Chapter 7
A Primer on Merger and Acquisition Cash-Flow Valuation
The greater danger for most of us is not that our aim is too high and we might miss it, but that it is too low and we reach it.
—Michelangelo
Inside M&A: the importance of distinguishing between operating and nonoperating assets
In 2006, Verizon Communications and MCI Inc. executives completed a deal in which MCI shareholders received $6.7 billion for 100% of MCI stock. Verizon's management argued that the deal cost their shareholders only $5.3 billion in Verizon stock, with MCI having agreed to pay its shareholders a special dividend of $1.4 billion contingent on their approval of the transaction. The $1.4 billion special dividend reduced MCI's cash in excess of what was required to meet its normal operating cash requirements.
To understand the actual purchase price, it is necessary to distinguish between operating and nonoperating assets. Without the special dividend, the $1.4 billion in cash would have transferred automatically to Verizon as a result of the purchase of MCI's stock. Verizon would have had to increase its purchase price by an equivalent amount to reflect the face value of this nonoperating cash asset. Consequently, the purchase price would have been $6.7 billion. With the special dividend, the excess cash transferred to Verizon was reduced by $1.4 billion, and the purchase price was $5.3 billion.
In fact, the alleged price reduction was no price reduction at all. It simply reflected Verizon's shareholders' receiving $1.4 billion less in net acquired assets. Moreover, since the $1.4 billion represents excess cash that would have been reinvested in MCI or paid out to shareholders anyway, the MCI shareholders were simply getting the cash earlier than they may have otherwise.
Chapter overview
The five basic methods of valuation are income or discounted cash flow (DCF), market based, asset oriented, replacement cost, and the contingent claims or real-options approach. This chapter provides an overview of the basics of valuing mergers and acquisitions (M&A) using discounted-cash-flow methods. The remaining valuation methods are discussed in Chapter 8.
In addition to these methods, investment bankers often use the leveraged buyout method (LBO) of valuation to assess whether a particular target firm may be of interest to private equity investors (i.e., so-called financial sponsors) as an acquisition opportunity. As is true of DCF methods, the LBO approach requires the projection of cash flows to identify an internal rate of return (IRR) for a private equity investor. The IRR is the discount rate that equates the projected cash flows and terminal value or expected value of the target firm when sold with the initial equity investment. The LBO method is discussed in detail in Chapter 13. The special challenges of valuing private firms, distressed companies, and cross-border transactions are addressed in detail in Chapters 10, 16, and 17, respectively.
This chapter begins with a brief review of rudimentary finance concepts, including measuring risk and return, the capital asset pricing model, and the effects of operating and financial leverage on risk and return. The cash-flow definitions, free cash flow to equity (equity value) or to the firm (enterprise value), discussed in this chapter are used in valuation problems in subsequent chapters. The chapter concludes with an illustration of the commonly used enterprise method to value a firm's operating and nonoperating assets and liabilities to determine equity value.1
A review of this chapter (including additional practice problems with solutions) is available in the file folder entitled “Student Study Guide” in the companion site to this book (www.elsevierdirect.com/companions/9780123854858). The companion site also contains a Learning Interactions Library, which gives students the opportunity to test their knowledge of this chapter in a “real-time” environment, and a discussion of how to project cash flows in a file entitled “Primer on Cash Flow Forecasting.”
Required returns
Investors require a minimum rate of return on an investment to compensate them for the level of perceived risk associated with that investment. The required rate of return must be at least equal to what the investor can receive on alternative investments exhibiting a comparable level of perceived risk.2
Cost of Equity and the Capital Asset Pricing Model
The cost of equity (ke ) is the rate of return required to induce investors to purchase a firm's equity. The cost of equity also can be viewed as an opportunity cost, because it represents the rate of return investors could earn by investing in equities of comparable risk. The cost of equity can be estimated using the capital asset pricing model (CAPM), which measures the relationship between expected risk and expected return. It postulates that investors require higher rates of return for accepting higher levels of risk. Specifically, the CAPM states that the expected return on an asset or security is equal to a risk-free rate of return plus a risk premium.
A risk-free rate of return is one for which the expected return is certain. It is the reward paid to an investor for postponing current consumption spending without taking any risk. It represents the time value of money. For a return to be considered risk free over some future period, it must be free of default risk, and there must be no uncertainty about the reinvestment rate (i.e., the rate of return that can be earned at the end of the investor's holding period). Despite widespread agreement on the use of U.S. Treasury securities as assets that are free of default risk, there is some controversy over whether a short- or long-term Treasury rate should be used in applying the CAPM.
Whether you should use a short- or long-term rate depends on how long the investor intends to hold the investment. Consequently, the investor who anticipates holding an investment for five or ten years needs to use either a five- or ten-year Treasury bond rate. A three-month Treasury bill rate is not free of risk for a five- or ten-year period, since interest and principal received at maturity must be reinvested at three-month intervals, resulting in considerable reinvestment risk. In this book, a ten-year Treasury bond rate is used to represent the risk-free rate of return. This would be most appropriate for a strategic acquirer interested in valuing a target firm with the intent of operating the firm over an extended time period.
Estimating Market Risk Premiums
The market risk or equity premium refers to the additional rate of return in excess of the risk-free rate that investors require to purchase a firm's equity. While the risk premium represents the perceived risk of the stock and should therefore be forward looking, obtaining precise estimates of future market returns often is exceedingly difficult. The objectivity of Wall Street analysts' projections is problematic, and efforts to develop sophisticated models show results that vary widely. Consequently, analysts often look to historical data, despite results that vary based on the time periods selected and whether returns are calculated as arithmetic or geometric averages. CAPM relates the cost of equity (ke ) to the risk-free rate of return and market risk premium as follows:
(7.1)
where
β = beta (See the section of this chapter entitled “Analyzing Risk.”)
Rm = expected rate of return on equities
Rm – Rf = 5.5% (i.e., the difference between the return on a diversified portfolio of stocks and the risk-free rate)
The 5.5% equity risk premium used in this book is consistent with long-term arithmetic and geometric averages calculated elsewhere.3 Despite its intuitive appeal, the CAPM has limitations. Betas tend to vary over time and are quite sensitive to the time period and methodology employed in their estimation.4 Some analysts argue that the “risk premium” should be changed to reflect fluctuations in the stock market. However, history shows that such fluctuations are relatively short term in nature. Consequently, the risk premium should reflect more long-term considerations, such as the expected holding period of the investor or acquiring company. Therefore, for the strategic or long-term investor or acquirer, the risk premium should approximate the 5.5% premium long-term historical average.5
Since CAPM measures a stock's risk only relative to the overall market and ignores returns on assets other than stocks, some analysts have begun using multifactor models. Such models adjust the CAPM by adding other risk factors that determine asset returns, such as firm size, bond default premiums, bond term structure (i.e., the difference between short- and long-term interest rates on securities that differ only by maturity), and inflation.
Studies show that, of these factors, firm size appears to be among the most important.6 The size factor serves as a proxy for factors such as smaller firms being subject to higher default risk and generally being less liquid than large capitalization firms.7 Table 7.1 provides estimates of the amount of the adjustment to the cost of equity to correct for firm size, as measured by market value, based on actual data since 1926. The analyst should use this data as a guideline only. Specific firm business risk is largely unobservable. Consequently, in applying a firm size premium, analysts should use their judgment in selecting a proper size premium. This magnitude of the firm size premium should be tempered by such factors as a comparison of the firm's key financial ratios (e.g., liquidity and leverage) with comparable firms and after interviewing management. The selection of the proper magnitude is addressed in more detail in Chapter 10.
Table 7.1. Estimates of the Size Premium
| Market Value (000,000) | Percentage Points Added to CAPM Estimate |
| >$18,600 | 0.0 |
| $7,400 to $18,600 | 0.6 |
| $2,700 to $7,400 | 1.0 |
| $1,100 to $2,700 | 1.5 |
| $450 to $1,100 | 2.3 |
| $200 to $450 | 2.7 |
| $100 to $200 | 5.8 |
| <$100 million | 9.2 |
Source: Adapted from estimates provided by Ibbotson's Stocks, Bills, Bonds, and Inflation Valuation Edition 2010 Yearbook.
Equation (7.1) can be rewritten to reflect an adjustment for firm size as follows:
(7.2)
where
Assume that a firm has a market value of less than $100 million and a β of 1.75. Also assume that the risk-free rates of return and equity premium are 5% and 5.5%, respectively. The firm's cost of equity using the CAPM method adjusted for firm size can be estimated as follows:
Pretax Cost of Debt
The cost of debt represents the cost of borrowing each additional dollar of debt. It reflects the current level of interest rates and the level of default risk as perceived by investors. Interest paid on debt is tax deductible by the firm; in bankruptcy, bondholders are paid before shareholders as the firm's assets are liquidated. Default risk, the likelihood the firm will fail to repay interest and principal on a timely basis, can be measured by the firm's credit rating. Default rates vary from an average of 0.52% for AAA-rated firms over a 15-year period to 54.38% for those rated CCC by Standard & Poor's Corporation.8
Interest paid by the firm on its current debt can be used as an estimate of the current cost of debt if the financial condition of the firm and the prevailing level of interest rates have not changed since the firm last borrowed. However, when conditions have changed, the analyst must estimate the cost of debt reflecting current market interest rates and default risk.
In estimating the current cost of debt, analysts commonly use the yield to maturity (YTM)9 of the company's long-term, option-free bonds.10 This requires knowing the price of the security and its coupon and face value.11 In general, the cost of debt is estimated by calculating the yield to maturity (YTM) on each of the firm's outstanding bond issues. We then compute a weighted average YTM, with the estimated YTM for each issue weighted by its percentage of total debt outstanding. In Table 7.2, Microsoft's weighted average YTM on the bulk of its long-term debt on January 24, 2011, was 2.4%. The source for the YTM for each debt issue was found in the Financial Industry Regulatory Authority's (FINRA) Trace database www.finra.org/marketdata.12 The book or face value of the debt comes from Microsoft's 2009 10K. Microsoft is rated AAA by Standard & Poor's Corporation.
Table 7.2. Weighted-Average Yield to Maturity of Microsoft's Long-Term Debt
YTM represents the most reliable estimate of a firm's cost of debt as long as the firm's debt is investment grade. Investment grade bonds are those whose credit quality is considered to be among the most secure by independent bond rating agencies. A rating of BBB or higher by Standard & Poor's and Baa or higher by Moody's Investors Service is considered to be investment grade.
For investment grade bonds, the difference between the expected rate of return and the promised rate of return is small. The promised rate of return assumes that the interest and principal are paid on time. The yield to maturity is affected by the cost of debt, the probability of default, and the expected recovery rate on the debt if the firm defaults, and it is a good proxy for actual future returns on investment grade debt, since the potential for default or bankruptcy is relatively low.
Noninvestment grade debt is rated less than BBB by Standard & Poor's and Baa by Moody's, and it represents debt with a default risk that is significant due to the firm's high leverage, deteriorating cash flows, or both. The difference between the expected rate of return and the promised rate can be substantial. Ideally, the expected yield to maturity would be calculated based on the current market price of the noninvestment grade bond, the probability of default, and the potential recovery rate following default.13 However, such data are frequently unavailable. A practical alternative is to use the YTM for a number of similarly rated bonds of other firms. Such bonds include a so-called default premium, which reflects the compensation that lenders require over the risk-free rate to buy noninvestment grade debt. This methodology assumes that the risk characteristics of the proxy firms approximate those of the firm being analyzed.
