hence less risky than growth stocks
and speculative stocks. However, over long periods of time, where the ups anddowns of the stock market can be waited out, common stocks as a group haveprovided higher returns. Common stocks provide the growth in a portfolio andshould be included among the investments. The percentage allocated to common stocks depends on your objectives and personal characteristics. For exam-

FIGURE 36.2 Types of investments and their risk levels
Speculative
stocksHigh risk

GrowthstocksBlue-chip stocks/ Intermediate
long-term bonds
bonds

Short-termbonds

Money market
securities

Low risk

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

ple, a retired widow who is dependent on the income generated from the investments in her portfolio may have a smaller percentage allocated to common
stocks. However, if the portfolio generates more than a sufﬁcient level of income
for the widow’s current needs, a larger portion of the portfolio could be invested
in common stocks to provide more growth in the portfolio for later years.
Bonds are sought by investors primarily for their ability to generate a steadystream of income. However, an often-overlooked fact is that long-term bonds(10- to 30-year maturities) can also be quite risky. Although long-term U.S. Treasury bonds are safe investments in that the U.S. government is not liable todefault on the interest and principal payments, they can be quite volatile in pricedue to changes in interest rates. Corporate and other types of long-term bonds
are more volatile than Treasuries due to the increased risk of default.
You need to weigh the advantages of taking on the greater risks of investing in other types of long-term bonds over Treasuries by examining their coupon
yields. If the yields are signiﬁcantly greater than those of long-term Treasuries,
you may want to contemplate purchasing these other types of long-term bonds.
Some of the volatility in the price of bonds is reduced by shortening thematurities to intermediate-term bonds. Shortening the length of time to maturity reduces returns, but intermediate-term bonds offer greater ﬂexibility. For
instance, if your personal circumstances change so you no longer need current income from investments, intermediate-term securities are generally
much more liquid than longer-term bonds and can be more easily changed
to more growth-oriented investments.
Low-risk, low-return securities such as certiﬁcates of deposit (CDs), Treasury bills, and money market funds should account for the percentage of yourportfolio that serves liquidity and emergency fund purposes. Many people
make the mistake of keeping too large a percentage of their portfolio inthese low-risk, low-return assets for various reasons.
If you are conservative and do not feel comfortable keeping only anamount equal to your liquidity and emergency needs in low-risk investments,
you should increase the percentage. Often, however, the returns from these
low-yielding money market investments do not even keep pace with inﬂation,
not to mention the effect of taxation on the interest. It is evident that risk can-Managing Your Personal Wealth—Investments

183

not be avoided even with the most conservative investments, such as savings
accounts and Treasury bills. By understanding and recognizing the different
levels of risk for each type of investment, the total risk can be better managed
in the construction of the portfolio.
There is a direct correlation between risk and return. The greater the riskin an investment, the greater the potential return to entice investors. In
most cases, however, investing in securities with the greatest return and, therefore, the greatest risk can lead to financial ruin if everything does not go
according to plan.
Being aware of the risks pertaining to the different types of investments
is of little consequence unless you are aware of your own feelings toward risk.
How much risk you can tolerate depends on many factors, such as the type of
person you are, your investment objectives, the amount of your assets, the sizeof your portfolio, and the time horizon for your investments.
How nervous are you as an investor? Do you check your stock prices every
morning in the ﬁnancial newspapers? Can you sleep well at night if your stocks
have declined below their acquisition prices? If you do watch the prices of yourstocks every day, call your broker every time that your stocks fall by a point,and do not sleep well at night when your stocks are down, you do not toleraterisk well. In this case, your portfolio should be weighted toward conservative
investments that generate income through capital preservation. The percentage of your portfolio allocated toward stocks may be low to zero, depending on
your comfort zone. If you are comfortable with accepting more risk, you would
invest a greater percentage of your portfolio in stocks. This would be so even if
you are the type of person who monitors your stocks on a daily basis. The difference is whether you can sleep well at night when your stocks go down in value.
Moving along the continuum of greater risk seeking, if you buy stocks
and forget about them until you are reminded about them by someone else,
your tolerance for risk is much greater, and your portfolio can include a large
percentage of stocks.
The risk seeker or speculator will look for investments with the greatest
rates of return even though the investments may be extremely volatile andthere may be a good chance that some of the principal could be lost.

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Bear in mind that there are other factors you need to consider when allocating your investment funds to different types of investments. Understanding your tolerance for risk is just one important step in determining how muchof your portfolio should be allocated to common stocks.
There is a wide range of returns associated with each type of investment.
Stocks have different classiﬁcations, such as growth stocks, income stocks, andspeculative stocks. Income stocks generally are lower risk and offer returns
mainly in the form of dividends, whereas growth stocks are more risky andgenerally offer higher returns in the form of capital gains. Similarly, there isa broad range of risks and returns for the different types of bonds; for example, junk bonds versus Treasury bonds of the same maturities. Investors should
be aware of the broad range of risks and returns for these different types ofinvestments so that an acceptable level of risk may be found. Figure 36.3 illustrates the risk-return trade-off, in general, for the different types of investments. Bear in mind that with the broad range of risks and returns for each

FIGURE 36.3 General levels of risk and returns for different types of investments
Small-cap
stocksGrowthstocksRate of returnGood-quality
municipal bonds
Blue-chipstocksTreasurybonds
Treasury
notes
CDs

Preferredstock

Treasury bills
Level of risk______________________________________________________________________

Manage Your Personal Wealth—Investments

185

type of investment, you may be exposed to more risk with certain junk bonds,
for example, than with certain blue-chip stocks. In general, the risk-return
relationship shows that for accepting a higher level of risk in an investment,
you should be rewarded with higher returns. Similarly, for lower levels of risk,
you can expect lower returns.
Use Worksheet 36.1 to determine your investments by balancing yourneed for returns with the risk levels.

WORKSHEET 36.1 Choose your investments by balancing your risk-return trade-off
Type ofinvestments

Risk
level

Return(percent)

Dollar amountof investment

Short term__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Intermediate term__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Long term__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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F I N A N C I A L C A LC U L ATO R # 37

How to Calculate a Simple Rate of
Return for Stocks and Bonds

T

he reason to invest is to earn a return that may be in the form ofincome (interest and dividends) and/or capital appreciation (when theprice of the investment rises between the time of purchase and sale). Some
investments, such as savings accounts and certificates of deposit (CDs),
offer only income with no capital appreciation; others, common stocks forexample, may or may not pay dividends, but also offer the potential for capital appreciation. If the price of the stock goes down, there will be a capital
loss. The simple deﬁnition of total return includes both income and capitalgains and losses.
Why is calculating a return so important? There are two reasons. First,
it is a measure of the growth or decline of your investments. Second, it is ayardstick with which to evaluate the performance of your investments against
your objectives. The formula for calculating a simple rate of return for stocks
or bonds is as follows:
Rate of return =(Ending Value − Beginning value) + Income
Gross purchase priceSpreads and commissions should be included in the calculations. For
example, if a stock was purchased at the beginning of the year for $1,000(including the commission), sold for $1,200 (net proceeds received after
deducting the commission) at the end of the year, and earned a dividend of$50, the rate of return is 25 percent:
Rate of return =(1,200 − 1,000) + 50
= 25%
1,000

This rate of return is not very accurate, particularly if the investment isheld for a long period of time. The reason is because the time value of money

Managing Your Personal Wealth—Investments

187

is not taken into account. The time value of money is a concept that recognizes that a dollar today is worth more in the future because of its earnings
potential. A dollar invested at 3 percent for one year would be worth $1.03
at the end of one year. Similarly, a dollar to be received at the end of one
year would be worth less than a dollar at the beginning of the year.
The simple average rate of return of 25 percent discussed above does nottake into account the earnings capacity of the interest received. In other words,
the $50 of dividends received would be reinvested, which would raise the rateof return above 25 percent.
Using the time value of money to calculate the rate of return gives a moreaccurate rate of return ﬁgure. However, it is more difﬁcult to calculate forstocks. The rate of return on a stock equates the discounted cash ﬂows of
the future dividends and the expected sale price of the stock to the current
purchase price of the stock. This formula works better for bonds than forcommon stocks because the cash ﬂows for bonds are much more certain thanthose for common stocks. The coupon rate for bonds is generally ﬁxed; dividend rates on common stocks may ﬂuctuate. When companies are experiencing losses, they may cut their dividends, as Ford Motor Company did in
2002. On the positive side, if earnings increase, companies may increase theirdividend payout ratios. There is even less certainty over the sale price of a stock
into the future. Bonds are retired at their par price ($1,000 per bond) at maturity, but when planning to sell a stock in the future, you would be guessing
at the sale price.
Whichever formula you use to calculate the rate of return on stocks,
you need to be aware that there could be wide ﬂuctuations in return from year
to year. This is due primarily to the ﬂuctuations in the price of the stock, sincedividend income tends to be relatively stable. Thus, at any point in the future,
the price of the stock could be up or down from the acquisition price.
Clearly, many investors dream of tripling their investments overnightby buying stocks. This could happen, but it is not the order of the day. In 1999,
many Internet company stocks rose 200 and 300 percent in short periods oftime, but unfortunately, they showed that they had the potential to go downby that much and more. The rate of return that investors ought to expect from

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

investing in a diversiﬁed stock portfolio should be greater than the returns
received on bonds and money market securities. Historically, over long
periods of time the stock market has outperformed both long-term and shortterm bonds, and although there are no guarantees, this trend will likely prevail in the future. The superior results obtained by stocks are compelling.
Use Worksheet 37.1 to determine the rate of return for your stock or bondinvestments.
Worksheet 37.2 illustrates the rate of return on a bond for different
time periods.

WORKSHEET 37.1 Determine your rate of return for a bond or stock
Ending value _________
Interest income/dividends _________
Rate of return =Beginning value _________
Gross purchase price _________(Ending value − beginning value) + income
Gross purchase price= __________= __________ %Step 1 Fill in the data and enter the ﬁgures into the formula.
Step 2 Determine the annualized return if the time period is greater or less than
one year.

Managing Your Personal Wealth—Investments

189

WORKSHEET 37.2 Calculation of rates of return on a bond for different
time periods
1. Determine the rate of return for a bond bought at $99 and sold two years
later at $101 with a coupon of 7% payable semiannually. (Bonds arequoted in hundreds but trade in thousands.)
Answer:Cash ﬂows
$35

$35

$35

$1,010$35$990
Rate of return = [(1,010 – 990) + 140] ÷ 990 = 16.16%
Annualized rate of return = 16.16% ÷ 2 years = 8.08%
Reason: The rate of return of 16.16% is for the two-year period, and for anannualized return this ﬁgure is divided by two.
2. Determine the rate of return for a bond bought at $98 and sold after six
months for $99 with a receipt of one interest payment of $40.
Answer:Rate of return = [( 990 − 980) + 40] ÷ 980 = 5.1%
Annualized rate of return = 5.1% × 2 = 10.2%
Reason: The rate of return for 6 months is 5.1%, which is multiplied by two foran annualized return.

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F I N A N C I A L C A LC U L ATO R # 38

How to Determine a Rate of
Return for a Mutual FundT

he total return of a mutual fund includes the following threecomponents:
1. Dividends and capital gains/capital losses
2. Changes in net asset value
3. Dividends (interest) on reinvested dividends

You can calculate an average total return by taking into account the threesources of return (dividends distributed, capital gains distributed, and thechanges in share price) and by using the following formula:

Average total return =(Dividend + capital (Ending NAV − Beginning NAV+
gain distributions
Year+(Ending NAV + Beginning NAV
2

Example:Assume the following information:
Beginning net asset value (NAV) = $10.00 per share
Ending net asset value (NAV) = $10.30 per share
Dividends = $0.37 per share
Capital gains distributed = $0.70

Managing Your Personal Wealth—Investments

191

0.37 + 0.70) + (10.30 – 10.00
1
Average total return = ________________________
10.30 + 10.00
2= 13.5%This simple yield of 13.5 percent indicates that an investor in this fundwould have received double-digit returns, resulting mainly from realized gains
and increases in the NAV share price. The more volatile the net asset valueof the fund, the greater the likelihood of unstable returns. Thus, when considering whether to invest in a particular fund, don’t go by the advertised yieldalone, but look at the total return.
Worksheet 38.1 provides the outline to determine a rate of return on yourmutual funds.

WORKSHEET 38.1 How to determine the rate of return on your mutual funds
Step 1 Fill in your mutual fund data.
Beginning NAV (purchase price)
Ending NAV (sale price)
Dividends
Capital gains distributed________________________________

Step 2 Enter the data into the formula.

Average total return =(Dividend + capital (Ending NAV − Beginning NAV+
gain distributions
Year+(Ending NAV + Beginning NAV
2( ____ − _____ )( ___ + ____ ) +1= __________________________( ___ + ____ )__________
2= _____ %Step 3 Analyze your return.
Does the major portion of the return come from dividends, capital gains, or an
increase in net asset value?

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F I N A N C I A L C A LC U L ATO R # 39

How to Determine theYield on Treasury BillsT

reasury bills are the most popular of the short-term individual
investments after money market mutual funds.

What Are Treasury Bills?
Treasury bills (T-bills) are short-term, safe-haven investments that are issued
by the U.S. Treasury and fully backed by the U.S. government. The risk ofdefault is extremely low. In fact, if the U.S. government defaulted on any of its
obligations, all investments in the United States would be suspect. Treasury
bills are considered to be the safest of all short-term ﬁxed-income investments.
Treasury bills are negotiable, non–interest-bearing securities that mature
in four weeks, three months, or six months. They are available in a minimum
denomination of $10,000 and multiples of $1,000 above that. See Table 39.1
for details on the different Treasury bill issues.
The 4-, 13-, and 26-week bills are auctioned every week. The 4-week Treasury bill cannot be bought through the Treasury Direct program, but the othertwo maturities may be bought directly. The announcements for auctions
are generally made two weeks before each auction.
TABLE 39.1 Treasury bills
Term(weeks)Minimum

Multiples

AuctionAuction
time

Issue
date

4
13
26

$10,000$10,000$10,000$1,000$1,000$1,000WeeklyWeeklyWeeklyMondayMondayMondayThursdayThursdayThursdayWORKSHEET 39.1 How to determine the yield on Treasury bills
Although there is no stated rate of interest, the yield on Treasury bills can be
determined as follows:
Yield =

(Face value − price paid)
365
×Price paid
Days to maturity

A six-month, $10,000 Treasury bill purchased for $9,908.50 and redeemed atface value has an annual yield of 1.85 percent:
Yield = (10,000 − 9,908.50 ÷ 9,908.50) × (365 ÷ 182)
= 1.85%
However, to make matters more complex, bids submitted to the Federal
Reserve Banks are not quoted on an annual basis, as above, but on a bankdiscount basis which is computed as follows:
Yield = (Face value − price paid ÷ 100*) × (360** ÷ days to maturity)* Yield is quoted for each $100 of face value.
** Note the use of 360 as opposed to 365 days.
Using the same example as above, the discount is $0.915 for the T-bill sellingat $99.085 per $100 face value with a maturity of six months.
The bank discount yield is:= (100 − 99.085 ÷ 100) × (360 ÷ 180)
= 1.83%The bank discount yield is always less than the annual yield.

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195

Treasury bills are issued at a discount from their face value. The amountof the discount depends on the prices bid in the Treasury bill auctions. At
maturity, the bills are redeemed at full face value. The difference in the amountbetween the discount value and the face value is treated as interest income.
See Worksheet 39.1 for the determination of Treasury bill yields, shown on
an annual basis and on a bank discount basis. The distinction between these
two methods of determining the yields is important, because if you are submitting a competitive bid you would need to use the yield computed on a bankdiscount basis. The yield would need to be stated to two decimal places.
Worksheet 39.2 outlines the steps for you to determine the yields on yourTreasury bills.

WORKSHEET 39.2 How to determine the yield on your Treasury bills
Step 1 Fill in the following information on your Treasury bill:
Price paid ______________ Face Value ($1,000 per T-bill) ________
Days to maturity ___________
Step 2 Enter this information into the formula to determine the annual yield.
Yield =

365
(Face value − price paid)×Price paid
Days to maturity=(______ − ______)
365×(______)(______)= _______
To determine the bank discount yield:
Step 1 Fill in the following information:
Price paid (in hundreds) __________ Days to maturity ______________
Step 2 Enter this information into the formula to determine the bank discount yield.
Yield = (Face value − price paid ÷ 100) × (360 ÷ days to maturity)=

360(100 − ______)
×100
Days to maturity= ______
Step 3 The bank discount yield is always less than the annual yield.
The bank discount yield is used to place your competitive bid when buying
Treasury bills directly from the Treasury.

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F I N A N C I A L C A LC U L ATO R # 4 0

How to Determine the Purchase andSelling Price of Treasury BillsW

hen you buy Treasury bills that are quoted in the secondary market, you do not see a price quote. Instead, these issues are quoted on a
bid and ask spread. Consequently, you need to determine the purchase andselling prices of the issues in which you are interested.
Table 40.1 shows a listing of a Treasury bill quote in a daily newspaper:• Treasury bills are short-term securities, so all listed T-bills will
mature within six months—in this case on August 15, 2002.
• There are 176 days from this date until maturity of this issue. Treasury bills are sold at a discount, which is less than the par or face
amount of $1,000, and then redeemed at par at maturity. This difference is attributed to interest. The bid discount of 1.80 percent is thediscount (price) that buyers are willing to pay for this bill on thatday, and the ask discount of 1.79 percent is the discount at which
sellers are willing to sell this security on that day. The spread between
the bid and the ask price is $0.05 per T-bill (0.01 percent).
• The ask yield is 1.83 percent, which is the return an investor would
get on this issue if bought at the ask price and held to maturity.

TABLE 40.1 Treasury bill quote
Maturity
Aug 15 02

Days to Mat.
176

Bid
1.80

Ask
1.79

Chg
...

Ask Yld
1.83

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

The formulas for calculating the dealer’s selling and purchase price areshown in Worksheet 40.1.
From the ask discount, you can determine the price at which dealers
will be willing to sell the Treasury bill. In this example, it is $991.25, and at
maturity (in 176 days’ time) you will receive the face value of the Treasury
bill—$1,000. The bid discount indicates what dealers are willing to pay for
Treasury bills that you want to sell to them, on the day of this quote. In thiscase it is $991.20 per bill.
Worksheet 40.2 outlines the steps for determining the purchase and selling price of Treasury bills in which you are interested.

