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**Module 6.1 Cost of equity and debt McGraw-Hill/Irwin**

Copyright © 2013 by the McGraw-Hill Companies, Inc. All rights reserved.

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Where Do We Stand? Earlier chapters on capital budgeting focused on the appropriate size and timing of cash flows. This chapter discusses the appropriate discount rate when cash flows are risky. Will also now be employing our CAPM tools as well. The terms discount rate, required return, and cost of capital are all synonymous.

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**13.1 The Cost of Equity Capital**

Shareholder invests in financial asset Firm with excess cash Pay cash dividend A firm with excess cash can either pay a dividend or make a capital investment Therefore, the discount rate of a project should be the expected return on a financial asset of comparable risk. Shareholder’s Terminal Value Invest in project Because stockholders can reinvest the dividend in risky financial assets, the expected return on a capital-budgeting project should be at least as great as the expected return on a financial asset of comparable risk.

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**The Cost of Equity Capital**

From the firm’s perspective, the expected return is the Cost of Equity Capital: To estimate a firm’s cost of equity capital, we need to know three things: The risk-free rate, RF The market risk premium, The company beta,

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Example Suppose the stock of Stansfield Enterprises, a publisher of PowerPoint presentations, has a beta of 1.5. The firm is 100% equity financed. Assume a risk-free rate of 3% and a market risk premium of 7%. What is the appropriate discount rate for an expansion of this firm? You may want to note that this example assumes expansion into projects that are similar to the existing nature of the business. Also, point out that the firm is all equity, thus its discount rate is the cost of equity.

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Example Suppose Stansfield Enterprises is evaluating the following independent projects. Each costs $100 and lasts one year. Project Project b Project’s Estimated Cash Flows Next Year IRR NPV at 13.5% A 1.5 $125 25% $10.13 B $113.5 13.5% $0 C $105 5% -$7.49

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Using the SML Good project 30% 2.5 A B C Project IRR Bad project 5% This, again, assumes independent projects. This is a good point at which to review the relation between IRR and NPV. Firm’s risk (beta) An all-equity firm should accept projects whose IRRs exceed the cost of equity capital and reject projects whose IRRs fall short of the cost of capital.

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13.3 Estimation of Beta Market Portfolio - Portfolio of all assets in the economy. In practice, a broad stock market index, such as the S&P 500, is used to represent the market. Beta - Sensitivity of a stock’s return to the return on the market portfolio. 3

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**Estimation of Beta Problems Solutions Betas may vary over time.**

The sample size may be inadequate. Betas are influenced by changing financial leverage and business risk. Solutions Problems 1 and 2 can be moderated by more sophisticated statistical techniques. Problem 3 can be lessened by adjusting for changes in business and financial risk. Look at average beta estimates of comparable firms in the industry.

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Stability of Beta Most analysts argue that betas are generally stable for firms remaining in the same industry. That is not to say that a firm’s beta cannot change. Changes in product line Changes in technology Deregulation Changes in financial leverage

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Using an Industry Beta It is frequently argued that one can better estimate a firm’s beta by involving the whole industry. If you believe that the operations of the firm are similar to the operations of the rest of the industry, you should use the industry beta. If you believe that the operations of the firm are fundamentally different from the operations of the rest of the industry, you should use the firm’s beta. Do not forget about adjustments for financial leverage (details in Module 6.3).

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**13.4 Determinants of Beta Business Risk Financial Risk**

1. Cyclicality of Revenues 2. Operating Leverage Financial Risk 3. Financial Leverage

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**Cyclicality of Revenues**

Highly cyclical stocks have higher betas. Empirical evidence suggests that retailers and automotive firms fluctuate with the business cycle. Transportation firms and utilities are less dependent on the business cycle. Note that cyclicality is not the same as variability—stocks with high standard deviations need not have high betas. Movie studios have revenues that are variable, depending upon whether they produce “hits” or “flops,” but their revenues may not be especially dependent upon the business cycle.

