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fund and health care benefits yet to be paid, and to the government in the form of taxes deferred. In the past two decades accountants have increasingly moved toward quantifying these liabilities and showing them as long-term liabilities. Leases Firms often choose to lease long-term assets rather than buy them. Lease payments create the same kind of obligation that interest payments on debt create, and they must be viewed in a similar light. If a firm is allowed to lease a significant portion of its assets and keep it off its financial statements, a perusal of the statements will give a very misleading view of the company's financial strength. Consequently, accounting rules have been devised to force firms to reveal the extent of their lease obligations on their books. There are two ways of accounting for leases. In an operating lease, the lessor (or owner) transfers only the right to use the property to the lessee. At the end of the lease period, the lessee returns the property to the

to force firms to reveal the extent of their lease obligations on their books. There are two ways of accounting for leases. In an operating lease, the lessor (or owner) transfers only the right to use the property to the lessee. At the end of the lease period, the lessee returns the property to the lessor. Since the lessee does not assume the risk of ownership, the lease expense is treated as an operating expense in the income statement and the lease does not affect the balance sheet. In a capital lease, the lessee assumes some of the risks of ownership and enjoys some of the benefits. Consequently, the lease, when signed, is recognized both as an asset and as a liability (for the lease payments) on the balance sheet. The firm gets to claim depreciation each year on the asset and also deducts the interest expense component of the lease payment each year. In general, capital leases recognize expenses sooner than equivalent operating leases. Since firms prefer to keep leases off the boo

ments) on the balance sheet. The firm gets to claim depreciation each year on the asset and also deducts the interest expense component of the lease payment each year. In general, capital leases recognize expenses sooner than equivalent operating leases. Since firms prefer to keep leases off the books and sometimes to defer expenses, they have a strong incentive to report all leases as operating leases. Consequently the Financial Accounting Standards Board has ruled that a lease should be treated as a capital lease if it meets any one of the following four conditions: 1. The lease life exceeds 75 percent of the life of the asset. 2. There is a transfer of ownership to the lessee at the end of the lease term. 3. There is an option to purchase the asset at a bargain price at the end of the lease term. 4. The present value of the lease payments, discounted at an appropriate discount rate, exceeds 90 percent of the fair market value of the asset. The lessor uses the same criteria for deter

f the lease term. 3. There is an option to purchase the asset at a bargain price at the end of the lease term. 4. The present value of the lease payments, discounted at an appropriate discount rate, exceeds 90 percent of the fair market value of the asset. The lessor uses the same criteria for determining whether the lease is a capital or operating lease and accounts for it accordingly. If it is a capital lease, the lessor records the present value of future cash flows as revenue and recognizes expenses. The lease receivable is also shown as an asset on the balance sheet, and the interest revenue is recognized over the term of the lease as paid. From a tax standpoint, the lessor can claim the tax benefits of the leased asset only if it is an operating lease, though the tax code uses slightly different criteria for determining whether the lease is an operating lease.4 Employee Benefits Employers can provide pension and health care benefits to their employees. In many cases, the obligati

e tax benefits of the leased asset only if it is an operating lease, though the tax code uses slightly different criteria for determining whether the lease is an operating lease.4 Employee Benefits Employers can provide pension and health care benefits to their employees. In many cases, the obligations created by these benefits are extensive, and a failure by the firm to adequately fund these obligations needs to be revealed in financial statements. Pension Plans In a pension plan, the firm agrees to provide certain benefits to its employees, either by specifying a defined contribution (wherein a fixed contribution is made to the plan each year by the employer, without any promises as to the benefits that will be delivered in the plan) or a defined benefit (wherein the employer promises to pay a certain benefit to the employee). In the latter case, the employer has to put sufficient money into the plan each period to meet the defined benefits. Under a defined contribution plan, the fir

benefits that will be delivered in the plan) or a defined benefit (wherein the employer promises to pay a certain benefit to the employee). In the latter case, the employer has to put sufficient money into the plan each period to meet the defined benefits. Under a defined contribution plan, the firm meets its obligation once it has made the prespecified contribution to the plan. Under a defined benefit plan, the firm's obligations are much more difficult to estimate, since they will be determined by a number of variables, including the benefits that employees are entitled to, the prior contributions made by the employer and the returns they have earned, and the rate of return that the employer expects to make on current contributions. As these variables change, the value of the pension fund assets can be greater than, less than, or equal to pension fund liabilities (which include the present value of promised benefits). A pension fund whose assets exceed its liabilities is an overfund

yer expects to make on current contributions. As these variables change, the value of the pension fund assets can be greater than, less than, or equal to pension fund liabilities (which include the present value of promised benefits). A pension fund whose assets exceed its liabilities is an overfunded plan, whereas one whose assets are less than its liabilities is an underfunded plan, and disclosures to that effect have to be included in financial statements, generally in the footnotes. When a pension fund is overfunded, the firm has several options. It can withdraw the excess assets from the fund, it can discontinue contributions to the plan, or it can continue to make contributions on the assumption that the overfunding is a transitory phenomenon that could well disappear by the next period. When a fund is underfunded, the firm has a liability, though accounting standards require that firms reveal only the excess of accumulated pension fund liability5 over pension fund assets on the

assumption that the overfunding is a transitory phenomenon that could well disappear by the next period. When a fund is underfunded, the firm has a liability, though accounting standards require that firms reveal only the excess of accumulated pension fund liability5 over pension fund assets on the balance sheet. Health Care Benefits A firm can provide health care benefits in either of two ways—by making a fixed contribution to a health care plan without promising specific benefits (analogous to a defined contribution plan) or by promising specific health benefits and setting aside the funds to provide these benefits (analogous to a defined benefit plan). The accounting for health care benefits is very similar to the accounting for pension obligations. Deferred Taxes Firms often use different methods of accounting for tax and financial reporting purposes, leading to a question of how tax liabilities should be reported. Since accelerated depreciation and favorable inventory valuation me

its is very similar to the accounting for pension obligations. Deferred Taxes Firms often use different methods of accounting for tax and financial reporting purposes, leading to a question of how tax liabilities should be reported. Since accelerated depreciation and favorable inventory valuation methods for tax accounting purposes lead to a deferral of taxes, the taxes on the income reported in the financial statements will generally be much greater than the actual tax paid. The same principles of matching expenses to income that underlie accrual accounting suggest that the deferred income tax be recognized in the financial statements. Thus a company that pays taxes of $55,000 on its taxable income based on its tax accounting, and that would have paid taxes of $75,000 on the income reported in its financial statements, will be forced to recognize the difference ($20,000) as deferred taxes. Since the deferred taxes will be paid in later years, they will be recognized when paid. It is w

e income based on its tax accounting, and that would have paid taxes of $75,000 on the income reported in its financial statements, will be forced to recognize the difference ($20,000) as deferred taxes. Since the deferred taxes will be paid in later years, they will be recognized when paid. It is worth noting that companies that actually pay more in taxes than the taxes they report in the financial statements create an asset called a deferred tax asset. This reflects the fact that the firm's earnings in future periods will be greater as the firm is given credit for the deferred taxes. The question of whether the deferred tax liability is really a liability is an interesting one. On one hand, the firm does not owe the amount categorized as deferred taxes to any entity, and treating it as a liability makes the firm look more risky than it really is. On the other hand, the firm will eventually have to pay its deferred taxes, and treating the amount as a liability seems to be the conserva

, the firm does not owe the amount categorized as deferred taxes to any entity, and treating it as a liability makes the firm look more risky than it really is. On the other hand, the firm will eventually have to pay its deferred taxes, and treating the amount as a liability seems to be the conservative thing to do. Preferred Stock When a company issues preferred stock, it generally creates an obligation to pay a fixed dividend on the stock. Accounting rules have conventionally not viewed preferred stock as debt because the failure to meet preferred dividends does not result in bankruptcy. At the same time, the fact the preferred dividends are cumulative makes them more onerous than common equity. Thus, preferred stock is a hybrid security, sharing some characteristics with equity and some with debt. Preferred stock is valued on the balance sheet at its original issue price, with any cumulated unpaid dividends added on. Convertible preferred stock is treated similarly, but it is treate

quity. Thus, preferred stock is a hybrid security, sharing some characteristics with equity and some with debt. Preferred stock is valued on the balance sheet at its original issue price, with any cumulated unpaid dividends added on. Convertible preferred stock is treated similarly, but it is treated as equity on conversion. Equity The accounting measure of equity is a historical cost measure. The value of equity shown on the balance sheet reflects the original proceeds received by the firm when it issued the equity, augmented by any earnings made since (or reduced by losses, if any) and reduced by any dividends paid out during the period. While these three items go into what we can call the book value of equity, three other points need to be made about this estimate: 1. When companies buy back stock for short periods, with the intent of reissuing the stock or using it to cover option exercises, they are allowed to show the repurchased stock as treasury stock, which reduces the book va

book value of equity, three other points need to be made about this estimate: 1. When companies buy back stock for short periods, with the intent of reissuing the stock or using it to cover option exercises, they are allowed to show the repurchased stock as treasury stock, which reduces the book value of equity. Firms are not allowed to keep treasury stock on the books for extended periods, and have to reduce their book value of equity by the value of repurchased stock in the case of stock buybacks. Since these buybacks occur at the current market price, they can result in significant reductions in the book value of equity. 2. Firms that have significant losses over extended periods or carry out massive stock buybacks can end up with negative book values of equity. 3. Relating back to the discussion of marketable securities, any unrealized gain or loss in marketable securities that are classified as available for sale is shown as an increase or a decrease in the book value of equity i

y out massive stock buybacks can end up with negative book values of equity. 3. Relating back to the discussion of marketable securities, any unrealized gain or loss in marketable securities that are classified as available for sale is shown as an increase or a decrease in the book value of equity in the balance sheet. As part of their financial statements, firms provide a summary of changes in shareholders' equity during the period, where all the changes that occurred to the accounting measure of equity value are summarized. As a final point on equity, accounting rules still seem to consider preferred stock, with its fixed dividend, as equity or near-equity, largely because of the fact that preferred dividends can be deferred or cumulated without the risk of default. To the extent that there can still be a loss of control in the firm (as opposed to bankruptcy), we have already argued that preferred stock shares almost as many characteristics with unsecured debt as it does with equity.

