BA 504 - Chapter 12 HW

You are a consultant to a firm evaluating an expansion of its current business. The cash-flow forecasts (in millions of dollars) for the project are as follows: Years | Cash Flow 0 | -100 1-10 | 15 On the basis of the behavior of the firm's stock, you believe that the beta of the firm is 1.4. Assuming that the rate of return available on risk-free investments is 4% and that the expected rate of return on the market portfolio is 12%, what is the net present value of the project?

-25.29

What is the beta of a 3-stock portfolio including 25% of stock A with a beta of 0.90, 40% of stock B with a beta of 1.05, and 35% of stock C with a beta of 1.73?

1.25

The following table shows betas for several companies. Calculate each stock's expected rate of return using the CAPM. Assume the risk-free rate of interest is 4%. Use a 7% risk premium for the market portfolio. Caterpillar: Beta = 1.63 Cisco: Beta = 1.24 Harley-Davidson: Beta = 0.82 Hershey: Beta = 0.24

Caterpillar: 0.04 + (1.63 x 0.07) = 0.1541 or 15.41% Cisco: 0.04 + (1.24 x 0.07) = 0.1268 or 12.68% Harley: 0.04 + (0.82 x 0.07) = 0.0974 or 9.74% Hershey: 0.04 + (0.24 x 0.07) = 0.0568 or 5.68%

The Treasury bill rate is 4% and the market risk premium is 7%. Project | Beta | Internal ROR % P | 1.0 | 14% Q | 0 | 6% R | 2.0 | 18% S | 0.4 | 7% T | 1.6 | 20% a. What are the project costs of capital for new ventures with betas of 0.75 and 1.75? b. Which of the capital investments shown above have positive (non-zero) NPV's?

a) 0.04 + (0.75 x 0.07) = 9.25% 0.04 + (1.75 x 0.07) = 16.25% b) Project P, Project Q, Project S, Project T

You are considering acquiring a firm that you believe can generate expected cash flows of $10,000 a year forever. However, you recognize that those cash flows are uncertain. a. Suppose you believe that the beta of the firm is 0.4. How much is the firm worth if the risk-free rate is 4% and the expected rate of return on the market portfolio is 11%? b. By how much will you overvalue the firm if its beta is actually 0.6?

a) Discount rate = 0.04 + (0.4 x (0.11-0.04) = 6.80% Value of firm = $10,000/6.80% = $147,058.82 b) Discount rate = 0.04 + (0.6 x (0.11-0.04) = 8.20% Value of firm = $10,000/8.20% = $121,951.22 Overvaluation= $147,058.82 - $121,951.22 = $25,107.60

We Do Bankruptcies is a law firm that specializes in providing advice to firms in financial distress. It prospers in recessions when other firms are struggling. Consequently, its beta is negative, −0.2. a. If the interest rate on Treasury bills is 5% and the expected return on the market portfolio is 15%, what is the expected return on the shares of the law firm according to the CAPM? b. Suppose you invested 90% of your wealth in the market portfolio and the remainder of your wealth in the shares in the law firm. What would be the beta of your portfolio?

a) .05 + (-0.20 x (0.15-0.05)) = 3% b) Market beta is 1 (0.90 x 1) + (1-0.90)*(-0.20) = 0.88

A project under consideration has an internal rate of return of 14% and a beta of 0.6. The risk-free rate is 4%, and the expected rate of return on the market portfolio is 14%. a. What is the required rate of return on the project? b. Should the project be accepted? c. What is the required rate of return on the project if its beta is 1.6? d. Should the project be accepted?

a) 0.04 + (0.6 x (0.14-0.04)) = 10% b) Yes c) 0.04 + (1.6 x (0.14-0.04)) = 20% d) No

State whether the following statements are true or false. a) Investors demand higher expected rates of return on stocks with more variable rates of return. b) The capital asset pricing model predicts that a security with a beta of zero will provide an expected return of zero. c) An investor who puts $10,000 in Treasury bills and $20,000 in the market portfolio will have a portfolio beta of 2.0. d) Investors demand higher expected rates of return from stocks with returns that are highly exposed to macroeconomic changes. e) Investors demand higher expected rates of return from stocks with returns that are very sensitive to fluctuations in the stock market. f) The CAPM implies that if you could find an investment with a negative beta, its expected return would be less than the interest rate. g) If a stock lies below the security market line, it is undervalued.

a) False b) False c) False d) True e) True f) True g) False

Ford: Beta = 1.31 STDV = 25.3% Pfizer: Beta = 0.90 STDV = 15.3% Walmart: Beta = 0.26 STDV = 16.5% a. Which stock is safest for a diversified investor? b. Which stock is safest for an un-diversified investor who puts all her funds in one of these stocks?. c. Consider a portfolio with equal investments in each stock. What would this portfolio's beta have been? d. Consider a well-diversified portfolio made up of stocks with the same beta as Ford. What are the beta and standard deviation of this portfolio's return? The standard deviation of the market portfolio's return is 20%. e. What is the expected rate of return on each stock? Use the capital asset pricing model with a market risk premium of 8%. The risk-free rate of interest is 4%.

a) Walmart. The company with the lowest Beta b) Pfizer. The company with the lowest STDV c) (1.31x0.33) + (0.90x0.33) + (0.26x 0.33) = 0.82 d) Beta = 1.31 ; STVD = 1.31 x 0.20 = 26.20% e) Ford: 0.04 + (1.31 x 0.08) = 0.1448 or 14.48% Pfizer: 0.04 + (0.90 x 0.08) = 0.1120 or 11.20% Walmart: 0.04 + (0.26 x 0.08) = 0.0608 or 6.08%

The risk-free rate is 6% and the expected rate of return on the market portfolio is 13%. a. Calculate the required rate of return on a security with a beta of 1.25. b. If the security is expected to return 16%, is it overpriced or underpriced?

a. Required return = 0.06 + (1.25 x (0.13-0.06)) = 0.1475 or 14.75% b. Underpriced

A stock with a beta greater than 1.0 would be termed:

an aggressive stock, expected to increase more than the market increases

A stock's total risk depends on the stock's _________ and __________.

beta; specific risk

A stock's beta measures the:

sensitivity of the stock's returns to those of the market portfolio.