WORKSHEET 40.1 How to calculate the purchase and sale price of Treasury bills
The dealer’s selling price can be calculated as follows:= Par value − Par value × Asked discount ×= $100 − 100 × 0.0179 ×

Days to maturity
360

176
360

= $99.125, or $991.25 per T-bill
The dealer’s purchase price can be calculated as follows:= Par value − Par value × Bid discount ×= $100 − 100 × (0.018) ×

176
360

= $99.12 or $991.20 per T-billDays to maturity
360

WORKSHEET 40.2 How to determine the purchase and sale price of yourTreasury bills
Step 1 Fill in the following information on your Treasury bill.
Days to maturity __________________ Bid discount __________________
Ask discount __________________
Step 2 If you are buying Treasury bills, use the ask discount.
The purchase price is calculated as follows:= Par value − Par value × Asked discount ×= _______ − _______ × _______ ×

Days to maturity360_______
360= _______
Step 3 If you are selling Treasury bills, use the bid discount.
The selling price can be calculated as follows:= Par value − Par value × Bid discount ×= _______ − _______ × _______ ×= _______

Days to maturity360_______
360

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F I N A N C I A L C A LC U L ATO R # 41

How to Buy and Sell
Treasury Securities Directlyfrom the Federal ReserveN

ew issues of Treasury securities can be bought directly from anyof the Federal Reserve Banks in the primary market with no commissions or fees charged. New Treasury issues can also be bought indirectly
through banks and brokerage ﬁrms, which charge commissions for their services. Existing Treasury securities that trade in the secondary markets arebought and sold through banks and brokerage ﬁrms.

Direct Purchase
An investor can buy directly from the Treasury by opening an account andthen submitting a tender form. See Figures 41.1 and 41.2 for a copy of a
new account request form and a copy of a tender form for Treasury securities, respectively. See Worksheet 41.1 on page 204 for an explanation of theprocess for purchasing securities directly through the Federal Reserve Banks.
See Worksheet 41.2 on page 205 to determine whether to submit a competitive or a noncompetitive bid.
Worksheet 41.3 on page 206 summarizes the steps for buying Treasury
securities directly through the Federal Reserve Bank or branches.

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

FIGURE 41.1 New account request

FIGURE 41.2 Treasury bill, note, and bond tender form

WORKSHEET 41.1 Process for buying Treasury securities directly
Step 1 The ﬁrst step is to ﬁll out the new account request form (Figure 41.1) to establish an account with the Department of the Treasury. The routing number requestedon the form is the nine-digit identiﬁcation number of your ﬁnancial institution. It canbe found on the bottom line of a check before the account number or on a deposit
slip before the account number. This step can be done on the Internet.
Step 2 Submit this form to the Federal Reserve Bank/branch. A conﬁrmation of theestablishment of the account and an account number will be issued. Purchases ofTreasury securities are recorded in this account, which is maintained at no charge up
to $100,000 of securities. Over this amount, the Federal Reserve charges $25 to maintainthe account.
Step 3 Fill in the tender form to buy Treasury securities directly from the Federal
Reserve Bank. See Figure 41.2 for a copy of a tender form.
Step 4 The Federal Reserve Bank auctions new issues of Treasury securities on a weekly
basis and investors may submit their bids either on a competitive or noncompetitive basis.
Step 5 Treasury bills purchased directly through the Federal Reserve are held in the TreasuryDirect book-entry system, which is designed primarily for investors who hold theirsecurities to maturity. Should an investor decide to sell Treasury securities before maturity,
he or she would have to ﬁll out a Transfer Request Form (PD 5179), which transfers theaccount to the commercial book-entry system, at which point the Treasury securities
could be sold. The commercial book-entry system records those Treasuries bought
through ﬁnancial institutions and government securities dealers. Information on Treasury
bills can be obtained from the government’s website at (www.publicdebt.treas.gov).

WORKSHEET 41.2 Competitive or noncompetitive bids?
Competitive bids
• Submit a bid on a bank discount basis, to two decimal places. For example, if an investor wanted to buy $100,000 of six-month Treasury bills andpay $99,125, the competitive bid submitted to the Federal Reserve Bank
would be 1.79 percent.
• The Federal Reserve accepts those bids with the lowest discount rates(the highest prices) from all the bids received. For the accepted bids there
is a range of yields, from the lowest to the highest known as the “stopout
yield,” which the Federal Reserve will pay. Investors with accepted bids at
the “stopout yield” or close to it receive greater returns than those withaccepted bids at the lowest accepted yield.
• The yields that investors bid depend upon the money market rates thatare currently being offered by competing short-term instruments as well
as expectations of what current short-term rates for T-bills will be. By
studying these rates, an investor has a better chance of submitting a bidthat will be accepted. However, with a competitive bid, investors face
the risk of not having their bids accepted, if their bids are above thestopout yields.
Noncompetitive bids
• Less expert investors who may not want to work out their bids or for
those who want to be assured of their bids being accepted can submit
noncompetitive bids. With noncompetitive bids, investors are able to buy
Treasury securities at the average accepted competitive bid in the auction.
Generally, all noncompetitive bids of up to $1 million per investor per
auction are accepted, which means that investors are assured of theirpurchases.
• Tender forms to submit bids may be sent by mail, delivered in person to
the Federal Reserve Banks and branches before the close of the auction,or submitted on the Internet. Competitive bids must be received by thetime designated in the offering circular. Noncompetitive bids that are
mailed must be postmarked by no later than midnight the day before theauction and received on or before the issue date of the securities.
(continued overleaf)

WORKSHEET 41.2 Competitive or noncompetitive bids? (continued)• Payment must accompany the tender form. Check the type of payment:
cash, check, securities, or other. The amount of the payment should be
no less than the amount of the tender for a noncompetitive bid and noless than the bid amount for a competitive bid. If the payment amount is
not correct, the tender will be rejected and returned.
• On acceptance of the bid, the investor receives a conﬁrmation receipt
from the Federal Reserve and a payment, which is the difference between
the tender amount submitted and the discounted price of the T-bills.
Investors can stipulate on the tender form whether they want the Federal
Reserve to reinvest the T-bills when they mature. If the reinvestment
option is not chosen, the Federal Reserve credits the investor’s accountfor the face value of the Treasury bills at maturity.
• The advantage of buying T-bills directly and holding them to maturity isthat the investor avoids paying commissions or fees.

WORKSHEET 41.3 Steps for buying Treasury securities directly through the Federal
Reserve Bank.
Step 1 Fill in the following data on the Treasury Security tender form:
Par amount ________ Competitive ________ or Noncompetitive bid ________
TreasuryDirect account number ______________ (If you do not have one, ﬁll in
the new account form.)
Social Security # _______________
Type of Treasury security ____________ Maturity date ____________
Routing number (9 digits) ____________ Account # ____________
Type of account ____________ Name of your ﬁnancial institution ____________
Purchase method ____________
Step 2 Determine whether you will submit a competitive or a noncompetitive bid.
Competitive bid
Fill in the bid/ask yield to two decimal places. ____________
Noncompetitive Bid
Limited to $1 million per auction for Treasury bills
Limited to $5 million in a note and bond auction(continued)

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207

WORKSHEET 41.3 Steps for buying Treasury securities directly through the Federal
Reserve Bank (continued)
Step 3 Submit your bid.
This can be done by mail, in person, by touch-tone phone, or through theInternet. Be aware of the time deadline for the auction.
Step 4 File account statements from the Federal Reserve in a safe place.
Step 5 Make a note of the dates of the interest payments.
Interest payment date ____________ Amount ____________
Maturity date ____________
These payments are made directly to the bank account that you wrote on yourform. Check to see that these transfers have come in on the due dates.
Step 6 At maturity, TreasuryDirect allows you to reinvest the principal.
If you decide to reinvest the principal, you may do so by mail, by phone, or
through the Internet.
Reinvest principal? Yes ____ No ____F I N A N C I A L C A LC U L ATO R # 4 2

How to Convert Municipal Bond
Yields to Before-Tax Yields

M

unicipal bonds are debt securities issued by state and local governments, their agencies, and enterprises with a public purpose. The
most important feature of municipal bonds is that the interest income isexempt from federal income taxes and state taxes if the holder lives in the stateissuing the municipal bond. The federal tax exemption beneﬁts not only individuals who buy municipal bonds but also the states and localities issuingthem, since they can pay lower coupon yields than regular taxable bonds.

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

Most investors look to lower their tax bills, but municipal bonds may not
be the right investment for everyone. Buying tax-exempt issues purely to lower
tax liability may mean that some investors in some cases may not be earning as much as they could on an after-tax basis if they had bought taxablebonds. This may be especially true for investors in low tax brackets, who could
earn more from taxable bonds even after paying the taxes.
In order to compare municipal bonds with taxable bonds, you need toconvert the tax-exempt yield of a municipal bond to the equivalent yield ofa taxable bond. See Table 42.1 for some examples of what taxable bonds would
have to yield in order to equal the yields of municipal bonds.
The equivalent yield of a taxable bond at the investor’s tax bracket isthe yield an investor would have to earn on a taxable bond to equal the yield
on a municipal bond. For example, an investor in the 15 percent tax bracket
purchasing a taxable bond with a yield of 7.65 percent would earn the equivalent from a 6.5 percent tax-exempt municipal bond. Put another way, theinvestor in the 15 percent tax bracket would purchase a municipal bond yielding 6.5 percent only if taxable bonds of similar maturities were yielding lessthan 7.65 percent. If this investor could earn more than 7.65 percent on tax-

TABLE 42.1 Comparison of taxable bond yields to those of municipals at different
tax brackets
Municipal bond yield
5.0%
Federal income
tax bracket
10%
15%
27%
30%
35%
38.6%

5.5%

6.0%

6.5%

Taxable bond yield
5.50%
5.88%
6.85%
7.14%
7.69%
8.14%

6.11%
6.47%
7.53%
7.86%
8.46%
8.96%

6.67%
7.06%
8.22%
8.57%
9.23%
9.77%

7.22%
7.65%
8.90%
9.29%
10.00%
10.59%

Managing Your Personal Wealth—Investments

209

able bonds, municipal bonds would not be considered. However, for investors
in higher tax brackets, the taxable equivalent yield is much greater. In the 35
percent tax bracket, the taxable equivalent yield on a 6.5 percent municipal
bond is 10.00 percent. Thus, as tax brackets (rates) increase, the taxable equivalent yields increase, and municipal bonds become more attractive. For a taxpayer in the highest marginal tax bracket of 38.6 percent, a 5 percent municipal
coupon is the equivalent of an 8.14 percent taxable bond coupon.
This presents earnings opportunities for investors in the highest tax brackets when comparing these yields with 10-year Treasury bonds, which are currently yielding under 5 percent. With the current declines in the stock markets
around the world, the high yields of municipal bonds, due to their tax-exempt
status, make them very appealing to high-income taxpayers.
Before buying tax-free municipal bonds, you should decide whether
the yield at your tax bracket is high enough to warrant the purchase.
Brokerage ﬁrms publish tables of taxable equivalent yields, like Table 42.1,
but it is a simple calculation to convert municipal bond yields to taxable yield
equivalents. See Worksheet 42.1 for the formula to convert municipal bondyields to before-tax yields or taxable equivalent yields.
Some states have higher rates of taxation than other states, which brings
the next question to mind: Should you buy an in-state or out-of-state bond?

WORKSHEET 42.1 How to convert municipal bond yields to taxable equivalentyieldsTaxable equivalent yield =Municipal bond yield
1 − Investor’s marginal tax rate

A 6 percent municipal bond bought by an investor in the 27 percent marginal
tax bracket will have a before-tax return of 8.22 percent.
Taxable equivalent yield =6%
1 − 0.27= 8.22%

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

Most states give favorable tax treatment to in-state municipals by exempting the income from state taxes. This also applies at the local tax level if theissue is a local issue. This exemption from state and local taxes increases thetaxable equivalent yield when comparing an in-state municipal bond with ataxable bond. To answer the question of whether to buy an in-state or out-ofstate bond requires another simple calculation.
Suppose that you are considering an out-of-state municipal bond witha yield of 6.5 percent and an in-state bond with a yield of 5.75 percent, andthe state and local taxes combined are 6 percent.
The after-tax out-of-state yield = (1 − tax rate) × the out-of-state yield= (1 − 0.06) × 0.065= 6.11%

The after-tax yield on the out-of-state bond is 6.11 percent, which is higher
than the in-state bond yield, and so the out-of-state bond would be more attractive in this case. High-tax states like New York and California have such ahigh demand for their in-state issues that their yields are often lower than outof-state municipal bond issues. Bear in mind for comparison purposes that
Treasury issues and certain government agency issues are also exempt fromstate and local taxes. These, however, are not exempt from federal taxes.
Investors who are subject to the alternative minimum tax should consult theirtax advisors or accountants to determine their equivalent yields.
Worksheet 42.2 outlines the steps to determine your before-tax or taxable equivalent yields.
Tax laws change continually and the marginal tax rates are set to be
reduced over the early years of the twenty-ﬁrst century. Investors should keep
abreast of these changes as to the effects on their investments. Municipal bonds
are probably the last great tax shelter left in the code. However, they do not
beneﬁt all investors. Generally, investors in the higher tax brackets beneﬁt themost from municipal bonds, while those in the lower tax brackets may not
ﬁnd them particularly advantageous to own.

Managing Your Personal Wealth—Investments

211

WORKSHEET 42.2 How to convert municipal bond yields to before-tax yields
Step 1 Fill in the following information:
Municipal bond yield _______________ Your marginal tax rate ________________
Step 2 Plug this data into the formula:
Before tax yield ==Municipal bond yield
1 − Investor’s marginal tax rate(________)(1 − _____)= _____
Step 3 Compare the before-tax yields of municipals with those of Treasuries and agency
and corporate bonds to assist in the purchase decision. If the before-tax yield/taxable
equivalent yield of the municipal bond yield is greater than the other bond yields, thenit is advantageous to go with the municipal bond issue, assuming the risk level is similar.
Taxable equivalent yield of municipal ______ Treasury/other bond yield ______F I N A N C I A L C A LC U L ATO R # 4 3

Duration and How It
Can Help You in the Choice ofBonds for Your Portfolio

Duration is deﬁned as the average time that it takes for a bondholder
to receive the total interest and principal. It is the point in time in thelife of the bond where the bond’s return remains the same despite the movement of market rates of interest. For example, the duration on a $1,000 facevalue bond with a coupon of 6 percent, maturing in three years with a market

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

price of $973.44 and a current market rate of interest of 7 percent, is calculated using the following formula:
Duration =(1 + y) (1 + y) + n(c − y)−c[(1 + y)n − 1] + yyWherec = coupon ratey = yield to maturityn = number of years to maturity
Substituting the ﬁgures from the example above:
Duration =(1 + 0.07) (1 + 0.07) + 3(0.06 – 0.07)−
0.07
0.06[1 + 0.07)3 − 1] + 0.07

= 2.83 years

Another method of determining the duration of a bond is to use the timevalue of money concept. Using the same example as above, a bond with acoupon of 6 percent maturing in three years with a market price of $973.44
and a current market rate of interest of 7 percent, duration is determined asshown in Table 43.1.
Duration is a time-weighted average of the summation of the present values of the coupon and interest payments multiplied by the time periods ofthe payments, then divided by the market price of the bond. The present value
is the opposite of the future or compound value in the time value of money
concept. A dollar today is worth more in the future because of its earnings
potential. Similarly, a dollar in the future can be discounted to today’s value
and is worth less now than in the future.
The duration means that the bondholder will collect the average of the
coupon and the principal payments of the bond in 2.83 years.
The impact of interest rate risk can be lessened using the concept of duration. Bonds with different maturities and different coupons have different

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213

TABLE 43.1 Duration using the time value of money formula

Time periodof payment
12
3

Present valueinterest factor
of 7%

Payment amount(Coupon & principal)
×××

Duration =

=

$60
60
1,060

×
×
×

0.93460.87340.8163Present value oftime-weighted
payments===$56.08104.802,595.83$2,756.71

Summation of present value of time-weighted payments
Market price of the bond
$2,756.71$973.44= 2.83 years/periods

durations. Bonds with higher durations experience greater price volatility as
market rates of interest change, and bonds with lower durations have lower
price volatility. Different bonds with the same durations experience similar
price ﬂuctuations due to changes in market rates of interest.
These points are illustrated in Table 43.2, which shows the prices of 6 percent coupon bonds with different maturities when market rates of interest change.
When market rates of interest decline below the coupon rate (6 percent) to 5 percent, the price of the bond increases above par value. Correspondingly, as the maturities increase from two years to 20 years, so do theprices of the bond. The opposite is true when market rates of interest rise to
7 percent (above the coupon rate of 6 percent) as shown in Table 43.2. Bond
prices fall below par and decline further as maturities extend into the future.
The following generalizations for bonds help to better explain duration:
1. The longer the maturity of a bond, the greater the price volatility.
2. There is an inverse relationship between bond prices and market

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

TABLE 43.2 Impact of market ﬂuctuations in interest rates on a par value bond witha coupon rate of 6% with different maturities
Maturity

Market rate of interest
5%Market rate of interest
7%

2 years
5 years
10 years
20 years$1,018.56
1,042.27
1,077.21
1,124.63$981.88959.01
929.72894.04rates of interest: When market rates of interest rise, bond prices fall,
and when market rates of interest fall, bond prices rise.
As pointed out, a bondholder with a coupon of 6 percent with a maturity of 30 years faces greater price volatility than a bondholder with a similar coupon bond with a shorter maturity. A lower-coupon bond (for example,
4 percent) with the same maturity experiences even greater price volatility
with changes in market rates of interest. A bondholder with the lower-couponbond receives lower cash ﬂows ($40 per year through maturity versus $60 peryear), which when reinvested produces lower future values. The longer thematurity of the bond, the longer the bondholder has to wait to receive the faceor par value of the bond. Hence, the present value of the par value of the bondis discounted to a lesser amount than the present value of the par value of abond maturing earlier.
Duration accounts for this reinvestment rate risk, the coupon rate, andthe term to maturity of a bond as follows:• The lower the coupon, the higher the duration.
• The higher the coupon, the lower the duration.
• The longer the term to maturity, the higher the duration.
• The shorter the term to maturity, the lower the duration.
• The smaller the duration, the smaller the price volatility of the bond.
• The greater the duration, the greater the price volatility of the bond.