preferred dividends can be deferred or cumulated without the risk of default. To the extent that there can still be a loss of control in the firm (as opposed to bankruptcy), we have already argued that preferred stock shares almost as many characteristics with unsecured debt as it does with equity. ILLUSTRATION 3.2: Measuring Liabilities and Equity in Boeing and the Home Depot in 1998 The following table summarizes the accounting estimates of liabilities and equity at Boeing and the Home Depot for the 1998 financial year in millions of dollars: Boeing Home Depot Accounts payable and other liabilities $10,733 $ 1,586 Accrued salaries and expenses 0 $ 1,010 Advances in excess of costs $ 1,251 $ 0 Taxes payable $ 569 $ 247 Short-term debt and current long-term debt $ 869 $ 14 Total current liabilities $13,422 $ 2,857 Accrued health care benefits $ 4,831 0 Other long-term liabilities 0 $ 210 Deferred income taxes 0 $ 83 Long-term debt $ 6,103 $ 1,566 Minority interests $ 9 $ 0 Shareholder

$ 0 Taxes payable $ 569 $ 247 Short-term debt and current long-term debt $ 869 $ 14 Total current liabilities $13,422 $ 2,857 Accrued health care benefits $ 4,831 0 Other long-term liabilities 0 $ 210 Deferred income taxes 0 $ 83 Long-term debt $ 6,103 $ 1,566 Minority interests $ 9 $ 0 Shareholders' Equity Par value $ 5,059 $ 37 Additional paid-in capital $ 0 $ 2,891 Retained earnings $ 7,257 $ 5,812 Total shareholders' equity $12,316 $ 8,740 Total liabilities $36,672 $13,465 The most significant difference between the companies is the accrued health care liability shown by Boeing, representing the present value of expected health care obligations promised to employees in excess of health care assets. The shareholders' equity for both firms represents the book value of equity and is significantly different from the market value of equity. The follwing table summarizes the difference at the end of 1998 (in millions of dollars): Boeing Home Depot Book value of equity $12,316 $ 8,740 Ma

care assets. The shareholders' equity for both firms represents the book value of equity and is significantly different from the market value of equity. The follwing table summarizes the difference at the end of 1998 (in millions of dollars): Boeing Home Depot Book value of equity $12,316 $ 8,740 Market value of equity $32,595 $85,668 One final point needs to be made about the Home Depot's liabilities. The Home Depot has substantial operating leases. Because these leases are treated as operating expenses, they do not show up in the balance sheet. Since they represent commitments to make payments in the future, we would argue that operating leases should be capitalized and treated as part of the liabilities of the firm. How best to do this is considered in Chapter 9. MEASURING EARNINGS AND PROFITABILITY How profitable is a firm? What did it earn on the assets that it invested in? These are fundamental questions we would like financial statements to answer. Accountants use the income sta

the liabilities of the firm. How best to do this is considered in Chapter 9. MEASURING EARNINGS AND PROFITABILITY How profitable is a firm? What did it earn on the assets that it invested in? These are fundamental questions we would like financial statements to answer. Accountants use the income statement to provide information about a firm's operating activities over a specific time period. The income statement is designed to measure the earnings from assets in place. This section examines the principles underlying earnings and return measurement in accounting, and the way they are put into practice. Accounting Principles Underlying Measurement of Earnings and Profitability Two primary principles underlie the measurement of accounting earnings and profitability. The first is the principle of accrual accounting. In accrual accounting, the revenue from selling a good or service is recognized in the period in which the good is sold or the service is performed (in whole or substantially).

ciples underlie the measurement of accounting earnings and profitability. The first is the principle of accrual accounting. In accrual accounting, the revenue from selling a good or service is recognized in the period in which the good is sold or the service is performed (in whole or substantially). A corresponding effort is made on the expense side to match expenses to revenues.6 This is in contrast to a cash-based system of accounting, where revenues are recognized when payment is received and expenses are recorded when paid. The second principle is the categorization of expenses into operating, financing, and capital expenses. Operating expenses are expenses that, at least in theory, provide benefits only for the current period; the cost of labor and materials expended to create products that are sold in the current period is a good example. Financing expenses are expenses arising from the nonequity financing used to raise capital for the business; the most common example is interes

ide benefits only for the current period; the cost of labor and materials expended to create products that are sold in the current period is a good example. Financing expenses are expenses arising from the nonequity financing used to raise capital for the business; the most common example is interest expenses. Capital expenses are expenses that are expected to generate benefits over multiple periods; for instance, the cost of buying land and buildings is treated as a capital expense. Operating expenses are subtracted from revenues in the current period to arrive at a measure of operating earnings of the firm. Financing expenses are subtracted from operating earnings to estimate earnings to equity investors or net income. Capital expenses are written off over their useful lives (in terms of generating benefits) as depreciation or amortization. Measuring Accounting Earnings and Profitability Since income can be generated from a number of different sources, generally accepted accounting p

quity investors or net income. Capital expenses are written off over their useful lives (in terms of generating benefits) as depreciation or amortization. Measuring Accounting Earnings and Profitability Since income can be generated from a number of different sources, generally accepted accounting principles (GAAP) require that income statements be classified into four sections—income from continuing operations, income from discontinued operations, extraordinary gains or losses, and adjustments for changes in accounting principles. Generally accepted accounting principles require the recognition of revenues when the service for which the firm is getting paid has been performed in full or substantially, and the firm has received in return either cash or a receivable that is both observable and measurable. Expenses linked directly to the production of revenues (like labor and materials) are recognized in the same period in which revenues are recognized. Any expenses that are not directly

stantially, and the firm has received in return either cash or a receivable that is both observable and measurable. Expenses linked directly to the production of revenues (like labor and materials) are recognized in the same period in which revenues are recognized. Any expenses that are not directly linked to the production of revenues are recognized in the period in which the firm consumes the services. Accounting has resolved one inconsistency that bedeviled it for years, with a change in the way it treats employee options. Unlike the old rules, these option grants were not treated as expenses when granted but only when exercised, the new rules require that employee options be valued and expensed, when granted (with allowances for amortization over periods). Since employee options are part of compensation, which is an operating expense, the new rules make more sense. While accrual accounting is straightforward in firms that produce goods and sell them, there are special cases where a

xpensed, when granted (with allowances for amortization over periods). Since employee options are part of compensation, which is an operating expense, the new rules make more sense. While accrual accounting is straightforward in firms that produce goods and sell them, there are special cases where accrual accounting can be complicated by the nature of the product or service being offered. For instance, firms that enter into long-term contracts with their customers are allowed to recognize revenue on the basis of the percentage of the contract that is completed. As the revenue is recognized on a percentage-of-completion basis, a corresponding proportion of the expense is also recognized. When there is considerable uncertainty about the capacity of the buyer of a good or service to pay for it, the firm providing the good or service may recognize the income only when it collects portions of the selling price under the installment method. Reverting back to the discussion of the difference

there is considerable uncertainty about the capacity of the buyer of a good or service to pay for it, the firm providing the good or service may recognize the income only when it collects portions of the selling price under the installment method. Reverting back to the discussion of the difference between capital and operating expenses, operating expenses should reflect only those expenses that create revenues in the current period. In practice, however, a number of expenses are classified as operating expenses that do not seem to meet this test. The first is depreciation and amortization. While the notion that capital expenditures should be written off over multiple periods is reasonable, the accounting depreciation that is computed on the original historical cost often bears little resemblance to the actual economic depreciation. The second expense is research and development expenses, which accounting standards classify as operating expenses, but which clearly provide benefits over

the accounting depreciation that is computed on the original historical cost often bears little resemblance to the actual economic depreciation. The second expense is research and development expenses, which accounting standards classify as operating expenses, but which clearly provide benefits over multiple periods. The rationale used for this classification is that the benefits cannot be counted on or easily quantified. Much of financial analysis is built around the expected future earnings of a firm, and many of these forecasts start with the current earnings. It is therefore important to know how much of these earnings comes from the ongoing operations of the firm and how much can be attributed to unusual or extraordinary events that are unlikely to recur on a regular basis. From that standpoint, it is useful that firms categorize expenses into operating and nonrecurring expenses, since it is the earnings prior to extraordinary items that should be used in forecasting. Nonrecurring

ributed to unusual or extraordinary events that are unlikely to recur on a regular basis. From that standpoint, it is useful that firms categorize expenses into operating and nonrecurring expenses, since it is the earnings prior to extraordinary items that should be used in forecasting. Nonrecurring items include: Unusual or infrequent items, such as gains or losses from the divestiture of an asset or division, and write-offs or restructuring costs. Companies sometimes include such items as part of operating expenses. As an example, Boeing in 1997 took a write-off of $1,400 million to adjust the value of assets it acquired in its acquisition of McDonnell Douglas, and it showed this as part of operating expenses. Extraordinary items, which are defined as events that are unusual in nature, infrequent in occurrence, and material in impact. Examples include the accounting gain associated with refinancing high-coupon debt with lower-coupon debt, and gains or losses from marketable securitie