To illustrate this process, on January 24, 2011, HCA Healthcare Inc.'s 9% fixed rate noncallable bond that would reach maturity on December 15, 2015 (rated CCC by Standard & Poor's and Caa1 by Moody's) had a YTM of 7.41% on that date, according to FINRA's TRACE database. With five-year U.S. Treasury bonds offering a yield to maturity of 1.94%, the implied default risk premium was 5.47% (i.e., 7.41 minus 1.94). This same process could then be repeated for a number of similarly rated bonds in order to calculate an average YTM.
For nonrated firms, the analyst may estimate the current pretax cost of debt for a specific firm by comparing debt-to-equity ratios, interest coverage ratios, and operating margins with those of similar rated firms. The analyst would then use the interest rates paid by these comparably rated firms as the pretax cost of debt for the firm being analyzed. Much of this information can be found in local libraries in such publications as Moody's Company Data; Standard & Poor's Descriptions, the Outlook, and Bond Guide; and Value Line's Investment Survey. In the United States, the FINRA TRACE database also is an excellent source of interest rate information.
Cost of Preferred Stock
Preferred stock exhibits some of the characteristics of long-term debt in that its dividend is generally constant and preferred stockholders are paid before common shareholders in the event the firm is liquidated. Unlike interest payments on debt, preferred dividends are not tax deductible. Because preferred stock is riskier than debt but less risky than common stock in bankruptcy, the cost to the company to issue preferred stock should be less than the cost of equity but greater than the cost of debt. Viewing preferred dividends as paid in perpetuity, the cost of preferred stock (k pr) can be calculated as dividends per share of preferred stock (d pr) divided by the market value of the preferred stock (PR) (see the section of this chapter entitled “Zero-Growth Valuation Model”). Consequently, if a firm pays a $2 dividend on its preferred stock whose current market value is $50, the firm's cost of preferred stock is 4% (i.e., $2 ÷ $50). The cost of preferred stock can be generalized as follows:
(7.3)
Cost of Capital
The weighted-average cost of capital (WACC) is the broadest measure of the firm's cost of funds and represents the return that a firm must earn to induce investors to buy its common stock, preferred stock, and bonds. The WACC is calculated using a weighted average of the firm's cost of equity (ke ), cost of preferred stock (k pr), and pretax cost of debt (i):
(7.4)
where
A portion of interest paid on borrowed funds is recoverable by the firm because of the tax deductibility of interest. For every dollar of taxable income, the tax owed is equal to $1 multiplied by t. Since each dollar of interest expense reduces taxable income by an equivalent amount, the actual cost of borrowing is reduced by (1 – t). Therefore, the after-tax cost of borrowed funds to the firm is estimated by multiplying the pretax interest rate, i, by (1 – t).
Note that the weights, [E/(D + E + PR)], [D/(D + E + PR)], and [PR/(D + E + PR)], associated with the cost of equity, preferred stock, and debt, respectively, reflect the firm's target capital structure or capitalization. These are targets in that they represent the capital structure the firm hopes to achieve and sustain in the future. The actual market value of equity, preferred stock, and debt as a percentage of total capital (i.e., D + E + PF) may differ from the target. Market values rather than book values are used because the WACC measures the cost of issuing debt, preferred stock, and equity securities. Such securities are issued at market and not book value. The use of the target capital structure avoids the circular reasoning associated with using the current market value of equity to construct the weighted average cost of capital, which is subsequently used to estimate the firm's current market value.
Non-interest-bearing liabilities, such as accounts payable, are excluded from the estimation of the cost of capital for the firm to simplify the calculation of WACC.14 Estimates of industry betas, cost of equity, and WACC are provided by firms such as Ibbotson Associates, Value Line, Standard & Poor's, and Bloomberg. Such estimates provide a “reality check,” since they serve as a benchmark against which the analyst's estimate of a firm's WACC can be compared.
Analyzing risk
Risk is the degree of uncertainty associated with the outcome of an investment. It takes into consideration the probability of a loss as well as a gain on an investment. Risk consists of a diversifiable risk (also called nonsystematic risk) component, such as strikes, defaulting on debt repayments, and lawsuits, that are specific to a firm, and a nondiversifiable risk (also called systematic risk) component, such as inflation and war, that affects all firms. Beta (β) is a measure of nondiversifiable risk or the extent to which a firm's (or asset's) return changes because of a change in the market's return.
An equity beta is a measure of the risk of a stock's financial returns compared with the risk of the financial returns to the general stock market, which in turn is affected by the overall economy. When β = 1, the stock is as risky as the general market. When β < 1, the stock is less risky, whereas when β > 1, the stock is more risky than the overall stock market. Investors are compensated only for risk that cannot be eliminated through diversification (i.e., systematic or nondiversifiable risk).
The value of β may be estimated by applying linear regression analysis to explain the relationship between the dependent variable, stock returns (Rj ), and the independent variable, market returns (Rm ). The intercept or constant term (also referred to as alpha) of the regression equation provides a measure of Rj 's performance compared with the general market during the regression period. In Wall Street parlance, alpha is the premium (or discount) an investment earns above (below) some performance benchmark, such as the S&P 500 index.
The following equations express Rj as defined by the linear regression model and Rj as defined by the CAPM:
If α is greater than Rf (1 – β), this particular stock's rate of return, Rj , performed better than would have been expected using the CAPM during the same time period. The cumulative daily difference between α (i.e., actual returns) and Rf (1 – β) (i.e., expected returns) is a measure of “abnormal” or “excess return” for a specified number of days around the announcement of a transaction (see Exhibit 7.1).
In practice, betas are frequently estimated using the most recent three to five years of data. Consequently, betas are sensitive to the time period selected. The relationship between the
Exhibit 7.1 Estimating β for Publicly Traded Companies
Calculate the return to the jth company's shareholders as capital gains (or losses) plus dividends paid during the period adjusted for stock splits that take place in the current period. This adjusted return should then be regressed against a similarly defined return for a broadly defined market index.
Notes:
1. SP is equal to 2 for a two-for-one stock split, 1.5 for a three-for-two split, and 1.33 for a four-for-three split, and so on. If we do not adjust for stock splits that may take place in the current period, the stock price will drop, resulting in a negative return.
2. Betas for public companies can be obtained from estimation services such as Value Line, Standard & Poor's, Ibbotson, and Bloomberg. Betas for private companies can be obtained by substituting a beta for comparable publicly traded companies (see Chapter 10).
overall market and a specific firm's equity beta may change significantly if a large sector of stocks that make up the overall index increase or decrease substantially.15 Estimates of public company equity betas may be obtained by going to finance.yahoo.com, finance.google.com, and reuters.com.
Alternatively, a firm's beta may be calculated based on the betas of a sample of similar firms—that is, firms facing similar business risk (usually in the same industry) and those with similar capital structures. We unlever the betas of the firms in the sample to eliminate the effects of their current capital structures on their betas. Finally, we average the unlevered betas and relever them to reflect the capital structure of the firm whose beta we are trying to estimate. This process is described in detail in the next section.
Effects of Financial and Operating Leverage on Beta
The volatility of a firm's financial returns is affected by the cyclicality of the industry in which it competes, its cost structure, and its capital structure. The following discussion introduces the concepts of unlevered and levered betas as ways to measure the effects of a firm's cost and capital structures on its beta and, in turn, the firm's financial returns.
In the absence of debt, the equity β is called an unlevered β, denoted βu . The unlevered beta of a firm is determined by the type of industry in which the firm operates (e.g., cyclical or noncyclical) and its operating leverage (i.e., the firm's ratio of fixed expenses to total cost of sales). Operating leverage magnifies the volatility of a firm's earnings and financial returns.16 Table 7.3 illustrates the effects of operating leverage on financial returns.
Table 7.3. How Operating Leverage Affects Financial Returnsa
a All figures are in millions of dollars unless otherwise noted.
b In Case 1, variable costs represent 32% of revenue. Assuming this ratio is maintained, variable costs in Cases 2 and 3 are estimated by multiplying total revenue by 0.32.
The three cases reflect the same level of fixed expenses but varying levels of revenue and the resulting impact on after-tax earnings and financial returns. The Case 1 illustration assumes that the firm's total cost of sales is 80% of revenue and that fixed expenses comprise 60% of the total cost of sales. Note the volatility of the firm's return on equity resulting from fluctuations of 25% in the firm's revenue in Cases 2 and 3.
If a firm borrows, the unlevered equity beta must be adjusted to reflect the additional risk associated with financial leverage (i.e., the firm's ratio of debt to equity). The resulting beta is called a leveraged or levered β, denoted βl . Table 7.4 illustrates the effects of financial leverage on financial returns. The three cases reflect varying levels of debt but the same earnings before interest and taxes. Note how increasing leverage magnifies financial returns to equity.
Table 7.4. How Financial Leverage Affects Financial Returnsa
a All figures are in millions of dollars unless otherwise noted.
If a firm's stockholders bear all the risk from operating and financial leverage and interest paid on debt is tax deductible, levered and unlevered betas can be calculated as follows for a firm whose debt-to-equity ratio is denoted by D/E:
(7.5)
(7.6)
Shareholders view risk as the potential for a firm not to earn sufficient future cash flow to satisfy their minimum required financial returns. Equation (7.5) implies that increases in a firm's leverage denoted by (D/E) will, other things unchanged, increase this risk as measured by the firm's levered beta because the firm's interest payments represent fixed expenses that must be paid before any payments can be made to shareholders. However, this increased risk is offset somewhat by the tax deductibility of interest, which reduces shareholder risk by increasing after-tax cash flow available for shareholders. The reduction in the firm's tax liability due to the tax deductibility of interest is often referred to as a tax shield. Therefore, the levered beta will, unless offset by other factors, increase with an increase in leverage and decrease with an increase in tax rates.
In summary, βu is determined by the characteristics of the industry in which the firm competes and its degree of operating leverage. The value of βl is determined by the same factors and the degree of the firm's financial leverage. Estimating a firm's beta by regressing the percent change in its share price plus dividends against the percent change in a broadly defined index plus dividends over some historical period, as illustrated in Exhibit 7.1, assumes the historical relationship will hold in the future. However, this often is not the case.
An alternative to using historical information is to estimate beta using a sample of similar firms and applying Eqs. (7.5) and (7.6). This involves a three-step procedure (Table 7.5). In step 1, select a sample of firms with similar cyclicality and operating leverage (i.e., firms usually in the same industry). Step 2 requires calculating the average unleveraged beta for firms in the sample to eliminate the effects of their current capital structures on their betas. Finally, in step 3, we relever the average unleveraged beta using the debt-to-equity ratio and the marginal tax rate of the firm whose beta we are trying to estimate (i.e., the target firm).
Table 7.5. Estimating Abbot Labs' Equity Beta Using Similar Firms
a Yahoo! Finance (1/29/2011). Beta estimates are based on the historical relationship between the firm's share price and a broadly defined stock index.
b β u = βl / [1 + (1 – t)(D/E)], where β u and βl are unlevered and levered betas; marginal tax rate is 0.4.Abbot Labs (β u ) = 0.2900 / [1 + (1 – 0.4)0.2662)] = 0.2501Johnson & Johnson (β u ) = 0.6000 / [1 + (1 – 0.4)0.0762)] = 0.5738Merck (β u ) = 0.6600 / [1 + (1 – 0.4)0.3204)] = 0.5536Pfizer (β u ) = 0.6800 / [1 + (1 – 0.4)0.3044)] = 0.5750
c βl = β u [1 + (1 – t)(D/E)] using the target firm's (Abbot Labs') debt/equity ratio and marginal tax rate.Abbot Labs' relevered beta = 0.4881[1 + (1 – 0.4)0.2662)] = 0.4209
Using Eqs. (7.5) and (7.6), the effects of different amounts of leverage on the cost of equity also can be analyzed.17 The process is as follows:
1. Determine a firm's current equity β* and (D/E)*;
2. Estimate the unleveraged beta to eliminate the effects of the firm's current capital structure:
3. Estimate the firm's leveraged beta: β l = βu [1 + (1 – t)(D/E)**]; and
4. Estimate the firm's cost of equity for the new leveraged beta
where β* and (D/E)* represent the firm's current equity beta and the market value of the firm's debt-to-equity ratio before additional borrowing takes place; (D/E)** is the firm's debt-to-equity ratio after additional borrowing occurs; and t is the firm's marginal tax rate.
