Top hedge fund manager Diana Sauros believes that a stock with the same market r

Question

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 $56. The stock will pay a dividend at year-end of $4.00. Assume that risk-free Treasury securities currently offer an interest rate of 1.9%. Average rates of return on Treasury bills, government bonds, and common stocks. 1900-2013 (figures in percent per year) are as follows. Average Annual Average Premium (Extra return versus Treasury bills) Portfolio Rate of Return Treasury bills 3.9 Treasury bonds 5.2 1.3 Common stocks 11.5 7.6 What is the discount rate if the interest rate is 4.0%? (Enter your answer as a percent rounded to 2 decimal places.) Discount rate What price should she be willing to pay for the stock today? (Do not round intermediate calculation. Round your answer to 2 decimal places.) Stock price

Explanation / Answer

Discoun rate = T- bill rate + market premium

=4% +7.6% =11.6%

First we will have to calculat the growth rate of stock

= R- d1/p

R= required return = 1.9% +7.6%=9.5%

growth rate =9.5% -4/56

9.15% -7.14%= 2.01%

Now interst rate 4% hence discoun rate = 4% +7.6% =11.6%

Hence the Price of the stock =4/(11.6% -2.01%) = 4/9.59% =41.71

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