f operating expenses. Extraordinary items, which are defined as events that are unusual in nature, infrequent in occurrence, and material in impact. Examples include the accounting gain associated with refinancing high-coupon debt with lower-coupon debt, and gains or losses from marketable securities that are held by the firm. Losses associated with discontinued operations, which measure both the loss from the phaseout period and any estimated loss on sale of the operations. To qualify, however, the operations have to be separable from the firm. Gains or losses associated with accounting changes, which measure earnings changes created by both accounting changes made voluntarily by the firm (such as a change in inventory valuation) and accounting changes mandated by new accounting standards. ILLUSTRATION 3.3: Measures of Earnings—Boeing and the Home Depot in 1998 The following table summarizes the income statements of Boeing and the Home Depot for the 1998 financial year: Boeing (in $ m

such as a change in inventory valuation) and accounting changes mandated by new accounting standards. ILLUSTRATION 3.3: Measures of Earnings—Boeing and the Home Depot in 1998 The following table summarizes the income statements of Boeing and the Home Depot for the 1998 financial year: Boeing (in $ millions) Home Depot (in $ millons) Sales and other operating revenues $56,154 $30,219 – Operating costs and expenses $51,022 $27,185 – Depreciation $ 1,517 $ 373 – Research and development expenses $ 1,895 $ 0 Operating income $ 1,720 $ 2,661 + Other income (includes interest income) $ 130 $ 30 – Interest expenses $ 453 $ 37 Earnings before taxes $ 1,397 $ 2,654 – Income taxes $ 277 $ 1,040 Net earnings (Loss) $ 1,120 $ 1,614 Boeing's operating income is reduced by the research and development expense, which is treated as an operating expense by accountants. The Home Depot's operating expenses include operating leases. As noted earlier, the treatment of both these items skews earnings, and h

rnings (Loss) $ 1,120 $ 1,614 Boeing's operating income is reduced by the research and development expense, which is treated as an operating expense by accountants. The Home Depot's operating expenses include operating leases. As noted earlier, the treatment of both these items skews earnings, and how best to adjust earnings when such expenses exist is considered in Chapter 9. Measures of Profitability While the income statement allows us to estimate how profitable a firm is in absolute terms, it is just as important that we gauge the profitability of the firm in terms of percentage returns. Two basic ratios measure profitability. One examines the profitability relative to the capital employed to get a rate of return on investment. This can be done either from the viewpoint of just the equity investors or by looking at the entire firm. Another examines profitability relative to sales, by estimating a profit margin. Return on Assets and Return on Capital The return on assets (ROA) of a

ed to get a rate of return on investment. This can be done either from the viewpoint of just the equity investors or by looking at the entire firm. Another examines profitability relative to sales, by estimating a profit margin. Return on Assets and Return on Capital The return on assets (ROA) of a firm measures its operating efficiency in generating profits from its assets, prior to the effects of financing. Return on assets = Earnings before interest and taxes(1 – Tax rate)/Total assets Earnings before interest and taxes (EBIT) is the accounting measure of operating income from the income statement, and total assets refers to the assets as measured using accounting rules—that is, using book value (BV) for most assets. Alternatively, return on assets can be written as: Return on assets = [Net income + Interest expenses(1 – Tax rate)]/Total assets By separating the financing effects from the operating effects, the return on assets provides a cleaner measure of the true return on these

k value (BV) for most assets. Alternatively, return on assets can be written as: Return on assets = [Net income + Interest expenses(1 – Tax rate)]/Total assets By separating the financing effects from the operating effects, the return on assets provides a cleaner measure of the true return on these assets. By dividing by total assets, the return on assets does understate the profitability of firms that have substantial current assets. ROA can also be computed on a pretax basis with no loss of generality, by using the earnings before interest and taxes and not adjusting for taxes: Pretax ROA = Earnings before interest and taxes/Total assets This measure is useful if the firm or division is being evaluated for purchase by an acquirer with a different tax rate. A more useful measure of return relates the operating income to the capital invested in the firm, where capital is defined as the sum of the book value of debt and equity, net of cash. This is the return on invested capital (ROC or

ing evaluated for purchase by an acquirer with a different tax rate. A more useful measure of return relates the operating income to the capital invested in the firm, where capital is defined as the sum of the book value of debt and equity, net of cash. This is the return on invested capital (ROC or ROIC), and provides not only a truer measure of return but one that can be compared to the cost of capital, to measure the quality of a firm's investments. The denominator is generally termed invested capital and measures the book value of operating assets. For both measures, the book value can be measured at the beginning of the period or as an average of beginning and ending values. ILLUSTRATION 3.4: Estimating Return on Capital—Boeing and the Home Depot in 1998 The following table summarizes the after-tax return on assets and return on capital estimates for Boeing and the Home Depot, using both average and beginning measures of capital in 1998: Boeing Home Depot (in $millions) (in $milli

N 3.4: Estimating Return on Capital—Boeing and the Home Depot in 1998 The following table summarizes the after-tax return on assets and return on capital estimates for Boeing and the Home Depot, using both average and beginning measures of capital in 1998: Boeing Home Depot (in $millions) (in $millions) After-tax operating income $ 1,118 $ 1,730 Book value of capital—beginning $19,807 $ 8,525 Book value of capital—ending $19,288 $10,320 Book value of capital—average $19,548 $ 9,423 Return on capital (based on average) 5.72% 18.36% Return on capital (based on beginning) 5.64% 20.29% Boeing had a terrible year, in 1998, in terms of after-tax returns. The Home Depot had a much better year in terms of those same returns. Decomposing Return on Capital The return on capital of a firm can be written as a function of the operating profit margin it has on its sales, and its capital turnover ratio. Thus, a firm can arrive at a high ROC by either increasing its profit margin or utilizing its capi

rms of those same returns. Decomposing Return on Capital The return on capital of a firm can be written as a function of the operating profit margin it has on its sales, and its capital turnover ratio. Thus, a firm can arrive at a high ROC by either increasing its profit margin or utilizing its capital more efficiently to increase sales. There are likely to be competitive constraints and technological constraints on both variables, but a firm still has some freedom within these constraints to choose the mix of profit margin and capital turnover that maximizes its ROC. The return on capital varies widely across firms in different businesses, largely as a consequence of differences in profit margins and capital turnover ratios. mgnroc.xls: This is a dataset on the Web that summarizes the operating margins, turnover ratios, and returns on capital of firms in the United States, classified by industry. Return on Equity While the return on capital measures the profitability of the overall fi

argins and capital turnover ratios. mgnroc.xls: This is a dataset on the Web that summarizes the operating margins, turnover ratios, and returns on capital of firms in the United States, classified by industry. Return on Equity While the return on capital measures the profitability of the overall firm, the return on equity (ROE) examines profitability from the perspective of the equity investor, by relating the equity investor's profits (net profit after taxes and interest expenses) to the book value of the equity investment. Since preferred stockholders have a different type of claim on the firm than do common stockholders, the net income should be estimated after preferred dividends, and the book value should be that of only common equity. Determinants of Noncash ROE Since the ROE is based on earnings after interest payments, it is affected by the financing mix the firm uses to fund its projects. In general, a firm that borrows money to finance projects and that earns a ROC on those

he book value should be that of only common equity. Determinants of Noncash ROE Since the ROE is based on earnings after interest payments, it is affected by the financing mix the firm uses to fund its projects. In general, a firm that borrows money to finance projects and that earns a ROC on those projects that exceeds the after-tax interest rate it pays on its debt will be able to increase its ROE by borrowing. The return on equity, not including cash, can be written as follows:7 where ROC = EBIT(1 – t)/(BV of debt + BV of equity – Cash) D/E = BV of debt/BV of equity i = Interest expense on debt/BV of debt t = Tax rate on ordinary income The second term captures the benefit of financial leverage. ILLUSTRATION 3.5: Return on Equity Computations: Boeing and the Home Depot in 1998 The following table summarizes the return on equity for Boeing and the Home Depot in 1998: Boeing Home Depot Return Ratios (in $millions) (in $millions) Net income $ 1,120 $1,614 Book value of equity—beginning

verage. ILLUSTRATION 3.5: Return on Equity Computations: Boeing and the Home Depot in 1998 The following table summarizes the return on equity for Boeing and the Home Depot in 1998: Boeing Home Depot Return Ratios (in $millions) (in $millions) Net income $ 1,120 $1,614 Book value of equity—beginning $12,953 $7,214 Book value of equity—ending $12,316 $8,740 Book value of equity—average $12,635 $7,977 Return on equity (based on average) 8.86% 20.23% Return on equity (based on beginning) 8.65% 22.37% The results again indicate that Boeing had a substandard year in 1998, while the Home Depot reported healthier returns on equity. The returns on equity can also be estimated by decomposing into the components just specified (using the adjusted beginning-of-the-year numbers): Boeing Home Depot (in $millions) (in $millions) After-tax return on capital 5.82% 16.37% Debt-equity ratio 35.18% 48.37% Book interest rate(1 – Tax rate) 4.22% 4.06% Return on equity 6.38% 22.33% Note that a tax rate of 3