In an acquisition, an acquirer may anticipate increasing significantly the target firm's current debt level after the closing. To determine the impact on the target's beta of the increased leverage, the target's levered beta, which reflects its preacquisition leverage, must be converted to an unlevered beta, reflecting the target firm's operating leverage and the cyclicality of the industry in which the firm competes. To measure the increasing risk associated with new borrowing, the resulting unlevered beta is then used to estimate the levered beta for the target firm (see Exhibit 7.2).
Exhibit 7.2 Estimating the Impact of Changing Debt Levels on the Cost of Equity
Assume that a target's current or preacquisition debt-to-equity ratio is 25%, current levered beta is 1.05, and marginal tax rate is 0.4. After the acquisition, the debt-to-equity ratio is expected to rise to 75%. What is the target's postacquisition levered beta?
Answer: Using Eqs. (7.5) and (7.6):
where (D/E)* and (D/E)** are the target's pre- and postacquisition debt-to-equity ratios and β l* is the target's preacquisition equity beta.
Calculating free cash flows
Two common definitions of cash flow used for valuation purposes are free cash flow to the firm (FCFF), or enterprise cash flow, and cash flow to equity investors (FCFE), or equity cash flow. These cash flows (often referred to as valuation cash flows) require adjusting GAAP-based cash flows provided in companies' financial statements. How valuation cash flows are constructed is discussed next.
Free Cash Flow to the Firm (Enterprise Cash Flow)
Free cash flow to the firm represents cash available to satisfy all investors holding claims against the firm's resources. These claim holders include common stockholders, lenders, and preferred stockholders. This definition assumes implicitly that a firm can always get financing if it can generate sufficient future cash flows to meet or exceed minimum returns required by investors and lenders. Consequently, enterprise cash flow is calculated before the sources of financing are determined and, as such, is not affected by the firm's financial structure. However, in practice, the financial structure may affect the firm's cost of capital and, therefore, its value due to the potential for bankruptcy (see Chapter 16 for a more detailed discussion of financial distress).
FCFF can be calculated by adjusting operating earnings before interest and taxes (EBIT) as follows:
(7.7)
Under this definition, only cash flow from operating and investment activities, but not financing activities, is included. The tax rate refers to the firm's marginal tax rate. Net working capital is defined as current operating assets less cash balances in excess of the amount required to meet normal operating requirements less current operating liabilities. In some instances, firms may have negative working capital. While this is possible for a certain time period, it is unlikely to be sustained; consequently, it is preferable to set net working capital to zero in this instance.
Assets lose value or wear out over time. There is a cash outflow when the asset is acquired initially; however, because assets can continue to generate revenue over many years, GAAP accounting requires that the initial cost of the asset be spread over the expected useful life of the asset to better align costs with the revenue generated in each year. Since such depreciation and amortization expenses do not constitute an actual cash outlay, they are added back to operating income in the calculation of cash flow.
Selecting the Right Tax Rate
The calculation of after-tax operating income requires multiplying EBIT by either a firm's marginal tax rate (i.e., the rate paid on each additional dollar of earnings) or effective tax rate (i.e., taxes due divided by taxable income). The effective tax rate is calculated from actual taxes paid, based on accounting statements prepared for tax-reporting purposes. The marginal tax rate in the United States is usually 40%—35% for federal taxes for firms earning more than $10 million and 5% for most state and local taxes—and it is typically used to calculate after-tax income from new investment projects.
The effective rate is usually less than the marginal tax rate and varies among firms due to the use of tax credits to reduce actual taxes paid or accelerated depreciation to defer the payment of taxes. While favorable tax rules may temporarily reduce the effective tax rate, it is unlikely to be permanently reduced. Once tax credits have been used and the ability to further defer taxes has been exhausted, the effective rate can exceed the marginal rate at some point in the future.
Because favorable tax treatment cannot be extended indefinitely, the marginal tax rate should be used if taxable income is going to be multiplied by the same tax rate during each future period. However, an effective tax rate lower than the marginal rate may be used in the early years of cash-flow projections and eventually increased to the firm's marginal tax rate if the analyst has reason to believe that the current favorable tax treatment is likely to continue into the foreseeable future. However, whatever the analyst chooses to do with respect to the selection of a tax rate, it is critical to use the marginal rate in calculating after-tax operating income in perpetuity. Otherwise, the implicit assumption is that taxes can be deferred indefinitely.
Dealing with Operating Leases
For many firms, their future operating lease commitments are substantial. Leased assets qualifying as operating leases do not require a firm to record an asset or a liability on the balance sheet; instead, the lease charge is recorded as an expense on the firm's income statement, and future lease commitments are recorded in footnotes to the firm's financial statements.
As noted later in this chapter, future lease commitments should be discounted to the present at the firm's pretax cost of debt (i), since leasing equipment represents an alternative to borrowing to buy a piece of equipment, and its present value (PVOL) should be included in the firm's total debt outstanding. Once operating leases are converted to debt, operating lease expense (OLEEXP) must be added to EBIT because it is a financial expense and EBIT represents operating income before such expenses. Lease payments include both an interest expense component to reflect the cost of borrowing and a depreciation component to reflect the anticipated decline in the value of the leased asset.
An estimate of depreciation expense associated with the leased asset (DEPOL) then must be deducted from EBIT, as is depreciation expense associated with other fixed assets owned by the firm, to calculate an “adjusted” EBIT (EBITADJ). DEPOL may be estimated by dividing the firm's gross plant and equipment by its annual depreciation expense. Studies show that the median asset life for leased equipment is 10.9 years.18 The EBITADJ then is used to calculate free cash flow to the firm. EBIT may be adjusted as follows:
(7.8)
For example, if EBIT, OLEEXP, PVOL, and the estimated useful life of the leased equipment are $15 million, $2 million, $30 million, and ten years, respectively, EBITADJ equals $14 million (i.e., $15 + $2 – ($30/10)).
Free Cash Flow to Equity Investors (Equity Cash Flow)
Free cash flow to equity investors is the cash flow remaining for returning cash through dividends or share repurchases to current common equity investors or for reinvesting in the firm after the firm satisfies all obligations.19 These obligations include debt payments, capital expenditures, changes in net working capital, and preferred dividend payments. FCFE can be defined as follows:
(7.9)
Exhibit 7.3 summarizes the key elements of enterprise cash flow, Eq. (7.6), and equity cash flow, Eq. (7.9). Note that equity cash flow reflects operating, investment, and financing activities, whereas enterprise cash flow excludes cash flow from financing activities.
Exhibit 7.3 Defining Valuation Cash Flows: Equity and Enterprise Cash Flows
Free Cash Flow to Common Equity Investors (Equity Cash Flow: FCFE)
FCFE = {Net Income + Depreciation and Amortization – ΔWorking Capital}a – Gross Capital Expendituresb + {New Preferred Equity Issues – Preferred Dividends + New Debt Issues – Principal Repayments}c
Cash flow (after taxes, debt repayments and new debt issues, preferred dividends, preferred equity issues, and all reinvestment requirements) available for paying dividends and/or repurchasing common equity.Applying income or discounted-cash-flow methods
The firm's ability to generate future cash flows often is referred to as its economic value. DCF methods provide estimates of the economic value of a company at a moment in time, which do not need to be adjusted if the intent is to acquire a small portion of it. However, if the intention is to obtain a controlling interest in the firm, a control premium must be added to the firm's estimated economic value to determine the purchase price. A controlling interest generally is considered more valuable to an investor than is a minority interest because the investor has the right to approve important decisions affecting the business. Minority investment positions often are subject to discounts because of their lack of control. Control premiums and minority discounts are discussed in detail in Chapter 10.
Enterprise Discounted-Cash-Flow Model (Enterprise or FCFF Method)
The enterprise valuation method, or FCFF, approach discounts the after-tax free cash flow available to the firm from operations at the weighted-average cost of capital to obtain the estimated enterprise value. The firm's enterprise value (often referred to as firm value) reflects the market value of the entire business. It represents the sum of investor claims on the firm's cash flows from all those holding securities. These include those holding long-term debt, preferred stock, common shareholders, and minority shareholders.
Enterprise value is commonly calculated as the market value of the firm's common equity plus long-term debt, preferred stock, and minority interest less cash and cash equivalents.20 It is commonly assumed that cash and cash equivalents are available to meet such obligations.21
The firm's estimated common equity value then is determined by subtracting the market value of the firm's debt and other investor claims on cash flow, such as preferred stock, from the enterprise value. The estimate of equity derived in this manner equals the value of equity determined by discounting the cash flow available to the firm's shareholders at the cost of equity, if assumptions about cash flow and discount rates are consistent. The enterprise method is used when the analyst has limited information about the firm's debt repayment schedules or interest expense.
Equity Discounted-Cash-Flow Model (Equity or FCFE Method)
The equity valuation, or FCFE approach, discounts the after-tax cash flows available to the firm's shareholders at the cost of equity. This approach is more direct than the enterprise method when the objective is to value the firm's equity, and may be appropriate for financial services firms in which the cost of capital for various operations within the firm may be very difficult to estimate.22 By focusing on FCFE, the analyst needs to estimate only the financial services firm's cost of equity. The enterprise or FCFF method and the equity or FCFE method are illustrated in the following sections of this chapter using three cash-flow growth scenarios: zero-growth, constant-growth, and variable-growth rates.
The Zero-Growth Valuation Model
This model assumes that free cash flow is constant in perpetuity. The value of the firm at time zero (P 0) is the discounted or capitalized value of its annual cash flow. In this instance (see Exhibit 7.4), the discount rate and the capitalization rate are the same (see Chapter 10 for further discussion of the difference between discount and capitalization rates).23 The subscript FCFF or FCFE refers to the definition of cash flow used in the valuation.
(7.10)
where FCFF0 is free cash flow to the firm at time 0 and WACC is the cost of capital.
(7.11)
where FCFE0 is free cash flow to common equity at time 0 and ke is the cost of equity.
While simplistic, the zero-growth method has the advantage of being easily understood by all parties involved in a negotiation. Moreover, there is little evidence that more complex methods provide consistently better valuation estimates, due to their greater requirement for more inputs and assumptions. This method is often used to value commercial real estate transactions and small privately owned businesses.
Exhibit 7.4 The Zero-Growth Valuation Model
1. What is the enterprise value of a firm whose annual FCFF0 of $1 million is expected to remain constant in perpetuity and whose cost of capital is 12% (see Eq. (7.10))?
2. Calculate the weighted-average cost of capital (see Eq. (7.4)) and the enterprise value of a firm whose capital structure consists only of common equity and debt. The firm desires to limit its debt to 30% of total capital.a The firm's marginal tax rate is 0.4 and its beta is 1.5. The corporate bond rate is 8% and the ten-year U.S. Treasury bond rate is 5%. The expected annual return on stocks is 10%. Annual FCFF is expected to remain at $4 million indefinitely.