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Operating Leverage The degree of operating leverage measures how sensitive a firm (or project) is to its fixed costs. Operating leverage increases as fixed costs rise and variable costs fall. Operating leverage magnifies the effect of cyclicality on beta. The degree of operating leverage is given by: DOL = EBIT D Sales Sales D EBIT ×

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Operating Leverage EBIT Total costs Total costs $ Fixed costs Sales Fixed costs Sales Operating leverage increases as fixed costs rise and variable costs fall (the firm with green line has EBIT more sensitive to changes in sales).

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**Financial Leverage and Beta**

Operating leverage refers to the sensitivity to the firm’s fixed costs of production. Financial leverage is the sensitivity to a firm’s fixed costs of financing. The relationship between the betas of the firm’s debt, equity, and assets is given by: bAsset = Debt + Equity Debt × bDebt + Equity × bEquity Financial leverage always increases the equity beta relative to the asset beta.

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**Example: positive relation between financial leverage and equity betas**

Consider Grand Sport, Inc., which is currently all-equity financed and has a beta of 0.90. The firm has decided to lever up to a capital structure of 1 part debt to 1 part equity. Since the firm will remain in the same industry, its asset beta should remain 0.90 (it is not changing it’s assets) However, assuming a zero beta for its debt, its equity beta would become twice as large: bAsset = 0.90 = 1 + 1 1 × bEquity bEquity = 2 × 0.90 = 1.80

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**13.5 Dividend Discount Model**

The DDM is an alternative to the CAPM for calculating a firm’s cost of equity. The DDM and CAPM are internally consistent, but academics generally favor the CAPM and companies seem to use the CAPM more consistently. The CAPM explicitly adjusts for risk and it can be used on companies that do not pay dividends. Note that even if a firm pays no dividend, there is still a cost to equity, as investors expect to receive future payouts (i.e., the growth). Further, investors also face opportunity costs for investing in one firm versus another, implying that dividend yield is only a piece of the whole issue.

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**Capital Budgeting & Project Risk**

Project IRR The SML can tell us why: Incorrectly accepted negative NPV projects Hurdle rate bFIRM Incorrectly rejected positive NPV projects To estimate the cost of capital for a division, a “pure play” approach could be used, although finding exactly similar firms may be difficult, particularly considering underlying financial and operational structure. rf Firm’s risk (beta) A firm that uses one discount rate for all projects may, over time, increase the risk of the firm while decreasing its value.

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**Capital Budgeting & Project Risk**

Suppose the Conglomerate Company has a cost of capital, based on the CAPM, of 17%. The risk-free rate is 4%, the market risk premium is 10%, and the firm’s beta is Then, 17% = 4% × 10% This is a breakdown of the company’s investment projects: 1/3 Automotive Retailer b = 2.0 1/3 Computer Hard Drive Manufacturer b = 1.3 1/3 Electric Utility b = 0.6 average b of assets = 1.3 When evaluating a new electrical generation investment, which cost of capital should be used? 17

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**Capital Budgeting & Project Risk**

SML 24% Investments in hard drives or auto retailing should have higher discount rates. 17% Project IRR 10% Project’s risk (b) 0.6 1.3 2.0 R = 4% + 0.6×(14% – 4% ) = 10% 10% reflects the opportunity cost of capital on an investment in electrical generation, given the unique risk of the project.

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Cost of Debt Interest rate required on new debt issuance (i.e., yield to maturity on outstanding debt) This is simply solving for the YTM on a new debt issue. A firm will need to adjust for the tax deductibility of interest expense

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**Cost of Preferred Stock**

Preferred stock is a bit less prevalent than in the past. Preferred stock is a perpetuity, so its price is equal to the coupon paid divided by the current required return. Rearranging, the cost of preferred stock is: RP = C / PV There is no tax adjustment because dividends are not tax deductible.

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