components just specified (using the adjusted beginning-of-the-year numbers): Boeing Home Depot (in $millions) (in $millions) After-tax return on capital 5.82% 16.37% Debt-equity ratio 35.18% 48.37% Book interest rate(1 – Tax rate) 4.22% 4.06% Return on equity 6.38% 22.33% Note that a tax rate of 35% is used on both the return on capital and the book interest rate. This approach results in a return on equity that is different from the one estimated using the net income and the book value of equity. rocroe.xls: This is a dataset on the Web that summarizes the return on capital, debt equity ratios, book interest rates, and returns on equity of firms in the United States, classified by industry. MEASURING RISK How risky are the investments the firm has made over time? How much risk do equity investors in a firm face? These are two more questions that we would like to find the answers to in the course of an investment analysis. Accounting statements do not really claim to measure or quant

y. MEASURING RISK How risky are the investments the firm has made over time? How much risk do equity investors in a firm face? These are two more questions that we would like to find the answers to in the course of an investment analysis. Accounting statements do not really claim to measure or quantify risk in a systematic way, other than to provide footnotes and disclosures where there might be risk embedded in the firm. This section examines some of the ways in which accountants try to assess risk. Accounting Principles Underlying Risk Measurement To the extent that accounting statements and ratios do attempt to measure risk, there seem to be two common themes. The first is that the risk being measured is the risk of default—that is, the risk that a fixed obligation, such as interest or principal due on outstanding debt, will not be met. The broader equity notion of risk, which measures the variance of actual returns around expected returns, does not seem to receive much attention. T

eing measured is the risk of default—that is, the risk that a fixed obligation, such as interest or principal due on outstanding debt, will not be met. The broader equity notion of risk, which measures the variance of actual returns around expected returns, does not seem to receive much attention. Thus, an all-equity-financed firm with positive earnings and few or no fixed obligations will generally emerge as a low-risk firm from an accounting standpoint, in spite of the fact that its earnings are unpredictable. The second theme is that accounting risk measures generally take a static view of risk, by looking at the capacity of a firm at a point in time to meet its obligations. For instance, when ratios are used to assess a firm's risk, the ratios are almost always based on one period's income statement and balance sheet. Accounting Measures of Risk Accounting measures of risk can be broadly categorized into two groups. The first is disclosures about potential obligations or losses in

when ratios are used to assess a firm's risk, the ratios are almost always based on one period's income statement and balance sheet. Accounting Measures of Risk Accounting measures of risk can be broadly categorized into two groups. The first is disclosures about potential obligations or losses in values that show up as footnotes on balance sheets, which are designed to alert potential or current investors to the possibility of significant losses. The second measure is ratios that are designed to measure both liquidity and default risk. Disclosures in Financial Statements In recent years, the disclosures that firms have to make about future obligations have proliferated. Consider, for instance, the case of contingent liabilities. These refer to potential liabilities that will be incurred under certain contingencies, as is the case, for instance, when a firm is the defendant in a lawsuit. The general rule that has been followed is to ignore contingent liabilities that hedge against ris

nce, the case of contingent liabilities. These refer to potential liabilities that will be incurred under certain contingencies, as is the case, for instance, when a firm is the defendant in a lawsuit. The general rule that has been followed is to ignore contingent liabilities that hedge against risk, since the obligations on the contingent claim will be offset by benefits elsewhere.8 In recent periods, however, significant losses borne by firms from supposedly hedged derivatives positions (such as options and futures) have led to FASB requirements that these derivatives be disclosed as part of a financial statement. In fact, pension fund and health care obligations have moved from mere footnotes to actual liabilities for firms. Financial Ratios Financial statements have long been used as the basis for estimating financial ratios that measure profitability, risk, and leverage. Earlier, the section on earnings looked at two of the profitability ratios—return on equity and return on capi

notes to actual liabilities for firms. Financial Ratios Financial statements have long been used as the basis for estimating financial ratios that measure profitability, risk, and leverage. Earlier, the section on earnings looked at two of the profitability ratios—return on equity and return on capital. This section looks at some of the financial ratios that are often used to measure the financial risk in a firm. Short-Term Liquidity Risk Short-term liquidity risk arises primarily from the need to finance current operations. To the extent that the firm has to make payments to its suppliers before it gets paid for the goods and services it provides, there is a cash shortfall that has to be met, usually through short-term borrowing. Though this financing of working capital needs is done routinely in most firms, financial ratios have been devised to keep track of the extent of the firm's exposure to the risk that it will not be able to meet its short-term obligations. The two ratios most

t, usually through short-term borrowing. Though this financing of working capital needs is done routinely in most firms, financial ratios have been devised to keep track of the extent of the firm's exposure to the risk that it will not be able to meet its short-term obligations. The two ratios most frequently used to measure short-term liquidity risk are the current ratio and the quick ratio. Current Ratios The current ratio is the ratio of the firm's current assets (cash, inventory, accounts receivable) to its current liabilities (obligations coming due within the next period). A current ratio below 1, for instance, would indicate that the firm has more obligations coming due in the next year than assets it can expect to turn into cash. That would be an indication of liquidity risk. While traditional analysis suggests that firms maintain a current ratio of 2 or greater, there is a trade-off here between minimizing liquidity risk and tying up more and more cash in net working capital (

ar than assets it can expect to turn into cash. That would be an indication of liquidity risk. While traditional analysis suggests that firms maintain a current ratio of 2 or greater, there is a trade-off here between minimizing liquidity risk and tying up more and more cash in net working capital (Net working capital = Current assets – Current liabilities). In fact, it can be reasonably argued that a very high current ratio is indicative of an unhealthy firm that is having problems reducing its inventory. In recent years firms have worked at reducing their current ratios and managing their net working capital better. Reliance on current ratios has to be tempered by a few concerns. First, the ratio can be easily manipulated by firms around the time of financial reporting dates to give the illusion of safety; second, current assets and current liabilities can change by an equal amount, but the effect on the current ratio will depend on its level before the change.9 Quick or Acid Test Ra

e ratio can be easily manipulated by firms around the time of financial reporting dates to give the illusion of safety; second, current assets and current liabilities can change by an equal amount, but the effect on the current ratio will depend on its level before the change.9 Quick or Acid Test Ratios The quick or acid test ratio is a variant of the current ratio. It distinguishes current assets that can be converted quickly into cash (cash, marketable securities) from those that cannot (inventory, accounts receivable). The exclusion of accounts receivable and inventory is not a hard-and-fast rule. If there is evidence that either can be converted into cash quickly, it can, in fact, be included as part of the quick ratio. Turnover Ratios Turnover ratios measure the efficiency of working capital management by looking at the relationship of accounts receivable and inventory to sales and to the cost of goods sold: These statistics can be interpreted as measuring the speed with which the

luded as part of the quick ratio. Turnover Ratios Turnover ratios measure the efficiency of working capital management by looking at the relationship of accounts receivable and inventory to sales and to the cost of goods sold: These statistics can be interpreted as measuring the speed with which the firm turns accounts receivable into cash or inventory into sales. These ratios are often expressed in terms of the number of days outstanding: A similar pair of statistics can be computed for accounts payable, relative to puchases: Since accounts receivable and inventory are assets, and accounts payable is a liability, these three statistics (standardized in terms of days outstanding) can be combined to get an estimate of how much financing the firm needs to raise to fund working capital needs. The greater the financing period for a firm, the greater is its short-term liquidity risk. wcdata.xls: This is a dataset on the Web that summarizes working capital ratios for firms in the United Stat

ined to get an estimate of how much financing the firm needs to raise to fund working capital needs. The greater the financing period for a firm, the greater is its short-term liquidity risk. wcdata.xls: This is a dataset on the Web that summarizes working capital ratios for firms in the United States, classified by industry. finratio.xls: This spreadsheet allows you to compute the working capital ratios for a firm, based upon financial statement data. Long-Term Solvency and Default Risk Measures of long-term solvency attempt to examine a firm's capacity to meet interest and principal payments in the long term. Clearly, the profitability ratios discussed earlier in the section are a critical component of this analysis. The ratios specifically designed to measure long-term solvency try to relate profitability to the level of debt payments in order to identify the degree of comfort with which the firm can meet these payments. Interest Coverage Ratios The interest coverage ratio measures

component of this analysis. The ratios specifically designed to measure long-term solvency try to relate profitability to the level of debt payments in order to identify the degree of comfort with which the firm can meet these payments. Interest Coverage Ratios The interest coverage ratio measures the capacity of the firm to meet interest payments from predebt, pretax earnings. The higher the interest coverage ratio, the more secure is the firm's capacity to make interest payments from earnings. This argument, however, has to be tempered by the recognition that the amount of earnings before interest and taxes is volatile and can drop significantly if the economy enters a recession. Consequently, two firms can have the same interest coverage ratio but be viewed very differently in terms of risk. The denominator in the interest coverage ratio can be easily extended to cover other fixed obligations such as lease payments. If this is done, the ratio is called a fixed charges coverage rati

ntly, two firms can have the same interest coverage ratio but be viewed very differently in terms of risk. The denominator in the interest coverage ratio can be easily extended to cover other fixed obligations such as lease payments. If this is done, the ratio is called a fixed charges coverage ratio: Finally, this ratio, while stated in terms of earnings, can be restated in terms of cash flows by using earnings before interest, taxes, depreciation, and amortization (EBITDA) in the numerator and cash fixed charges in the denominator. Both interest coverage and fixed charges coverage ratios are open to the criticism that they do not consider capital expenditures, a cash flow that may be discretionary in the very short term, but not in the long term if the firm wants to maintain growth. One way of capturing the extent of this cash flow, relative to operating cash flows, is to compute a ratio of the two: While there are a number of different definitions of cash flows from operations, the