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215

Duration explains why a zero-coupon bond has the same duration as
its term to maturity. With a zero-coupon bond, there are no coupon payments
and only the principal is received at maturity. Thus, except for zero-coupon
bonds, the durations for all bonds are less than their terms to maturities.
Duration is a tool that can be used to manage interest rate risk and thematurity of the bonds with the timing of the investor’s need for the funds. By
matching the duration of bonds with the timing of the need for the funds,
investors can lessen their risk of loss on their bonds.
For instance, assume that you need $17,100 in seven years’ time and you
have $10,000 to invest. You could buy 10 bonds at par, which have a coupon of
8 percent and mature in seven years’ time. The cash ﬂow per bond is:$80 per year for seven years and $1,000 at maturity in seven years
The future value of an annuity of $80 reinvested at 8 percent = $ 713.84
The par value of the bond at maturity
1,000.00
Total proceeds from bond at maturity
1,713.84
Multiplied by 10 bonds
× 10
Total proceeds in seven years’ time

$17,138.40

This is fine if interest rates stay at 8 percent. If interest rates fall, youwill have to reinvest your interest proceeds ($80 per year per bond) at lower
interest rates, and you will have less than the $17,100 that you need.
Consequently, if you buy a bond with a duration of seven instead ofmatching the term to maturity of your bond, you will have the amount ofmoney that you need. This is because if interest rates rise and you have a longer
maturity bond, the interest is reinvested at higher interest rates, and you would
sell your bond at a discount in seven years’ time. Similarly, if interest rates fall,your interest will be reinvested at lower interest rates, but you will be able tosell your bond at a premium.
Worksheet 43.1 shows how you can use the concept of duration in the
choice of your bonds.

WORKSHEET 43.1 How to use duration in the choice of your bonds
Step 1 Determine the length of time until you will need your funds. _______________
Step 2 Determine the duration for each of the bonds you are considering purchasing.
Duration =(1 + y) (1 + y) + n(c − y)−yc[(1 + y)n − 1] + y

Wherec = coupon rate________________
y = yield to maturity (reinvestment rate) ________________
n = number of years to maturity________________=(1 + __ ) (1 + __ ) + __ ( __ − __ )−____ [(1 + __ ) __ − 1] + __= _____
Step 3 Match the duration to the length of time until you need the funds.
Length of time for funds __________ = Duration ______________

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F I N A N C I A L C A LC U L ATO R # 4 4

How to Value Bonds

B

ond prices ﬂuctuate due to the relationship between their coupon
and market rates of interest, their creditworthiness, and the length oftime to maturity. After bonds are issued, they rarely trade at their par values($1,000) in the secondary markets because interest rates are always changing.
Some bonds sell at premiums and others sell at discounts.
There is a mathematical formula for determining the price of a bond,but bear in mind that this is conceptual. The market price of a bond depends
on the stream of the bond’s coupon payments and the principal repayment in
the future. Using the time value of money, this stream of future payments is
discounted at market rates of interest to its present value in today’s dollars.
For example, a bond that pays coupon interest of $100 per year andmatures in three years’ time with market rates of interest projected at an average of 6 percent per year will have a price of $1,106.92, according to the calculation shown in Worksheet 44.1. Thus, the price of the bond is linked to the
coupon yield, market rates of interest, discount rate, and the length of time
to maturity.
Comparing the price of a U.S. Treasury note with that of a corporate bondwith the same coupon rate and maturity, the prices of the two bonds will differ. Generally, the Treasury note will trade at a higher price than that of thecorporate bond because there is a greater risk of default with the corporatebond, and thus the price will be calculated with a higher discount rate (or yield
to maturity). The reason is because investors require a greater yield on thecorporate bond for assuming the greater risk of default. This conﬁrms why
an AAA-rated corporate bond trades at a higher price than a BBB-rated
corporate bond if the coupon and maturity are the same. The difference inyield between the AAA- and BBB-rated bonds is referred to as the excess yield,
which issuers must pay for the extra grade of credit risk.
Bond prices ﬂuctuate depending on investors’ assessment of risk. The
greater the risk, the greater the discount rate or required rate of return (and218

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WORKSHEET 44.1 Determining the value of a sample bondStep1 List the data for the bond:Coupon interest per year: $100
Market rate of interest: 6%
Maturity: 3 years
Step 2 Determine the present value or price of the bond using Microsoft Excel. The
price of the bond is $1,106.92.
Rate

6%

Nper

3

Pmt

$100

FV

$1,000

Formula result = $1,106.92

the lower the market price). Therefore, a bond with a greater degree of risk
will be discounted at a greater rate of return. Worksheet 44.2 outlines the steps
for determining the value of a bond.
For bonds that pay their coupon interest on a semiannual basis, you needto make the following changes. Since the coupon payment is made twice a year,
you need to divide the coupon amount by two. For example, a 6 percent coupon
payable semiannually results in a coupon amount of $30 per six-month period.
Consequently, the rate needs to be adjusted to a six-month period and the Nperor time to maturity is measured in six-month periods. Three years results in six
6-month periods, so six would be entered in the Nper row.

WORKSHEET 44.2 How to determine the value of a bond
Step 1 List the data of the bond you are interested in buying:
Coupon interest _______________
Years to maturity_______________
Bond rating_______________
Market rate of interest _______________
Risk premium _______________
Discount rate = Risk premium + market rate of interest____ + _____ = _________
Step 2 Using Microsoft Excel, determine the price of the bond:
Click on function in the row of tools.
In the left dialog box, highlight ﬁnancial.
In the right dialog box, highlight PV.
Step 3 Enter the data in the dialog box as shown in Worksheet 44.1:
Rate _________ Enter the discount rate or market rate of interest
Nper _________ Time to maturity
Pmt _________ Coupon interest payments
FV _________ Future value of the bond, which is the par value ($1,000)
Type _________ Enter 1 if the interest payments are made at the beginningof the period or 0 if the payments are made at the endof the period.
Step 4 The formula result is the price of the bond.

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F I N A N C I A L C A LC U L ATO R # 4 5

How to Value Common StockIt is not as easy to value common stock as it is to value bonds. Theoretically, the value of any securities, stocks, bonds, and preferred stock isequal to the discounted future cash ﬂows of dividends/interest and the saleprice of the securities or maturity value of the bonds. Bondholders can counton ﬁxed payments of interest, but for common stockholders both the receiptof the dividend and the amount of the dividend are not assured. Similarly,
there is uncertainty as to the future date of the sale of the common stockand the price of the common stock. Bonds have a stated maturity date, atwhich time bondholders receive the par value ($1,000 per bond) of the bond.
There are exceptions, where bonds can be called in at their call price (which
is mostly above par, as it includes a call premium).
The payment of dividends to common stockholders is largely based on
two factors:
1. The proﬁtability of the company
2. The decision by the board of directors to declare and pay dividends
rather than retain the proﬁts in the company
Proﬁtable companies may decide not to pay dividends, as in the case oflarge companies such as Microsoft, Cisco, and Oracle. These companies
have accumulated large amounts of cash, so they are able to sustain the dividend payouts but choose not to pay dividends. Instead these companies havechosen to retain their proﬁts and reinvest in their future earnings. Consequently, companies fuel their own growth by retaining proﬁts and reinvesting them in future business projects. Generally, when a company’s earnings
increase, this is reﬂected in a higher price for the common stock.

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Thus, shareholders value stocks on earnings potential (growth) and direct
returns in the form of dividends. The dividend growth model is one method
for valuing a stock. This model makes a number of assumptions:• Common stock does not have a maturity date.
• Dividends may ﬂuctuate over time depending on proﬁtability andthe board of directors’ decision to either pay dividends or retain the
proﬁts for internal reinvestment purposes.
• Companies can grow in different ways, which may or may not affectthe valuation of the company.
To get around these difﬁculties in the valuation of a stock, the dividend
growth model makes the following assumptions:• Future dividends will be paid and will grow at a constant rate.
• The company will have constant growth rate.
The equation shown in Worksheet 45.1 is used to value a common stock
based on future dividends that are expected to grow at a constant rate, divided
by the investor’s expected rate of return minus the growth rate.
See Worksheet 45.2 to determine the value of your common stocks. A
good place to start in the determination of the required rate of return is theTreasury bill rate. Add a percentage for the risk premium of the stock to thisrate. Small-cap growth stocks in the technology group would fetch higher risk
premiums than an established mid-cap regional bank stock, which is in a morestable type of business.
See section 46 for a method to determine the growth rate of a stock.
Using the valuation equation in Worksheet 45.2, you can determine yourexpected rate of return for any stock by making the same assumption that dividends increase at a constant growth rate. The expected rate of return is thedividend yield of a stock plus its growth rate. See Worksheet 45.3 for how to
use the formula to determine the expected rate of return of a stock.

WORKSHEET 45.1 Dividend-growth model to determine the value of acommon stock
Stock value =Future dividend
Expected rate of return − Growth rate

Future dividend = Existing dividend (1 + Growth rate)
Expected rate of return of the investor includes a risk element for the stock.
Growth rate: see section 46 for one method to determine the growth rate.
ExampleCompany X has just paid a dividend of $1.20 per share and is expected to
grow at 9 percent for the foreseeable future. The investor’s required rate of
return for such a stock is 12 percent. Using this information, the value of thecommon stock is determined as follows.
Step 1 Determine the future dividend.
Future dividend = Existing dividend (1 + Growth rate)= 1.20 (1 + 0.09)= $1.31
Step 2 Determine the value of the common stock.
Value

=

Future dividend
Required rate of return − Growth rate=

1.31
0.12 − 0.09

= $43.67
In order to achieve the required rate of return of 12 percent, the investor
would pay no more than $43.67 for each share of this stock.

WORKSHEET 45.2 How to value your common stock
Step 1 Fill in the data:
Dividend
Growth rate of the stock
Required rate of return_________________________________

Step 2 Determine the future dividend:
Future dividend = Existing dividend (1 + Growth rate)= ______(1 + ___)
= _______
Step 3 Insert values into the formula to determine the value of the common stock.
Value =

Future dividend
Required rate of return − Growth rate=

( _______ )___ − ___

= ____224

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WORKSHEET 45.3 Determining the expected rate of return of a common stock

Expected rate of return =Future dividend+ Growth rate
Market price of the stock

ExampleIf Johnson & Johnson Inc. pays a dividend of $0.72, and has a market price of$57.24 per share, and is expected to grow at 10 percent for the foreseeable
future, the expected rate of return is:
Expected rate of return =Future dividend+ Growth rate
Market price of the stock=

Existing dividend + (1 + Growth rate)+ Growth rate
Market price of the stock=

0.72 (1 + 0.10)+ 0.1057.24= 11.4%This expected rate of return on Johnson & Johnson is based on a 1 percent dividend yield and a 10 percent growth rate. However, there is a stronger
relationship between a company’s future growth and earnings than between
growth and dividends in the valuation of a common stock. In reality, a company’s earnings and the amount that is retained to fuel the internal growth ofthe company have a greater inﬂuence on the value of common stock.
Worksheet 45.4 outlines the steps to determine the expected rate of returnon your stock.

WORKSHEET 45.4 How to determine the expected rate of return on your stock
Step 1 Fill in the data for your stock:
Dividend___________
Purchase price of the stock ___________
Growth rate___________
Step 2 Determine the expected rate of return:Expected rate of return ==Future dividend+ Growth rate
Purchase price of the stock( _______ )+ ______( ____ )= _______
Step 3 Evaluate whether this return is sufﬁcient.

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F I N A N C I A L C A LC U L ATO R # 4 6

How to Determine theGrowth Rate of a StockTo understand what drives the market price of a stock, it is important to examine a company’s dividends, earnings, and growth rate.
In general, when the earnings of a company increase over a period of time,it has a positive impact on the market price of the stock. The equation showing the valuation of common stock (see section 45) highlights the importanceof dividends and the constant growth rate of a company. However, a company’s sustained earnings are a major determinant when it comes to whether
the company can afford to pay out dividends, maintain its dividend payments,
or increase dividend payouts. If the company decides to retain earnings insteadof paying them out and reinvest the proﬁts in its business, it can accelerate its
earnings growth. Consequently, by measuring the increase in a company’s
earnings over a period of time, the growth rate can be determined.
Earnings are just one measure of a company’s growth rate. Other measures are the growth of a company’s assets or sales. These, however, do not haveas direct a relationship to the price of the stock as does growth in earnings.Worksheet 46.1 illustrates how the growth rate of a stock can be determined.
Worksheet 46.2 provides the outline for you to determine the growth rateand expected rate of return for your common stock.

WORKSHEET 46.1 How to determine the growth rate of a stock and expected rateof return
Step 1 List the earnings per share (EPS) and dividends per share (DPS) for your stock
for the past ﬁve years.
This can be found on the company’s website, by clicking on ﬁnancial statements or in the company’s annual report. The following EPS and dividends per
share for Merck, Inc. were found on Merck’s website, www.merck.com.

Earnings per share
Dividends per share

1997

1998

1999

2000

2001

$1.87
0.84

$2.15
0.94

$2.45
1.10

$2.90
1.21

$3.14
1.37

Price per share in 2001: $59.80
Step 2 Determine the growth rate.
The growth rate is determined by solving for the rate of growth of the earnings
per share. EPS was $1.87 in 1997 and this grew to $3.14 in four years. Solve forthe rate using a ﬁnancial calculator or Microsoft’s Excel spreadsheet as follows:
Click on f *; two boxes appear on
the screen.

Nper

4

Highlight ﬁnancial in the left box andrate in the right box.

Pmt

0

PV

$ −1.87

Enter the data in the box to the right.

FV

$3.14

Type

0

Merck’s growth rate is 13.834%.
Step 3 Determine the expected rate of return.
Expected rate of return =Formula result = 0.13834

Future dividend+ Growth rate
Price of stock

Future dividend = Current dividend (1 + Growth rate)= 1.37(1 + 0.1383)= $1.56
Expected rate of return =1.56+ 0.1383
59.80= 0.0261 + 0.1383= 16.44%
The expected return is 16.44% if Merck is bought at the current price of $59.80 per share.

WORKSHEET 46.2 How to determine the growth rate and expected rate of returnfor your stocks
Step 1 List the earnings per share (EPS) and dividends per share (DPS) for your stock
for different periods.
Year________________________________________EPS
DPS
Market price per share _____________
Step 1 Determine the growth rate of the stock using a ﬁnancial calculator ora computer.
Number of periods _________
Present value_________
Future value_________
Solve for the rate_________

Step 3 Determine the expected rate of return for the stock.
Current dividend __________ Growth rate __________
Purchase price of stock _________
Future dividend = Current dividend (1 + Growth rate)= _______ ( 1 + _______ )= _______
Expected rate of return ==Future dividend+ Growth rate
Price of stock( ______________ )+ ___________( _____________ )= _______________
Step 4 Evaluate the growth rate and expected return for this stock.

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F I N A N C I A L C A LC U L ATO R # 47

How to Analyze and EvaluateYour Common Stocks

Although the dividend growth model for valuing common stock istheoretically sound, there are other approaches to analyzing and evaluating the value of a common stock. One such approach is to examine a company’s potential sales and earnings growth, proﬁtability returns, cash ﬂows, andother fundamental factors that affect the value of the company’s stock. Aftersuch an analysis of the company’s ﬁnancial statements, you will be able to assess
the past and present strengths and weaknesses of the company. With this information you can make a better assessment of the company’s future trends.
The following ratios can be calculated from the company’s financial
statements.

Current Ratio
The current ratio is a liquidity measure that indicates the ease or difﬁcultywith which a company can pay off its current liabilities as they become due.
Current ratio =Current assets
Current liabilities

A current ratio of less than 1 indicates that there are fewer current assets
than current liabilities. This means that if the company does not have othersources of raising cash (short term or long term), it may have difﬁculty covering its short-term liabilities as they become due. Generally speaking, it isdesirable for companies to have their current assets exceed their current liabilities, so that if their current assets decline they will still be able to pay off
their current liabilities. A low current ratio may indicate weakness, in that thecompany may not be able to borrow additional funds, or sell off assets, to raise
enough cash to meet its current liabilities.

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There are exceptions to the foregoing assessment of a low current ratio.
The current ratio for Exxon, one of the strongest companies in the oil industry, has dipped below 1 from time to time, but it has the capacity to borrowon a short-term basis to pay off its current obligations. In fact, the notes to
Exxon’s 1998 ﬁnancial statements showed that Exxon had unused lines ofshort-term ﬁnancing with its banks as well as access to the commercial paper
market. Potential investors should always read the footnotes, which containadditional information that can provide more insight into the ﬁgures on
the ﬁnancial statements.
It is not a good idea to look at one ratio for one period in isolation. By
examining the current ratio of a company for a few years and identifying a
trend, it is easier to see whether the current ratio has deteriorated, stayed
the same, or improved over time.
What may be the norm for one industry may not hold for another. Utility companies, for example, tend to have current ratios of less than 1, but
the quality of their accounts receivable is so good that virtually all of theaccounts will be converted into cash. (Most people pay their utility bills,
because if they don’t they ﬁnd themselves without power.) Creditors of andinvestors in utility companies are therefore not as concerned with a low current ratio.

Quick Ratio (Acid Test Ratio)
The major weakness of the current ratio is that it does not distinguish the difference in liquidity among the different types of current assets. In general,
inventory is the least liquid, in that it normally takes more time for it to be
sold and converted into cash. A more reﬁned measure of a company’s ability to pay off its current liabilities as they turn over into cash is the quick ratio.
The reason is because inventory is omitted from the calculation.
Quick ratio =Current assets − Inventory
Current liabilities

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231

The quick ratio will always be less than the current ratio unless thecompany has no inventory. The quick ratio indicates the degree of coverageof the current liabilities from cash and other liquid assets. A low quick ratio
indicates that the company may have difﬁculty paying off its current liabilities as they become due. However, this may not always be true for a company,
because there are many other factors that inﬂuence a company’s ability to pay
off current debts. These are:
• The company’s ability to raise additional funds, long term or short term.
• The willingness of creditors to roll over their debt.
• The rate at which current assets such as accounts receivable andinventory turn over into cash.
The following two ratios indicate the rate at which two of the current
assets turn over into cash. They are the accounts receivable turnover and inventory turnover.

Accounts Receivable Turnover
Accounts receivable turnover =Annual credit sales
Accounts receivable

The larger the accounts receivable turnover, the faster the company turns
its credit sales into cash. For example, an account receivable turnover of 8 indicates that sales turn over into cash every 45 days (365 ÷ 8), or one-and-ahalf months (12 ÷ 8). A receivables turnover that is too high indicates that thecompany may be too stringent in giving credit, which lowers sales and proﬁt.
This ratio may also be misleading for companies with seasonal sales orhighly ﬂuctuating sales in that it uses year-end receivable ﬁgures. It is a goodidea to compare this ratio and all other ratios over a ﬁve-year period, and if
possible compare them to those of the industry. For example, if the norm
for the industry is 30 days, you would not want to see a signiﬁcantly higher
deviation in the company’s collection period.