The Constant-Growth Valuation Model
The constant-growth model is applicable for firms in mature markets, characterized by a moderate and somewhat predictable rate of growth. Examples of such industries include beverages, cosmetics, personal care products, prepared foods, and cleaning products. To project growth rates, extrapolate the industry's growth rate over the past five to ten years. The constant-growth model assumes that cash flow grows at a constant rate, g, which is less than the required return, ke . The assumption that ke is greater than g is a necessary mathematical condition for deriving the model. In this model, next year's cash flow to the firm (FCFF1), or the first year of the forecast period, is expected to grow at the constant rate of growth, g. Therefore, FCFF1 = FCFF0 (1 + g):
(7.12)
(7.13)
where FCFE1 = FCFE0 (1 + g).24
This simple valuation model also provides a means of estimating the risk premium component of the cost of equity as an alternative to relying on historical information, as is done in the capital asset pricing model. This model was developed originally to estimate the value of stocks in the current period (P 0) using the level of expected dividends (d 1) in the next period. This formulation provides an estimate of the present value of dividends growing at a constant rate forever. Assuming the stock market values stocks correctly and we know P 0, d 1, and g, we can estimate ke . Therefore,
(7.14)
For example, if d 1 is $1, g is 10%, and P 0 = $10, ke is 20%. See Exhibit 7.5 for an illustration of how to apply the constant-growth model.
Exhibit 7.5 The Constant-Growth Model
1. Determine the enterprise value of a firm whose projected free cash flow to the firm (enterprise cash flow) next year is $1 million, WACC is 12%, and expected annual cash-flow growth rate is 6% (see Eq. (7.12)).
2. Estimate the equity value of a firm whose cost of equity is 15% and whose free cash flow to equity holders (equity cash flow) in the prior year is projected to grow 20% this year and then at a constant 10% annual rate thereafter. The prior year's free cash flow to equity holders is $2 million (see Eq. (7.13)).
The Variable-Growth (Supernormal or Nonconstant) Valuation Model
Many firms experience periods of high growth followed by a period of slower, more stable growth. Examples of such industries include cellular phones, personal computers, and cable TV. Firms within such industries routinely experience double-digit growth rates for periods of five to ten years because of low penetration of these markets in the early years of the product's life cycle. As the market becomes saturated, growth inevitably slows to a rate more in line with the overall growth of the economy or the general population. The PV of such firms is equal to the sum of the PV of the discounted cash flows during the high-growth period plus the discounted value of the cash flows generated during the stable growth period. The discounted value of the cash flows generated during the stable growth period is often called the terminal, sustainable, horizon, or continuing growth value.
The terminal value may be estimated using the constant-growth model. Free cash flow during the first year beyond the nth or final year of the forecast period, FCFF n +1, is divided by the difference between the assumed cost of capital and the expected cash-flow growth rate beyond the nth-year forecast period. The terminal value is the value in the nth year of all future cash flows beyond the nth year. Consequently, to convert the terminal value to its value in the current year, it is necessary to discount the terminal value by applying the discount rate used to convert the nth-year value to a present value.
The use of the constant-growth model provides consistency in estimating the value of the firm created beyond the end of the forecast period. It enables the application of discounted-cash-flow methodology in estimating value during both variable and stable growth periods. However, the selection of the earnings growth rate and cost of capital must be done very carefully. Small changes in assumptions can result in dramatic swings in the terminal value and, therefore, in the valuation of the firm.
Table 7.6 illustrates the sensitivity of a terminal value of $1 million to different spreads between the cost of capital and the stable growth rate. Note that, using the constant-growth model formula, the terminal value declines dramatically as the spread between the cost of capital and expected stable growth for cash flow increases by 1 percentage point. Note also that terminal values can be estimated in numerous other ways.25
Table 7.6. Impact of Changes in Assumptions on Terminal Value
| Difference between Cost of Capital and Cash-Flow Growth Rate | Terminal Value ($ millions) |
| 3% | 33.3a |
| 4% | 25.0 |
| 5% | 20.0 |
| 6% | 16.7 |
| 7% | 14.3 |
a $1.0/0.03
Using the definition of free cash flow to the firm, P 0,FCFF can be estimated using the variable-growth model as follows:
(7.15)
where
WACC = weighted-average cost of capital through year n
WACC m = cost of capital assumed beyond year n (Note: WACC > WACC m )
Pn = value of the firm at the end of year n (terminal value)
gt = growth rate through year n
gm = stabilized or long-term growth rate beyond year n (Note: gt > gm )
Similarly, the value of the firm to equity investors can be estimated using Eq. (7.15). However, projected free cash flows to equity (FCFE) are discounted using the firm's cost of equity.
The cost of capital is assumed to differ between the high-growth and the stable-growth period when applying the variable-growth model. High-growth rates usually are associated with increased levels of uncertainty. In applying discounted-cash-flow methodology, the discount rate reflects risk. Consequently, the discount rate during the high-growth (i.e., less predictable) period or periods should generally be higher than during the stable-growth period. For example, a high-growth firm may have a beta significantly above 1. However, when the growth rate becomes stable, it is reasonable to assume that the beta should approximate 1. A reasonable approximation of the discount rate to be used during the stable-growth period is the industry average cost of equity or weighted average cost of capital.
Equation (7.15) can be modified to use the growing-annuity model26 to approximate growth during the high-constant-growth period and the constant-growth model for the terminal period. This formulation requires fewer computations if the number of annual cash-flow projections is large. As such, P0,FCFF also can be estimated as shown in the following equation.
(7.16)
See Exhibit 7.6 for an illustration of when and how to apply the variable-growth model.
Exhibit 7.6 The Variable-Growth Valuation Model
Estimate the enterprise value of a firm (P 0) whose free cash flow is projected to grow at a compound annual average rate of 35% for the next five years. Growth then is expected to slow to a more normal 5% annual growth rate. The current year's cash flow to the firm is $4 million. The firm's weighted-average cost of capital during the high-growth period is 18% and 12% beyond the fifth year, as growth stabilizes. The firm's cash in excess of normal operating balances is assumed to be zero. Therefore, using Eq. (7.15), the present value of cash flows during the high-growth forecast period is as follows:
Calculation of the terminal value is as follows:
Alternatively, using the growing annuity model to value the high-growth period and the constant-growth model to value the terminal period (see Eq. (7.16)), the present value of free cash flow to the firm could be estimated as follows:
Valuing firms subject to multiple growth periods
Some companies display initial periods of what could be described as hypergrowth, followed by an extended period of rapid growth, before stabilizing at a more normal and sustainable growth rate. Initial public offerings and start-up companies may follow this model. This pattern reflects growth over their initially small revenue base, the introduction of a new product, or the sale of an existing product to a new or underserved customer group. Calculating the discounted cash flows is computationally more difficult for firms expected to grow for multiple periods, each of whose growth rates differ, before assuming a more normal long-term growth rate. Because each period's growth rate differs, the cost of capital in each period differs. Consequently, each year's cash flows must be discounted by the “cumulative cost of capital” from prior years. A more detailed discussion of this method is provided on the companion site to this book in the file folder entitled “Example of Supernormal Growth Model.”
Determining Growth Rates
Projected growth rates for sales, profit, cash flow, or other financial variables can be readily calculated based on the historical experience of the firm or of the industry. See the document entitled “Primer on Cash-Flow Forecasting” on the companion site to this text for a discussion of how to apply regression analysis to projecting a firm's cash flow.
The Duration of the High-Growth Period
Intuition suggests that the length of the high-growth period should be longer when the current growth rate of a firm's cash flow is much higher than the stable growth rate. This is particularly true when the high-growth firm has a relatively small market share and there is little reason to believe that its growth rate will slow in the foreseeable future. For example, if the industry is expected to grow at 5% annually and the target firm, which has only a negligible market share, is growing at three times that rate, it may be appropriate to assume a high-growth period of five to ten years.
Moreover, if the terminal value constitutes a substantial percentage (e.g., three-fourths) of the total PV, the annual forecast period should be extended beyond the customary five years to at least ten years. The extension of the time period reduces the impact of the terminal value in determining the market value of the firm. Historical evidence shows that sales and profitability tend to revert to normal levels within five to ten years.27 This suggests that the conventional use of a five- to ten-year annual forecast before calculating a terminal value makes sense.28
The Stable or Sustainable Growth Rate
The stable growth rate generally is going to be less than or equal to the overall growth rate of the industry in which the firm competes or the general economy. Stable growth rates in excess of these levels implicitly assume that the firm's cash flow eventually will exceed that of its industry or the general economy. Similarly, for multinational firms, the stable growth rate should not exceed the projected growth rate for the world economy or a particular region of the world.
Determining the Appropriate Discount Rate
The appropriate discount rate is generally the target's cost of capital if the acquirer is merging with a higher-risk business, resulting in an increase in the cost of capital of the combined firms. However, either the acquirer's or the target's cost of capital may be used if the two firms are equally risky and based in the same country.
Valuing firms under special situations
A firm's cash flows may be affected by temporary, long-term, or cyclical factors. Each scenario requires a different solution. How each scenario can be addressed is discussed next.
Firms with Temporary Problems
When cash flow is temporarily depressed as a result of strikes, litigation, warranty claims, employee severance, or other one-time events, it is generally safe to assume that cash flow will recover in the near term. One solution is to base projections on cash flow prior to the one-time event. Alternatively, actual cash flow could be adjusted for the one-time event by adding back the pretax reduction in operating profits of the one-time event and recalculating after-tax profits. If the cost of the one-time event is not displayed on the firm's financial statements, it is necessary to compare each expense item as a percentage of sales in the current year with the prior year. Any expense items that look abnormally high should be “normalized” by applying an average ratio from prior years to the current year's sales. Alternatively, the analyst could use the prior year's operating margin to estimate the current year's operating income.
Firms with Longer-Term Problems
Deteriorating cash flow may be symptomatic of a longer-term deterioration in the firm's competitive position due to poor strategic decisions having been made by management. Under such circumstances, the analyst must decide whether the firm is likely to recover and how long it would take to restore the firm's former competitive position. The answer to such questions requires the identification of the cause of the firm's competitive problems. Firms with competitive problems often are less profitable than key competitors or the average firm in the industry.
Therefore, the firm's recovery can be included in the forecast of cash flows by allowing its operating profit margin to increase gradually to the industry average or the level of the industry's most competitive firm. The speed of the adjustment depends on the firm's problems. For example, replacing outmoded equipment or back-office processing systems may be done more quickly than workforce reductions when the labor force is unionized or if the firm's products are obsolete.
Cyclical Firms
The projected cash flows of firms in highly cyclical industries can be distorted, depending on where the firm is in its business cycle. The most straightforward solution is to project cash flows based on an average historical growth rate during a prior full business cycle for the firm. Alternatively, if the recovery from a recession is expected to be sluggish, the analyst may extend the forecast period to as much as ten years and allow the currently depressed level of cash flow to gradually grow to its more normal historical level.
Using the enterprise method to estimate equity value
A firm's common equity value often is determined by first estimating its enterprise value, adding the value of nonoperating assets, and then deducting the value of debt and other nonequity claims on future cash flows. What follows is a discussion of how to value nonequity claims and nonoperating assets. If these factors already are included in the projections of future cash flows, they should not be deducted from the firm's enterprise value. This approach is especially useful when a firm's capital structure (i.e., debt–to–total capital ratio) is expected to remain stable.
Valuing Nonequity Claims
Nonequity claims commonly include long-term debt, operating leases, deferred taxes, unfunded pension liabilities, preferred stock, employee options, and minority interests. How to value these items is discussed next.