etionary in the very short term, but not in the long term if the firm wants to maintain growth. One way of capturing the extent of this cash flow, relative to operating cash flows, is to compute a ratio of the two: While there are a number of different definitions of cash flows from operations, the most reasonable way of defining it is to measure the cash flows from continuing operations, before interest but after taxes and after meeting working capital needs. covratio.xls: This is a dataset on the Web that summarizes the interest coverage and fixed charges coverage ratios for firms in the United States, classified by industry. ILLUSTRATION 3.6: Interest and Fixed Charges Coverage Ratios: Boeing and the Home Depot in 1998 The following table summarizes interest and fixed charges coverage ratios for Boeing and the Home Depot in 1998: Boeing Home Depot EBIT $1,720 $2,661 Interest expense $ 453 $ 37 Interest coverage ratio 3.80 71.92 EBIT $1,720 $2,661 Operating lease expenses $ 215 $ 290

eing and the Home Depot in 1998 The following table summarizes interest and fixed charges coverage ratios for Boeing and the Home Depot in 1998: Boeing Home Depot EBIT $1,720 $2,661 Interest expense $ 453 $ 37 Interest coverage ratio 3.80 71.92 EBIT $1,720 $2,661 Operating lease expenses $ 215 $ 290 Interest expenses $ 453 $ 37 Fixed charges coverage ratio 2.90 9.02 EBITDA $3,341 $3,034 Cash fixed charges $ 668 $ 327 Cash fixed charges coverage ratio 5.00 9.28 Cash flows from operations $2,161 $1,662 Capital expenditures $1,584 $2,059 Cash flows/Capital expenditures 1.36 0.81 Boeing, based on its operating income in 1998, looks riskier than the Home Depot on both the interest coverage ratio basis and fixed charges coverage ratio basis. On a cash flow basis, however, Boeing does look much better. In fact, when capital expenditures are considered, the Home Depot has a lower ratio. For Boeing, the other consideration is the fact that operating income in 1998 was depressed relative to inco

basis and fixed charges coverage ratio basis. On a cash flow basis, however, Boeing does look much better. In fact, when capital expenditures are considered, the Home Depot has a lower ratio. For Boeing, the other consideration is the fact that operating income in 1998 was depressed relative to income in earlier years, and this does have an impact on the ratios across the board. It might make more sense when computing these ratios to look at the average operating income over time. finratio.xls: This spreadsheet allows you to compute the interest coverage and fixed charges coverage ratios for a firm based on financial statement data. Debt Ratios Interest coverage ratios measure the capacity of the firm to meet interest payments, but do not examine whether it can pay back the principal on outstanding debt. Debt ratios attempt to do this, by relating debt to total capital or to equity: The first ratio measures debt as a proportion of the total capital of the firm and cannot exceed 100 per

f the firm to meet interest payments, but do not examine whether it can pay back the principal on outstanding debt. Debt ratios attempt to do this, by relating debt to total capital or to equity: The first ratio measures debt as a proportion of the total capital of the firm and cannot exceed 100 percent. The second measures debt as a proportion of the book value of equity in the firm and can be easily derived from the first, since: While these ratios presume that capital is raised from only debt and equity, they can be easily adapted to include other sources of financing, such as preferred stock. Although preferred stock is sometimes combined with common stock under the equity label, it is better to keep the two sources of financing separate and to compute the ratio of preferred stock to capital (which will include debt, equity, and preferred stock). There are two close variants of debt ratios. In the first, only long-term debt is used rather than total debt, with the rationale that sh

etter to keep the two sources of financing separate and to compute the ratio of preferred stock to capital (which will include debt, equity, and preferred stock). There are two close variants of debt ratios. In the first, only long-term debt is used rather than total debt, with the rationale that short-term debt is transitory and will not affect the long-term solvency of the firm. Given the ease with which some firms can roll over short-term debt and the willingness of many firms to use short-term financing to fund long-term projects, these variants can provide a misleading picture of the firm's financial leverage risk. The second variant of debt ratios uses market value (MV) instead of book value, primarily to reflect the fact that some firms have a significantly greater capacity to borrow than their book values indicate. Many analysts disavow the use of market value in their calculations, contending that market values, in addition to being difficult to get for debt, are volatile and

value, primarily to reflect the fact that some firms have a significantly greater capacity to borrow than their book values indicate. Many analysts disavow the use of market value in their calculations, contending that market values, in addition to being difficult to get for debt, are volatile and hence unreliable. These contentions are open to debate. It is true that the market value of debt is difficult to get for firms that do not have publicly traded bonds, but the market value of equity not only is easy to obtain, but it also is constantly updated to reflect marketwide and firm-specific changes. Furthermore, using the book value of debt as a proxy for market value in those cases where bonds are not traded does not significantly shift most market value-based debt ratios.10 ILLUSTRATION 3.7: Book Value Debt Ratios and Variants—Boeing and the Home Depot The following table summarizes different estimates of the debt ratio for Boeing and the Home Depot, in 2008, using book values of d

bonds are not traded does not significantly shift most market value-based debt ratios.10 ILLUSTRATION 3.7: Book Value Debt Ratios and Variants—Boeing and the Home Depot The following table summarizes different estimates of the debt ratio for Boeing and the Home Depot, in 2008, using book values of debt and equity for both firms: Boeing Home Depot (in $millions) (in $millions) Long-term debt $ 6,103 $1,566 Short-term debt $ 869 $ 14 Book value of equity $12,316 $8,740 Long-term debt/Equity 49.55% 17.92% Long-term debt/(Long-term debt + Equity) 33.13% 15.20% Debt/Equity 56.61% 18.08% Debt/(Debt + Equity) 36.15% 15.31% In 2008, Boeing has a much higher book value debt ratio, considering either long-term or total debt, than the Home Depot. dbtfund.xls: This is a dataset on the Web that summarizes the book value debt ratios and market value debt ratios for firms in the United States, classified by industry. OTHER ISSUES IN ANALYZING FINANCIAL STATEMENTS There are significant differences in

long-term or total debt, than the Home Depot. dbtfund.xls: This is a dataset on the Web that summarizes the book value debt ratios and market value debt ratios for firms in the United States, classified by industry. OTHER ISSUES IN ANALYZING FINANCIAL STATEMENTS There are significant differences in accounting standards and practices across countries and these differences may color comparisons across companies. Differences in Accounting Standards and Practices Differences in accounting standards across countries affect the measurement of earnings. These differences, however, are not so great as they are made out to be by some analysts, and they cannot explain away radical departures from fundamental principles of valuation. Choi and Levich, in a 1990 survey of accounting standards across developed markets, note that most countries subscribe to basic accounting notions of consistency, realization, and historical cost principles in preparing accounting statements. As countries increasingl

amental principles of valuation. Choi and Levich, in a 1990 survey of accounting standards across developed markets, note that most countries subscribe to basic accounting notions of consistency, realization, and historical cost principles in preparing accounting statements. As countries increasingly move toward international financial reporting standards (IFRS), it is worth noting that IFRS and U.S. GAAP are more similar than dissimilar on many issues. It is true that there are areas of differences that still remain, and we note some of them in Table 3.1. Table 3.1 Key Differences between IFRS and GAAP Most of these differences can be accounted and adjusted for when comparisons are made between companies in the United States and companies in other financial markets. Statistics such as price-earnings ratios, which use stated and unadjusted earnings, can be misleading when accounting standards vary widely across the companies being compared. CONCLUSION Financial statements remain the pr

ween companies in the United States and companies in other financial markets. Statistics such as price-earnings ratios, which use stated and unadjusted earnings, can be misleading when accounting standards vary widely across the companies being compared. CONCLUSION Financial statements remain the primary source of information for most investors and analysts. There are differences, however, between how accounting and financial analysts approach answering a number of key questions about the firm. The first question relates to the nature and the value of the assets owned by a firm. Assets can be categorized into investments already made (assets in place) and investments yet to be made (growth assets); accounting statements provide a substantial amount of historical information about the former and very little about the latter. The focus on the original price of assets in place (book value) in accounting statements can lead to significant differences between the stated value of these asset

ssets); accounting statements provide a substantial amount of historical information about the former and very little about the latter. The focus on the original price of assets in place (book value) in accounting statements can lead to significant differences between the stated value of these assets and their market value. With growth assets, accounting rules result in low or no values for assets generated by internal research. The second issue is the measurement of profitability. The two principles that govern how profits are measured are accrual accounting—in which revenues and expenses are shown in the period in which transactions occur rather than when the cash is received or paid—and the categorization of expenses into operating, financing, and capital expenses. While operating and financing expenses are shown in income statements, capital expenditures are spread over several time periods and take the form of depreciation and amortization. Accounting standards miscategorize opera

he categorization of expenses into operating, financing, and capital expenses. While operating and financing expenses are shown in income statements, capital expenditures are spread over several time periods and take the form of depreciation and amortization. Accounting standards miscategorize operating leases and research and development expenses as operating expenses (when the former should be categorized as financing expenses and the latter as capital expenses). Financial statements also deal with short-term liquidity risk and long-term default risk. While the emphasis in accounting statements is on examining the risk that firms may be unable to make payments that they have committed to make, there is very little focus on risk to equity investors. QUESTIONS AND SHORT PROBLEMS In the problems following, use an equity risk premium of 5.5 percent if none is specified. Coca-Cola's balance sheet for December 1998 is summarized (in millions of dollars) for problems 1 through 9: 1. Conside

ake, there is very little focus on risk to equity investors. QUESTIONS AND SHORT PROBLEMS In the problems following, use an equity risk premium of 5.5 percent if none is specified. Coca-Cola's balance sheet for December 1998 is summarized (in millions of dollars) for problems 1 through 9: 1. Consider the assets on Coca-Cola's balance sheet and answer the following questions: a. Which assets are likely to be assessed closest to market value? Explain. b. Coca-Cola has net fixed assets of $3,669 million. Can you estimate how much Coca-Cola paid for these assets? Is there any way to know the age of these assets? c. Coca-Cola seems to have far more invested in current assets than in fixed assets. Is this significant? Explain. d. In the early 1980s, Coca-Cola sold off its bottling operations, and the bottlers became independent companies. How would this action have impacted the assets on Coca-Cola's balance sheet? (The manufacturing plants are most likely to be part of the bottling operation

