Problem 1. You are considering three insurance settlement offers. The first offer includes annual payments of $5,000, $10,000, $15,000, etc., where the payment for each year is $5,000 more than the payment for the previous year, over the next ten years. The first payment of $5,000 will be made exactly one year from today and the last payment, equal to $50,000 will be made ten years from today. The second offer is the payment of one lump sum amount today. The third offer is to receive an equal amount at the end of each year, over the next ten years. Assume there are no tax effects and your discount rate is 12% per year. What is the minimum amount that you will accept today if you are to select the lump sum offer? What is the minimum amount of each of the 10 equal annual payments that you should be willing to accept?
Problem 2. Joan Collins wishes to choose the best of four immediate-retirement annuities available to her. In each case, in exchange for paying a single premium today, she will receive equal annual end-of-year cash benefits for a specified number of years. She considers the annuities to be equally risky and is not concerned about their differing lives. Her decision will be based solely on the rate of return she will earn on each annuity. The key terms of each of the four annuities are shown in the following table.
Calculate the rate of return on each of the four annuities Joan is considering. Given Joan's stated decision criterion, which annuity would you recommend?
Problem 3. Junior Sayou, a financial analyst for Chargers Investments, a mutual fund management company, must evaluate the risk and return of two stocks, X and Y. The firm is considering adding these stocks to its diversified stock portfolio. To assess the return and risk of each stock, Junior gathered data on the annual dividends and beginning- and end-of-year prices of each stock over the immediately preceding 10 years, 2002-2011. These data are summarized in the accompanying table. Junior's investigation suggests that both stocks, on average, will tend to perform in the future just as they have during the past 10 years. He therefore believes that the expected annual return can be estimated by finding the average annual return for each stock over the past 10 years. Junior believes that each stock's risk can be assessed in two ways: in isolation and as part of the firm's diversified portfolio of stocks. The risk of the stocks in isolation can be found by using the standard deviation and coefficient of variation of returns over the past 10 years. The capital assets pricing model (CAPM) can be used to assess the stock's risk as part of the firm's portfolio of stocks. Applying some sophisticated quantitative techniques, Junior estimated betas for stocks X and Y of 1.60 and 1.10, respectively. In addition, he found that the risk-free rate is currently 7% and that the market return is 10%. Note: you may find it easier and time effective to solve the problems using Excel or any other spreadsheet software. If you do, please use the drop box to submit your spreadsheet file.
a) Calculate the annual rate of return for each stock in each of the 10 preceding years, and use those values to find the average annual return for each stock over the 10-year period.
b) Use the returns calculated in part (a) to find (i) the standard deviation and (ii) the coefficient of variation of the returns for each stock over the 10-year period 2002-2011.
c) Use your findings in parts (a) and (b) to evaluate and discuss the return and risk associated with each stock. Which stock appears to be preferable? Explain.
d) Use the CAPM to find the required return for each stock. Compare this value with the average annual returns calculated in part (a).
e) Compare and contrast your findings in parts (c) and (d). What recommendations would you give Junior with regard to investing in either of the two stocks? Explain to Junior why he is better off using beta rather than the standard deviation and coefficient of variation to assess the risk of each stock.
Problem 4. Assume that you have been hired as a consultant by S- Corporation, a major producer of chemicals and plastics, including plastic grocery bags, Styrofoam cups, and fertilizers, to estimate the firm's weighted average cost of capital. S-Corporation has 500 million shares of common stock outstanding, 75 million shares of preferred stock outstanding, and 25 million 11% semiannual coupon bonds outstanding, par value $1,000 each. The common stock currently sells for $40 per share and has a beta of 1.2, the preferred stock currently sells for $75 per share and pays an annual dividend of $7 per share, and the bonds have 15 years to maturity and sell for 93.5 percent of par. The market risk premium is 6%, the yield on Treasury bills is 4%, and S Corporation's tax rate is 35%. What is the firm's weighted average cost of capital?