Determining the Market Value of Long-Term Debt
The current value of a firm's debt generally is independent of its enterprise value for stable or financially healthy companies. This is not true for financially distressed or unstable firms and for hybrid securities such as convertible debt and convertible preferred stock.
Financially Stable Firms
In some instances, the analyst may not know the exact principal repayment schedule for the target firm's debt. To determine the market value of debt, treat the book value of all of the firm's debt as a conventional coupon bond, in which interest is paid annually or semiannually and the principal is repaid at maturity. The coupon is the interest on all of the firm's debt, and the principal at maturity is a weighted average of the maturity of all of the debt outstanding. The weighted-average principal at maturity is the sum of the amount of debt outstanding for each maturity date multiplied by its share of total debt outstanding. The estimated current market value of the debt then is calculated as the sum of the annuity value of the interest expense per period plus the present value of the principal (see Exhibit 7.7).29
Note that the book value of debt may be used unless interest rates have changed significantly since the debt was incurred or the likelihood of default is high. In these situations, value each bond issued by the firm separately by discounting cash flows at yields to maturity for comparably rated debt with similar maturities issued by similar firms. Book value also may be used for floating rate debt, since its market value is unaffected by fluctuations in interest rates.
In the United States, the current market value of a company's debt can be determined using the FINRA TRACE database. For example, the Home Depot Inc.'s 5.40% fixed coupon bond maturing on March 1, 2016, was priced at $112.25 on September 5, 2010, or 1.1225 times par value. Multiply this number by the amount of debt outstanding, which is $3,040,000, to determine its market value of $3,412,400 on that date.
Financially Distressed Firms
Valuing debt for distressed or troubled firms is more challenging than for healthier companies. The value of the debt reflects the riskiness of the firm and fluctuates with the cash flows of the firm and will usually be a fraction of its book value. Because the debt takes on the riskiness of equity, debt and equity are not independent, and the calculation of a firm's equity value cannot be calculated by simply subtracting the market value of the firm's debt from the firm's enterprise value.
One method is to utilize scenarios as described in Chapter 8 (see Exhibit 8.11) in which the firm's enterprise value is estimated using two scenarios: one in which the firm is able to return to financial health and one in which the firm's position deteriorates. For each scenario, calculate the firm's enterprise value and deduct the book value of the firm's debt and other nonequity claims. Each scenario is weighted by the probability the analyst attaches to each scenario, such that the resulting equity value estimate represents a probability weighted average of the scenarios.
Hybrid Securities (Convertible Bonds and Preferred Stock)
Convertible bonds and stock represent conventional debt and preferred stock plus a conversion feature or call option to convert the bonds or stock to shares of common equity at a stipulated price per share. Since the value of the debt reflects the value of common equity, it is not independent of the firm's enterprise value and therefore cannot be deducted from the firm's enterprise value to estimate equity value. One approach to valuing such debt and preferred stock is to assume that all of it will be converted into equity when a target firm is acquired. This makes the most sense when the offer price for the target exceeds the price per share at which the debt can be converted. See Exhibit 9.8 in Chapter 9 for an illustration of this method.
Exhibit 7.7 Estimating the Market Value of a Firm's Debt and Capitalized Operating Leases
According to its 10K report, Gromax, Inc. has two debt issues outstanding, with a total book value of $220 million. Annual interest expense on the two issues totals $20 million. The first issue, whose current book value is $120 million, matures at the end of five years; the second issue, whose book value is $100 million, matures in ten years. The weighted average maturity of the two issues is 7.27 years (i.e., 5 × (120/220) + 10 × (100/220)). The current cost of debt maturing in seven to ten years is 8.5%.
The firm's 10K also shows that the firm has annual operating lease expenses of $2.1, $2.2, $2.3, and $5 million in the fourth year and beyond (the 10K indicated the firm's cumulative value in the fourth year and beyond to be $5 million). (For our purposes, we may assume that the $5 million is paid in the fourth year.) What is the total market value of the firm's total long-term debt, including conventional debt and operating leases?
a The present value of debt is calculated using the PV of an annuity formula for 7.27 years and an 8.5% interest rate plus the PV of the principal repayment at the end of 7.27 years. Alternatively, rather than using the actual formulas, a present value interest factor annuity table and a present value interest factor table could have been used to calculate the PV of debt.
Determining the Market Value of Operating Leases
Both capital and operating leases also should be counted as outstanding debt of the firm. When a lease is classified as a capital lease, the present value of the lease expenses is treated as debt. Interest is imputed on this amount that corresponds to debt of comparable risk and maturity. This imputed interest is shown on the income statement. Although operating lease expenses are treated as operating expenses on the income statement, they are not counted as part of debt on the balance sheet for financial reporting purposes. For valuation purposes, operating leases should be included in debt because failure to meet lease payments results in the loss of the leased asset, which contributes to the generation of operating cash flows.
Future operating lease expenses are shown in financial statement footnotes. These future expenses should be discounted at an interest rate comparable to current bank lending rates for unsecured assets. The discount rate may be approximated using the firm's current pretax cost of debt, reflecting the market rate of interest that lessors would charge the firm. If future operating lease expenses are not available, the analyst can approximate the principal amount of the operating leases by discounting the current year's operating lease payment as a perpetuity using the firm's cost of debt (see Exhibit 7.7).
Determining the Cash Impact of Deferred Taxes
Deferred tax assets and liabilities arise when the tax treatment of an item is temporarily different from its financial accounting treatment. Deferred taxes can arise from many sources, such as uncollectible accounts receivable, warranties, options expensing, pensions, leases, net operating losses, depreciable assets, inventories, installment receivables, and intangible drilling and development costs. Deferred taxes have a current and a future or noncurrent impact on cash flow. The current impact is reflected by adding the change in deferred tax liabilities and subtracting the change in deferred tax assets in the calculation of working capital. The noncurrent impact of deferred assets generally is shown in other long-term assets and deferred tax liabilities in other long-term liabilities on the firm's balance sheet.
For example, GAAP may allow the current deduction of a $20,000 product warranty expense, reducing taxable income for reporting the firm's financial performance in the current accounting period to its shareholders. However, the tax authorities may allow only an $8,000 current tax deduction—that is, the amount actually paid by the firm during the current period to satisfy claims. The remaining $12,000 represents a balance sheet reserve set up by the firm in anticipation of future claims. Consequently, there will be a temporary difference if the tax authorities allow for the remaining $12,000 to be deducted in subsequent years. Assuming the firm's marginal tax rate is 40%, the firm would show a tax savings of $8,000 (i.e., $20,000 × 0.4) for financial reporting purposes; for tax purposes, however, tax savings would only be $3,200 (i.e., $8,000 × 0.4). Therefore, actual taxes paid during the current period are $4,800 (i.e., $8,000 – $3,200) higher than they would have been had the IRS allowed the deduction of the entire expense.
A deferred tax asset is a future tax benefit in that deductions not allowed in the current period may be realized in some future period. In the preceding example, the $12,000 is deductible when an equivalent amount of warranty claims are paid, resulting in future tax savings of $4,800 (i.e., 0.4 × $12,000).30 In this instance, the deferred tax asset would equal $4,800. A deferred tax liability represents the increase in taxes payable in future years as a result of taxable temporary differences existing at the end of the current year. The excess of accelerated depreciation taken for tax purposes over straight-line depreciation often used for financial reporting results in a reduction in the firm's current tax liability but an increase in future tax liabilities when the rate of the firm's spending on plant and equipment slows. The amount of the deferred tax liability would equal the excess of accelerated over straight-line depreciation times the firm's marginal tax rate.
For valuation purposes, noncurrent deferred taxes may be valued separately, with deferred tax assets added to and deferred tax liabilities subtracted from the present value of the firm's operating cash flows in the estimation of the firm's equity value. Alternatively, the PV of net deferred tax liabilities (i.e., deferred tax assets less deferred tax liabilities) may be deducted from the firm's enterprise value in calculating equity value. The use of net deferred tax liabilities is appropriate, since deferred tax liabilities generally are larger than deferred tax assets for most firms in the absence of significant NOLs.31
The impact of timing differences can be incorporated into present value estimates by including the impact of the factors affecting a firm's effective tax rate in projections of the individual components of cash flow.32 Alternatively, the analyst could make assumptions about how the firm's effective tax rate will change and value current and future deferred tax liabilities separately from the calculation of the present value of the projected cash flows. As such, the impact on free cash flow of a change in deferred taxes can be approximated by the difference between a firm's marginal and effective tax rate multiplied by the firm's operating income before interest and taxes. The author recommends calculating the impact of deferred taxes separately, since they can arise from many sources.
The greatest challenge with deferred taxes is determining when they are likely to come due. The choice of tax rate in estimating future after-tax operating income has different implications under alternative scenarios. The first scenario assumes after-tax operating income is calculated using the firm's current effective tax rate indefinitely, implicitly assuming that the firm's deferred tax liabilities will never have to be repaid. In the second scenario, the analyst estimates after-tax operating income using the firm's marginal rate indefinitely, which implies that the firm cannot defer taxes beyond the current period. In the final scenario, the analyst assumes the effective tax rate is applicable for a specific number of years (e.g., five years) before reverting to the firm's marginal tax rate.
The use of the effective tax rate for five years increases the deferred tax liability to the firm during that period as long as the effective rate is below the marginal rate. The deferred tax liability at the end of the fifth year can be estimated by adding to the current cumulated deferred tax liability the incremental liability for each of the next five years. This incremental liability is the sum of projected EBIT times the difference between the marginal and effective tax rates. Assuming tax payments on the deferred tax liability at the end of the fifth year will be spread equally over the following ten years, the present value of the tax payments during that ten-year period is then estimated and discounted back to the current period (see Exhibit 7.8).
Exhibit 7.8 Estimating Common Equity Value by Deducting the Market Value of Debt, Preferred Stock, and Deferred Taxes from the Enterprise Value
Operating income, depreciation, working capital, and capital spending are expected to grow 10% annually during the next five years and 5% thereafter. The book value of the firm's debt is $300 million, with annual interest expense of $25 million and term to maturity of four years. The debt is a conventional “interest only” note with a repayment of principal at maturity. The firm's annual preferred dividend expense is $20 million. The prevailing market yield on preferred stock issued by similar firms is 11%. The firm does not have any operating leases, and pension and healthcare obligations are fully funded. The firm's current cost of debt is 10%. The firm's weighted-average cost of capital is 12%. Because it is already approximating the industry average, it is expected to remain at that level beyond the fifth year. Because of tax deferrals, the firm's current effective tax rate of 25% is expected to remain at that level for the next five years. The firm's current net deferred tax liability is $300 million. The projected net deferred tax liability at the end of the fifth year is expected to be paid off in ten equal amounts during the following decade. The firm's marginal tax rate is 40% and will be applied to the calculation of the terminal value. What is the value of the firm to common equity investors?
Financial Data (in $ million)
Notes:
a See Eq. (7.16).
b The terminal value reflects the recalculation of the fifth year after-tax operating income using the marginal tax rate of 40% and applying the constant-growth model. Fifth-year free cash flow equals $322.1(1 − 0.4) + $12.9 − $48.3 − $64.4 = $93.5.
c The present value of debt is calculated using the PV of an annuity for four years and a 10% interest rate plus the PV of the principal repayment at the end of four years. The firm's current cost of debt of 10% is higher than the implied interest rate of 8% ($25/$300) on the loan currently on the firm's books. This suggests that the market rate of interest has increased since the firm borrowed the $300 million “interest only” note.
d The market value of preferred stock (PVPFD) is equal to the preferred dividend divided by the cost of preferred stock.