Is this significant? Explain. d. In the early 1980s, Coca-Cola sold off its bottling operations, and the bottlers became independent companies. How would this action have impacted the assets on Coca-Cola's balance sheet? (The manufacturing plants are most likely to be part of the bottling operations.) 2. Examine the liabilities on Coca-Cola's balance sheet. a. How much interest-bearing debt does Coca-Cola have outstanding? (You can assume that other short-term liabilities represent sundry payables, and other long-term liabilities represent health care and pension obligations.) b. How much did Coca-Cola obtain in equity capital when it issued stock originally to the financial markets? c. Is there any significance to the fact that the retained earnings amount is much larger than the original paid-in capital? d. The market value of Coca-Cola's equity is $140 billion. What is the book value of equity in Coca-Cola? Why is there such a large difference between the market value of equity and

there any significance to the fact that the retained earnings amount is much larger than the original paid-in capital? d. The market value of Coca-Cola's equity is $140 billion. What is the book value of equity in Coca-Cola? Why is there such a large difference between the market value of equity and the book value of equity? 3. Coca-Cola's most valuable asset is its brand name. Where in the balance sheet do you see its value? Is there any way to adjust the balance sheet to reflect the value of this asset? 4. Assume that you have been asked to analyze Coca-Cola's working capital management. a. Estimate the net working capital and noncash working capital for Coca-Cola. b. Estimate the firm's current ratio. c. Estimate the firm's quick ratio. d. Would you draw any conclusions about the riskiness of Coca-Cola as a firm by looking at these numbers? Why or why not? Coca-Cola's income statements for 1997 and 1998 are summarized (in millions of dollars) for problems 5 through 9: 1997 1998 Net

urrent ratio. c. Estimate the firm's quick ratio. d. Would you draw any conclusions about the riskiness of Coca-Cola as a firm by looking at these numbers? Why or why not? Coca-Cola's income statements for 1997 and 1998 are summarized (in millions of dollars) for problems 5 through 9: 1997 1998 Net revenues $18,868 $18,813 Cost of goods sold 6,015 5,562 Selling, general, and administrative expenses 7,852 8,284 Earnings before interest and taxes 5,001 4,967 Interest expenses 258 277 Nonoperating gains 1,312 508 Income tax expenses 1,926 1,665 Net income 4,129 3,533 Dividends 1,387 1,480 The following questions relate to Coca-Cola's income statements. 5. How much operating income did Coca-Cola earn, before taxes, in 1998? How does this compare to how much Coca-Cola earned in 1997? What are the reasons for the difference? 6. The biggest expense for Coca-Cola is advertising, which is part of the selling, generals and administrative (G&A) expenses. A large portion of these expenses is desig

earn, before taxes, in 1998? How does this compare to how much Coca-Cola earned in 1997? What are the reasons for the difference? 6. The biggest expense for Coca-Cola is advertising, which is part of the selling, generals and administrative (G&A) expenses. A large portion of these expenses is designed to build up Coca-Cola's brand name. Should advertising expenses be treated as operating expenses or are they really capital expenses? If they are to be treated as capital expenses, how would you capitalize them? (Use the capitalization of R&D as a guide.) 7. What effective tax rate did Coca-Cola have in 1998? How does it compare with what the company paid in 1997 as an effective tax rate? What might account for the difference? 8. You have been asked to assess the profitability of Coca-Cola as a firm. To that end, estimate the pretax operating and net margins in 1997 and 1998 for the firm. Are there any conclusions you would draw from the comparisons across the two years? 9. The book valu

might account for the difference? 8. You have been asked to assess the profitability of Coca-Cola as a firm. To that end, estimate the pretax operating and net margins in 1997 and 1998 for the firm. Are there any conclusions you would draw from the comparisons across the two years? 9. The book value of equity at Coca-Cola in 1997 was $7,274 million. The book value of interest-bearing debt was $3,875 million. Estimate: a. The return on equity (beginning of the year) in 1998. b. The pretax return on capital (beginning of the year) in 1998. c. The after-tax return on capital (beginning of the year) in 1998, using the effective tax rate in 1998. 10. SeeSaw Toys reported that it had a book value of equity of $1.5 billion at the end of 1998 and 100 million shares outstanding. During 1999, it bought back 10 million shares at a market price of $40 per share. The firm also reported a net income of $150 million for 1999, and paid dividends of $50 million. Estimate: a. The book value of equity a

of equity of $1.5 billion at the end of 1998 and 100 million shares outstanding. During 1999, it bought back 10 million shares at a market price of $40 per share. The firm also reported a net income of $150 million for 1999, and paid dividends of $50 million. Estimate: a. The book value of equity at the end of 1999. b. The return on equity, using beginning book value of equity. c. The return on equity, using the average book value of equity. 1 Depreciation is treated as an accounting expense. Hence, the use of straight-line depreciation (which is lower than accelerated depreciation in the first few years after an asset is acquired) will result in lower expenses and higher income. 2 Firms have evaded the requirements of consolidation by keeping their share of ownership in other firms below 50 percent. 3 Once an acquisition is complete, the difference between market value and book value for the target firm does not automatically become goodwill. Existing assets can be reappraised first

ve evaded the requirements of consolidation by keeping their share of ownership in other firms below 50 percent. 3 Once an acquisition is complete, the difference between market value and book value for the target firm does not automatically become goodwill. Existing assets can be reappraised first to fair value and the difference becomes goodwill. 4 The requirements for an operating lease in the tax code are: (1) The property can be used by someone other than the lessee at the end of the lease term, (2) the lessee cannot buy the asset using a bargain purchase option, (3) the lessor has at least 20 percent of its capital at risk, (4) the lessor has a positive cash flow from the lease independent of tax benefits, and (5) the lessee does not have an investment in the lease. 5 The accumulated pension fund liability does not take into account the projected benefit obligation, where actuarial estimates of future benefits are made. Consequently, it is much smaller than the total pension liab

dent of tax benefits, and (5) the lessee does not have an investment in the lease. 5 The accumulated pension fund liability does not take into account the projected benefit obligation, where actuarial estimates of future benefits are made. Consequently, it is much smaller than the total pension liabilities. 6 If a cost (such as an administrative cost) cannot easily be linked with particular revenues, it is usually recognized as an expense in the period in which it is consumed. 7 8 This assumes that the hedge is set up competently. It is entirely possible that a hedge, if sloppily set up, can end up costing the firm money. 9 If the current assets and current liabilities increase by an equal amount, the current ratio will go down if it was greater than 1 before the increase, and go up if it was less than 1. 10 Deviations in the market value of equity from book value are likely to be much larger than deviations for debt, and are likely to dominate in most debt ratio calculations. HAPTER 4

mount, the current ratio will go down if it was greater than 1 before the increase, and go up if it was less than 1. 10 Deviations in the market value of equity from book value are likely to be much larger than deviations for debt, and are likely to dominate in most debt ratio calculations. HAPTER 4The Basics of Risk When valuing assets and firms, we need to use discount rates that reflect the riskiness of the cash flows. In particular, the cost of debt has to incorporate a default spread for the default risk in the debt, and the cost of equity has to include a risk premium for equity risk. But how do we measure default and equity risk? More importantly, how do we come up with the default and equity risk premiums? This chapter lays the foundations for analyzing risk in valuation. It presents alternative models for measuring risk and converting these risk measures into acceptable hurdle rates. It begins with a discussion of equity risk and presents the analysis in three steps. In the fi

d equity risk premiums? This chapter lays the foundations for analyzing risk in valuation. It presents alternative models for measuring risk and converting these risk measures into acceptable hurdle rates. It begins with a discussion of equity risk and presents the analysis in three steps. In the first step, risk is defined in statistical terms to be the variance in actual returns around an expected return. The greater this variance, the more risky an investment is perceived to be. The next step, the central one, is to decompose this risk into risk that can be diversified away by investors and risk that cannot. The third step looks at how different risk and return models in finance attempt to measure this nondiversifiable risk. It compares the most widely used model, the capital asset pricing model (CAPM), with other models and explains how and why they diverge in their measures of risk and the implications for the equity risk premium. The final part of this chapter considers default r

o measure this nondiversifiable risk. It compares the most widely used model, the capital asset pricing model (CAPM), with other models and explains how and why they diverge in their measures of risk and the implications for the equity risk premium. The final part of this chapter considers default risk and how it is measured by ratings agencies. By the end of the chapter, we should have a way of estimating the equity risk and default risk for any firm. WHAT IS RISK? Risk, for most of us, refers to the likelihood that in life’s games of chance we will receive an outcome that we will not like. For instance, the risk of driving a car too fast is getting a speeding ticket or, worse still, getting into an accident. Merriam-Webster’s Collegiate Dictionary, in fact, defines the verb to risk as “to expose to hazard or danger.” Thus risk is perceived almost entirely in negative terms. In finance, our definition of risk is both different and broader. Risk, as we see it, refers to the likelihood

