# Financial Management Case Study

MARY AND ROBERT TRENTICOSTA CASE STUDY:Georgetown CFP:Booher, Perdue, Pryor, Shi, Waldron

## 27. What is the weighted Alpha of the entire stock portfolio?

First, we calculate the weighted average return from all stocks. In order to do this, we used the historical average return for the stocks in the brokerage account and the conservative “large company” 11% return given in the case for the High-Tech and Brown Foreman (easier, and probably more reliable than calculating returns). Beta for the High-Tech and Brown Foreman was calculated using a correlation of 1 and the 12% standard deviation given for the S&P 500 index—rough estimates indeed.
| | Market Value | Return | Beta | Weight |
| Big | 29,000 | 12.5 | .88 | 17% |
| Small | 24,666 | 15 | 1.24 | 15% |
| Oil | 30,300 | 8 | 1 | 18% |
| Auto | 32,276 | 10 | 1.12 | 19% |
| Brown Foreman | 10,000 | 11 | 1 | 6% |
| High-Tech | 40,000 | 11 | 1 | 24% |
| | Weighted Average | 11.1 | 1.038 |
Using the assumption provided in the yield-curve for the risk-free rate of return as 3.70%, we apply the definition to solve for Jensen’s alpha, denoted by $\alpha _{j}$ or,
    ${\begin{alignedat}{2}\alpha _{j}&=r-R_{f}-\beta \times (K_{m}-R_{f})\\&=0.111-0.037+1.038\,(.12-.037)=-1.3\%\end{alignedat}}$.
where $r$ is the fund's return rate, $R_{f}$ is the risk-free return rate, and $K_{m}$ is the return of the index (here we use the S&P 500). The same calculation for just the brokerage account is,
    $\alpha =.112-.037+(.12-.037)\,1.054=-1.2\%$.

## 28. Assuming an income tax rate of 30%, what is the pretax equivalent yield to maturity for the Texas municipal bonds?

The yield to maturity (YTM) from today using the current market value is 7.56%. In order to calculate this, we first determine the YTM rate using the following formula: N=15, PV=55,232.58, PMT =(3000), FV=(50,000) which produces 5.29% as the YTM. In order to arrive at the pre-tax equivalent yield we use the following calculation,
    ${\text{Taxable eqivalent yield}}={\frac {0.0529}{(1-.3)}}=7.56\%.$

## 29. How does the return on the municipal bond compare with other interest rates?

The municipal bond has a tax equivalent interest rate that is comparable to the other bonds. The return on the municipal bond is 7.56%, while the average coupon on their other bonds is around 8.67%.

## 30. On the basis of other prevailing interest rates, does the pretax return for the Texas municipal bond seem reasonable? Why?

Yes, it does seem reasonable. Higher than the federal government, but lower than the corporate bonds

## 31. Determine the holding period return for each of the stocks in the brokerage account. Ignore dividends for this purpose.

HPR is the percentage by which the value of a portfolio (or asset) has grown for a particular period. It is the sum of net income and capital gains divided by the initial period value (asset value at the beginning of the period). Mathematically,
    ${\text{HPR}}_{n}\ =\ {\frac {{\text{Income}}+(P_{n+1}-P_{n})}{P_{n}}},$
where $P_{n}$ is the return in period $n$. Performing this computation on the stocks in the portfolio produces the results shown below.
| Company | Holding Period Return |
| Big | 80.2% |
| Small | 15.00% |
| Oil | 36.05% |
| Auto | 33.10% |
| Portfolio | 38.28% |
In order to compute the HPR for the portfolio we computed the difference between the aggregate basis and aggregate fair market value divided by the total basis,
    ${\text{Portfolio Return}}={\frac {\sum FMV-\sum Basis}{\sum Basis}}.$

## 32. What percentage of the change in the value of the brokerage account can be explained by changes in the stock market?

The exact correlation of portfolio returns requires equities' individual standard deviations as well as the complete covariance matrix. In this case, we were simply given a correlation coefficient between the portfolio and the market of 0.80. The correlation coefficient quantifies the extent of correlation between two sets of returns and $R^{2}$ represents the proportion of the total variance of portfolio return that is attributable to market movements but, unlike market risk, is a relative measure of risk.
    $R=0.80\implies R^{2}=64\%$
Therefore 64% of the portfolio’s movement is attributable to market movement.

