Problem Set 2 Dr. Zacharias Sautner If no information about the premium has been given in the questions below, you can use the data form the following table:
Arithmetic average Geometric Average Stocks ‐ Stocks ‐ Stocks ‐ Stocks ‐ Historical Period T.Bills T.Bonds T.Bills T.Bonds 1928‐2004 7.92% 6.53% 6.02% 4.84% 1964‐2004 5.82% 4.34% 4.59% 3.47% 1994‐2004 8.60% 5.82% 6.85% 4.51% For a long‐term investor the geometric average with treasury bonds (4.84%) is used. For a short‐term investor the arithmetic average with treasury bills (7.92%) is used. In both cases the longest possible period is taken.
Solutions 1. In December 1995, Boise Cascade’s stock had a beta of 0.95. The treasury bill rate at the time was 5.8%, and the treasury bond rate was 6.4%. The firm had debt outstanding of $1.7 billion and a market value of equity of $1.5 billion; the corporate marginal tax rate was 36%. a. Estimate the expected return on the stock for a short term investor in the company. b. Estimate the expected return on the stock for a long‐term investor in the company. c. Estimate the cost of equity for the company. a. We use the CAPM: The Expected Return on the stock = 0.058 + 0.95(0.0792) = 0.1332 = 13.32% Since the investor is a short‐term investor, we use the T‐bill rate, and the arithmetic mean. Since the focus is short‐term, we don’t need to take compounding into account.
b. For a long‐term investor, we would use the T‐bond rate, and the geometric mean: The expected return = 0.064 + 0.95(0.0484) = 0.11 or 11%, where 4.84% is used as the estimate of the market risk premium, since that is the geometric average of the market premium using the long‐term T‐bond rate as the riskfree rate. c. The cost of equity for the company is more appropriately the long‐term required rate of return, since most projects for the company