# Homework 4

### Homework 4

HW#4 Assigned on Friday, November 16, 2012 / Due on Thursday, November 29, 2012 Please turn in a hard-copy of your homework to the class. Show all your work to receive full credit for each question. 1. Suppose a stock had an initial price of \$91 per share, paid a dividend of \$2. 40 per share during the year, and had an ending share price of \$102. Compute the percentage total return. What was the dividend yield? The capital gains yield? 2. Suppose you bought a 7 percent coupon bond one year ago for \$1,040. The bond sells for \$1,070 today. a.

Assuming a \$1,000 face value, what was your total dollar return on this investment over the past year? b. What was your total nominal rate of return on this investment over the past year? c. If the inflation rate last year was 4 percent, what was your total real rate of return on this investment? (Hint: use the Fisher equation) 3. Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. 4. You bought one of Great White Shark Repellant Co. ‘s 8 percent coupon bonds one year ago for \$1,030.

These bonds make annual payments and mature six years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 7 percent. If the inflation rate was 4. 2 percent over the past year, what was your total real return on investment? (Hint: calculate the current bond price and then compute the nominal return) 5. Consider the following information: a. Your portfolio is invested 25 percent each in A and C, and 50 percent in B. What is the expected return of the portfolio? b. What is the variance of this portfolio?

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The standard deviation? 6. Asset W has an expected return of 15 percent and a beta of 1. 25. If the risk-free rate is 5 percent, complete the following table for portfolios of Asset W and a risk-free asset. Illustrate the relationship between portfolio expected return and portfolio beta by plotting the expected returns against the betas. What is the slope of the line that results? 7. Consider the following information about Stocks I and II: The market risk premium is 10 percent, and the risk-free rate is 5 percent.

Which stock has the most systematic risk? Explain. (Hint: use the CAPM to find betas of the stocks) 8. Stock in Country Road Industries has a beta of . 85. The market risk premium is 8 percent, and T-bills are currently yielding 5 percent. The company’s most recent dividend was \$1. 60 per share, and dividends are expected to grow at a 6 percent annual rate indefinitely. If the stock sells for \$37 per share, what is your best estimate of the company’s cost of equity? (Use both the CAPM and the dividend growth model to get the cost of equity)