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Inventory Turnover
Inventory turnover =Sales
Average inventory

The inventory turnover ratio shows the speed with which inventory issold. The higher the inventory turnover, the more rapidly the company is able
to turn over its inventory into accounts receivable and cash. For example, aninventory turnover of 5 indicates that it takes the average inventory 73 days
to turn over (365 days ÷ 5). If the inventory turnover for the same company
increases to 7, the inventory turns over in roughly 52 days (365 ÷ 7).
With both the accounts receivable turnover and inventory turnover,
you do not want to see extremely low values, which indicate that the company’s cash is tied up for long periods. Similarly, extremely high turnover ﬁgures indicate poor inventory management, which could lead to stock-outs,
and hence customer dissatisfaction.

Proﬁtability
The proﬁts of a company are important to investors because these earnings
are either retained or paid out in dividends to shareholders, both of which
affect the stock price. Many different measures of proﬁtability indicate howmuch the company is earning relative to the base used, such as sales, assets,
and shareholders’ equity. The different proﬁtability ratios are relative measures of the success of the company.
Using sales as a base, the income statement is the starting point. The sales
for a selected period can be compared with the sales ﬁgures for previous years
to see whether there has been growth or a decline. For example, sales may haveincreased from the previous year, yet the company may report a net loss forthe year. This indicates that expenses have risen signiﬁcantly. An investor would
then examine the income statement to see whether the additional expenses
were nonrecurring (a one-time write-off) or due to increased operating costs

Managing Your Personal Wealth—Investments

233

incurred in the normal course of business. If the latter, the investor should
question management’s ability to contain these costs. Identifying a trend ofthese expenses over a period of time is useful in the evaluation process.
There are several proﬁtability ratios that use sales as a base: gross proﬁt,
operating proﬁt, and net proﬁt.

Gross Proﬁt
Gross proﬁt reﬂects not only a company’s markup on its cost of goods soldbut also management’s ability to control these costs in relation to sales. The
gross proﬁt ratio is computed as follows:
Gross proﬁt ratio =Sales − Cost of goods soldNet sales

The gross proﬁt ﬁgure is found in the income statement. The gross proﬁt
is sales minus cost of goods sold.

Operating Proﬁt
Operating proﬁt =

EBIT
Sales

The operating proﬁt ratio is the income from operations (also known
as the earnings before interest and taxes, or EBIT) divided by sales. This
includes the cost of goods sold and the selling, general, and administrative
expenses. This ratio shows the proﬁtability of the company in its normal
course of operations and provides a measure of the operating efﬁciency of thecompany.
The operating proﬁt or loss often provides the truest indicator of a company’s earning capacity, as it excludes the nonoperating income and expenses.

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

Net Proﬁt
The net proﬁt margin includes the nonoperating income and expenses suchas taxes, interest expense, and extraordinary items. The net proﬁt ratio is
calculated as follows:
Net proﬁt =Net income
Net sales

To the lay investor, it may not seem that important to calculate all these
proﬁt ratios. Instead, there may be an emphasis on the net proﬁt margin only.
This could be misleading because if tax rates or interest expenses increase,or if there are some large, extraordinary items in the year, there will be a significant change in the net profit even though operating profits have notchanged.
Other measures of profitability, which are more specific to commonshareholders in that they measure the returns on the invested funds of theshareholders, are the returns on equity and common equity.

Return on Equity
The return on equity ratio indicates how well management is performing forthe stockholders and is calculated as follows:
Return on equity =Net income
Shareholders’ equity

If the company increases its use of debt instead of using equity ﬁnancing, it can increase its return on equity. The reason is because the earnings are
spread over a smaller equity base. This is the use of ﬁnancial leverage (leverage ratios are discussed later in this section).

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235

For common stock investors, a highly leveraged company means there
is great risk, which will require a greater rate of return to justify the risk.
This increase in the required rate of return may have a negative impact on theshare price.
Thus, the use of leverage can increase the value of the stock when the levelof debt used is not perceived as adding a great amount of risk to the company.
When considering the leverage of a company, compare it to the typical leverage for that industry. Investors should look at the debt and coverage ratios ofa company to see the extent of its borrowing and its ability to service the debt.

Return on Common Equity
When a company has preferred stock, the common shareholders may be moreconcerned with the return attributable to the common equity rather than to
the total equity. To determine this return, adjustments are made for the preferred dividends and preferred stock outstanding.
Return on common equity =Net income − Preferred dividends
Equity – Preferred stock

Leverage Ratios
While leverage is a major concern for bondholders who use leverage ratios todetermine the level of debt and the servicing of the contractual payments ofinterest and principal, it is also an important issue for common stockholders.

Debt Ratio
The debt ratio indicates how much of the ﬁnancing of the total assets comesfrom debt. The ratio is calculated as follows:

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Debt ratio =Total current and noncurrent liabilities
Total assets

A company with a large debt ratio becomes increasingly vulnerable if
there is a downturn in sales and/or the economy, particularly in the latter case,
if it is a cyclical company.
When examining the financial statements of a company, you should
always check the footnotes to see if there is any debt that has not been included
on the balance sheet. If a company does not consolidate the ﬁnancial subsidiaries into its ﬁnancial statements, any debt that the parent company is
responsible for will be reported in the footnotes to the ﬁnancial statements.

Coverage Ratios
The coverage ratios measure a company’s ability to cover the interest payments
associated with its debt.
The times interest earned ratio indicates the company’s coverage of its
interest payments. It is calculated as follows:
Times interest earned ratio =Earnings before interest and taxes
Annual interest expense

If a company has low coverage of its interest payments, a slight downturnin sales or an increase in costs could have disastrous consequences in thatthe company may not be able to meet its interest payments.

The Price-Earnings (P/E) Ratio
The most commonly used guide to interpret the relationship between stock
prices and earnings is the price-earnings (P/E) ratio. It is calculated as follows:Managing Your Personal Wealth—Investments

Price-earnings ratio =237

Market price of the stock
Earnings per share

The P/E ratio shows the number of times that a stock’s price is trading
relative to its earnings. The P/E ratios for listed common stocks are publisheddaily in ﬁnancial newspapers. For example, the P/E ratio for Exxon Corporation as of March 18, 2002, was 20, and the closing price of the stock on thatday was $43.61 per share. This means that shareholders were willing to pay 20
times Exxon’s earnings for its stock. Looked at another way, it would take 20
years of these earnings to equal the invested amount of $43.61 per share.
By rearranging the formula, the earnings per share can be determined for
Exxon:
Earnings per share ==Market price of the stock
P/E ratio$43.6120= $2.18

Investors who obtain company information from service organizations,such as Standard & Poor’s and Value Line, may ﬁnd discrepancies between the
P/E ratios reported in the newspapers and those reported by information services companies. The reason is because the ﬁnancial newspapers quote theP/E ratio based on annual earnings of the previous year, whereas the information services companies may quote the P/E ratio based on earnings ofthe current quarter and projected future quarters.
Theoretically, if the earnings per share increase, the stock price should
rise so that the P/E ratio stays much the same. In reality, this does not often
happen. P/E ratios may be volatile and ﬂuctuate considerably.
As a rule of thumb, the P/E ratios of drug companies on average tradearound the low 20s, while the P/E ratios of many small, emerging growth companies, such as the biotech companies, may be greater than the 50s. P/E ratios

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of companies whose stock prices have been driven down due to pessimism
may be very low. Boeing Corporation, for example, is trading at 14 times earnings, while computer companies are trading at higher P/E multiples. Dell
Computer is trading around 56 times earnings.
Thus, P/E ratios by themselves are not relied on very greatly to selectstocks. For example, why would an investor pay 200 times earnings for thestock of a company that may or may not succeed when there are solid companies with steady, ﬂat earnings trading at low P/E multiples?
What the P/E ratio of a company will do is show how expensive the stock
is relative to its earnings. High P/E ratios (above 20, as a rule of thumb) arecharacteristic of growth companies—although with the average market multiple currently around 28, a P/E ratio of 20 almost seems like a value stock.
Investors may be optimistic about a company’s potential growth, and hence
the stock price is driven up in anticipation. This results in a high stock pricerelative to the company’s current earnings. Some investors may be willing to
pay a high price for a company’s potential earnings; other investors may consider such stocks to be overpriced.
What becomes apparent is that high P/E ratios indicate high risk. If the
anticipated growth of these high P/E ratio stocks is not achieved, their stock
prices will be punished and will fall very quickly. On the other hand, if they
do live up to their promise, investors will beneﬁt substantially.
Low–P/E ratio stocks (under 10) are characteristic of either mature companies with low growth potential or companies that are undervalued or in
ﬁnancial difﬁculty.
By comparing the P/E ratios of companies with the averages in the industries and the markets, investors can get a feeling for the relative value of thestock. For example, the average P/E ratios for companies on the U.S. stock
markets are currently around 28 times earnings. During bull markets theseratios go up, and during bear markets the average declines (to as low as 6 times
earnings, which happened in 1974).
P/E ratios ﬂuctuate considerably, differing among companies due to manyfactors, such as growth rates, popularity, earnings, and other financial
characteristics.

Managing Your Personal Wealth—Investments

239

Earnings Per Share (EPS)
Besides the market price of the stock, the other ﬁgure used to determine theP/E ratio is the earnings per share (EPS). The earnings per share indicate
the amount of earnings allocated to each share of common stock outstanding. EPS ﬁgures can be used to compare the growth (or lack of growth) inearnings from year to year and to project future growth in earnings. EPS pershare is calculated as follows:

Earnings per share =Net income minus preferred dividends
Number of common shares outstanding

The number of shares outstanding equals the number of shares issued
minus the number of shares that the company has bought back, called treasury stock. In many cases, companies will report two sets of EPS ﬁgures; theregular earnings per share, and the fully diluted earnings per share. For the
beginning investor, this can be confusing.
When companies have convertible bonds, convertible preferred stock,rights, options, and/or warrants, their EPS ﬁgures may be diluted due to theincreased number of common shares outstanding, if and when these securities are converted into common stock. Companies are then required todisclose their fully diluted EPS ﬁgures as well.
It is the trend of EPS ﬁgures over a period of time that is important forinvestors. If earnings per share are increasing steadily due to growth in sales, thisshould translate into increasing stock prices. However, earnings per share canalso increase through companies buying back their own shares. This reduces thenumber of shares outstanding, and if earnings stay the same, there will be anincrease in earnings per share. Conceivably, earnings per share could increase
when sales and earnings decrease if a signiﬁcant amount of stock is bought back.
The astute investor examines the ﬁnancial statements to determine whether
the increase in earnings per share is due to growth in sales and earnings or due
to stock buybacks. If the increase is due to the latter, the result could be a loss of
conﬁdence in the stock, which could lead to a decline in the stock price.

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Companies with poor fundamentals may try this tactic of buying theirshares back to improve their earnings per share and ultimately their stock
prices, but over the long term this strategy may not work.
Decreasing earnings per share over a period of time generally has anegative impact on stock prices. However, the reasons for the decrease areimportant. A decrease in EPS due to an increase in the number of shares outstanding from conversions of convertible bonds or preferred stock issues is
not as negative a factor as decreasing sales. If a decrease in EPS is due todecreasing sales, further investigation is required to determine if this is a temporary or permanent situation.
Consequently, when comparing current EPS ﬁgures with those of previous periods, it is important to examine the reasons for the changes in orderto get a better feeling for the potential changes in the stock price.

Dividends and Dividend Yields
Investors buy stocks for their potential capital gains and/or their dividend payments. Companies either share their proﬁts with their shareholders by paying dividends or retain their earnings and reinvest them in different projects
in order to boost their share prices. A company’s dividend policy is generally made public. For example, some growth companies and other companies
choose not to pay dividends, while some of the established blue-chip companies, utility companies, and real estate investment trusts (REITs) are wellknown for their dividend payments.
The dividend amount that listed companies pay can be found in the stocklistings in newspapers. Generally, companies try to maintain these stated dividend payments even if they suffer declines in earnings. Similarly, increases inearnings do not always translate into increases in dividends. Certainly there
are many examples where companies experience earnings increases that resultin increases in dividend payments, but this is not always the case. There isManaging Your Personal Wealth—Investments

241

an imprecise relationship between dividends and earnings. There are times
when increases in earnings exceed increases in dividends and other times whenincreases in dividends exceed increases in earnings. Thus, growth in dividends
cannot be interpreted as a sign of a company’s ﬁnancial strength.
Dividends are important from the standpoint that they represent tangible returns. The cash ﬂow from dividends may be reinvested by shareholders.
In contrast, investors in growth stocks that pay little or no dividends are
betting on capital appreciation rather than current returns.
To determine the dividend yield, which shows the percentage return that
dividends represent relative to the market price of the common stock, the following calculation is used:
Dividend yield =Annual dividendMarket price of the stock

A strategy of buying high-dividend–yielding stocks may offer some protection against a fall in stock market prices due to rising interest rates. Dividend yields of many utility companies, REITS, and energy companies may be
as high as 5 to 7 percent. High dividend yields are characteristic of a few bluechip and large companies, and utility companies.
It is risky, however, to choose stocks purely because of their high dividend
yields. Dividends can always be reduced, which in general puts downward
pressure on the price of the stock.
When choosing high-dividend–yield stocks, you should look at the earnings to see that they are sufﬁcient to support the dividend payments. According to Geraldine Weiss, editor of the newsletter Investment Quality Trends,
earnings should be equal to at least 150 percent of the dividend payout *Dividend payout ratio =Dividend per share
Earnings per share* Earl C., Jr. Gottschalk.“Nervous About Growth Stocks? Try some High-Dividend Ones,”
The Wall Street Journal, May 2, 1994, p. C1.

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Book Value
Some investors look for stocks whose market prices are trading below theirbook values. This may or may not be a sound strategy because there are manyfactors that overstate or understate the book value of a stock, which makes
it a less meaningful measure.
Book value =Shareholders’ equity
Number of shares outstanding

Investors looking for value stocks would place more emphasis on ﬁnding
stocks whose book values are greater than their market values.

Price-to-Sales Ratio
The price-to-sales ratio indicates how much an investor pays for every dollar of sales for a company.

Price-to-sales ratio =Market price per share
Sales per share

This ratio measures the valuation of a company on the basis of sales rather
than earnings. The price-to-sales ratio should be compared with those of othercompanies in the industry to determine whether the company is trading at
a compelling valuation to its sales base.

Price-Earnings to Growth Ratio
The price-earnings to growth ratio indicates how much an investor pays forthe growth of the company.

Managing Your Personal Wealth—Investments

Price-earnings to growth ratio =243

Price-earnings ratio
Growth rate

The lower the ratio, the greater the potential increase in stock price,assuming that the company can grow at its projected rate.

What About a Company’s Cash?
Earnings are an important determinant of a company’s value and stock price,
but the company’s cash position is another important place to assess value.
The statement of changes in cash position is a good starting point to assess
cash ﬂow. This statement can be found in the annual report of a company.
The statement of changes in cash has three sections:• Cash from operating activities• Cash from investing activities• Cash from ﬁnancing activities
The ﬁrst section, cash from operating activities, shows the inﬂows andoutﬂows of cash from operations for the period. Noncash expenses such as
depreciation, deferred income tax charges, and annuity and accrued liability
provisions are added back to the net income to provide cash ﬂow.
A more reﬁned measure is free cash ﬂow, which is the cash ﬂow minus
capital spending. Companies that do not generate strong cash ﬂows haveless ﬂexibility, and this is most often reﬂected in their stock prices.
Worksheet 47.1 provides a framework to evaluate your company’s common stock. After completing this worksheet, you will have a better feelingfor the strengths and weaknesses of the company.

Return on common equity
Net income − Preferred dividends=
Equity − Preferred stock

Company name _____________________
Current assets
Current ratio =Current liabilities
Current assets − Inventory
Quick ratio =Current liabilities
Annual credit sales
Acc. rec. turnover =Acc. rec.
Sales
Inv. turnover =Average inventory
Sales − Cost of goods sold
Gross proﬁt ratio =
Sales
EBIT
Operating proﬁt =Sales
Net income
Net proﬁt =Sales
Net income
Return on equity =Shareholders’ equity____________________________________________________________________________________________________________

Year______

Year______

WORKSHEET 47.1 Framework to evaluate common stock______________________________________________________

Year____________________________________________________________

Year____________________________________________________________

Year____________________________________________________________

Year____________________________________________________________

Year______

Total liabilities
Total assets____________________________________________________________________________________________________________Cash ﬂow

Free cash ﬂow

Year____________

Year____________

Coverage ratio =EBIT
Annual interest expense
Market price of the stock
P/E ratio =Earnings per share
Net income − Preferred dividends
EPS =No. of shares outstanding
Annual dividend
Dividend yield =Price of stock
Dividend per share
Dividend payout ratio =EPS
Shareholders’ equity
Book value =No. of shares outstanding
Price per share
Price-to-sales ratio =Sales per share
P/E ratio
P/E to growth ratio =Growth rate

Debt ratio =WORKSHEET 47.1 Framework to evaluate common stock (continued)____________________________________________________________

Year__________________________________________________________________

Year__________________________________________________________________

Year__________________________________________________________________

Year__________________________________________________________________

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T H E P E R SO N A L F I N A N C E C A LC U L ATO R

F I N A N C I A L C A LC U L ATO R # 4 8

How to Choose a Mutual Fund*T

here are more than 8,000 mutual funds on the market, and they are
all vying for an investor’s savings. Many of the messages in their advertisements lead you to believe that they have attained superior performance.
Even if funds do well during good times, however, you need to examine howthese funds have performed during a down market. Several business magazines track the overall performance records (during up and down markets)of many of the mutual funds, which is a better yardstick than the advertising
messages of the mutual funds themselves. From these publications, potential
investors can see how well funds have performed in up markets as well as
how the funds have protected their capital during periods of declining prices.
New funds do not have track records. Therefore, a yardstick on performance during a period of declining prices may not be available.
You can evaluate a mutual fund on the basis of performance; namely,
yield and total return, and the total expense ratio of the fund. But before doingthat you should begin with the objectives of the fund.
Mutual funds are required to send a prospectus to a potential investor before
accepting investment funds. Although prospectuses are written in a manner thatranks them high on the list of best cures for insomnia, they still provide investors
with information about the fund that they may not be able to get anywhere else.
Obtain a prospectus for each of the funds that you are considering so that you
can compare them in terms of the following criteria.

*Portions of this section have been previously published by Esmé Faerber in All About
Stocks (New York: McGraw-Hill, 2000).