## 33. On the basis of the Constant Dividend Growth Model, what must the Trenticostas’ required rate of return be for the high tech stock to be priced fairly? What are the implications of buying, selling or holding the stock?
### Required rate of return be for the high tech stock to be priced fairly

    $r={\frac {D}{V}}+g={\frac {.824}{20}}+.03=7.1\%$

### What are the implications of buying, selling or holding the stock?

Based on Mary and Robert's actual required rate of return of 9%, the High Tech stock is overpriced using a dividend model for valuation. The stock has more than doubled since it was purchased at the pit of the bear market, however, and tech stocks generally pay low dividends, so a dividend growth model may not be an appropriate valuation model for this stock. Buying more of this stock would be a bet that it will return to, or exceed, its previous high, but buying Tech also would not diversify the portfolio. Holding on to the stock avoids capital gains tax, but if the dividend model is an accurate predictor of future growth, it is likely to produce suboptimal returns. Selling it would generate a capital gain of $23,000, but this could be offset by loss sales in the bond portfolio and the proceeds could be reinvested in an index fund to diversify the portfolio.

## 34. Mary only recently made Dominic the co-owner of Mary’s checking account.
### What are the consequences to Mary?

Mary has given Dominic full rights over the account, including the right to withdraw funds for his own use. the account will not pass under her will, but will become fully owned by dominic at her death. As noted below, there may also be gift tax consequences.

### When does this become a taxable gift from Mary to Dominic?

It becomes a taxable gift when Dominic writes checks for more than $12,000 more than he contributed into the account.

## 35. Crescent City publications used a cross-purchase life insurance program to protect themselves from early and untimely death of a principal shareholder. Mary owns 80%; two other individuals (A and C) own 10% each. Assume that Crescent City Publications is worth 700K. How many policies did they have and for what amounts?

Six policies are needed. Mary owns a $35,000 policy on the life of A and a similar policy on the life of C each. A and C each have a $280,000 policy on the life of Mary and $35,000 policies on each other's lives. Upon the death of any partner, the insurance would provide funds for each of the surviving partners to buy out the deceased partner's interest from his or her estate in equal shares.
If Mary wished only to keep her 80% interest upon the death of A or C, she would not need policies on their lives and wouldn't incurr the premium expense. If A or C died, the survivor would buy out the other's shares and become a 20% owner.

## 36. Determine the basis in Robert’s Brown Foreman stock.

His basis in Brown Forman is $3,600 or $18 per split share. Based on 100 shares priced at the average between the high and low prices on the day of his Aunt’s death.

## 37. If Robert were to sell the Brown Foreman stock today, what would be the income tax consequences?

$6,400 in long term capital gain (all inherited stock is long term), taxed at 15%= $960 in taxes due.

## 38. How much qualified residence interest can the Trenticostas deduct for income tax in 2007?

The mortgage interest on both the house and the condo is qualified residence interest. On the tax return the Trenticostas will file in 2007 for tax year 2006, the mortgage interest deduction for the personal residence is $15,920.98. This is equal to 9 monthly payments of $1,957.80 = $17,620.20 minus the reduction in the loan balance of (350,000 x 0.80) - 278,300.78 = $1,699.22.
For the condo, 12 monthly payments of principle and interest in 2006 totals $25,886.16. The current loan balance is $215,254.14. One year ago, after making 18 payments, the loan balance was 225,673.49 (N=18, i=7/12, PV=240,000, PMT=(2157.18), compute FV). Therefore, the principle reduction in 2006 was $10,419.35. Subtract from total payments of $25,886.15 yields 15,466.81 in qualified interest on the condo.
The Trenticostas can deduct $31,387.79 in qualified residence interest on their 2006 tax return.

## 39. By using the dividend growth model, determine the intrinsic value per share for each of the following stocks.

The intrinsic value of a security whose dividend is growing at a constant rate is V = D1/k-g, where D1 is the annual dividend expected in the next year, k is the required rate of return, and g is the annual rate of growth in dividends. For the Trenticosta's stocks, k = 0.09 and g = 0.03. Plugging these values and the dividend yield for each stock into the formula results in the following:
| | Current $/share | Dividend in period 1 | 'Intrinsic value' |
| Big | $14.50 | $.597 | $9.96 |
| Oil | $15.15 | $.546 | $9.10 |
| Auto | $16.14 | $.499 | $8.31 |

## 40. Since Mary has been diagnosed with cancer, she has been distracted by her health concerns and forgot to make her IRA contribution for 2006. Can she still make a 2006 contribution in 2007?

Yes. She can do so until April 15th 2007.

## 41. This is a three-part question.
### 41a: What is the probability of a positive return for Big Company?

The probability of a return greater than zero for Big Company is 84%.
The mean return for Big Company is 12.5% and the standard deviation is also 12.5%. One standard deviation above and below the mean covers 68% of all returns in a normal distribution. At one standard deviation below the mean, the return is 0. Therefore, 34% of all returns lie between 0 and 12.5%, and 50% of all returns lie above 12.5%. Adding 50% and 34% equals 84%. (The actual percentage is 84.13%)
For this answer and parts b and c, a normal distribution of returns is assumed. In the real world, returns are skewed toward the "tails" of the curve. This is called leptokurtosis. It means that any prediction about the probability of future returns can't be taken as exact.

