CHAPTER 7DISCOUNT RATES IN VALUATION

LEARNING OBJECTIVES

1. Why different valuation models use different discount rates.2. The capital asset pricing model and how it relates to discount rates.3. How to estimate the discount rate for each model.4. How to alter the analysis of discount rates for private companies.

TRUE/FALSE QUESTIONS

1. Different valuation models rely on different components of the firm’s cash flows because the components of cash flow belong to different capital suppliers.(moderate, L.O. 1, Section 1, true)

2. Unlevered cost of equity is the discount rate used in the adjusted present value model.(moderate, L.O. 1, Section 1, true)

3. Like other sources of capital, common equity has a promised rate of return.(easy, L.O. 1, Section 1, false)

4. The degree to which a stock’s returns are correlated with market movements is known as systematic risk.(moderate, L.O. 2, Section 1, true)

5. Beta is the variable which measures a stock’s correlation with the market.(moderate, L.O. 2, Section 1, true)

6. Diversification eliminates systematic risk.(easy, L.O. 2, Section 1, false)

7. The systematic risk of a portfolio is the total of the individual systematic risks of each stock in the portfolio.(difficult, L.O. 2, Section 1, false)

8. The volatility of an individual stock has significant effect on the volatility of a well-diversified portfolio.(moderate, L.O. 2, Section 1, false)

9. When a firm’s economic balance sheet has only core operations, debt, and common equity, the weighted-average cost of capital is the average of the after-tax cost of debt and cost of equity.(difficult, L.O. 3, Section 2, true)

10. Under the concept of negative debt, a firm that holds equal amounts of debt and nonoperating securities is viewed as not being leveraged at all.(difficult, L.O. 3, Section 2, true)

11. Under the weighted-average cost of capital, the weights of all components must equal.(moderate, L.O. 3, Section 2, true)

12. Under the weighted-average cost of capital, the discount rate for core operations is the weighted-average of the demanded return on all economic balance sheet items other than core operations.(difficult, L.O. 3, Section 2, true)

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13. Analysts cannot infer the value of the unlevered beta from either the levered beta or the firm’s capital structure since no theoretical relationship among these elements exist.(moderate, L.O. 3, Section 2, false)

14. The beta for a private company is identical to the beta for a publicly held company as long as the two are of similar sizes in the same industry.(moderate, L.O. 4, Section 4, false)

15. Precision is a statistical measure of the unlevered cost of capital, and it is equal to the reciprocal of the variance.(moderate, L.O. 4, Section 4, false)

MULTIPLE CHOICE QUESTIONS

16. The valuation models that use the weighted-average cost of capital as a discount rate are the:a. free cash flow and the adjusted present value modelsb. residual income and flows to equity modelsc. dividend discount and adjusted present value modelsd. free cash flow and residual income models(moderate, L.O. 1, Section 1, d)

17. The valuation models that use the cost of common equity as a discount rate are the:a. dividend discount and flows to equity modelsb. dividend discount and free cash flow modelsc. free cash flows and flows to equity modelsd. free cash flows and dividend discount models(moderate, L.O. 1, Section 1, a)

18. Using the capital asset pricing model (CAPM), the variable known as the risk-free interest rate best approximates the interest rate on the:a. 30-year Treasury bondb. average 5-year bank certificate of depositc. average systematic risk computed for the general domestic bond market over the last 30 monthsd. prime interest rate as established by the Federal Reserve Bank(moderate, L.O. 2, Section 1, a)

19. In the capital asset pricing model formula, the additional expected return above the risk-free rate that an investor requires to hold an average-price stock is known as:a. historical equity premium earnedb. equity risk premiumc. betad. risk-free rate of interest(moderate, L.O. 2, Section 1, b)

20. Regarding beta in the capital asset pricing model, it is true that __________ can be eliminated through diversification, however __________ cannot be eliminated in the same way.a. systematic risk; unsystematic riskb. systematic risk; equity risk premiumc. unsystematic risk; systematic riskd. unsystematic risk; equity risk premium(moderate, L.O. 2, Section 1, c)

21. Beta represents the firm’s sensitivity to market performance when using CAPM. If a firm has a beta that 43

is greater than 1 on a particular day, then we can conclude that the firm’s expected return:a. is greater than market movement in both directions on that dayb. is less than market movement in both directions on that dayc. is whatever the market’s return was on that dayd. It is impossible for a firm to have a beta greater than 1.(moderate, L.O. 2, Section 1, a)