Determining the Cash Impact of Unfunded Pension Liabilities
Publicly traded firms are required to identify the present value of their unfunded pension obligations. If not shown as a separate line item on the firm's balance sheet, they typically are shown in the company's notes to the balance sheet. If the unfunded liability is not shown explicitly in the footnote, the footnote should indicate where it has been included.
Determining the Cash Impact of Employee Options
Firms commonly offer key employees incentive compensation in the form of options to buy stock. Holders of such options have the right, but not the obligation, to buy a firm's common stock at a stipulated price (i.e., exercise price). Since such options may be exercised over a number of years, the firm's share price could eventually exceed the exercise price, making such options valuable. Exercising these options impacts cash flows as firms attempt to repurchase shares to mitigate the dilution in earnings per share and the wealth transfer from current shareholders to option holders who buy newly issued shares at a discount to the prevailing share price at the time options are exercised. Consequently, the present value of these future cash outlays to repurchase stock should be deducted from the firm's enterprise value.33 Accounting rules require firms to report the present value of all stock options outstanding based on estimates provided by option pricing models (see Chapter 8) in the footnotes to financial statements.
Determining the Cash Impact of Other Provisions and Contingent Liabilities
Provisions (i.e., reserves set up for anticipated charges) for future layoffs due to restructuring usually are recorded on the balance sheet in undiscounted form, since they usually represent cash outlays to be made in the near term. Such provisions should be deducted from enterprise value because they are equivalent to debt.
Contingent liabilities, whose future cash outlays depend on the occurrence of certain events, are not shown on the balance sheet but rather in footnotes. Examples include pending litigation and loan guarantees. Since such expenses are tax deductible, estimate the present value of future after-tax cash outlays discounted at the firm's cost of debt and deduct from the firm's enterprise value.
Determining the Market Value of Minority Interests
When a firm owns less than 100% of another business, it is shown on the firm's consolidated balance sheet. That portion of the business not owned by the firm is shown as a minority interest. Note that for valuation purposes the minority interest has a claim on the assets of the majority-owned subsidiary and not on the parent firm's assets. If the less than wholly-owned subsidiary is publicly traded, value the minority interest by multiplying the minority's ownership share by the market value of the subsidiary. If the subsidiary is not publicly traded and you as an investor in the subsidiary have access to its financials, value the subsidiary by discounting the subsidiary's cash flows at the cost of capital appropriate for the industry in which it competes. Alternatively, value the subsidiary using multiples of earnings or cash flow available for comparable publicly traded firms (see Chapter 8).
Valuing nonoperating assets
Other assets not directly used in operating the firm also may contribute to the value of the firm, including such nonoperating assets as cash in excess of normal operating requirements, investments in other firms, and unused or underutilized assets. The value of such assets should be added to the value of the discounted cash flows from operating assets to determine the total value of the firm.
Cash and Marketable Securities
Cash and short-term marketable securities, held in excess of the target firm's minimum operating cash balance, represent value that should be added to the present value of net operating assets to determine the value of the firm. If a firm has cash balances in excess of those required to satisfy operating requirements at the beginning of the forecast period, the valuation approach outlined in this chapter, which focuses on cash flow generated from net operating assets, assumes implicitly that it is treated as a one-time cash payout to the target firm's shareholders. Otherwise, the excess cash should be added to the present value of the firm's operating cash flows. On an ongoing basis, projected excess cash flows are assumed implicitly to be paid out to shareholders either as dividends or share repurchases. Note that the estimate of the firm's minimum cash balance should be used in calculating net working capital in determining free cash flow from operations.
What constitutes the minimum cash balance depends on the firm's cash conversion cycle. This cycle reflects the firm's tendency to build inventory, sell products on credit, and later collect accounts receivable. The delay between the investment of cash in the production of goods and the eventual receipt of cash in this process reflects the amount of cash tied up in working capital. The length of time cash is committed to working capital can be estimated as the sum of the firm's inventory conversion period plus the receivables collection period less the payables deferral period.
The inventory conversion period is the average length of time in days required to produce and sell finished goods. The receivables collection period is the average length of time in days required to collect receivables. The payables deferral period is the average length of time in days between the purchase of and payment for materials and labor. To finance this investment in working capital, a firm must maintain a minimum cash balance equal to the average number of days its cash is tied up in working capital times the average dollar value of sales per day. The inventory conversion and receivables collection periods are calculated by dividing the dollar value of inventory and receivables by average sales per day. The payments deferral period is estimated by dividing the dollar value of payables by the firm's average cost of sales per day. See Exhibit 7.9 for an illustration of how to estimate minimum and excess cash balances.
Exhibit 7.9 Estimating Minimum and Excess Cash Balances
Prototype Incorporated's current inventory, accounts receivable, and accounts payable are valued at $14 million, $6.5 million, and $6 million, respectively. Projected sales and cost of sales for the coming year total $100 million and $75 million, respectively. Moreover, the value of the firm's current cash and short-term marketable securities is $21,433,000. What minimum cash balance should the firm maintain? What is the firm's current excess cash balance?
While excess cash balances should be added to the present value of operating assets, any cash deficiency should be subtracted from the value of operating assets to determine the value of the firm. This reduction in the value reflects the need for the acquirer to invest additional working capital to make up any deficiency.
The method illustrated in Exhibit 7.9 may not work for firms that manage working capital aggressively, so receivables and inventory are very low relative to payables. An alternative is to compare the firm's cash and marketable securities as a percent of revenue with the industry average. If the firm's cash balance exceeds the industry average, the firm has excess cash balances, assuming there are no excess cash balances for the average firm in the industry. For example, if the industry average cash holdings as a percent of annual revenue is 5% and the target firm has 8%, the target holds excess cash equal to 3% of its annual revenue.
Investments in Other Firms
Many target firms have investments in other firms. These investments generally have value and need to be included in any valuation of the target's nonoperating assets. Such investments, for financial reporting purposes, may be classified as minority passive investments, minority active investments, or majority investments. These investments need to be valued individually and added to the present value of the firm's operating assets to determine the total value of the firm. Table 7.7 describes their accounting treatment and valuation methodology.
Table 7.7. Investments in Other Firms
| Percent Ownership of Firm | Accounting Treatment | Valuation Methodology |
| Minority, Passive Investments (Investment <20% of other firm) | • Assets held to maturity are carried at book value with interest or dividends shown on income statement • Investments available for sale are carried at market value, with unrealized gains/losses included as equity and not as income • Trading investments are shown at market value with unrealized gains/losses shown on the income statementa |
• For investments recorded on investing firm's balance sheet at book value: 1. Value firm in which investment held 2. Multiply the firm's value by the proportionate share held by the investing firm to determine the investment's market value 3. Add the investment's market value to the value of the investing firm's nonoperating assets • For investments recorded at market value, add to the investing firm's nonoperating assets |
| Minority, Active Investments—Equity Method (Investment is between 20% and 50% of the other firm's value) | ||
| Majority Investments (Investment >50% of other firm's value) | • Requires consolidation of both firms' balance sheetsb • Shares held by other investors are shown as a noncontrolling or minority interest in the shareholders' equity account of the consolidated firms' balance sheet |
a Financial services firms may have to revalue their assets more frequently to reflect changes in their market value. Under so-called “mark to market” requirements, banks could be required to revalue their assets daily.
b A firm may be required to consolidate both firms' balance sheets even if it owns less than 50% if its ownership position gives it effective control of the other firm.
c If the subsidiary is in a different industry from the parent, a weighted-average cost of capital reflecting the different costs of capital for the two businesses should be used to discount cash flows generated by the consolidated businesses.
d If a subsidiary is valued at $500 million and the parent owns 75% of the subsidiary, the value of the subsidiary to the parent is $375 million (i.e., $500 million – 0.25 × $500 million to reflect the value owned by minority shareholders).
Unutilized and Undervalued Assets
Real estate on the books of the target firm at historical cost may have an actual market value substantially in excess of the value stated on the balance sheet. In other cases, a firm may have more assets on hand to satisfy future obligations than it currently might need (e.g., an overfunded pension fund). Examples of intangible assets include patents, copyrights, licenses, and trade names. Intangible assets may represent significant sources of value on a target firm's balance sheet. However, they tend to be difficult to value. There is evidence that the value of intangible spending, such as R&D expenditures, is indeed factored into a firm's current share price.34 Despite this evidence, it is doubtful that the value of intellectual property rights, such as patents, which a firm may hold but not currently use, is reflected fully in the firm's current share price. In the absence of a predictable cash-flow stream, their value may be estimated using the Black–Scholes model (see Chapter 8) or the cost of developing comparable inventions or technologies.
Patents
How patents are valued depends on whether they have current applications, are linked to existing products or services, or can be grouped and treated as a single patent portfolio. Many firms have patents for which no current application within the firm has yet been identified. However, the patent may have value to an external party. Before closing, the buyer and seller may negotiate a value for a patent that has not yet been licensed to a third party based on the cash flows that can reasonably be expected to be generated over its future life. In cases where the patent has been licensed to third parties, the valuation is based on the expected future royalties to be received from licensing the patent over its remaining life.
When a patent is linked to a specific product, it is normally valued based on the “cost avoidance” method. This method uses after-tax market-based royalty rates paid on comparable patents multiplied by the projected future stream of revenue from the products whose production depends on the patent discounted to its present value at the cost of capital.
Products and services often depend on a number of patents. This makes it exceedingly difficult to determine the amount of the cash flow generated by the sale of the products or services to be allocated to each patent. In this case, the patents are grouped together as a single portfolio and valued as a group using a single royalty rate applied to a declining percentage of the company's future revenue. The declining percentage of revenue reflects the likely diminishing value of the patents with the passage of time. This cash-flow stream is then discounted to its present value.
Trademarks and Service Marks
A trademark is the right to use a name associated with a company, product, or concept. A service mark is the right to use an image associated with a company, product, or concept. Trademarks and service marks have recognition value. Examples include Bayer Aspirin and Kellogg's Corn Flakes. Name recognition reflects the firm's longevity, cumulative advertising expenditures, the overall effectiveness of its marketing programs, and the consistency of perceived product quality. The cost avoidance approach,35 the PV of projected license fees,36 or the use of recent transactions can be helpful in estimating a trademark's value.
Overfunded Pension Plans
Defined benefit pension plans require firms to accumulate financial assets to enable them to satisfy estimated future employee pension payments. During periods of rising stock markets, such as during the 1990s, firms with defined benefit pension plans routinely accumulated assets in excess of the amount required to meet expected obligations. As owners of the firm, shareholders have the legal right to these excess assets. In practice, if such funds are liquidated and paid out to shareholders, the firm has to pay taxes on the pretax value of these excess assets. Therefore, the after-tax value of such funds may be added to the present value of projected operating cash flows.
Putting it all together
Table 7.8 shows how Home Depot's equity value is estimated by first determining the firm's total operating value, adding the value of nonoperating assets to derive enterprise value, and subtracting the value of all nonequity claims to calculate equity value. Home Depot is the largest home improvement materials retailer in the United States.
Table 7.8. Determining Home Depot's Equity Value Using the Enterprise Method
Explanatory Notes
a WACC calculation:
ke = 0.0265 + 1.10 (0.055) = 8.43%, where 2.65% is the ten-year Treasury bond rate on September 5, 2010, and 1.21 is the firm's beta provided by
I = 6.85%, pretax cost of debt estimated as the yield to maturity on BBB+ rated debt per Yahoo! Finance on 9/5/2010. Weights for debt and equity of 31% and 69%, respectively, are based on firm's current debt–to–capital ratio held constant throughout the forecast period.
