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Business Administration 130

Problem Set # 3 Answers

http://www.j-bradford-delong.net/Intro_Finance/BA130PS3A.html


1. "I don't see why a thirty-year U.S. Treasury Bond pays a higher interest rate than the risk-free rate. After all, if you hold it for thirty years you are guaranteed to get all your money." Criticize this statement.

2. Suppose you find a company, Abbott Aeronautics, with a beta of -1. Suppose, further, that the risk-free (nominal) rate is 3% per year and that the required rate of return on the market is 10% per year.

3. Suppose you invest 25% of your funds in Interesting Industries and 75% of your funds in Boring Buildings. The standard deviation of the annual return on the first is 15%; the standard deviation of the annual return on the second is 5%.

4. Suppose that the standard deviation of the market return per year is 0.2 (20%), the standard deviation of the annual return on Zed Industries is 0.8 (40%) [oops! Let's solve for the case where it is 80%], and that the correlation between the excess return on the market and the excess return on Zed industries is 0.5.

5. Suppose that you can invest in any of the following eight portfolios:

A
   B C D E F G H
 Expected Return  12%  8% 6%  3%  2%  5%  21%  0%
 Standard Deviation  25% 15% 12% 0% 3% 10% 50% 8%

Which portfolios are "efficient"? Which portfolios are "inefficient"? If security returns follow the CAPM, and portfolio A represents the market, which portfolios are fully diversified? What are the betas of the fully diversified portfolios?

6. Thermo-Electron Corporation has a beta of 1.4; Tyson Foods (a major campaign contributor to former Governor Clinton) has a beta of 1.0. Tyson Foods has a standard deviation of annual returns of about 26%; Thermo-Electron has a standard deviation of annual returns of about 24%. Which stock contributes more risk if added to a diversified portfolio? Which stock does the CAPM predict will have a higher expected return?

7. Suppose that Bankers' Trust Corporation announces that it intends to acquire Bank of America, paying the Bank of America's shareholders a premium of $25 a share over Bank of America's most recent stock price. In response to this announcement, Bank of America stock jumps by $12.50 a share. Your assessment--and it is a good assessment: you are a Wall Street professional with better information than anyone else--is that there is a 60% chance that the acquisition will go through.

8. The benefits of diversification from a portfolio of one to a portfolio of two stocks are greatest:

9. Suppose that your corporation's securities have a required rate of return of 8% per year, the risk-free rate is 3%, and the market's required rate of return is 10%. You have the opportunity to undertake an investment with the following set of expected cash flows (with all numbers in thousands):

 Year  0 1 2 3 4 5 6 7
 Cash Flow  -$10,000  $1,200 $6,200 $600 $600 $600 $3,100 $2,800
 NPV  -1336 10137  10457  4980  5125  5295  5493  

Your financial advisors say that this investment carries an incremental beta of two. Will undertaking this project raise or lower your company's total stock market value? By how much?

10. Suppose that the Nordhaus Lighting Corporation will pay a dividend of $4 a share next year, and that thereafter its dividend will grow at 7% per year; suppose further that the risk-free rate is 3%, the market required rate of return is 10%, and that the Nordhaus Lighting Corporation has a beta of two. What does the CAPM predict for the current price of a share of the Nordhaus Lighting Corporation?


Adam Smith
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