### 41b: What is the probability of a return above 30% for Auto Company?

There is a 2.5% probability of Auto Company earning 30% or more per year.
The mean return is 10% and one standard deviation is also 10%. A 30% return is therefore two standard deviation above the mean. Two standard deviations cover 95% of all returns. Divide the remaining 5% in half to obtain the percentage of all returns above 30%. (The actual figure is 2.27%).

### 41c: What is the probability of a return between 15% and 33% for Small Company?

There is a 34% probability that Small Company will earn between 15% and 33%.
The mean return for Small Company is 15% and the standard deviation is 18%. Returns of 15% to 33% are within one standard deviation above the mean. One standard deviation encompasses 68% of all returns above and below the mean, so 34% of all returns are within one standard deviation above the mean. (The actual percentage is 34.13%)

## 42. How much will be invested in Big Company and Small Company at a 40/60 ratio for Mary’s brokerage account after taxes and rebalancing?

Adjusting to purchase whole shares at current market values, Mary will own 3140 shares of Big Company worth $45530, and 5539 shares of Small Company worth $68296, with a cash balance of $8. Using whole numbers, the calculation is as follows:

## 43. What is the expected return for the new portfolio?

The expected return for the reallocated portfolio is 14%.
Take the return for Small Company (15%) times its weight of 60%, and the return for Big Company (12.5%) times its weight of 40%. Added together they equal 14%.

## 44. What is the standard deviation of the new portfolio?

The standard deviation of this two-asset portfolio is 13.19%.
The formula for the standard deviation of a two-asset portfolio is:
    $\sigma _{p}={\sqrt {w_{1}^{2}\sigma _{1}^{2}+w_{2}^{2}\sigma _{2}^{2}+2\,w_{1}\,w_{2}\rho _{12}\sigma _{1}\sigma _{2}}}$
where $w_{1}$ and $w_{2}$ are the weights of asset 1 and 2, $s_{1}$ and $s_{2}$ are the standard deviations of the assets, and $\rho _{ij}$ is the correlation coefficient between the returns of assets 1 and 2.
Plugging in values for Big Company as asset 1 and Small Company as asset 2:
.16 x .0156 + .36 x .0324 + 2 x .4 x .6 x 0.3 x .125 x .18 = 0.0174, the square root of which is .1319.

## 45. What is the tax treatment for the Condo income and expenses for 2006?

Because it was rented less than 15 days, the condo is a vacation property for which the rental income is excluded from income and the interest and taxes are itemized deductions. Depreciation and utilities are not deductible.

## 46. What part of Mary’s surgery expenses of $3200 is not covered by insurance?

Mary will pay $1440 out of pocket.
| Loss | $3200 |
| Deductible | (1000) |
| Covered loss | 2200 |
| Less 20% | (440) |
| Insurance payment | 1760 |
| Patient responsibility | $1440 |

## 47. Crescent City Publication had earnings of $54,000 last year. How does the capitalized earning approach method of valuation compare with Mary’s guess of what Crescent City is worth? Use the Treticosta required rate of return.

Assuming no growth in earnings, the company’s value is $54,000/.09 = 600,000. Mary’s 80 percent share would be worth $480,000 (not including any control premium) as compared to the balance sheet value of $320,000.
If earnings are assumed to grow at the rate of inflation, the value is $54,000/.09 - .04 = $1,080,000, or $864,000 for Mary’s share.

## 48. Based on the earnings of $54,000, how does Mary’s guess of the value of Crescent City compare with using the PE Ratio of similar companies to determine the value of Crescent City? (Assume the PE ratio for similar companies is 12:1)

A PE ratio of 12:1 means the price (value) of the security (company) is 12 times earnings. Crescent City's earnings of $54,000 x 12 = $648,000. Mary's 80% interest would be worth $518,400--considerably more than the balance sheet value.

## 49. If Mary sold the ski condo and all the contents in 2007 for $320000. How much tax would she pay from this sale? (Assume a real estate commission of 6%

Mary will experience a loss of $17,600 on the sale of her condo and contents. This is a personal loss that is not deductible.
$300,000 (purchase price) + $18,400 (restoration cost) = $318,400 adjusted basis
$320,000 (sales cost) X .06 (commission rate) = $19,200 commission
$320,000 -$318,400 - $19,200 = $17,600 loss
Since the condo was rented less than 15 days a year, it’s considered personal, not investment, property. The transaction is a sale of the condo "and contents". The furniture is not a capital improvement to the condo, but the furniture was sold along with the condo and the furniture is a capital asset. Mary is selling improved real property with a basis of $311,400 and personal property (the furniture) with a basis of $7000 together in one transaction. The total basis of all property being sold--real and personal--is $318,400. The proceeds of all the property being sold is $300,800 net of the commission. The loss is $17,600.
== Use the following information to answer questions 50-55
Mary is concerned about the price of Big Company. During July 2007 she decides to buy a put option to protect her position in the stock. The price of the stock has dropped to $14. Per share. The put option has an expiration of January 2008, an exercise price of $13 and a premium of $2.00.