WACC = 8.70 × 0.69 + 6.85 (1 – 0.4) × 0.31 = 7.28
WACC for terminal period equal to average for comparable retail companies per Yahoo! Finance.
b Operating Leases:
Capitalized value of operating leases = PV of lease expense provided in financial statement footnotes discounted at firm's cost of debt.
Operating lease equipment estimated useful life = 25 years; estimated annual operating lease depreciation expense = $6,450/25 = $258.
c Working Capital $3,537 $3,812 $3,850 $3,927 $4,084 $4,288 $4,503 $4,683 $4,870 $5,040 $5,192.
d Terminal period enterprise cash flow recalculated using 40% marginal tax rate.
e Excess cash is zero, since minimum balances estimated using Exhibit 7.9 method exceed actual year-end 2009 cash balances.
f Excludes goodwill but includes $33 million in notes receivable.
g Market Value of Home Depot Debt:
h PV of Net Noncurrent DTLs (Net Deferred Tax Assets – Deferred Tax Liabilities) Calculation:
| Future Value as of 2019 = $3,570Adds current net deferred tax liability to the sum of the projected EBIT times the difference between marginal and effective tax rates. |
| Present Value= $1,1022019 net deferred tax liability paid off in equal amounts during following decade. |
The exhibit is divided into three panels. The top panel displays the primary assumptions underlying the valuation. The second panel shows how the total operating value of the firm is determined. The bottom panel—“Explanatory Notes”—provides details on how various line items in the exhibit were calculated. Cash flow is projected for ten years, reflecting the anticipated slow recovery of the firm's free cash flow from the 2008–2009 recession. The actual formula used to construct the Excel-based model underlying this exhibit is provided in an Excel file entitled “Determining Home Depot's Equity Value Using the Enterprise Method” on the companion site to this book.
Some things to remember
Value is created for shareholders when firms invest capital that generates future cash flows at financial returns exceeding their cost of capital. Therefore, firms earning financial returns in excess of their cost of capital should focus on growth, while those earning less than their cost of capital should concentrate on improving their returns.
Discounted-cash-flow methods such as the zero-, constant-, and variable-growth methods are widely used to estimate the value of the firm. GAAP-based cash flows must be adjusted to create valuation cash flows for this purpose. Such cash flows include FCFF or enterprise cash flow, cash available for investors and lenders, which reflects cash from operating and investing activities. Alternatively, FCFE, free cash flow to equity investors or equity cash flow, includes cash from operating, investing, and financing activities. The present value of enterprise cash flows often is referred to as the enterprise value of the firm. Valuation estimates based on equity cash flows are called the equity value. A common technique for estimating equity value is to deduct the market value of the target firm's debt and other nonequity claims from its enterprise value.
Discussion Questions
7.1. What is the significance of the weighted-average cost of capital? How is it calculated? Do the weights reflect the firm's actual or target debt–to–total capital ratio? Explain your answer.
7.2. What does a firm's β measure? What is the difference between an unlevered and levered β? Why is this distinction significant?
7.3. Under what circumstances is it important to adjust the capital asset pricing model for firm size? Why?
7.4. What are the primary differences between FCFE and FCFF?
7.5. Explain the conditions under which it makes the most sense to use the zero-growth and constant-growth DCF models. Be specific.
7.6. Which DCF valuation methods require the estimation of a terminal value? Why?
7.7. Do small changes in the assumptions pertaining to the estimation of the terminal value have a significant impact on the calculation of the total value of the target firm? If so, why?
7.8. How would you estimate the equity value of a firm if you knew its enterprise value and the present value of all nonoperating assets, nonoperating liabilities, and long-term debt?
7.9. Why is it important to distinguish between operating and nonoperating assets and liabilities when valuing a firm? Be specific.
7.10. Explain how you would value a patent under the following situations: a patent with no current application, a patent linked to an existing product, and a patent portfolio.Answers to these Chapter Discussion Questions are available in the Online Instructor's Manual for instructors using this book.
Practice Problems and Answers
7.11. ABC Incorporated shares are currently trading for $32 per share. The firm has 1.13 billion shares outstanding. In addition, the market value of the firm's outstanding debt is $2 billion. The ten-year Treasury bond rate is 6.25%. ABC has an outstanding credit record and earned a AAA rating from the major credit rating agencies. The current interest rate on AAA corporate bonds is 6.45%. The historical risk premium over the risk-free rate of return is 5.5 percentage points. The firm's beta is estimated to be 1.1, and its marginal tax rate, including federal, state, and local taxes, is 40%.
a. What is the cost of equity?
b. What is the after-tax cost of debt?
7.12 HiFlyer Corporation does not currently have any debt. Its tax rate is 0.4 and its unlevered beta is estimated by examining comparable companies to be 2.0. The ten-year bond rate is 6.25%, and the historical risk premium over the risk-free rate is 5.5%. Next year, HiFlyer expects to borrow up to 75% of its equity value to fund future growth.
a. Calculate the firm's current cost of equity.
b. Estimate the firm's cost of equity after the firm increases its leverage to 75% of equity.
7.13. Abbreviated financial statements are given for Fletcher Corporation in Table 7.9. Year-end working capital in 2009 was $160 million, and the firm's marginal tax rate was 40% in both 2010 and 2011. Estimate the following for 2010 and 2011:
7.14. In 2011, No Growth Incorporated had operating income before interest and taxes of $220 million. The firm was expected to generate this level of operating income indefinitely. The firm had depreciation expense of $10 million that year. Capital spending totaled $20 million during 2011. At the end of 2010 and 2011, working capital totaled $70 million and $80 million, respectively. The firm's combined marginal state, local, and federal tax rate was 40%, and its outstanding debt had a market value of $1.2 billion. The ten-year Treasury bond rate is 5%, and the borrowing rate for companies exhibiting levels of creditworthiness similar to No Growth is 7%. The historical risk premium for stocks over the risk-free rate of return is 5.5%. No Growth's beta was estimated to be 1.0. The firm had 2.5 million common shares outstanding at the end of 2011. No Growth's target debt–to–total capital ratio is 30%.
a. Estimate free cash flow to the firm in 2011.
b. Estimate the firm's weighted average cost of capital.
c. Estimate the enterprise value of the firm at the end of 2011, assuming that it will generate the value of free cash flow estimated in (a) indefinitely.
d. Estimate the value of the equity of the firm at the end of 2011.
7.15. Carlisle Enterprises, a specialty pharmaceutical manufacturer, has been losing market share for three years because several key patents have expired. Free cash flow to the firm is expected to decline rapidly as more competitive generic drugs enter the market. Projected cash flows for the next 5 years are $8.5 million, $7 million, $5 million, $2 million, and $0.5 million. Cash flow after the fifth year is expected to be negligible. The firm's board has decided to sell the firm to a larger pharmaceutical company that is interested in using Carlisle's product offering to fill gaps in its own product line until it can develop similar drugs. Carlisle's WACC is 15%. What purchase price must Carlisle obtain to earn its cost of capital?
7.16. Ergo Unlimited's current year's free cash flow to equity is $10 million. It is projected to grow at 20% per year for the next five years. It is expected to grow at a more modest 5% beyond the fifth year. The firm estimates that its cost of equity will be 12% during the next five years and then will drop to 10% beyond the fifth year as the business matures. Estimate the firm's current market value.
7.17. In the year in which it intends to go public, a firm has revenues of $20 million and net income after taxes of $2 million. The firm has no debt, and revenue is expected to grow at 20% annually for the next five years and 5% annually thereafter. Net profit margins are expected to remain constant throughout. Annual capital expenditures equal depreciation, and the change in working capital requirements is minimal. The average beta of a publicly traded company in this industry is 1.50 and the average debt-to-equity ratio is 20%. The firm is managed conservatively and will not borrow through the foreseeable future. The Treasury bond rate is 6%, and the marginal tax rate is 40%. The normal spread between the return on stocks and the risk-free rate of return is believed to be 5.5%. Reflecting the slower growth rate in the sixth year and beyond, the discount rate is expected to decline to the industry average cost of capital of 10.4%. Estimate the value of the firm's equity.
7.18. The information in Table 7.10 is available for two different common stocks: Company A and Company B.
a. Estimate the cost of equity for each firm.
b. Assume that the companies' growth rates will continue at the same rate indefinitely. Estimate the per share value of each company's common stock.
7.19. You have been asked to estimate the beta of a high-technology firm that has three divisions with the characteristics shown in Table 7.11.
a. What is the beta of the equity of the firm?
b. If the risk-free return is 5% and the spread between the return on all stocks is 5.5%, estimate the cost of equity for the software division.
c. What is the cost of equity for the entire firm?
d. Free cash flow to equity investors in the current year (FCFE) for the entire firm is $7.4 million and for the software division is $3.1 million. If the total firm and the software division are expected to grow at the same 8% rate into the foreseeable future, estimate the market value of the firm and of the software division.
d. PV (total firm) = $147.96; PV (software division) = $41.88
7.20 Financial Corporation wants to acquire Great Western Inc. Financial has estimated the enterprise value of Great Western at $104 million. The market value of Great Western's long-term debt is $15 million, and cash balances in excess of the firm's normal working capital requirements are $3 million. Financial estimates the present value of certain licenses that Great Western is not currently using to be $4 million. Great Western is the defendant in several outstanding lawsuits. Financial Corporation's legal department estimates the potential future cost of this litigation to be $3 million, with an estimated present value of $2.5 million. Great Western has 2 million common shares outstanding. What is the adjusted equity value of Great Western per common share?
Table 7.9. Abbreviated Financial Statements for Fletcher Corporation ($ million)
| 2010 | 2011 | |
| Revenues | $600 | $690 |
| Operating expenses | 520 | 600 |
| Depreciation | 16 | 18 |
| Earnings before interest and taxes | 64 | 72 |
| Less interest expense | 5 | 5 |
| Less taxes | 23.6 | 26.8 |
| Equals: net income | 35.4 | 40.2 |
| Addendum | ||
| Year-end working capital | 150 | 200 |
| Principal repayment | 25 | 25 |
| Capital expenditures | 20 | 10 |
Table 7.10. Common Stocks in Problem 7.18
| Company A | Company B | |
| Free cash flow per-share at the end of year 1 | $1.00 | $5.00 |
| Growth rate in cash flow per share | 8% | 4% |
| Beta | 1.3 | 0.8 |
| Risk-free return | 7% | 7% |
| Expected return on all stocks | 13.5% | 13.5% |
Table 7.11. High-Technology Company in Problem 7.19
| Division | Beta | Market Value ($ million) |
| Personal computers | 1.60 | 100 |
| Software | 2.00 | 150 |
| Computer mainframes | 1.20 | 250 |
Answers to these Practice Problems are available in the Online Instructor's Manual for instructors using this book.
Chapter business cases
Case Study 7.1
Hewlett-Packard Outbids Dell Computer to Acquire 3PAR
On September 2, 2010, a little more than two weeks after Dell's initial bid for 3PAR, Dell Computer withdrew from a bidding war with Hewlett-Packard when HP announced that it had raised its previous offer by 10% to $33 a share. Dell's last bid had been for $32 per share, which had trumped HP's previous bid the day before of $30 per share. The final HP bid valued 3PAR at $2.1 billion versus Dell's original offer of $1.1 billion.
3Par was sought after due to the growing acceptance of its storage product technology in the emerging “cloud computing” market. 3PAR's storage products enable firms to store and manage their data more efficiently at geographically remote data centers accessible through the Internet. While 3Par has been a consistent money loser, its revenues had been growing at more than 50% annually since it went public in 2007. The deal valued 3Par at 12.5 times 2009 sales in an industry that has rarely spent more than 5 times sales to acquire companies. HP's motivation for its rich bid seems to have been a bet on a fast-growing technology that could help energize the firm's growth. While impressive at $115 billion in annual revenues and $7.7 billion in net income in 2009, the firm's revenue and earnings has slowed due to the 2008–2009 global recession and the maturing personal computer market.
