Top hedge fund manager Sally Buffit believes that a stock with the same market risk as the S&P 500 will sell at year-end at a price of $59. The stock will pay a dividend at year-end of $4.00. Assume that risk-free Treasury securities currently offer an interest rate of 1.6%.

Average rates of return on Treasury bills, government bonds, and common stocks, 1900–2017 (figures in percent per year) are as follows.

PortfolioAverage Annual

Rate of Return (%)Average Premium (Extra return

versus Treasury bills) (%)Treasury bills 3.8 Treasury bonds 5.3 1.5 Common stocks 11.5 7.7

a. What is the discount rate on the stock? (Enter your answer as a percent rounded to 2 decimal places.)

b. What price should she be willing to pay for the stock today? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Consider the following scenario analysis:

Rate of ReturnScenarioProbabilityStocksBondsRecession0.2-4%15%Normal economy0.716 11 Boom0.125 3

Assume a portfolio with weights of 0.60 in stocks and 0.40 in bonds.

a. What is the rate of return on the portfolio in each scenario? (Enter your answer as a percent rounded to 1 decimal place.)

b. What are the expected rate of return and standard deviation of the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Consider the following two scenarios for the economy and the expected returns in each scenario for the market portfolio, an aggressive stock A, and a defensive stock D.

Rate of ReturnScenario Market Aggressive

Stock A Defensive

Stock D Bust –8% –11% –6% Boom 30 40 24

Required:a. Find the beta of each stock.b. If each scenario is equally likely, find the expected rate of return on the market portfolio and on each stock.c. If the T-bill rate is 3%, what does the CAPM say about the fair expected rate of return on the two stocks?d. Which stock seems to be a better buy on the basis of your answers to (a) through (c)?