## 50. How many option contacts should she buy to fully hedge her long position in Big Company stock?

A put option contract covers 100 shares. To hedge all 2000 shares that Mary owns, she should buy 20 contracts (2000/100=20)

## 51. Mary fully hedges her position with the above option. On Dec, 31, 2007, the price of the stock has dropped $10
### a. What is her gain or loss on the option contract?

The gain is the difference between the strike price ($13) and the market price of the stock ($10) less the cost of the put.
((13-10)- 2) x 2000 = $4000

### b. How much gain or loss does she have to recognize for this put on her 2007 form 1040?

Since Mary did not exercise the option, there will be no tax consequences in 2007.

### c. How much is the gain or loss on her long position in Big Company for the time she has held this option?

Big Company stock was worth $14 when Mary bought the option and $10 at the end of the year. Mary's unrealized loss for the period is $8000.

### d. Based on your analysis, has Mary done an effective job of hedging Big company stock? If not, why? What alternative strategy might you suggest? Describe the pros. And cons of the put and your suggestions, if applicable.

She only hedged 25% of her loss. Not very effective. She might have been able to buy a put at a higher strike price, but probably only at a higher cost. She could have shorted a call on Big Company. She could have sold short the stock itself (shorting against the box) if there was an uptick in the stock. Whether these strategies would have worked better depends on the prices and terms she could get.

## 52. In January 2008, the option expires unexercised, the price of Big. Co. has increased to $15 per share. How should Mary treat this on her 2008 individual tax return from 1040?

Mary has a short term capital loss of $4000 computed as follows: $2 (premium) x 2000 (shares) = $4000.
Mary can write off $3000 against ordinary income even if she has no offsetting capital gains. She can write off the remaining $1000 against any ST or LT capital gain she incurrs in 2007, or carry it forward.

## 53. Because the price of Big Co. stock has rebounded and the entire market is doing well, Mary believes that the price of Big Co. will continue to increase above the $14.5 lever (current price). How do you advise her as her financial planner?

Mary can buy a short put, a long call, or simply hold the stock as a long position. Given that Mary and Robert describe themselves as only moderately aggressive investors, I would advise them to avoid speculating in the options market and just hold the stock.

## 54. After your discussion with her, Mary decided to enter into a future contract on S&P 500 to take advantage of the rising market. The contract expires January 2009
### a. Should she buy or sell contract?

If Mary believes the market will rise, she should buy the futures contract.

### b. The S&P 500 contract has had the following price:

Upon entering into contract--$100 At 12/31/07--$110 Expiration--$125

### How much gain or loss should Mary report for tax purposes in 2006 and 2007?

Since Mary did not own the futures contract in 2006 she has no gain or loss to report for tax year 2006. For 2007, however, under IRS code section 1256, Mary must "mark to market" any regulated futures contract she holds at the end of 2007. The cash value of an S&P 500 contract is 250 times the market price. Mary's contract had a value of $25,000 when entered into, and a value of $27,500 at 12/31/2007. Mary must report a gain of $2500 on the contract on her 2007 return.

### What is the nature of this gain or loss?

The gain on a section 1256 asset is 60% long term and 40% short term capital gain regardless of when the futures contract was actually purchased. See IRS publication 550 p.40.

## 55. What are two methods Mary could use to value her option against the market values?

The two options Mary could use to value her option are (1) the intrinsic value, which is the difference between the strike price of the option and the market price of the underlying security, and (2) the Black-Scholes pricing model.

## 56. If Mary and Robert died, how should their beneficiary treat the inherited IRAs?

The answer depends on when they died.
Each spouse is the beneficiary of the other's IRA. A spouse who inherits an IRA can make it his or her own and defer distributions to his or her RBD.
If they both die simultaneously, their IRAs go to their estates and the 5 year rule applies.
If they die after distributions have begun, their heirs have two options: 1) continue taking distributions on the same schedule as the orginial owner or 2) stretch the distributions over their own life expectancy.
IRA assets do not receive a basis adjustment at the death of the owner, and when distributions are taken, the income will be Income in Respect of a Decedent to the recipient.