Table 7.12 provides selected financial data on 3PAR and a set of valuation assumptions. Note that HP's marginal tax rate is used rather than 3PAR's much lower effective tax rate to reflect potential tax savings to HP from 3PAR's cumulative operating losses. Given HP's $10 billion plus pretax profit, HP is expected to fully utilize 3PAR's deferred tax assets in the current tax year. The continued 3PAR high sales growth rate reflects the HP expectation that its extensive global sales force can expand the sale of 3PAR products.
Table 7.12. 3PAR Valuation Assumptions and Selected Historical Data
To support further development of the 3PAR products, the valuation assumptions reflect an increase in plant and equipment spending in excess of depreciation and amortization through 2015; however, beyond 2015, capital spending is expected to grow at the same rate as depreciation as the business moves from a growth to a maintenance mode. 3PAR's operating margin is expected to show a slow recovery, reflecting the impact of escalating marketing expenses and the cost of training the HP sales force in the promotion of the 3PAR technology.
Discussion Questions
1. Estimate 3PAR's equity value per share based on the assumptions and selected 3PAR data provided in Table 7.12.
2. Why is it appropriate to utilize at least a ten-year annual time horizon before estimating a terminal value in valuing firm's such as 3PAR?
3. What portion of the purchase price can be financed by 3PAR's nonoperating assets?
4. Does the deal still make sense to HP if the terminal period growth rate is 3% rather than 5%? Explain your answer.
Answers to these questions are found in the Online Instructor's Manual available to instructors using this book.
Case Study 7.2
Creating a Global Luxury Hotel Chain
Fairmont Hotels & Resorts Inc. announced on January 30, 2006, that it had agreed to be acquired by Kingdom Hotels and Colony Capital in an all-cash transaction valued at $45 per share. The transaction is valued at $3.9 billion, including assumed debt. The purchase price represents a 28% premium over Fairmont's closing price on November 4, 2005, the last day of trading when Kingdom and Colony expressed interest in Fairmont. The combination of Fairmont and Kingdom will create a luxury global hotel chain with 120 hotels in 24 countries. Discounted cash-flow analyses, including estimated synergies and terminal value, value the firm at $43.10 per share. The net asset value of Fairmont's real estate is believed to be $46.70 per share.
Discussion Questions
1. Is it reasonable to assume that the acquirer could actually be getting the operation for “free,” since the value of the real estate per share is worth more than the purchase price per share? Explain your answer.
2. Assume the acquirer divests all of Fairmont's hotels and real estate properties but continues to manage the hotels and properties under long-term management contracts. How would you estimate the net present value of the acquisition of Fairmont to the acquirer? Explain your answer.
Answers to these questions are found in the Online Instructor's Manual available to instructors using this book.
1 For more exhaustive analyses of valuation, see Copeland, Koller, and Murrin (2005).
2 For an excellent discussion of the basic concepts of finance, see Gitman (2008).
3 Based on survey results of 510 finance and economics professors, Welch (2001) estimates an equity premium over a 30-year horizon of 5.5%. Using data provided by Dimson, March, and Staunton (2003), the equity risk premium relative to bonds during the period from 1900 to 2002 was 5.75% in the United States and 4.9% for a 16-country average.
4 For a detailed discussion of these issues, see Fama and French (1992, 1993, 2006). Other studies show that the market risk premium is unstable—lower during periods of prosperity and higher during periods of economic slowdowns (Claus and Thomas, 2001; Easton et al., 2001).
5 In a survey of 200 companies, Escherich (1998) found that most firms estimate the cost of equity using CAPM and use an equity risk premium of between 5 and 7%. In a survey of 1,500 finance professors, Fernandez (2011) found that the average equity risk premium used in 2010 was 6% in the United States and 5.3% in Europe. Fernanadez also found in a survey of 2,400 analysts and companies that analysts in the United States and Europe used 5.1% and 5%, respectively, while companies used 5.3% in the United States and 5.7% in Europe. Similar results were found in a survey of 150 finance textbooks in which the five-year moving average ending in 2009 was 5.7%.
6 Bernard, Healy, and Palepu, 2000
9 Yield to maturity is the internal rate of return on a bond held to maturity, assuming scheduled payment of principal and interest, that takes into account the capital gain or loss on a discount bond or capital loss on a premium bond.
10 To calculate the yield to maturity using a Hewlett-Packard 12C calculator, enter the quoted price (as a percent of par), using PV; enter the annual coupon rate (as a percentage), using PMT; key in the settlement (purchase) date; and press ENTER. Key in the maturity (redemption) date. Press f and YTM.Note: Using day-month-year format, key in 1 or 2 digits of the day and press decimal point. Key in 2 digits of the month and 4 digits of the year.
11 YTM is distorted by corporate bonds, which also have conversion or callable features, since their value will affect the bond's value.
12 FINRA is the largest independent regulator for all securities firms in the Unites States. See http://cxa.marketwatch.com/finra/MarketData/CompanyInfo/default.aspx.
13 Titman and Martin (2011), pp. 144–147.
14 Although such liabilities have an associated cost of capital, it is assumed to have been included in the price paid for the products and services whose purchase generated the accounts payable. Consequently, the cost of capital associated with these types of liabilities affects cash flow through its inclusion in operating expenses (e.g., the price paid for raw materials).
15 While over longer periods of time the impact on beta is problematic, it may be quite substantial over relatively short time periods. For example, the telecommunications, media, and technology sectors of the S&P 500 rose dramatically in the late 1990s and fell precipitously after 2000. Other sectors were relatively unaffected by the wild fluctuations in the overall market, resulting in a reduction in their betas. To illustrate, the equity beta for electric utilities fell to 0.1 in 2001 from 0.6 in 1998, falsely suggesting that the sector's risk and, in turn, cost of equity had declined.
16 Recall that operating profits equal total revenue less fixed and variable costs. If revenue, fixed, and variable costs are $100, $50, and $25 million, respectively, the firm's operating profits are $25 million. If revenue doubles to $200 million, the firm's profit increases fourfold to $100 million (i.e., $200 – $50 – $50).
17 The reestimation of a firm's beta to reflect a change in leverage requires that we first deleverage the firm to remove the effects of the firm's current level of debt on its beta and then releverage the firm using its new level of debt to estimate the new levered beta.
a Cash from operating activities.
b Cash from investing activities.
c Cash from financing activities.
20 Other long-term liabilities such as the firm's pension and healthcare obligations may be ignored if they are fully funded. However, the unfunded portion of such liabilities should be added to enterprise value, while any recoverable surplus should be deducted.
21 The total amount of cash and cash equivalents would only be available to meet investor claims if the firm were being liquidated. Otherwise, some portion of such cash would be required to meet continuing operations of the company.
22 For example, a retail commercial banking operation typically finances its operations using interest-free checking accounts. Determining the actual cost of acquiring such accounts is often quite arbitrary.
23 The present value of a constant payment in perpetuity is a diminishing series because it represents the sum of the PVs for each future period. Each PV is smaller than the preceding one; therefore, the perpetuity is a diminishing series that converges to 1 divided by the discount rate.
a If you only know a firm's debt-to-equity ratio (D/E), it is possible to calculate the firm's debt-to-total capital ratio (D/D + E) by dividing (D/E) by (1 + D/E), since D/(D + E) = (D/E)/(1 + D/E) = [(D/E)/(D + E)/E]= (D/E) × (E/D + E) = D/(D + E).
24 Note that the zero growth model is a special case of the constant-growth model for which g equals 0.
25 The price-to-earnings, price-to-cash-flow, or price-to-book techniques value the target as if it were sold at the end of a specific number of years. At the end of the forecast period, the terminal year's earnings, cash flow, or book value is projected and multiplied by a P/E, cash-flow, or book-value multiple believed to be appropriate for that year. The terminal value also may be estimated by assuming the firm's cash flow or earnings in the last year of the forecast period will continue in perpetuity. This is equivalent to the zero-growth valuation model discussed previously.
26 Ross et al. (2009), pp. 238–240.
27 Between 1979 and 1998, sales growth for the average U.S. firm reverted to an average of 7 to 9% within five years. Firms with initial growth rates in excess of 50% experience a decline to about 6% growth within three years; those with the lowest initial growth rate tend to increase to about 8% by year 5. See Palepu, Healy, and Bernard (2004), pp. 10-2 and 10-3.
28 More sophisticated forecasts of growth rates involve an analysis of the firm's customer base. Annual revenue projections are made for each customer or product and summed to provide an estimate of aggregate revenue. A product or service's life cycle (see Chapter 4) is a useful tool for making such projections. In some industries, a product's life cycle may be a matter of months (e.g., software) or years (e.g., an automobile). This information is readily available by examining the launch dates of new products and services in an industry in publications provided by the industry's trade associations. By determining where the firm's products are in their life cycle, the analyst can project annual unit volume by product.
29 The only debt that must be valued is the debt outstanding on the valuation date. Future borrowing is irrelevant if we assume that cash inflows generated from investments financed with future borrowings are sufficient to satisfy interest and principal payments associated with these borrowings.
30 GAAP requires a firm to reduce the amount of a deferred tax asset by an offsetting valuation allowance if, based on available information, it is more likely than not that that some portion of or the entire deferred asset will not be realized.
31 In some instances, differences between the tax liability for financial reporting and for tax purposes are permanent. Examples include nondeductible goodwill and the 50% limitation on the deductibility of meals and entertainment expenses for tax purposes. The tax treatment of goodwill depends on the expenditures that created the goodwill. If an acquisition is structured as a stock purchase (unless the parties agree to a 338 election), no amortization of goodwill is permitted under current accounting practices. If the purchase is structured as an asset purchase, goodwill is amortized over 15 years using straight-line depreciation. For financial reporting to shareholders, goodwill is not normally amortized unless the assets are viewed as impaired. When goodwill is tax deductible and is being amortized on the firm's tax return, it creates a deferred tax liability once the amortization period is up (see Chapter 12 for more details on the tax treatment of goodwill and other intangibles).
33 The effects of this cash outflow may be more than offset by the additional shareholder value created by the incentive of option holders to work more efficiently and to innovate more to increase the value of their options. Note also that because such options represent employee compensation, they are tax deductible for firms.
34 Chan, Lakonishok, and Sougiannis, 1999
35 The underlying assumption in applying the cost-avoidance approach to the valuation of trademarks and service marks is that cumulative advertising and promotion campaigns build brand recognition. The initial outlays for promotional campaigns are the largest and tend to decline as a percentage of sales over time as the brand becomes more recognizable. Consequently, the valuation of a trademark associated with a specific product or business involves multiplying projected revenues by a declining percentage to reflect the reduced level of spending, as a percentage of sales, required to maintain brand recognition. These projected expenditures then are adjusted for taxes (because marketing expenses are tax deductible) and discounted to the present at the acquiring firm's cost of capital.
36 Companies may license the right to use a trademark or service mark. The acquiring company may apply the license rate required to obtain the rights to comparable trademarks and service marks to a percentage of the cash flows that reasonably can be expected to be generated by selling the products or services under the licensed trademark or service mark. The resulting cash flows then are discounted to the present using the acquirer's cost of capital. Alternatively, a value may be determined by examining recent outright purchases of comparable trademarks or, in the case of the Internet, Web addresses or domain names.