Managing Your Personal Wealth—Investments247

1. Objectives: Are They Compatible withYour Level of Risk?
The objectives and policies of the fund generally appear near the front of
the prospectus. The objectives describe the type of securities the fund invests
in as well as the risk factors associated with the securities. For instance, if
the prospectus states that the fund will buy growth securities, the investor
should not be surprised to ﬁnd that most of the stocks will have high priceearnings ratios and may include risky small-cap stocks.
The investment policies outline the latitude of the fund manager to invest
in other types of securities. This could include trading futures contracts, writing options to hedge bets on the direction of interest rates or the market, orinvesting in derivative securities to boost the yield of the fund. Many so-called
conservative funds, which supposedly only hold blue-chip stocks, have on
occasion resorted to small-company and offshore stocks to boost returns. The
greater the latitude in investing in these other types of securities, the greater
the risk if events backﬁre.
Determine whether the objectives of each of the funds are compatible
with your level of risk tolerance.

2. The Performance of the Fund
Most funds can boast they have attained the number one position in somearea of performance at some point in time during their existence. Similarly,
good past performance may not be indicative of good future performance.
Some funds that have performed well in the past have had poor performance
thereafter. In fact, some funds that did well in the past no longer exist.
Organizations such as Morningstar rate a mutual fund’s performance relative to other funds with the same investment objectives, but this too can bemisleading for investors trying to choose a fund. (Morningstar’s Internet
address is www.morningstar.com.) First, the funds may not be comparable,
even though they have similar objectives. One may have riskier assets than

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another, for instance. Second, past performance may not be a reliable indicator of future performance.
In choosing a fund, investors are best off looking at what the fund invests
in (as well as can be determined), and then trying to determine the volatility in terms of up and down markets.

3. The Total Return for the Fund
Yield is one aspect of performance. Yield is deﬁned as the interest and/or dividends paid to shareholders as a percentage of the net asset value price. Money
market funds quote yields over a seven-day period. This is an average dividend yield for seven days, and it can be annualized. Long-term bond funds
also quote an annualized average yield, but it is generally over 30 days.
In 1988, the Securities and Exchange Commission (SEC) ruled that fundswith average maturities longer than those of money market mutual funds
must quote the SEC standardized yield. The SEC standardized yield includes
the interest or dividends accrued by the fund over 30 days as well as an adjustment to the prices of the bonds for the amount of the amortization of any
discount or premium that was paid for the bond assets. The SEC standardized yield makes the comparison of different mutual funds more meaningful.
Make sure that you are not comparing the yield of one fund to that of anotherfund that is calculated differently.
The SEC standardized yield should be used for comparison purposes only
and not as a means to predict future yields. This yield is a measure of the fund’s
dividend distribution over a 30-day period and is only one aspect of the fund’s
total return. Mutual funds pass on any gains or losses to shareholders, which
can increase or decrease the fund’s total return.
Another factor that affects total return is the ﬂuctuations in net asset value.
When the share price increases by 6 percent, it effectively increases the total
return by an additional 6 percent. Similarly, when the net asset value price ofthe fund declines, total return will decrease. This explains why funds with apositive yield can have a negative total return. During the bear market of 2001,

Manage Your Personal Wealth—Investments249

funds distributed dividends and capital gains, but the total returns for the funds
were negative due to the decline in net asset values (prices of the funds).
The interest on reinvested dividends is another factor that may also be in
the total return. When the interest or dividends paid out by the fund are reinvested to buy more shares, the yield earned on these reinvested shares boosts
the overall return on the invested capital.
Therefore, when comparing the total returns quoted by different funds,
you need to make sure you are comparing the same type of total return.
The total return of a mutual fund includes the following three components in its makeup:
1. Dividends and capital gains or losses
2. Changes in net asset value
3. Dividends (interest) on reinvested dividends
When comparing the total returns quoted by funds, you should determine whether all of these components are included in the computation. However, there are funds that choose not to advertise a total cumulative return.
Some high-yield junk bond funds have at times chosen not to emphasize total
returns, since deep declines in junk bond prices caused them to be negative.
Instead they touted their high yields. Thus, basing your choice of fund on yieldalone can be misguided, since yields may be easier to manipulate. Investors
should, therefore, look at both the yield and the total return of the fund to geta more balanced picture.

4. The Expenses of the Fund
Expenses are a key factor in differentiating the performances of different funds.
By painstakingly looking for funds with the highest yields, investors are looking at only half the picture. A fund with a high yield may also be one thatcharges higher expenses, which could put that fund behind some of the lowercost funds with lower yields. Fees reduce the total return earned by funds.

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The mutual fund industry has been criticized for the proliferation of fees
and charges. Granted, these are all disclosed by the mutual funds, but besides
the conspicuous charges, investors need to know where to look to ﬁnd the lessobvious fees. Load charges are obvious expenses.
A no-load mutual fund is one where the investor pays no commission or
fee to buy or sell the shares of the fund. With an investment of $10,000 in a
no-load fund, every cent of the $10,000 goes to buying shares in the fund. You
can no longer easily identify no-load funds in the newspapers. However,you can easily ﬁnd out whether the fund that you are interested in is a no-loadfund by calling the mutual fund family, looking at its website, or examining
the prospectus.
A load fund charges a sales commission for buying shares in the fund.
These fees can be quite substantial, ranging to as much as 8.5 percent of thepurchase price of the shares. The amount of the sales (load) charge pershare can be determined by deducting the net asset value price from the offer
price. Some funds give quantity discounts on their loads to investors who buy
shares in large blocks. For example, the sales load might be 5 percent for
amounts under $100,000, 4.25 percent for investments between $100,000 to$200,000, and 3.5 percent for amounts in excess of $200,000. When buying
load funds, you need to check whether a load is charged on reinvested dividends as well.
Some funds also charge a back-load or exit fee when you sell shares in thefund. This can be a straight percentage, or the percentage charged may decline
the longer the shares are held.
The ultimate effect of load charges is to reduce the total return. The
impact of the load charge is felt more keenly if the fund is held for a shortperiod of time. For instance, if a fund has a return of 6 percent and there isa 4 percent load to buy into the fund, the total return to the investor for theyear is sharply reduced. If there is a back-load fee to exit the fund, this could
be even more expensive for the investor. If the share price has increased, theload percentage will be calculated on a larger amount.
Don’t be fooled by some funds that tout themselves as no-load funds but
assess fees by another name that come right out of the investor’s investment

Managing Your Personal Wealth—Investments

251

dollars like a load. These fees are not called loads, but they work exactly likeloads. Their uses are to defray some of the costs of opening accounts orbuying stocks for the fund’s portfolio. They vary from 1 to 3 percent among
the different fund groups.
From the investor’s point of view, it should not matter how lofty the purpose is for these fees. They reduce your investment. If you invest $10,000
and there is a 3 percent fee, only $9,700 of your investment will go towardbuying shares.
You also need to watch out for redemption fees: sell $10,000 worth ofshares with a 3 percent redemption fee and you only receive $9,700.
Why then would so many investors invest in load funds when these commissions eat away so much of their returns? One can only speculate on possible answers:• Investors may not want to make decisions themselves as to whichfunds to invest in, so they leave the decisions to their brokers andﬁnancial planners.
• Brokers and ﬁnancial planners earn their livings from selling investments from which they are paid commissions. These include only
load funds.
• No-load funds do not pay commissions to brokers and ﬁnancial
planners and are, consequently, not promoted or sold by brokers
and planners.
Brokers and ﬁnancial planners often tout that load funds outperform noload funds, but there is no evidence to support this opinion. According to
CDA/Weisenberger, there was no difference between the performance of theaverage no-load fund and load fund over a ﬁve-year period (1988–1992).* Infact, when adjusting for sales commissions, investors would have been better off with no-load funds.
*Jonathan Clements, “The 25 Facts Every Fund Investor Should Know,” The Wall Street
Journal, March 5, 1993, p. C1.

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12 (b)-1 fees are less obvious than loads. These are charged by many funds
to recover expenses for marketing and distribution. These fees are assessedannually and can be quite steep when added together with load fees. Many
no-load funds tout the absence of sales commissions but tack on 12 (b)-1 fees,
which are like a hidden load. A 1 percent 12 (b)-1 fee may not sound like very
much, but it is $100 less per annum in your pocket on a $10,000 mutual fundinvestment.
In addition to the above-mentioned charges, funds have management
fees that are paid to the managers who administer the fund’s portfolio ofinvestments. These can range from 0.5 percent to 2 percent of assets. Highmanagement fees also take a toll on the investor’s total return.
Thus, all fees bear watching since they reduce yields and total returns.
Critics of the mutual fund industry have cultivated a sense of awarenessregarding the proliferation of these charges. Indeed, investors should not be
deceived by funds that claim to be what they are not. Lowering front-end loads
or eliminating them altogether doesn’t mean a fund can’t add fees somewhere
else. Funds have to disclose their fees, which means that investors can ﬁndthem in the fund’s prospectus. Management fees, 12 (b)-1 fees, redemption
fees (back-end loads), and any other fees charged are disclosed somewhere in
the fund’s prospectus. Financial newspapers also list the types of charges ofthe different funds in their periodic mutual fund performance reviews.
Worksheet 48.1 lists guidelines to assist you in the choice of a mutual fund.
WORKSHEET 48.1 Guidelines in the choice of a mutual fund
Step 1 List the objectives of each fund in which you are interested.
Names of the mutual funds _________________________________
Objectives ______________________________________________________________________________________________________________________
Risk level of fund: Conservative 䊐
Risk level of fund: Conservative 䊐
Risk level of fund: Conservative 䊐Moderate 䊐Moderate 䊐Moderate 䊐Aggressive 䊐
Aggressive 䊐
Aggressive 䊐(continued)

WORKSHEET 48.1 Guidelines in the choice of a mutual fund (continued)
Step 2 Examine the past performance of each fund.
Names of the funds
Rankings of the funds__________________________________________________________________

Step 3 List the returns of the funds in which you are interested.
Names of the funds
Yield
30-day yield
Annual yield
Dividends & gains
Net asset value (NAV)changes
Reinvested dividends_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Rank funds on the basis of total return.
_________________________________

Step 4 Compare the expenses and fees of the funds in which you are interested.
Names of the funds
Load/no-loadBack-end load
Redemption fees
12 (b)-1 fees
Ratio of operating
expenses to average
net assets______________________________________________________________________________________________________________________________________________________________________________________________________

Rank the funds on the basis of their fees, with the lowest expense ratio receiving the highest ranking.
_________________________________
Step 5 Choose the fund that has the lowest expense ratio if there is no difference in theperformance of the funds.
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F I N A N C I A L C A LC U L ATO R # 4 9

How to Determine theTax Consequences of Buying and
Selling Shares in a Mutual FundTax reporting on mutual funds can be complicated. Even if you buy
and hold shares in a mutual fund, there are tax consequences. Dividends paid to investors may be automatically reinvested in the fund to buy
more shares. At the end of the year, the mutual fund sends Form 1099 to eachmutual fund holder showing the amount of dividends and capital gains
received for the year. Individual shareholders pay taxes on these dividends andcapital gains. Therefore, these dividends and capital gains need to be added
into the cost basis when the investor sells shares in the fund.
For example, suppose you had invested $10,000 in a fund two years ago
and had received a total of $2,000 in dividends and capital gains in the fundto date. You now sell all the shares in the fund and receive $14,000. The costbasis is $12,000 (not $10,000), and the gain on the sale of the shares is $2,000($14,000 – $12,000), as shown in Worksheet 49.1.
When you sell only a portion of your total shares, the calculation is different and may be tricky. It is further complicated if you have actively bought
and sold shares. In fact, many mutual funds encourage shareholders to operate their funds like a checking account by providing check-writing services.
However, every time you write a check against a bond or stock fund, there isa capital gain or loss tax consequence. This does not include money market
funds due to their stable price of one dollar per share. Active trading can causea nightmare for you at tax time and produce extra revenue for your accountant for the additional time spent calculating the gains and losses.
The most important thing to do for an actively traded mutual fund (orany mutual fund for that matter) is to keep good records. For each fund, keep
a separate folder and store all the monthly statements showing purchases andsales of shares, and dividends and capital gains distributions.

Managing Your Personal Wealth—Investments

255

WORKSHEET 49.1 How to determine the capital gain from the sale of all shares ina mutual fund

Date

Transaction

Dollaramount

Share
price

1/1/02
12/31/02

InvestDividends$10,000
2,000

$10
8

Total adjusted cost

Number of Total number
sharesof shares
1,000
250

1,000
1,250

$12,000

Step 1 Determine the adjusted cost.
Add all the dollar amounts invested in the fund, including dividends andcapital gains transactions.
Step 2 Determine the capital gain/loss from the sale of all shares.
Subtract the adjusted cost of the shares from the proceeds of the sale.
12/01/03 (sold 1,250 shares @ $11.20 per share)minus (cost basis 1,250 shares)
Capital gain

$14,000
12,000$2,000By keeping records of all transactions, you will be able to determine the costbasis of shares sold. This can be done using either an average cost method, on a
FIFO basis, or using the speciﬁc identiﬁcation method. FIFO stands for ﬁrst in,ﬁrst out, which means that the cost of the ﬁrst shares purchased in the fund areused ﬁrst when shares are sold. Worksheet 49.2 illustrates the FIFO method of
calculating a capital gain or loss on the partial sale of shares in a mutual fund.
The example shows that the earliest shares purchased are the ﬁrst to be used in
the sale of shares. After all the shares of the invested fund are sold, the basis of thedividends and capital gains shares are used to determine any gain or loss.
Several funds provide the gains and losses on an average cost basis. The
average cost basis can get quite complex with additional sales and purchasesof shares. Hence, some funds don’t allow their shareholders to write checks
against their accounts. However, once you make a partial sale in a fund, some

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WORKSHEET 49.2 Calculation of gain/losses on the partial sale of shares

Date

Transaction

Dollaramount

Share
price

Numberof shares

Total numberof shares

06/14
11/26
11/30
12/31

InvestInvestRedeem (sell)
Dividends$10,000
4,500
12,0001,000$10.00
9.00
10.00
10.00

1,000
500
1,200
100

1,000
1,500
300
400

To calculate gain/loss on a FIFO basis:
Sold 1,200 shares at $10.00 per share; sale price$12,000

Cost basis
06/14
1,000 shares at
11/26
200 shares at
Total cost
Gain

$10.009.00$10,000
1,800$11,800$200

Cost basis of the growth and income fund after sale

Date

Transaction

Dollaramount

Share
price

Numberof shares

Total numberof shares

06/14
11/26

Invested
Dividends$2,700
1,000

$9.00
10.00

300
100

300
400

fund companies will no longer provide the average cost basis for that fund.
The speciﬁc identiﬁcation method allows shareholders to identify the speciﬁc shares that they wish to sell. Investors can minimize their gains by choosing to sell shares with the highest cost basis ﬁrst. However, in order to obtain
Internal Revenue Service acceptance of this method, the investor must ﬁrst
identify the shares to be sold and notify the mutual fund company in writing and then receive written conﬁrmation from the mutual fund company.

Managing Your Personal Wealth—Investments

257

Worksheet 49.3 outlines the steps for determining the capital gains/losses
on your mutual funds using the FIFO method, which is the usual method
used unless you have written conﬁrmation of a different method from yourmutual fund company.
To minimize potential tax hassles, you are better off not writing checks
on your stock funds for your short-term cash needs, which creates gains orlosses. You are better served investing the money needed for short-term
purposes in a money market fund, which alleviates tax complications.
Whether you trade actively or not, the solution to tax computations is tokeep good records. If you can’t determine the cost basis of your shares, anaccountant will be able to do so, provided you keep records. If you don’t have
all the records of your purchases and sales, you may not be able to prove yourcost basis to the Internal Revenue Service if it is disputed.

WORKSHEET 49.3 Steps to determine your capital gain/loss in the sale of shares
Step 1 List all the transactions in your fund.

Date

Transaction

Dollaramount

Share
price

_________________________________________________________________________________________________________________________________________________________________________________________

Number Total numberof sharesof shares____________________________________________________________________________________________________

Step 2 Determine the proceeds from the sale.

Date

Transaction

Number ofshares

Share
price

Total
proceeds______________________________________________

Step 3 Determine the cost basis for the shares sold.

Date
____
____
____

Transaction______________________________

Number ofshares______________________________

×

Share
price
________________________=

Cost__________________
Total cost ______

Step 4 Subtract total cost from total proceeds to equal total gain/loss.
Total proceeds from sale _________− Total cost_________
Total gain/(loss)_________
Step 5 List the shares left in your fund.

Date

Transaction

Dollaramount

Share
price

____________________________________________ ____________________ __________

Number Total numberof sharesof shares________________________________________

Managing Your Personal Wealth—Investments

259

F I N A N C I A L C A LC U L ATO R # 50

How to Determine the
Average Cost in Dollar Cost Averaging*Dollar cost averaging is a method of investing the same amountof money at regular intervals over a long period of time. This strategy
can be used for stocks, bonds, and mutual funds. Most people build their portfolios over time, and by investing amounts at different times they avoid therisk of putting all their money into stocks at one point in time. By consistently
investing the same amount in a security at regular intervals over a period oftime, the average cost of the security will be lower than the high price of the
security for the period, and higher than the low price of the security for theperiod. Table 50.1 shows the dollar cost averaging method when $1,000 isinvested every month to purchase the stock of Company X. The example
assumes fractional shares may be purchased, and commissions are ignored.
In January, $1,000 is invested at $7 per share, resulting in 142.86 shares
being purchased. The price of the stock goes up in February to $8 per share,
which means that the same investment amount ($1,000) will buy fewer shares(125.00) than in January. Conversely, when the price of the stock goes down
to $6.75 in September, more shares are purchased (148.15) with the sameinvestment dollars ($1,000).
Over the 12-month period, $12,000 was invested to purchase a total of
1,467.36 shares. The average cost per share is $8.18. In this example, an investor
would lose money if the price falls below $8.18 and would make money if thestock price is above the average cost per share when selling. This average
cost per share is $0.09 less than the average price per share during the
12-month period. Part of the reason for this is that during the months when
the price per share is low, more shares are purchased for the same dollar
amount. Thus, with ﬂuctuating stock prices, the average cost per share will
always be lower than the average price per share.
*Portions of this section have been previously published by Esmé Faerber in All About
Stocks (New York: McGraw-Hill, 2000).

260

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

TABLE 50.1 Dollar cost averaging

Date
January
February
March
April
May
June
July
AugustSeptember
OctoberNovember
December
Total

Investment
amountPrice
per share

Number ofshares purchased$1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
$12,000

$7.00
8.00
7.50
9.00
9.50
9.00
8.00
7.75
6.75
8.75
9.00
9.00
$99.25142.86125.00133.33111.11105.26111.11125.00129.03148.15114.29111.11111.11
1,467.36

Average price per share ==Total price per share
Number of investment periods
99.25
12

= $8.27
Average cost per share ==Total investment
Number of shares purchased
12,0001,467.36= $8.18

This does not mean that investors will always make a proﬁt by using dollar
cost averaging. If the price of the stock keeps going down, the average cost per
share will be lower than the average price per share, but the investor will still losemoney if the shares are sold at a declining price. If stock prices are volatile (goingup and down), investors can do very well as long as there are systematic and even
investments over the period, alleviating the need to time the market.

