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Unformatted text preview: t C to decrease until no arbitrage opportunity exists. In other words, the price of asset C should decrease until the return becomes 14.25 percent. Let: X1 = the proportion of Security 1 in the portfolio and X2 = the proportion of Security 2 in the portfolio and note that since the weights must sum to 1.0, X1 = 1 – X2 Recall from Chapter 10 that the beta for a portfolio (or in this case the beta for a factor) is the weighted average of the security betas, so β P1 = X1β 11 + X2β 21 β P1 = X1β 11 + (1 – X1)β 21 Now, apply the condition given in the hint that the return of the portfolio does not depend on F1. This means that the portfolio beta for that factor will be 0, so: β P1 = 0 = X1β 11 + (1 – X1)β 21 β P1 = 0 = X1(1.0) + (1 – X1)(0.5) and solving for X1 and X2: X1 = – 1 X2 = 2 Thus, sell short Security 1 and buy Security 2. To find the expected return on that portfolio, use RP = X1R1 + X2R2 so applying the above: E(RP) = –1(20%) + 2(20%) E(RP) = 20% β P1 = –1(1) + 2(0.5) β P1 = 0 10. a. 306 b. Following the same logic as in part a, we have β P2 = 0 = X3β 31 + (1 – X3)β 41 β P2 = 0 = X3(1) + (1 – X3)(1.5) and X3 = 3 X4 = –2 Thus, sell short Security 4 and buy Security 3. Then, E(RP2) = 3(10%) + (–2)(10%) E(RP2) = 10% β P2 = 3(0.5) – 2(0.75) β P2 = 0 Note that since both β P1 and β P2 are 0, this is a risk free portfolio! c. The portfolio in part b provides a risk free return of 10%, which is higher than the 5% return provided by the risk free security. To take advantage of this opportunity, borrow at the risk free rate of 5% and invest the funds in a portfolio built by selling short security four and buying security three with weights (3,–2) as in part b. First assume that the risk free security will not change. The price of security four (that everyone is trying to sell short) will decrease, and the price of security three (that everyone is trying to buy) will increase. Hence the return of security four will increase and the return of security three will decrease. The alternative is that the prices of securities three and four will remain the same, and the price of the risk-free security drops until its return is 10%. Finally, a combined movement of all security prices is also possible. The prices of security four and the risk-free security will decrease and the price of security three will increase until the opportunity disappears. d. 307 CHAPTER 13 RISK, COST OF CAPITAL, AND CAPITAL BUDGETING
Answers to Concepts Review and Critical Thinking Questions 1. 2. 3. 4. No. The cost of capital depends on the risk of the project, not the source of the money. Interest expense is tax-deductible. There is no difference between pretax and aftertax equity costs. You are assuming that the new project’s risk is the same as the risk of the firm as a whole, and that the firm is financed entirely with equity. Two primary advantages of the SML approach are that the model explicitly incorporates the relevant risk of the stock and the method is more widely applicable than is the DCF model, since the SML doesn’t make any assumptions about the firm’s dividends. The primary disadvantages of the SML method are (1) three parameters (the risk-free rate, the expected return on the market, and beta) must be estimated, and (2) the method essentially uses historical information to estimate these parameters. The risk-free rate is usually estimated to be the yield on very short maturity T-bills and is, hence, observable; the market risk premium is usually estimated from historical risk premiums and, hence, is not observable. The stock beta, which is unobservable, is usually estimated either by determining some average historical beta from the firm and the market’s return data, or by using beta estimates provided by analysts and investment firms. The appropriate aftertax cost of debt to the company is the interest rate it would have to pay if it were to issue new debt today. Hence, if the YTM on outstanding bonds of the company is observed, the company has an accurate estimate of its cost of debt. If the debt is privately-placed, the firm could still estimate its cost of debt by (1) looking at the cost of debt for similar firms in similar risk classes, (2) looking at the average debt cost for firms with the same credit rating (assuming the firm’s private debt is rated), or (3) consulting analysts and investment bankers. Even if the debt is publicly traded, an additional complication arises when the firm has more than one issue outstanding; these issues rarely have the same yield because no two issues are ever completely homogeneous. a. b. c. This only considers the dividend yield component of the required return on equity. This is the current yield only, not the promised yield to maturity. In addition, it is based on the book value of the liability, and it ignores taxes. Equity is inherently riskier than debt (except, perhaps, in the unusual case where a firm’s assets have a negative beta). For...
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