g into an accident. Merriam-Webster’s Collegiate Dictionary, in fact, defines the verb to risk as “to expose to hazard or danger.” Thus risk is perceived almost entirely in negative terms. In finance, our definition of risk is both different and broader. Risk, as we see it, refers to the likelihood that we will receive a return on an investment that is different from the return we expect to make. Thus, risk includes not only the bad outcomes (returns that are lower than expected), but also good outcomes (returns that are higher than expected). In fact, we can refer to the former as downside risk and the latter as upside risk, but we consider both when measuring risk. In fact, the spirit of our definition of risk in finance is captured best by the Chinese symbols for risk: Loosely defined, the first symbol is the symbol for “danger,” while the second is the symbol for “opportunity,” making risk a mix of danger and opportunity. It illustrates very clearly the trade-off that every investo

ur definition of risk in finance is captured best by the Chinese symbols for risk: Loosely defined, the first symbol is the symbol for “danger,” while the second is the symbol for “opportunity,” making risk a mix of danger and opportunity. It illustrates very clearly the trade-off that every investor and business has to make—between the higher rewards that come with the opportunity and the higher risk that has to be borne as a consequence of the danger. Much of this chapter can be viewed as an attempt to come up with a model that best measures the danger in any investment, and then attempts to convert this into the opportunity that we would need to compensate for the danger. In finance terms, we term the danger to be “risk” and the opportunity to be “expected return.” What makes the measurement of risk and expected return so challenging is that it can vary depending on whose perspective we adopt. When analyzing the risk of a firm, for instance, we can measure it from the viewpoint of t

, we term the danger to be “risk” and the opportunity to be “expected return.” What makes the measurement of risk and expected return so challenging is that it can vary depending on whose perspective we adopt. When analyzing the risk of a firm, for instance, we can measure it from the viewpoint of the firm’s managers. Alternatively, we can argue that the firm’s equity is owned by its stockholders, and that it is their perspective on risk that should matter. A firm’s stockholders, many of whom hold the stock as one investment in a larger portfolio, might perceive the risk in the firm very differently from the firm’s managers, who might have the bulk of their capital, human and financial, invested in the firm. We argue that risk in an investment has to be perceived through the eyes of investors in the firm. Since firms often have thousands of investors, often with very different perspectives, it can be asserted that risk has to be measured from the perspective of not just any investor in

sted in the firm. We argue that risk in an investment has to be perceived through the eyes of investors in the firm. Since firms often have thousands of investors, often with very different perspectives, it can be asserted that risk has to be measured from the perspective of not just any investor in the stock, but of the marginal investor, defined to be the investor most likely to be trading on the stock at any given point in time. The objective in valuation is to measure the value of an asset to those who will be pricing it. If we want to stay true to this objective, we have to consider the viewpoint of those who set the stock prices, and they are the marginal investors. EQUITY RISK AND EXPECTED RETURN To demonstrate how risk is viewed in finance, risk analysis is presented here in three steps: first, defining risk in terms of the distribution of actual returns around an expected return; second, differentiating between risk that is specific to one or a few investments and risk that af

ECTED RETURN To demonstrate how risk is viewed in finance, risk analysis is presented here in three steps: first, defining risk in terms of the distribution of actual returns around an expected return; second, differentiating between risk that is specific to one or a few investments and risk that affects a much wider cross section of investments (in a market where the marginal investor is well diversified, it is only the latter risk, called market risk, that will be rewarded); and third, alternative models for measuring this market risk and the expected returns that go with it. Defining Risk Investors who buy an asset expect to earn returns over the time horizon that they hold the asset. Their actual returns over this holding period may be very different from the expected returns, and it is this difference between actual and expected returns that is a source of risk. For example, assume that you are an investor with a one-year time horizon buying a one-year Treasury bill (or any other

ir actual returns over this holding period may be very different from the expected returns, and it is this difference between actual and expected returns that is a source of risk. For example, assume that you are an investor with a one-year time horizon buying a one-year Treasury bill (or any other default-free one-year bond) with a 5 percent expected return. At the end of the one-year holding period, the actual return on this investment will be 5 percent, which is equal to the expected return. The return distribution for this investment is shown in Figure 4.1. This is a riskless investment. Figure 4.1 Probability Distribution of Returns on a Risk-Free Investment To provide a contrast to the riskless investment, consider an investor who buys stock in a firm, say Boeing. This investor, having done her research, may conclude that she can make an expected return of 30 percent on Boeing over her one-year holding period. The actual return over this period will almost certainly not be equal

riskless investment, consider an investor who buys stock in a firm, say Boeing. This investor, having done her research, may conclude that she can make an expected return of 30 percent on Boeing over her one-year holding period. The actual return over this period will almost certainly not be equal to 30 percent; it might be much greater or much lower. The distribution of returns on this investment is illustrated in Figure 4.2. Figure 4.2 Return Distribution for Risky Investment In addition to the expected return, an investor now has to consider the following. First, note that the actual returns, in this case, are different from the expected return. The spread of the actual returns around the expected return is measured by the variance or standard deviation of the distribution; the greater the deviation of the actual returns from the expected return, the greater the variance. Second, the bias toward positive or negative returns is represented by the skewness of the distribution. The di

e expected return is measured by the variance or standard deviation of the distribution; the greater the deviation of the actual returns from the expected return, the greater the variance. Second, the bias toward positive or negative returns is represented by the skewness of the distribution. The distribution in Figure 4.2 is positively skewed, since there is a higher probability of large positive returns than large negative returns. Third, the shape of the tails of the distribution is measured by the kurtosis of the distribution; fatter tails lead to higher kurtosis. In investment terms, this represents the tendency of the price of this investment to jump (up or down from current levels) in either direction. In the special case where the distribution of returns is normal, investors do not have to worry about skewness and kurtosis, since there is no skewness (normal distributions are symmetric) and a normal distribution is defined to have a kurtosis of zero. Figure 4.3 illustrates the

either direction. In the special case where the distribution of returns is normal, investors do not have to worry about skewness and kurtosis, since there is no skewness (normal distributions are symmetric) and a normal distribution is defined to have a kurtosis of zero. Figure 4.3 illustrates the return distributions on two investments with symmetric returns. Figure 4.3 Return Distribution Comparisons When return distributions are normal, the characteristics of any investment can be measured with two variables—the expected return, which represents the opportunity in the investment, and the standard deviation or variance, which represents the danger. In this scenario, a rational investor, faced with a choice between two investments with the same standard deviation but different expected returns, will always pick the one with the higher expected return. In the more general case, where distributions are neither symmetric nor normal, it is still conceivable that investors will choose bet

aced with a choice between two investments with the same standard deviation but different expected returns, will always pick the one with the higher expected return. In the more general case, where distributions are neither symmetric nor normal, it is still conceivable that investors will choose between investments on the basis of only the expected return and the variance, if they possess utility functions that allow them to do so.1 It is far more likely, however, that they prefer positive skewed distributions to negatively skewed ones, and distributions with a lower likelihood of jumps (lower kurtosis) over those with a higher likelihood of jumps (higher kurtosis). In this world, investors will trade off the good (higher expected returns and more positive skewness) against the bad (higher variance and kurtosis) in making investments. In closing, it should be noted that the expected returns and variances that we run into in practice are almost always estimated using past returns rather

will trade off the good (higher expected returns and more positive skewness) against the bad (higher variance and kurtosis) in making investments. In closing, it should be noted that the expected returns and variances that we run into in practice are almost always estimated using past returns rather than future returns. The assumption made when using historical variances is that past return distributions are good indicators of future return distributions. When this assumption is violated, as is the case when the asset’s characteristics have changed significantly over time, the historical estimates may not be good measures of risk. optvar.xls: This is a dataset on the Web that summarizes standard deviations and variances of stocks in various sectors in the United States. Diversifiable and Nondiversifiable Risk Although there are many reasons why actual returns may differ from expected returns, we can group the reasons into two categories: firm-specific and marketwide. The risks that ari

dard deviations and variances of stocks in various sectors in the United States. Diversifiable and Nondiversifiable Risk Although there are many reasons why actual returns may differ from expected returns, we can group the reasons into two categories: firm-specific and marketwide. The risks that arise from firm-specific actions affect one or a few investments, while the risks arising from marketwide reasons affect many or all investments. This distinction is critical to the way we assess risk in finance. Components of Risk When an investor buys stock or takes an equity position in a firm, he or she is exposed to many risks. Some risk may affect only one or a few firms, and this risk is categorized as firm-specific risk. Within this category, we would consider a wide range of risks, starting with the risk that a firm may have misjudged the demand for a product from its customers; we call this project risk. For instance, consider Boeing’s investment in a Super Jumbo jet. This investment

orized as firm-specific risk. Within this category, we would consider a wide range of risks, starting with the risk that a firm may have misjudged the demand for a product from its customers; we call this project risk. For instance, consider Boeing’s investment in a Super Jumbo jet. This investment is based on the assumption that airlines want a larger airplane and are willing to pay a high price for it. If Boeing has misjudged this demand, it will clearly have an impact on Boeing’s earnings and value, but it should not have a significant effect on other firms in the market. The risk could also arise from competitors proving to be stronger or weaker than anticipated, called competitive risk. For instance, assume that Boeing and Airbus are competing for an order from Qantas, the Australian airline. The possibility that Airbus may win the bid is a potential source of risk to Boeing and perhaps some of its suppliers, but again, few other firms will be affected by it. Similarly, Disney rec