Managing Your Personal Wealth—Investments

261

The disadvantages of dollar cost averaging are as follows:• Transaction costs are higher using dollar cost averaging to purchaseshares on a systematic basis.
• The use of the dollar cost averaging method to buy stocks requires large
amounts of money for the regular payments in order to receive thelower commissions of buying shares in round lots over 100 shares. By
investing small amounts, investors buy shares in odd lots (fewer than
100 shares), which means that transaction costs are higher. The totaltransaction costs will also be higher if the shares were purchased in one
or two transactions rather than twelve. Dollar cost averaging works wellwith no-load mutual funds where there are no transaction fees.
• With a rising stock price, the use of dollar cost averaging will resultin a higher average cost per share than if the total amount wasinvested at the beginning of the period.
• When shares are sold, the calculation for the tax basis of the shares iscomplicated for most investors. Keeping records of all transactions isnecessary, and the use of a tax professional to compute the gains orlosses for tax purposes may be required. The success of dollar cost
averaging requires sticking to the plan and investing, particularly
when the stock price falls. However, from time to time, investors
should evaluate the stock with regard to its overall performance.
A stock that is going downhill with no bright prospects should beviewed as a sunk cost, and an investor should abandon it rather thansink more money into a bad investment. Thus, dollar cost averaging
does not alleviate the decision of which stocks to buy and sell.
Worksheet 50.1 lists the steps for determining your average cost in thedollar cost averaging of your investment.

WORKSHEET 50.1 How to determine your average cost in dollar cost averaging
Step1 List your transactions and total the columns.

Date

Investment
amountPrice
per share

Number ofshares purchased__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Step 2 Determine the total average price per share.
Average price per share ==Total price per share
Number of investment periods(______)()= ______
Step 3 Jot down your expectations for future changes in rates of interest.
Average cost per share ==Total investment
Number of shares purchased(______)()= ______
Step 4 Compare the average cost per share with the market price of the shares whenselling, if:
Average cost per share is greater than the market price per share, you have a loss.
Average cost per share equals the market price per share, you have neither a gain
nor a loss.
Average cost per share is less than the market price per share, you have a gain.

P A R T

F O U RPLANNING FOR
YOUR FUTURE

Copyright 2003 by Esme Faerber. Click Here for Terms of Use.

This page intentionally left blank.

F I N A N C I A L C A LC U L ATO R # 51

How to Determine Your
Future Financial Needs and
How to Fund ThemT

he ﬁrst step in determining your future ﬁnancial needs is to ﬁgure out how much money you will need when you decide to retire. The
ﬁgure that you come up with should include your assumptions about yourlifestyle in retirement. Do you expect to live with the same comforts and enjoy
the same spending level, or are you willing to do some belt tightening? For
example, if you don’t have any extravagant expenses currently, but when you
retire you plan to travel to different resorts around the world on a regular basis,
you may need to increase your anticipated yearly income to include these
expenditures in retirement. Alternatively, you may determine that the majority of your current expenses, such as education costs and other costs for children, and mortgage expenses, will not be a factor in retirement, and hence you
will need less to retire on. This may be so, but you may also need to bank on
increased health care costs. Thus, whatever your assumptions, you need to makeallowances for your projected lifestyle in retirement.
A common rule of thumb is that 80 percent of current living expenses should
be sufﬁcient in retirement. Thus, in your planning you need to determine whether
you need 100 percent of your current income in retirement or whether it could
be less or should be more. Another factor that you need to consider in this determination is inﬂation. If inﬂation rears its ugly head, you may not have sufﬁcient future purchasing power to maintain the lifestyle to which you areaccustomed. Consequently, you may have to assume an inﬂation rate for theperiod between now and retirement to maintain your current purchasing power.
Worksheet 51.1 outlines the steps for determining the amount of yourfuture retirement needs and how you plan on funding that amount.

265

WORKSHEET 51.1 Planning for retirement
Step 1 Anticipate the amount of money you will need at retirement.
Current income ___________ Number of years to retirement ______________
Projected inﬂation rate _______ % assumption of future income _________
Future value of 1 at inﬂation rate for the number of years to retirement* _____
Current Income × FV of 1 at inﬂation rate for # of years to retirement ×
Assumption % = Future Amount____________ × ________________ × __________ = _____________ (1)Step 2 Determine where the funds will come from for projected retirement needs.
Income source amount × FV of rate of return × Expected rate of return =Future assets in retirement
Investments
IRAs
401(k)s
Pensions
KeoghsHome equity
Other sources
Social Security
Total________ × ________ × _________ = ____________________________ × ________ × _________ = ____________________________ × ________ × _________ = ____________________________ × ________ × _________ = ____________________________ × ________ × _________ = ____________________________ × ________ × _________ = ____________________________ × ________ × _________ = ____________________= ______________________________________ (2)Step 3 Compare the projected amount needed in retirement with the total projectedsources of income.
If (1) − (2) = a positive amount, you need to save more in your different
source accounts.
If (1) = (2) you will have met your projected retirement needs.
If (1) − (2) = a negative amount, you will have exceeded your retirement needs.
*This factor can be obtained from Appendix A in the future value of 1 table. You can also
use a ﬁnancial calculator or computer to determine the future value of the income at
the projected inﬂation rate.

Planning for Your Future

267

Step 1: Determine Your AnticipatedYearly Amount in Retirement
Step 1 in the worksheet shows how to determine the amount of money thatyou will need on a yearly basis in retirement. Begin with your yearly current
income and determine the number of years until retirement. If you anticipate
an increase in inflation through the years to retirement, you will need totake this into account because inﬂation erodes future purchasing power.
The following example illustrates the process of determining the future
yearly income in retirement.
Current yearly income: $120,000
Projected inﬂation rate: 3%

Years to Retirement: 25
Assumption on lifestyle %: 80%

Current income × Future value factor of 1 at 3% for 25 years × 0.80
= Future retirement amount$120,000 × 2.094 × 0.80 = $201,024

In this example, with current income of $120,000, assuming an inﬂation
rate of 3 percent for the next 25 years and an 80 percent estimate of current
needs, the future yearly income needed in retirement is $201,024.

Step 2: Determine Where the Money Will
Come from to Finance Your Projected
Future Retirement Income Needs

Investments
Add your investment and savings account balances. Next, assume a rate of
return that these investments will earn per year over the period until yourretirement. If you expect your investments to return 5 percent after taxes on

268

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

average for each year in the 25 years to retirement, you can ﬁnd the future
value of 1 factor at 5 percent for 25 years in Appendix A. This ﬁgure is multiplied by the total investment amount to equal the future value of these investments at retirement. You then need to anticipate a rate of return in retirement,
which may or may not be a higher rate of return than your current projected rate. Assuming that your retirement nest egg will earn a rate of 7 percent per year, you can then determine what your total future investments will
earn per year in retirement, as illustrated below:
Investments × FV of 5 percent for 25 years × 0.07
= Future annual income from investments$150,000 × 3.386 × 0.07 = $35,553

The total investments of $150,000 invested at 5 percent for 25 years willproduce a nest egg of $507,900; multiplied by 7 percent, it will produce yearly
earnings of $35,553.

Individual Retirement Accounts (IRAs)
With IRAs you make tax-deductible contributions up to the allowable yearly
limit, and the principal and earnings on the principal are tax deferred untilmoney is withdrawn from the account. Withdrawals from IRA accounts may
be made penalty free after age 591⁄2. Thus, your money is tied up until you
reach this age, though there are some exceptions. The rate of return on an IRA
may be higher than that on a regular investment account due to the tax deferral of earnings on the former. The types of investment assets held in theaccount determine the rate of return.
You may need to use two different calculations with an IRA if you alreadyhave an account balance and you continue to make yearly contributions until
retirement.
Assume that you have a total of $20,000 in your IRA account and youplan on making yearly contributions of $2,000 for the next 20 years until

Planning for Your Future269

retirement. You expect these funds to earn 8 percent per annum during thisperiod.
Funds × FV factor of 8% for 20 years =Funds at retirement × Interest rate = Yearly amount$20,000 × 4.661* = $93,220 × 0.08 = $7,457.60$2,000 × 45.762**= 91,524 × 0.08 = 7,321.92
Total yearly retirement income from IRAs

$14,779.52*FV factor of a single sum from Appendix A.
**FV factor of an annuity from Appendix C.

401(k) and Employment Pension Plans
Another source of retirement income is from tax-deferred pension plans, suchas 401(k), 403(b), money purchase, and proﬁt-sharing plans. Each type ofplan has its own set of rules with regard to contribution amounts, employer
matching, and plan withdrawals. As with IRAs, dollar contribution amounts
are on a pretax basis, and the earnings on the contributed capital accrue ona tax-deferred basis.
To determine your retirement income from these plans, you would use
the same types of calculations as shown in the IRA example.

Social Security
You can begin to collect reduced Social Security beneﬁts at age 62 or, depending on the year that you were born, full benefits between ages 65 and 67.
The easiest way to determine the exact amount of your yearly beneﬁts is torequest it from the Social Security Administration.

270

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

Home Equity
If you own a house and you are paying off a mortgage, you have an equity
stake in the house. The amount of the equity is the current value of the houseminus the mortgage balance. The equity amount will increase with every
mortgage payment and over the years as house prices increase. At retirement if you sell your house and move into a smaller house or rent, you will
free up money, which can then be invested to generate income. Another option
is a reverse mortgage, where a bank will pay you a monthly amount andafter the term is up you (or your heirs) can sell the house to pay the bank back.
To quantify the amount of income generated from your home equity stake,you need to make several assumptions. The ﬁrst is the current value of yourhouse, and the second is the anticipated appreciation rate of your house. Currently, you are not taxed on the ﬁrst $250,000 of the capital gains on the saleof a house if you are single, or $500,000 if you ﬁle a joint return. Assume
that there are no tax consequences on these gains, although this is a large
assumption as Congress is constantly making changes to the tax code.
For example, if you have a house that has been appraised at $300,000 andyou have a mortgage of $125,000, you have $175,000 in equity ($300,000–$125,000). Assume that this equity will grow at 5 percent for the next 20 years
until retirement, when you plan on taking out a reverse mortgage. The amountof retirement income based on these assumptions is:
Equity × FV factor of 5% for 20 years =Future equity × Interest factor = Annual income$175,000 × 2.653 = $464,275 × 0.05 = $23,213.75

Step 3: Determine Whether You Will Have Met Your
Expected Needs in Retirement
Add up your total projected income in retirement and compare this to the anticipated amount needed in retirement. For example, if you anticipate that yourPlanning for Your Future271

yearly future needs will be $120,000, but you only come up with $100,000 a year
from all your sources of savings, investment accounts, and retirement accounts,
then you need to put aside greater amounts now to fund this shortfall.
You can use a computer or ﬁnancial calculator to determine the additional yearly amount that you would need to save to make up a shortfall.
Assuming that you have a $20,000 shortfall and you expect to earn 8 percent per year over the next 20 years until retirement, you will need to invest
an additional $437.04 each year for the next 20 years.
You can use the future value of an ordinary annuity table to determine
this, as shown below, or a spreadsheet program that has financial tables,such as Microsoft Excel.
Future value of annuity factor at 8% for 20 periods × Annuity = $20,000
45.762 × Annuity = $20,000
Annuity = 20,000 ÷ 45.762= $437.04

Using Microsoft Excel, click on f* in the top row of the toolbar. Highlightﬁnancial in the left box and PMT in the right box. A dialog box comes up
where you can enter your information as shown in Figure 51.1.
Thus, if you have a shortfall, determine the extra payment amounts
that you would need to invest to make up this shortfall.
FIGURE 51.1 Planning for retirement

Rate

8%

Nper

20

FV

$20,000

Type0

PMT = $437.04______________________________________________________________________

272

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

F I N A N C I A L C A LC U L ATO R # 52

How to Determine How Long Your
Money Will Last in Retirement andthe Amount of the Payment in a
Systematic Withdrawal PlanT

he aim of most withdrawal plans is to have the retirement funds lastthrough retirement. This means that you need to determine how muchyou can spend per year. If you spend too much you jeopardize the funding foryour later years, as you could run out of money. Similarly, if you spend too
little, you may not be enjoying the full comforts you can afford in retirement.
Consequently, you need to determine how much money you can withdraw
on an annual basis so that your funds will last you through your retirement.

Step 1: Determine Your Monthly
and Yearly Needs
Assume, for example, that you will need $10,000 per month to live on during
your retirement. You expect to receive close to $2,000 per month from Social
Security and $3,000 per month from your pension plan. You would then needto withdraw $5,000 per month or $60,000 annually from your other sources,
such as investments.

Step 2: Determine How Long Your
Investment Funds Will Last
How long your investment funds will last you in retirement depends on
several factors:

Planning for Your Future273• The amount of your investment account• Your withdrawal rate
• The rate of return earned on your investments• The projected length of time of your retirement
Determine your withdrawal rate, which is the annual withdrawal divided
by the total investment assets. For example, an annual withdrawal of $60,000
from an investment account of $800,000 is 7.5 percent.
Withdrawal rate ==Annual withdrawal
Total investment assets$60,000

800,000= 7.5%

With a 7.5 percent withdrawal rate, there is a good chance that the investment assets will be depleted in less than 20 years. A general rule of thumb isthat a withdrawal rate of less than 5 percent can stretch retirement to 30 years.
Of course, this depends on the rate of return earned on the investment assets.
Table 52.1 lists different withdrawal rates and the lengths of time that investment assets will last, assuming an annual rate of return of 5.5 percent. A withdrawal rate that equals the rate of return means that you will never deplete
your investment assets, as the principal will remain intact. You will be withdrawing only the interest earned on your investment assets. A 4 percent real
rate of return (adjusted for inﬂation) means that retirement assets will notlast as long with the same withdrawal rates.

274

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

TABLE 52.1 How long will your investment assets last?
Withdrawal rate*
12.8%
9.7%
7.3%
6.7%
5.5%

Length of time of withdrawals*
10 years
15 years
25 years
30 yearsIndeﬁnitely

Withdrawal rate**
8.6%
7.0%
6.1%
5.5%
4.0%

Length of time of withdrawals**
15 years
20 years
25 years
30 yearsIndeﬁnitely*This example assumes a rate of return of 5.5% per annum on the investment assets.
**This example assumes a 4% real rate of return that is adjusted for inﬂation.

Step 3: Determine the Projected Rate of
Return on Your Investment Funds
The composition of investment assets has a signiﬁcant impact on the projected rate of return and, hence, length of retirement income. Traditionally,
the greatest returns from ﬁnancial investments over long periods of time havecome from common stocks, followed by bonds, and then money market securities. The danger of investing all retirement funds in common stocks is that
if there is a bear market, common stocks might underperform other ﬁnancial
investments, and there could also be an erosion of principal. A protracted bearmarket would affect the amount of withdrawals and the length of time thatthe retirement funds would last.
Another argument, besides the volatility of the stock market, against
investing all retirement funds in common stock is that in retirement regular
payments of income are needed. Bonds provide these payments, while com-

Planning for Your Future275

mon stock provides long-term growth for the portfolio. A diversiﬁed portfolio of investments consisting of stocks, bonds, and money market securities
balances the trade-off between risk and return. Money market securities provide liquidity in the portfolio.
Your actual asset allocation plan depends on your individual personal circumstances, the amount of your retirement assets, your risk tolerance, theamount of funds you want to leave for your heirs, and so on. Stocks havereturned around 7 percent per year over long periods of time, while bonds
have earned around 4 to 5 percent. However, with the current low interest
rates and bear market, you should be conservative in projecting your future
rates of return on your retirement assets. Inﬂation should also be considered,as it erodes the future purchasing power of your withdrawals.
You should also have a plan for your withdrawals from your retirement
assets. The composition of your withdrawals should come mainly from money
market securities and regular income payments from bonds and stocks, without the bond and stock investments having to be liquidated. As you go along,
however, you will need to liquidate some of these investments and convert
them into money market securities for future withdrawals.

Step 4: Determine How Much You Can Withdraw overYour Projected Retirement Period
There are many Web sites on the Internet that have retirement calculators todetermine how much you can withdraw over your projected retirement
period. One such site is www.TrowePrice.com. In order to ﬁnd the calculator on this Web site, click on the arrow Select a Tool and highlight Retirement
Income Calculator. Enter your information to determine how much you can
withdraw. On completion of your information, you will get an annual withdrawal amount based on your retirement assets, your asset allocation, and thenumber of years for your retirement. Each retirement calculator makes its
own assumptions with regard to rates of return on stocks, bonds, and money
market securities, and rate of inﬂation.

276

T H E P E R SO N A L F I N A N C E C A LC U L ATO R

If necessary, you can always make changes to your withdrawal amounts
to keep up with changing economic circumstances.
Worksheet 52.1 outlines the steps for determining your withdrawal
amount.
WORKSHEET 52.1 How to determine your withdrawal amount
Step 1 Determine the monthly and annual income that you will need.
Projected income needs: Monthly _____________ Annual _____________
Step 2 Determine the withdrawal rate.
Withdrawal rate ==Annual withdrawal
Total investment assets
(
(

)
)

= ______%
Step 3 Determine the length of time that your retirement funds will last.
Compare your withdrawal rate to those in Table 52.1, using either the 5.5%
return rate or the more conservative 4% real rate of return to determine theapproximate length of time that your funds will last.
Withdrawal rate _____________ Length of time of withdrawals _____________
If the length of time is not sufﬁcient, go to step 4.
Step 4 Determine how much you can withdraw over your projected retirement period.
Go to a retirement calculator on the Internet and enter your information. There
are many websites that have retirement calculators, such as www.troweprice.com.
Enter your information to determine the amount that you can withdraw without depleting your retirement funds.
Monthly withdrawal _____________ Annual withdrawal _____________

Appendices

Copyright 2003 by Esme Faerber. Click Here for Terms of Use.

