Question

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 $44. The stock will pay a dividend at year-end of $2.00. Assume that risk-free Treasury securities currently offer an interest rate of 1.9%.Average rates of return on Treasury bills, government bonds, and common stocks, 1900–2017 (figures in percent per year) are as follows. Average Premium Average Annual (Extra returnPortfolio Rate of Return (%) versus Treasury bills) (%)Treasury bills 3.8 Treasury bonds 5.3 1.5 Common stocks 11.4 7.6 A. What is the discount rate on the stock? B. What price should she be willing to pay for the stock today?

Answer 1

Answer:

a. 9,50%

b. $47.09

Explanation:

a) Discount rate on the stock

Average Risk Premium of Stock = 7.60%

Current risk-free rate = 1.60%

Discount Rate = 7.60% + 1.90%

Discount Rate = 9.50%

b) Current Price = ($41 + $2) / (1 + 9.50%)^1

Current Price = $43 / (1.0950)^1

Current Price = $43 / (1.0950)^1

Current Price = $43 / 0.91324

Current Price = $47.0851035872278

Current Price = $47.09

Note: Stock price equals the present value of cash flows for a 1-year horizon (Fv + Dividend)/(1+ Discount rate)^n