22. A common approach to estimating beta is to go back in time five years and analyze a firm’s data. This time period usually provides sufficient daily intervals to obtain a reasonably narrow level of confidence. What factor can cause a company to change substantially and thus inhibit estimating beta during this five-year time period?a. an acquisitionb. a divestiturec. recapitalizationd. All of the above answers can cause a substantial change over a five-year period.(easy, L.O. 2, Section 1, d)

23. The cost of equity can be expressed as ke = rf + m · β when using the CAPM. In the formula, m represents:

a. the cost of equityb. the risk free interest ratec. the equity risk premiumd. systematic risk(difficult, L.O. 2, Section 1, c)

24. A fact that is critically important to an investor who holds a diversified portfolio is:a. systematic risk can be eliminated by holding a diversified portfoliob. unsystematic risk can be eliminated by holding a diversified portfolioc. all risk can be eliminated by holding a diversified portfoliod. the risk factors for diversified portfolios are approximately the same as risk factors for nondiversified

portfolios(moderate, L.O. 2, Section 1, b)

25. To understand what beta means we must formalize the distinction between correlation with the market and volatility. Rt = β · Rmt + Et is the formula that expresses this relationship. The variable Rmt stands for the:a. market return on date tb. firm’s return on date tc. additional volatility unrelated to the marketd. measure of correlation with the market(difficult, L.O. 2, Section 1, a)

26. In a situation in which a firm’s economic balance sheet consists of only core operations, debt, and common equity, the weighted-average cost of capital (WACC) is defined as the weighted average of the after-tax cost of debt and cost of equity. The weightings in this case are based on __________, not __________.a. historical costs; fair market valuesb. the proportion of debt to equity; debt to total capitalc. appraisals and industry guidelines; historical costsd. fair values of debt and equity; book values of debt and equity(difficult, L.O. 3, Section 2, d)

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27. A characteristic of the WACC is that:a. it is the discount rate used for the adjusted present value modelb. the only capital supplier considered in the WACC are debtholdersc. it is the discount rate used in the flows to equity valuation modeld. it blends the costs of equity and other sources of financing(moderate, L.O. 3, Section 2, d)

28. In a situation in which a firm’s economic balance sheet consists of only core operations, debt, and common equity, the combined risk of __________ and of __________ must equal the risk of __________.a. the firm’s debt; the firm’s equity; the firm’s core operationsb. the firm’s core operations; the firm’s equity; the marketplacec. the firm’s core operations; its nonoperating assets; the firm’s total debtd. the firm’s investors; the marketplace; the firm’s diversified portfolio(difficult, L.O. 3, Section 2, a)

29. In the WACC model, the effect of the firm holding other assets such as Treasury Bonds:a. does not affect the nature of the firm’s equityb. does affect the nature of its core operationsc. does not affect the nature of its core operationsd. does affect the nature of the firm’s debt(moderate, L.O. 3, Section 2, c)

30. Using the WACC model, Treasury Bonds that the firm holds is treated as a nonoperating asset. The Treasury Bonds in this situation would be treated in the WACC model as:a. positive debtb. negative debtc. a hedge against an inflationary spirald. a hedge against the discount rate applied to the firm’s core operations(moderate, L.O. 3, Section 2, b)

31. To estimate the firm’s unlevered cost of equity, the analyst must first find the unlevered beta. Formulas are employed to convert levered betas to unlevered betas. There are different formulas used to perform this task, because the relationship between levered and unlevered betas depends on:a. the pattern of the free cash flow streamb. whether the debt will remain as a fixed dollar amount, a fixed percentage of capital, or follow some

other patternc. the beta on the firm’s debtd. All of the answers are correct.(moderate, L.O. 3, Section 3, d)

32. The adjusted present value model uses the unlevered cost of equity as:a. a way to compute the levered betas required for the formulab. a way to estimate the unlevered beta directly from stock returnsc. its discount rated. None of the above answers are correct.(easy, L.O. 3, Section 3, c)

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33. Estimating a discount rate for privately held companies adds complications not faced with public companies. The degree of accuracy of the various estimated betas identified by the analyst is commonly known as:a. direct beta estimationb. the standard average beta formulac. precisiond. beta appraisal(moderate, L.O. 4, Section 4, c)

34. An analyst must adjust the beta estimates of comparable private companies for the difference in their capital structures. The analyst can approach this task by:a. choosing a firm with a comparable capital structure similar to the one being valued, if possibleb. choosing an estimated average beta based on public firm industry standardsc. estimating the cost of capital for the comparable firm.d. Answers a and c are both correct.(moderate, L.O. 4, Section 4, d)