2%

1.020
1.040
1.061
1.082
1.104

1.126
1.149
1.172
1.195
1.219

1.243
1.268
1.294
1.319
1.346

1.373
1.400
1.428
1.457
1.486

1.516
1.546
1.577
1.608
1.641

1.811

2.208

2.691

1%

1.010
1.020
1.030
1.041
1.051

1.062
1.072
1.083
1.094
1.105

1.116
1.127
1.138
1.149
1.161

1.173
1.184
1.196
1.208
1.220

1.232
1.245
1.257
1.270
1.282

1.348

1.489

1.645

n

1
2
3
4
5

6
7
8
9
10

11
12
13
14
15

16
17
18
19
20

21
22
23
24
25

30

40

50

APPENDIX A: Compound sum of $1

4.384

3.262

2.427

1.860
1.916
1.974
2.033
2.094

1.605
1.653
1.702
1.753
1.806

1.394
1.426
1.469
1.513
1.558

1.194
1.230
1.267
1.305
1.344

1.030
1.061
1.091
1.126
1.159

3%

7.106

4.801

3.243

2.279
2.370
2.465
2.563
2.666

1.873
1.948
2.026
2.107
2.191

1.539
1.601
1.665
1.732
1.801

1.265
1.316
1.169
1.423
1.480

1.040
1.082
1.125
1.170
1.217

4%

11.467

7.040

4.322

2.786
2.925
3.071
3.225
3.386

2.183
2.292
2.407
2.527
2.653

1.710
1.796
1.886
1.980
2.079

1.340
1.407
1.477
1.551
1.629

1.050
1.102
1.158
1.216
1.270

5%

18.41910.285

5.743

3.399
3.603
3.820
4.049
4.292

2.540
2.693
2.854
3.026
3.207

1.898
2.012
2.133
2.261
2.397

1.419
1.504
1.594
1.689
1.791

1.060
1.124
1.191
1.262
1.338

6%

29.45614.974

7.612

4.140
4.430
4.740
5.072
5.427

2.952
3.159
3.380
3.616
3.870

2.105
2.252
2.410
2.579
2.759

1.501
1.606
1.718
1.838
1.967

1.070
1.145
1.225
1.311
1.403

7%

46.90021.72410.062

5.034
5.436
5.871
6.341
6.848

3.426
3.700
3.996
4.316
4.661

2.332
2.518
2.720
2.937
3.172

1.587
1.714
1.851
1.999
2.159

1.080
1.166
1.260
1.360
1.469

8%

74.35431.40813.267

6.109
6.658
7.258
7.911
8.623

3.970
4.328
4.717
5.142
5.604

2.580
2.813
3.066
3.342
3.642

1.677
1.828
1.993
2.172
2.367

1.090
1.188
1.295
1.412
1.539

9%

117.38645.25817.449

7.400
8.140
8.954
9.850
10.834

4.595
5.054
5.560
6.116
6.727

2.853
3.138
3.452
3.797
4.177

1.772
1.949
2.144
2.358
2.594

1.100
1.210
1.111
1.464
1.611

10%

184.55950

288.996

29.960

21
22
23
24
25

93.04910.80412.10013.552
15.17817.0008.949
9.933
11.01612.23913.585

16
17
18
19
20

22.892

6.130
6.866
7.690
8.613
9.646

5.311
5.895
6.543
7.263
8.062

11
12
13
14
15

64.999

3.479
3.896
4.363
4.887
5.474

3.152
3.498
3.883
4.310
4.785

6
7
8
9
10

40

1.974
2.211
2.476
2.773
3.106

1.870
2.076
2.305
2.558
2.839

1
2
3
4
5

30

12%

1.120
1.254
1.405
1.574
1.762

11%

1.110
1.232
1.368
1.518
1.685

n
13%

450.711132.776

39.11513.02114.71316.62618.78821.230

7.067
7.986
9.024
10.197
11.523

3.836
4.334
4.898
5.535
6.254

2.082
2.353
2.658
3.004
3.395

1.130
1.277
1.443
1.630
1.842

14%

700.197188.876

50.94915.66717.86120.36123.21226.461

8.137
9.276
10.57512.05513.743

4.226
4.818
5.492
6.261
7.138

2.195
2.502
2.853
3.252
3.707

1.140
1.300
1.482
1.689
1.925

1,083.619

267.856

66.21018.82121.64424.89128.62532.9189.358
10.76112.37514.23216.366

4.652
5.350
6.153
7.076
8.137

2.313
2.660
3.059
3.518
4.046

1.150
1.322
1.521
1.749
2.011

15%

1,670.669

378.71585.84922.57426.18630.37635.23640.87410.74812.46814.462
16.77619.461

5.117
5.936
6.886
7.987
9.265

2.436
2.826
3.278
3.803
4.411

1.160
1.346
1.561
1.811
2.100

16%
17%

2,566.080

533.846111.061

27.03331.62937.00543.29650.65612.33014.42616.87919.74823.105

5.624
6.580
7.699
9.007
10.539

2.565
3.001
3.511
4.108
4.807

1.170
1.369
1.602
1.874
2.192

18%

3,927.189

750.353

143.367

32.32338.14145.00753.10862.667

14.12916.67219.67323.21427.393

6.176
7.288
8.599
10.147
11.974

2.700
3.185
3.759
4.435
5.234

1.180
1.392
1.643
1.939
2.288

5,988.730

1,051.642

184.672

38.59145.92354.64865.03177.387

16.171
19.24422.90027.25132.429

6.777
8.064
9.596
11.42013.589

2.840
3.379
4.021
4.785
5.695

1.190
1.416
1.685
2.005
2.386

19%

9,100.191

1,469.740

237.373

46.00555.20566.24779.49695.39518.48822.18626.62331.94838.3377.430
8.916
10.69912.83915.407

2.986
3.583
4.300
5.160
6.192

1.200
1.440
1.728
2.074
2.488

20%

2%

.980
.961
.942
.924
.906
.888
.871
.853
.837
.820
.804
.789
.773
.758
.743
.728
.714
.700
.686
.673
.660
.647
.634
.622
.610
.552
.453
.372

1%

.990
.990
.971
.961
.951
.942
.933
.923
.914
.905
.896
.887
.979
.870
.861
.853
.844
.836
.828
.820
.811
.803
.795
.788
.780
.742
.672
.608

n

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
30
40
50

APPENDIX B: Present value of $1
3%
.971
.943
.915
.888
.863
.837
.813
.789
.766
.744
.722
.701
.681
.661
.642
.623
.605
.587
.570
.554
.538
.522
.507
.492
.478
.412
.307
.228

4%
.962
.925
.889
.855
.822
.790
.760
.731
.703
.676
.650
.625
.601
.577
.555
.534
.513
.494
.475
.456
.439
.422
.406
.390
.375
.308
.208
.141

5%
.952
.907
.864
.823
.784
.746
.711
.677
.645
.614
.585
.557
.530
.505
.481
.458
.436
.416
.396
.377
.359
.342
.326
.310
.295
.231
.142
.087

6%
.943
.890
.840
.792
.747
.705
.665
.627
.592
.558
.527
.497
.469
.442
.417
.394
.371
.350
.331
.312
.294
.278
.262
.247
.233
.174
.097
.054

7%
.935
.873
.816
.763
.713
.666
.623
.582
.544
.508
.475
.444
.415
.388
.362
.339
.317
.296
.277
.258
.242
.226
.211
.197
.184
.131
.067
.034

8%
.926
.857
.794
.735
.681
.630
.583
.540
.500
.463
.429
.397
.368
.340
.315
.292
.270
.250
.232
.215
.199
.184
.170
.158
.146
.099
.046
.021

9%
.917
.842
.772
.708
.650
.596
.547
.502
.460
.422
.388
.356
.326
.299
.275
.252
.231
.212
.194
.178
.164
.150
.138
.126
.116
.075
.032
.013

.909
.826
.751
.683
.621
.564
.513
.467
.424
.386
.350
.319
.290
.263
.239
.218
.198
.180
.164
.149
.135
.123
.112
.102
.092
.057
.022
.009

10%

12%

.893
.797
.712
.636
.567

.507
.452
.404
.361
.322

.287
.257
.229
.205
.183

.163
.146
.130
.116
.104

.093
.083
.074
.066
.059

.033

.011

.003

11%

.901
.812
.731
.659
.593

.535
.482
.434
.391
.352

.317
.286
.258
.232
.209

.188
.170
.153
.138
.124

.112
.101
.091
.082
.074

.044

.015

.005

n

1
2
3
4
5

6
7
8
9
10

11
12
13
14
15

16
17
18
19
20

21
22
23
24
25

30

40

50
.002

.008

.026

.077
.068
.060
.053
.047

.141
.125
.111
.098
.087

.261
.231
.204
.181
.160

.480
.425
.376
.333
.295

.885
.783
.693
.613
.543

13%

.001

.005

.020

.064
.056
.049
.043
.038

.123
.108
.095
.083
.073

.237
.208
.182
.160
.140

.456
.400
.351
.308
.270

.877
.769
.675
.592
.519

14%

.001

.004

.015

.053
.046
.040
.035
.030

.107
.093
.081
.070
.061

.215
.187
.163
.141
.123

.432
.376
.327
.284
.247

.870
.756
.658
.572
.497

15%

.001

.003

.012

.044
.038
.033
.028
.024

.093
.080
.069
.060
.051

.195
.168
.145
.125
.108

.410
.354
.305
.263
.227

.862
.743
.641
.552
.476

16%

.000

.002

.009

.037
.032
.027
.023
.020

.081
.069
.059
.051
.043

.178
.152
.130
.111
.095

.390
.333
.285
.243
.208

.855
.731
.624
.534
.456

17%

.000

.001

.007

.031
.026
.022
.019
.016

.071
.060
.051
.043
.037

.162
.137
.116
.099
.084

.370
.314
.266
.225
.191

.847
.718
.609
.516
.437

18%

.000

.001

.005

.026
.022
.018
.015
.013

.062
.052
.044
.037
.031

.148
.124
.104
.088
.074

.352
.296
.249
.209
.176

.840
.706
.593
.499
.419

19%

.000

.001

.004

.022
.018
.015
.013
.010

.054
.045
.038
.031
.026

.135
.112
.093
.078
.065

.335
.279
.233
.194
.162

.833
.694
.579
.482
.402

20%

60.401

84.57764.46150

25.78327.29928.84530.42132.03023.23924.47125.71626.97328.243

21
22
23
24
25

40.56718.63920.01221.41222.84024.29717.25818.43019.61420.81122.019

16
17
18
19
20

34.78412.16913.41214.68015.97417.293

11.56712.68213.80914.94716.097

11
12
13
14
15

48.885

6.308
7.434
8.583
9.755
10.950

6.152
7.214
8.286
9.368
10.462

6
7
8
9
10

40

1.000
2.020
3.060
4.122
5.204

1.000
2.010
3.030
4.060
5.101

1
2
3
4
5

30

2%

1%

n

112.79475.40047.57528.67630.53632.45234.42636.45920.15721.76123.41425.11726.87012.80814.192
15.61817.08618.599

6.468
7.662
8.892
10.15911.464

1.000
2.030
3.091
4.184
5.309

3%

APPENDIX C: Sum of annuity for n periods

152.664

95.02456.08431.96934.24836.61839.08241.64521.82423.69725.64527.67129.77813.48615.02616.62718.29220.023

6.633
7.898
9.214
10.58312.006

1.000
2.040
3.122
4.246
5.416

4%

209.341120.79766.43835.71938.50541.43044.50147.72623.65725.84028.13230.53933.06614.20715.91717.71319.59821.578

6.802
8.142
9.549
11.027
12.578

1.000
2.050
3.152
4.310
5.526

5%

290.325

154.758

79.05739.99243.39246.99550.81554.86425.67228.21330.90533.76036.78514.972
16.87018.88221.01523.276

6.975
8.394
9.897
11.491
13.191

1.000
2.060
3.184
4.375
5.637

6%

406.516

199.630

94.45944.86549.00553.43558.17663.24827.88830.84033.99937.37940.99515.78417.88820.14122.55025.1297.153
8.654
10.26011.97813.816

1.000
2.070
3.215
4.440
5.751

7%

573.756

295.052

113.282

50.42255.45660.89366.76473.10530.32433.75037.45041.44645.76216.64518.97721.49524.21527.1527.336
8.923
10.63712.48814.487

1.000
2.080
3.246
4.506
5.867

8%

815.051

337.872

136.305

56.76462.87269.53176.78984.69933.00336.97341.30146.01851.15917.56020.14122.95326.01929.361

7.523
9.200
11.02813.021
15.193

1.000
2.090
3.278
4.573
5.985

9%

1,163.865

442.580

164.49164.00271.40279.54288.49699.34635.94940.54445.59951.15857.27418.53121.38424.52327.97531.7727.716
9.487
11.436
13.57915.937

1.000
2.100
3.310
4.641
6.105

10%

20.655
24.13328.02932.39237.28042.75348.88355.74963.43972.05281.69892.502104.602118.154133.333

241.330

767.080

19.56122.71326.21130.09534.40539.19044.50050.39656.93964.20272.26481.21391.147102.173
114.412199.018

581.812

1,668.723

1
2
3
4
5
6
7
8
9
10

11
12
13
14
15

16
17
18
19
20

21
22
23
24
25

30

40

50

2,399.975

12%

1.000
2.120
3.374
4.779
6.353
8.115
10.08912.30014.77617.549

11%

1.000
2.110
3.342
4.710
6.228
7.913
9.783
11.85914.16416.722n
13%

3,459.344

1,013.667

293.192

92.468105.489
120.203136.829
155.61646.67153.73861.72470.74880.94621.81425.65029.98434.88240.417

1.000
2.130
3.407
4.850
6.480
8.323
10.40512.75715.41618.42014%

4,994.301

1,341.979

356.778104.767
120.434138.295
158.656
181.867

50.98059.11768.39378.96891.02423.04427.27132.08837.58143.842

1.000
2.140
3.440
4.921
6.610
8.535
10.73013.23316.08519.33715%

7,217.488

1,779.048

434.738118.809137.630
159.274
184.166
212.790

55.71765.07575.83688.211102.443

24.34929.00134.35240.50447.580

1.000
2.150
3.472
4.993
6.742
8.754
11.06713.727
16.78620.30416%

10,435.449

2,360.724

530.306

134.840
157.414183.600
213.976249.21260.92571.67384.14098.603115.379

25.73330.85036.78643.67251.659

1.000
2.160
3.506
5.066
6.877
8.977
11.41414.24017.51821.321

17%

15,088.805

3,134.412

647.423

153.136
180.169
211.798248.803292.099

66.64878.97893.404110.283130.031

27.20032.82439.40447.10256.109

1.000
2.170
3.539
5.141
7.014
9.207
11.77214.77318.28522.39318%
19%

5,529.711

966.698

197.846236.436282.359
337.007402.03879.85096.021115.265
138.165
165.41730.40337.18045.24454.84166.260

1.000
2.190
3.606
5.291
7.297
9.683
12.52315.90219.92324.70921,812.273 31,514.492

4,163.094

790.932

174.019206.342244.483
289.490342.598

72.93887.067103.739
123.412146.62628.75534.93142.21850.81860.965

1.000
2.180
3.572
5.215
7.154
9.442
12.14115.32719.08623.521

20%

45,496.094

7,343.715

1,181.865

225.024271.028326.234
392.480
471.97687.442105.930128.116154.739186.687

32.15039.58048.49659.19672.035

1.000
2.200
3.640
5.368
7.442
9.930
12.91616.49920.79925.959

2%

.980
1.942
2.884
3.808
4.713

5.601
6.472
7.326
8.162
8.983

9.787
10.575
11.34812.10612.84913.57814.29214.99215.67916.35217.01117.65818.29218.91419.52422.39727.35631.424

1%

.990
1.970
2.941
3.902
4.853

5.795
6.728
7.652
8.566
9.471

10.36811.25512.13413.00413.86514.71815.562
16.39817.22618.04618.85719.66120.45621.24422.02325.80832.83539.197

n

1
2
3
4
5

6
7
8
9
10

11
12
13
14
15

16
17
18
19
20

21
22
23
24
25

30

40

50
25.73023.11519.60115.41515.93716.44416.93617.413

12.56113.16613.75414.32414.8789.253
9.954
10.63511.296
11.938

5.417
6.230
7.020
7.786
8.530

.971
1.913
2.829
3.717
4.580

3%

21.48219.79317.29214.02914.45114.85715.24715.62211.652
12.16612.65913.13413.590

8.760
9.385
9.986
10.56311.118

5.242
6.002
6.733
7.435
8.111

.962
1.886
2.775
3.630
4.452

4%

APPENDIX D: Present value of an annuity of $1 for n periods

18.25617.15915.37312.82113.16313.48913.79914.09410.838
11.274
11.69012.085
12.462

8.306
8.863
9.394
9.899
10.380

5.076
5.786
6.463
7.108
7.722

.952
1.859
2.723
3.546
4.329

5%

15.76215.04613.76511.76412.04212.30312.55012.78310.106
10.477
10.82811.15811.470

7.887
8.384
8.853
9.295
9.712

4.917
5.582
6.210
6.802
7.360

.943
1.833
2.673
3.465
4.212

6%

13.801

13.33212.40910.83611.061
11.272
11.46911.6549.447
9.763
10.05910.336
10.594

7.499
7.943
8.358
8.746
9.108

4.767
5.389
5.971
6.515
7.024

.935
1.808
2.624
3.387
4.100

7%

12.23411.925

11.25810.017
10.20110.371
10.52910.675

8.851
9.122
9.372
9.604
9.818

7.139
7.536
7.904
8.244
8.560

4.623
5.206
5.747
6.247
6.710

.926
1.783
2.577
3.312
3.993

8%

10.96210.757

10.274

9.292
9.442
9.580
9.707
9.823

8.313
8.544
8.756
8.950
9.129

6.805
7.161
7.487
7.786
8.061

4.486
5.033
5.535
5.995
6.418

.917
1.759
2.531
3.240
3.890

9%

9.915

9.779

9.427

8.649
8.772
8.883
8.985
9.077

7.824
8.022
8.201
8.365
8.514

6.495
6.814
7.103
7.367
7.606

4.355
4.868
5.335
5.759
6.145

.909
1.736
2.487
3.170
3.791

10%

12%

.893
1.690
2.402
3.037
3.605
4.111
4.564
4.968
5.328
5.650

5.938
6.194
6.424
6.628
6.811

6.974
7.120
7.250
7.366
7.469

7.562
7.645
7.718
7.784
7.843

8.055

8.244

8.305

11%

.901
1.713
2.444
3.102
3.696
4.231
4.712
5.146
5.537
5.889

6.207
6.492
6.750
6.982
7.191

7.379
7.549
7.702
7.839
7.963

8.075
8.176
8.266
8.348
8.442

8.694

8.951

9.042

n

1
2
3
4
5
6
7
8
9
10

11
12
13
14
15

16
17
18
19
20

21
22
23
24
25

30

40

50
7.675

7.634

7.496

7.102
7.170
7.230
7.283
7.330

6.604
6.729
6.840
6.938
7.025

5.687
5.918
6.122
6.303
6.462

.885
1.668
2.361
2.974
3.517
3.998
4.423
4.799
5.132
5.426

13%

7.133

7.105

7.003

6.687
6.743
6.792
6.835
6.873

6.265
6.373
6.467
6.550
6.623

5.453
5.660
5.842
6.002
6.142

.877
1.647
2.322
2.914
3.433
3.889
4.288
4.639
4.946
5.216

14%

6.661

6.642

6.566

6.312
6.359
6.399
6.434
6.464

5.954
6.047
6.128
6.198
6.259

5.234
5.421
5.583
5.724
5.847

.870
1.626
2.283
2.855
3.352
3.784
4.160
4.487
4.772
5.019

15%

6.246

6.233

6.177

5.973
6.011
6.044
6.073
6.097

5.669
5.749
5.818
5.877
5.929

5.029
5.197
5.342
5.468
5.575

.862
1.605
2.246
2.798
3.274
3.685
4.039
4.344
4.607
4.833

16%

5.880

5.871

5.829

5.665
5.696
5.723
5.747
5.766

5.405
5.475
5.534
5.585
5.628

4.836
4.988
5.118
5.229
5.324

.855
1.585
2.210
2.743
3.199
3.589
3.922
4.207
4.451
4.659

17%

5.554

5.548

5.517

5.384
5.410
5.432
5.451
5.467

5.162
5.222
5.273
5.316
5.353

4.656
4.793
4.910
5.008
5.092

.847
1.566
2.174
2.690
3.127
3.498
3.812
4.078
4.303
4.494

18%

5.262

5.258

5.235

5.127
5.149
5.167
5.182
5.195

4.938
4.990
5.033
5.070
5.101

4.487
4.611
4.715
4.802
4.876

.840
1.547
2.140
2.639
3.058
3.410
3.706
3.954
4.163
4.339

19%

4.999

4.997

4.979

4.891
4.909
4.925
4.937
4.948

4.730
4.775
4.812
4.843
4.870

4.327
4.439
4.533
4.611
4.675

.833
1.528
2.106
2.589
2.991
3.326
3.605
3.837
4.031
4.192

20%

This page intentionally left blank.