For instance, assume that Boeing and Airbus are competing for an order from Qantas, the Australian airline. The possibility that Airbus may win the bid is a potential source of risk to Boeing and perhaps some of its suppliers, but again, few other firms will be affected by it. Similarly, Disney recently launched magazines aimed at teenage girls, hoping to capitalize on the success of its TV shows. Whether it succeeds is clearly important to Disney and its competitors, but it is unlikely to have an impact on the rest of the market. In fact, risk measures can be extended to include risks that may affect an entire sector but are restricted to that sector; we call this sector risk. For instance, a cut in the defense budget in the United States will adversely affect all firms in the defense business, including Boeing, but there should be no significant impact on other sectors. What is common across the three risks described—project, competitive, and sector risk—is that they affect only a s

, a cut in the defense budget in the United States will adversely affect all firms in the defense business, including Boeing, but there should be no significant impact on other sectors. What is common across the three risks described—project, competitive, and sector risk—is that they affect only a small subset of firms. There is another group of risks that is much more pervasive and affects many if not all investments. For instance, when interest rates increase, all investments are negatively affected, albeit to different degrees. Similarly, when the economy weakens, all firms feel the effects, though cyclical firms (such as automobiles, steel, and housing) may feel it more. We term this risk market risk. Finally, there are risks that fall in a gray area, depending on how many assets they affect. For instance, when the dollar strengthens against other currencies, it has a significant impact on the earnings and values of firms with international operations. If most firms in the market h

k market risk. Finally, there are risks that fall in a gray area, depending on how many assets they affect. For instance, when the dollar strengthens against other currencies, it has a significant impact on the earnings and values of firms with international operations. If most firms in the market have significant international operations, it could well be categorized as market risk. If only a few do, it would be closer to firm-specific risk. Figure 4.4 summarizes the spectrum of firm-specific and market risks. Figure 4.4 Breakdown of Risk Why Diversification Reduces or Eliminates Firm-Specific Risk: An Intuitive Explanation As an investor, you could invest all your portfolio in one asset. If you do so, you are exposed to both firm-specific and market risk. If, however, you expand your portfolio to include other assets or stocks, you are diversifying, and by doing so you can reduce your exposure to firm-specific risk. There are two reasons why diversification reduces or, at the limit,

f you do so, you are exposed to both firm-specific and market risk. If, however, you expand your portfolio to include other assets or stocks, you are diversifying, and by doing so you can reduce your exposure to firm-specific risk. There are two reasons why diversification reduces or, at the limit, eliminates firm-specific risk. The first is that each investment in a diversified portfolio is a much smaller percentage of that portfolio than would be the case if you were not diversified. Any action that increases or decreases the value of only that investment or a small group of investments will have only a small impact on your overall portfolio, whereas undiversified investors are much more exposed to changes in the values of the investments in their portfolios. The second reason is that the effects of firm-specific actions on the prices of individual assets in a portfolio can be either positive or negative for each asset for any period. Thus, in very large portfolios this risk will ave

xposed to changes in the values of the investments in their portfolios. The second reason is that the effects of firm-specific actions on the prices of individual assets in a portfolio can be either positive or negative for each asset for any period. Thus, in very large portfolios this risk will average out to zero and will not affect the overall value of the portfolio. In contrast, the effects of marketwide movements are likely to be in the same direction for most or all investments in a portfolio, though some assets may be affected more than others. For instance, other things being equal, an increase in interest rates will lower the values of most assets in a portfolio. Being more diversified does not eliminate this risk. A Statistical Analysis of Diversification-Reducing Risk The effects of diversification on risk can be illustrated fairly dramatically by examining the effects of increasing the number of assets in a portfolio on portfolio variance. The variance in a portfolio is par

ied does not eliminate this risk. A Statistical Analysis of Diversification-Reducing Risk The effects of diversification on risk can be illustrated fairly dramatically by examining the effects of increasing the number of assets in a portfolio on portfolio variance. The variance in a portfolio is partially determined by the variances of the individual assets in the portfolio and partially by how they move together; the latter is measured statistically with a correlation coefficient or the covariance across investments in the portfolio. It is the covariance term that provides an insight into why diversification will reduce risk and by how much. Consider a portfolio of two assets. Asset A has an expected return of μA and a variance in returns of σ2A, while asset B has an expected return of μΒ and a variance in returns of σ2B. The correlation in returns between the two assets, which measures how the assets move together, is ρAB. The expected returns and variances of a two-asset portfolio c

n expected return of μA and a variance in returns of σ2A, while asset B has an expected return of μΒ and a variance in returns of σ2B. The correlation in returns between the two assets, which measures how the assets move together, is ρAB. The expected returns and variances of a two-asset portfolio can be written as a function of these inputs and the proportion of the portfolio going to each asset. where wA = Proportion of the portfolio in asset A The last term in the variance formulation is sometimes written in terms of the covariance in returns between the two assets, which is: The savings that accrue from diversification are a function of the correlation coefficient. Other things remaining equal, the higher the correlation in returns between the two assets, the smaller are the potential benefits from diversification. It is worth adding, though, that the benefits of correlation exist even for positively correlated assets and are non-existent only when the correlation is equal to one.

equal, the higher the correlation in returns between the two assets, the smaller are the potential benefits from diversification. It is worth adding, though, that the benefits of correlation exist even for positively correlated assets and are non-existent only when the correlation is equal to one. Mean-Variance Models Measuring Market Risk While most risk and return models in use in finance agree on the first two steps of the risk analysis process (i.e., that risk comes from the distribution of actual returns around the expected return and that risk should be measured from the perspective of a marginal investor who is well diversified), they part ways when it comes to measuring nondiversifiable or market risk. This section will discuss the different models that exist in finance for measuring market risk and why they differ. It begins with what still is the most widely used model for measuring market risk in finance—the capital asset pricing model (CAPM)—and then discusses the alternat

able or market risk. This section will discuss the different models that exist in finance for measuring market risk and why they differ. It begins with what still is the most widely used model for measuring market risk in finance—the capital asset pricing model (CAPM)—and then discusses the alternatives to this model that have developed over the past two decades. While the discussion will emphasize the differences, it will also look at what the models have in common. Capital Asset Pricing Model The risk and return model that has been in use the longest and is still the standard for most practitioners is the capital asset pricing model (CAPM). This section will examine the assumptions on which the model is based and the measures of market risk that emerge from these assumptions. WHY IS THE MARGINAL INVESTOR ASSUMED TO BE DIVERSIFIED? The argument that diversification reduces an investor’s exposure to risk is clear both intuitively and statistically, but risk and return models in finance

h the model is based and the measures of market risk that emerge from these assumptions. WHY IS THE MARGINAL INVESTOR ASSUMED TO BE DIVERSIFIED? The argument that diversification reduces an investor’s exposure to risk is clear both intuitively and statistically, but risk and return models in finance go further. These models look at risk through the eyes of the investor most likely to be trading on the investment at any point in time—the marginal investor. They argue that this investor, who sets prices for investments, is well diversified; thus, the only risk that he or she cares about is the risk added to a diversified portfolio or market risk. This argument can be justified simply. The risk in an investment will always be perceived to be higher for an undiversified investor than for a diversified one, since the latter does not shoulder any firm-specific risk and the former does. If both investors have the same expectations about future earnings and cash flows on an asset, the diversif

in an investment will always be perceived to be higher for an undiversified investor than for a diversified one, since the latter does not shoulder any firm-specific risk and the former does. If both investors have the same expectations about future earnings and cash flows on an asset, the diversified investor will be willing to pay a higher price for that asset because of his or her perception of lower risk. Consequently, the asset, over time, will end up being held by diversified investors. This argument is powerful, especially in markets where assets can be traded easily and at low cost. Thus, it works well for a stock traded in developed markets, since investors can become diversified at fairly low cost. In addition, a significant proportion of the trading in developed market stocks is done by institutional investors, who tend to be well diversified. It becomes a more difficult argument to sustain when assets cannot be easily traded or the costs of trading are high. In these marke

t fairly low cost. In addition, a significant proportion of the trading in developed market stocks is done by institutional investors, who tend to be well diversified. It becomes a more difficult argument to sustain when assets cannot be easily traded or the costs of trading are high. In these markets, the marginal investor may well be undiversified, and firm-specific risk may therefore continue to matter when looking at individual investments. For instance, real estate in most countries is still held by investors who are undiversified and have the bulk of their wealth tied up in these investments. Assumptions While diversification reduces the exposure of investors to firm-specific risk, most investors limit their diversification to holding only a few assets. Even large mutual funds rarely hold more than a few hundred stocks, and many of them hold as few as 10 to 20. There are two reasons why investors stop diversifying. One is that an investor or mutual fund manager can obtain most of

t investors limit their diversification to holding only a few assets. Even large mutual funds rarely hold more than a few hundred stocks, and many of them hold as few as 10 to 20. There are two reasons why investors stop diversifying. One is that an investor or mutual fund manager can obtain most of the benefits of diversification from a relatively small portfolio, because the marginal benefits of diversification become smaller as the portfolio gets more diversified. Consequently, these benefits may not cover the marginal costs of diversification, which include transactions and monitoring costs. Another reason for limiting diversification is that many investors (and funds) believe they can find undervalued assets and thus choose not to hold those assets that they believe to be fairly valued or overvalued. The capital asset pricing model assumes that there are no transaction costs, all assets are traded, and investments are infinitely divisible (i.e., you can buy any fraction of a unit