35. Most companies operate a number of different businesses. Each of these businesses faces different risks and therefore suitable discount rates will vary among divisions, product lines, or subsidiaries based on the risk profile of the particular business. To determine the cost of capital, an analyst should:a. use a single discount rate for the entire firmb. estimate the beta separately for each division, and then obtain a weighted average of all divisions to

compute the firm’s cost of capitalc. consult industry standards for publicly held firms in a similar industryd. None of the above answers are correct.(moderate, L.O. 4, Section 4, b)

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ESSAYS

36. Briefly explain the capital asset pricing model as a model that relates risk and return. What does beta represent in this model?

Suggested solution:

The capital asset pricing model (CAPM) is a formal model that relates risk and return. This model makes an assumption that investors do not like to take risks (that is, they are risk adverse), but if the reward for taking a risk by holding riskier stocks or riskier portfolios is sufficient, investors will take the risk to potentially gain a higher expected rate of return.

One assumption the CAPM makes is that stocks whose returns are highly correlated with the rest of the stock market are considered to produce more risk in an investor portfolio than a stock whose risk is not as highly correlated with the stock market. This means that a stock that is highly correlated with the market will be expected to produce a higher rate of return. The opposite holds true for stocks that are not highly correlated to the market, because it is not expected that such stocks will produce a higher rate of return. When a portfolio is well diversified, the volatility of an individual highly volatile stock (one that is not correlated with the market) will have almost no effect on the portfolio itself.

The degree to which stock returns are correlated with the movement of the markets is known as systematic risk, or beta. Beta (the symbol β is used to denote beta) represents systematic risk in the CAPM. A beta of 1 on a given day equals whatever the market’s return is for that day. A beta greater than 1 on a given day means that the firm’s expected return is greater than the movements of the markets, either positive or negative on that day. A beta that is less than 1 on a given day means that the firm’s expected return is worse than market movements on that day.(moderate, L.O. 2, Section 1)

37. Discuss the relationship among core operations, debt, and equity of a firm when the weighted-average cost of capital model is used for valuation purposes.

Suggested solution:

When working with the weighted-average cost of capital model (WACC), analysts want to know the appropriate expected return for the cash flows to be discounted for core operations. The expected return is dependent on the core operations’ risk factor. The analyst may not be able to clearly determine the level of risk associated with the firm’s core operations, so an assumption must be made in this case. Since the firm’s combined debt and equity must equal its core operations (so that an economic balance sheet will balance), we can conclude that the combined risk of the firm’s debt and equity must also equal the risk of its core operations. This assumption can be restated as, “the weighted average of the required returns on the debt and the common equity must be equal to the required return on the core operations.”

There is an important reason for this assumption. The risk associated with the firm’s core operations depends entirely on the characteristics of those operations. Depending on the valuation model used, an analyst can divide risk among debtholders and equityholders in a number of ways. How debt and equity risk is divided is irrelevant to the total risk of the firm’s assets. Therefore, the appropriate expected return on the firm’s assets can be inferred by determining the returns demanded on the combined claims (that is, debtholder and equityholder claims) against the firm’s assets.(moderate, L.O. 3, Section 2)

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38. Identify and comment on some of the issues an analyst faces when evaluating private companies.

Suggested solution:

It is more difficult to estimate a discount rate for privately held firms since an analyst cannot observe security returns for a privately held company, and therefore cannot estimate a beta with a regression. Also, a private firm may be a subsidiary of another firm, or be comprised of several subsidiaries, any of which may have different capital structures.

Companies in the same industry may share similar operating risks, but they may have different capital structures. Since capital structures affect betas, it may not be possible to compare companies in the same industry. One possible solution is to adjust the betas for the differences in capital structures. An analyst can algebraically adjust the beta of one firm to more closely match the capital structure of another firm, with the goal of generating a beta that is comparable for the firms. Although this method is inexact, it has some value. Unfortunately, there is no perfect solution in this situation.

An analyst can also adjust for a situation where a firm is a subsidiary of another firm, or is itself comprised of several subsidiaries by estimating a beta for each subsidiary and then taking the weighted average of the betas to generate a firm-wide beta. This method is preferable to merely taking a single discount rate for a firm that has divisions or subsidiaries, since this approach may overstate the value of high-risk divisions or subsidiaries and understate the value of lower-risk divisions or subsidiaries.(moderate, L.O. 4, Section 4)

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