IndexAAA-rated bonds, 173, 174, 217
accountant, preparing records for, 68–72
accounts receivable turnover, 23acid test ratio, 230–31
add-on method, for computing interest
on installment loans, 85, 88–90
adjustable rate mortgages (ARM),
114–16, 121, 122, 123–24
calculating an ARM schedule, 116–20
and reﬁnancing, 125
adjusted capitalized cost, 132age, as factor in investment planning,
153, 160
aggressive portfolio, 163
alternative minimum tax (AMT), 129
amortization schedule
for adjustable rate mortgages, 117,
118–19, 120
for house mortgages, 107–10
for installment loans: add-on method,89
precomputed, for purchase of a car,143
for simple interest loan, 145
AMT (alternative minimum tax), 129
annual percentage rate (APR), 30
of car loans, 136–37
for credit, 78–79, 81
for credit cards, 90, 91
for installment loans, 85–90
for single-payment loans, 82–84
annuities, 5, 20, 37–38. See also annuity
due; ordinary annuityof mortgage payments, 104–5
annuity due, 38
future value of, 40–42
determining future value of, using acomputer, 44–46
determining future value of, using aﬁnancial calculator, 42–43
determining present value of, using acomputer, 48, 52
determining present value of, using aﬁnancial calculator, 48, 51
present value of, 48
APR. See annual percentage rate
ARM. See adjustable rate mortgages
asset allocation plan, 158–61, 163

and rebalancing portfolio, 175–78
assets, 3, 5
and declaring bankruptcy, 98
current, 229
and net worth, 7
auctions, for Treasury bills, 193, 195
back-load fee, 250
balance sheet, 8balanced portfolio, 162
balloon mortgage, 127
bank loan, 96
bankruptcy, declaring, 98
Bankruptcy Code, 98
bank statements, 63, 65, 67
BBB-rated bonds, 173, 174, 217
blue-chip companies, 181, 240, 241
blue-chip stocks, 181, 247
bids, on Treasury bills, 201, 205–6
bond mutual fund, 171
bonds, 5, 57, 165, 171
assessing risk and return of, 182
calculating rate of return on, 186–89
corporate, 173, 217
determining value of, 217–19
duration, and choosing, 211–16
junk, 173, 181, 184, 249
maturity of, 171, 182, 213, 214, 215
municipal, 173, 207–11
ratings of, 174
Treasury, 172, 182, 209, 217
types of, 172–73
zero-coupon, 173, 215
book values, of stocks, 242
budget, 12
evaluating, 19
formulating, 12–18
canceled checks, 61–63
capital gains and losses, 186, 190, 254–58
capitalized cost reduction, 132
carsbuying versus leasing or ﬁnancing,
136–42determining value of, 5ﬁnancing, 136–40, 142–45
leasing, 131–36
loans for purchasing, 80, 136

287
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288

Index

cash ﬂow, 245
cash inﬂows and outﬂows statement, 8,245. See also income statement
certiﬁcates of deposit (CDs), 164, 182,
186
checkbook balance, determining, 63–64
checking accountreconciling, 61–68
reconciling, using a computer, 67–68
checkscanceled, marking off, 61–63
outstanding, listing, 65
writing, against bond or stock fund,254, 257
closed-end lease, 131, 132
closing costs, of house purchase, 100
common stocks, 153–54, 181
analyzing and evaluating, 229–45
determining growth rate of, 226–28
determining value of, 220–25
companies, and stock valuationaccounts receivable turnoverof, 231
cash position of, 220, 245
current ratio of, 229–30
dividend yields of, 220, 240–41
growth of, 220, 221, 226inventory turnover of, 232
leverage ratios of, 235–36
market capitalization of, 166
price-earnings ratio of, 236–40
proﬁtability of, 232–35
quick ratio of, 230–31
competitive bids, on Treasury bills, 201,
205–6
compound interest, 23–29
computer programs
to determine funding for ﬁnancial
objectives, 59–60
to determine future value, 28
to determine future value of anannuity, 44–46
to determine present value, 35–37
to determine present value of anannuity, 48, 52
to reconcile checking account, 67–68
conservative portfolio, 161–62
consumer ﬁnance companies, 78
convertible bonds, 173
corporate bonds, 173, 217
coupon rate, of bonds, 212–16
coverage ratios, 236
credit, 77–81
credit cards, 77, 78, 80
determining rate of interest on, 90–94
lower-rate, 91, 97
managing debt of, 96

credit counseling, 97
credit quality, of bonds, 171
credit unions, 80
current assets, 229
current liabilities, 229
current ratio, 7, 229–30
debt
managing, 94–96
paying down from savings, 96
setting limits, 75–77
debt ratio, 7–8, 235–36
debt securities, 207deﬁcitdetermining, 18
in net cash ﬂow, 11deﬁcit spending, 19
depreciation, 132discount interest, for single-payment
loans, 82, 84
dividend payout ratio, 241
dividends, 186, 190
on mutual funds, 248–49, 254
on stocks, 220, 221, 240–41
dividend yield, 241dollar cost averaging, 259–62
Dow Jones Industrial Average,
165, 167
down payment, for house purchase, 99
duration, 211–16
earnings before interest and taxes(EBIT), 233
earnings per share (EPS),
239–40EBIT (earnings before interest andtaxes), 233
education expenses, 54
effective interest rate, 31, 32
effective interest rate method, forcomputing the APR of installment
loans, 85–87
effective yield, 30
emergency fund, 53
EPS (earnings per share), 239–40
equityin home ownership, 129
in stock investments, 166,
234–35exit fee, 250
expenditures, 10–11
determining expected, 15–16
ﬁxed, 10, 15, 19
prioritizing, 19
recording actual, 18
variable, 11, 15, 19
Exxon, 230, 237

IndexFarrell, James L., 165
Federal Reserve Banks, 201
Federal Truth in Lending Act, 78
FIFO (ﬁrst in, ﬁrst out), 255, 257
ﬁnancial calculator
to determine funding for ﬁnancial
objectives, 58–59
to determine future value, 27–28
to determine future value ofannuities, 42–43
to determine mortgage balances, 107
to determine present value, 35
to determine present value ofannuities, 48
ﬁnancial goals
assessing cost and time frame for
each, 55–57
computing monthly amounts needed
to fund, 57–59
determining, 16–17
listing, 53–54
prioritizing, 16–17, 55
rates of return for each, 57
ﬁnancial statements, of companies, 229
ﬁnancial tables
to determine future value, 25–27
to determine present value, 34–35
ﬁnancing, a car, 136–37, 138, 140
manufacturer’s rebates for, 136, 137,
140
simple interest loans for, 142–45
special low–interest rate loans for,136, 137, 140
versus buying, 136, 137, 138, 139
versus leasing, 139, 141
ﬁrst in, ﬁrst out (FIFO), 255, 257
ﬁxed-rate mortgages, 103–4, 114, 121,
122, 123–24
and reﬁnancing, 125
future dividends, and value of common
stock, 221, 222–25
future value (FV), of money, 23, 24, 25
using a computer to determine, 28
using a ﬁnancial calculator todetermine, 27–28
using ﬁnancial tables to determine,
25–27
and present value, 33
graduated payment mortgages, 126
gross income, 10, 14
gross proﬁt ratio, 233
growth investing, 166
growth stocks, 166, 168, 169
high-quality bonds, 172
home equity loan, 96–97

289

house. See also mortgages
determining value of, 5
renting versus buying, 127–31
saving to buy, 53–54
incomeestimating future, 14–15
increasing, 11
listing sources of, 10
recording actual, 18
as return on investments, 180, 186
income statement, 8–11
income stocks, 184
index, of adjustable rate mortgages,
114–15installment loans, 85–90
interest, 20, 21–22
compound, 23–29, 30
market rates of, 121–22, 211, 213–14
simple, 22–23, 30, 31
interest expense, of simple interest loan,
143
interest rate caps, 115
interest rates, 22, 30
adjustable, for mortgages, 114–20,
121–22effective, 31
ﬁxed, for conventional mortgages,
103–4, 114, 121
market, 121–22, 211, 213–14
nominal, 31
intermediate-term bonds, 172, 182
Internal Revenue Service (IRS), 68, 256inventory turnover, 232
Investment Quality Trends (newsletter),241
investment objectives, 149–50, 151
and assessing investments, 180–85
of mutual funds, 247
investment portfolios, 158, 159
aggressive, 163
assessing risk and return, 180–86, 247
balanced, 162
bonds in, 171, 182
calculating rate of return on mutual
funds, 190–93
calculating rate of return on stocks
and bonds, 186–89
conservative, 161, 162
determining rate of doubling (rule of72), 179–80
determining yield on Treasury bills,
193–96and dollar cost averaging,
259–63rebalancing, 175–78
investment styles, 166

290

Index

investments. See also investment
portfolios
allocating, 158
bonds, 5, 57, 165, 171–74, 182,
186–89, 207–11
classifying, on a continuum of risk,
153–54, 181, 183choosing, 57
diversiﬁcation of, 158–59, 163,
168–69money market securities, 57, 164
mutual funds, 190–93
real estate, 5risk tolerance for, 152–57, 171,
180–85, 247
stocks, 5, 57, 153–54, 158, 159,
165–69, 186–89
Treasury bills, 193–96
IRS (Internal Revenue Service), 69,
256, 257
Johnson & Johnson, 221, 224
junk bonds, 173, 181, 184, 249
Kelley Blue Book, 5large-cap stocks, 166, 167, 169
leasinga car, 131–36
versus ﬁnancing a car, 139, 141, 142
leverage ratios, 235–36
liabilities
current, 229
determining, 5–6
and net worth, 7life insurance policies, value of, 5liquid current assets, 7
liquidity, of assets, 3load mutual funds, 250–51
loansbank, 96
car, 80, 136, 137, 140, 142–45
home equity, 96–97
installment, 85–90
simple interest, 142–45
single-payment, 82–84
special low–interest rate, 136, 137, 140
long-term bonds, 172, 182
low-quality bonds, 172
manufacturer’s rebates, 136, 137, 140
manufacturer’s suggested retail price(MSRP), 132
market capitalization, 166
market rates of interest, 121–22, 211,
213–14maturities, 171
maturityof bonds, 171, 182, 213, 214, 215
of Treasury bills, 195, 197
medium-quality bonds, 172
Microsoft’s Excel spreadsheet
to compute funding for ﬁnancial
objectives, 59–60
to compute future value, 28, 29
to compute future value of anannuity, 44, 45
to compute monthly mortgage
payments, 106
to compute present value,35, 37to compute present value of anannuity, 48–49, 52
Microsoft Money, 12
mid-cap stocks, 166, 167, 169
money, time value of. See time value ofmoneymoney factor, 134
money market securities, 57, 164, 182
Morning Star, and rating mutual funds,
166, 169, 170, 247
mortgage balance
determining, 107–10
and making additional principal
payments, 111–14
mortgage payments, 103–6
mortgage points, 100
mortgages, 6
adjustable rate, 114–21
calculating monthly payments of,
103–6
choosing, 121–24
determining balance of, 107–10
determining balance of, withadditional principal payments,
111–14determining affordable, 99–102
ﬁxed-rate, 103–4, 114, 121, 122,
123–24, 125
reﬁnancing, 125–27
MSRP (manufacturer’s suggested retailprice), 132
municipal bonds, 173, 207–11
mutual funds
calculating rate of return for, 190–93
choosing, 246, 252–53
determining value of, 5
expenses of, 249–52
objectives of, 247
performance of, 247–48
rating, using Morning Star, 166, 169,
170, 247

Indexreturn on, 248–49
tax consequences of buying
and selling shares in,
254–58
N.A.D.A. Ofﬁcial Used Car Guide, 5negative amortization, 116
net asset value (NAV), 190, 191, 192, 248
net cash ﬂow, 11
net proﬁt margin, 234
net worth, 3, 6
determining, 3–5, 6–8
increasing, 7
new loan balance, of simple interest
loan, 144–45
no-load mutual funds, 250, 251
nominal interest rate, 31
noncompetitive bids, on Treasury bills,
201, 205–6
open-end lease, 131
operating proﬁt ratio, 233
ordinary annuity, 38
future value of, 38–40
determining future valueof, using a computer, 44–46
determining future value of,using a ﬁnancial calculator,
42–43
determining present value of, using acomputer, 48–49, 52
determining present value of, using aﬁnancial
calculator, 48
present value of, 46–47
payment caps, 116
payroll tax deductions, 10, 14
P/E (price/earnings) ratios, 166, 236–40
pension funds, determining
value of, 5periodic rate, 90
personal balance sheet, 7personal effects, determining
value of, 5personal ﬁnance software programs, 12,28, 107. See also computer
programs; Microsoft Money;
Microsoft’s Excel spreadsheet;
Quicken software
portfolios. See investment portfolios
precomputed interest method, forcomputing the APR of installment
loans, 85present value (P), of money, 33
using a computer to determine, 35–37

291

using a ﬁnancial calculator todetermine, 35
using ﬁnancial tables to determine,
34–35
price/earnings (P/E) ratios, 166, 236–40
price-earnings to growth ratio,
242, 245
price-to-sales ratio, 242
principal amountin calculating compound interest,
23–24, 25
in calculating simple interest, 22–23
principal reduction
in paying mortgages, 111–14
in simple interest loans for car
ﬁnancing, 144
proﬁtability, 232–35
quality, of bonds, 171
Quicken software, 12, 28, 67–68
quick ratio, 230–31
rate of interest, 22
on credit cards, 90–94
rate of returnand assessing and balancing
investments, 180–85
for mutual funds, 190–93, 248–49
for stocks and bonds, 186–89, 221
and risk, 183–85, 217–18, 255
rule of 72, 179–80
of Treasury bills, 193–96
real estate investment trusts (REITs),
240, 241
rebates, manufacturer’s, 136, 137, 140
reﬁnancing, a mortgage, 125–26
REITs (real estate investment trusts),
240, 241
renting, versus home ownership, 127–31
residual value, 132
retirement, saving for, 54
return on common equity ratio, 235
return on equity ratio, 234–35
risk-return relationship, 183–85, 217–18,
255
risk tolerance
and assessing investments, 180–85
in bond investing, 171
in choosing a mortgage, 122
determining, 152–57
rule of 72, 179–80
Russell 200 Index, 165
salary, 10, 14
sales tax, in monthly lease
payments, 134

292

Index

Securities and Exchange Commission(SEC), 248
self-employment, and payroll tax
withholdings, 14
short-term bonds, 172
simple interest, 22–23
for single-payment loans, 82, 83
simple interest loans, for ﬁnancing a car,142–45
simple interest method, for computing
the APR of installment loans, 85,
87–88
single-payment loans, 82–84
small-cap stocks, 165, 166, 167, 169
special low–interest rate loans, 136,
137, 140
speculative stocks, 181, 184
Standard & Poor’s (S&P) 500 Index,
167, 237
stock market, 165–69, 181, 187–88, 238
and mutual funds, 246, 248
stock portfolios. See investment
portfolios
stocks, 5, 57, 158, 159
blue-chip, 181
classifying, 165–66
common, 153–54, 181, 220–25,
229–45determining rate of return on, 186–89
determining growth rate of, 226–28
and dollar cost averaging, 259–62
growth, 166, 168, 169, 184
income, 184large-cap, 166, 167, 169
management style of, 168
mid-cap, 166, 167, 169
small-cap, 165, 166, 167, 169
speculative, 181, 184
value, 166, 168, 169
surplusdetermining, 18
in cash net cash ﬂow, 11
tax accountant, preparing records for,68–72

tax records, 68–69
tax returns, 69
tax reporting, and mutual funds,
254–57teaser rates, 115
1099 forms, 68
time-frame
for ﬁnancial goals, 55
for investments, 149–50
time value of money, 17, 20–22
and calculating rate of return forstocks and bonds, 186–87
and determining duration of bonds,
212–13times interest earned ratio, 236
Treasury bills (T-bills), 182, 183buying and selling, from the Federal
Reserve, 201–7
determining purchase and selling
price of, 197–99
determining yield on, 193–96
Treasury bonds and notes, 172, 182,
209, 217
Treasury Direct program, 193
12 (b)-1 fees, 252
U.S. Treasury bills. See Treasury bills
U.S. Treasury bonds. See Treasury bonds
and notes
value investing, 166
Value Line, 237
value stocks, 166, 168, 169variances, 18, 19
wage earner’s plan, 98
wages, 10, 14
Weiss, Geraldine, 241
yield
on dividends, 241
on mutual funds, 248–49
zero-coupon bonds, 173, 215