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3 November, 06:13

Top hedge fund manager Diana Sauros believes that a stock with the same market risk as the S&P 500 will sell at year-end at a price of $60. The stock will pay a dividend at year-end of $2.00. Assume that risk-free Treasury securities currently offer an interest rate of 1.5%.

Average rates of return on Treasury bills, government bonds, and common stocks, 1900-2013 (figures in percent per year) are as follows.

Portfolio Average Annual Average Premium

Rate of Return (Extra return versus Treasury bills)

Treasury bills 3.9

Treasury bonds 5.2 1.3

Common stocks 11.5 7.6

Required:

(a) What is the discount rate if the interest rate is 4.0%? (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.)

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Answers (1)
  1. 3 November, 06:18
    0
    a. 7.71%

    b. $57.57

    Explanation:

    a. The computation of discount rate is shown below:-

    Discount rate = Risk free rate of return + Market Risk Premium * Beta

    Here Common stock will have the same market risk as S&P 500 i. e Beta of Common Stock is 1

    = 1.5% + 7.6 * 1

    = 7.71%

    b. The computation of stock price is shown below:-

    Stock price = Expected Stock Value at year End : (1 + Discount rate) + Expected Dividend : (1 + Discount Rate)

    = $60 : (1 + 7.71%) + $2 : (1 + 7.71%)

    = $60 : 1.0771 + 2 : 1.0771

    = $55.71 + $1.86

    = $57.57
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