Top hedge fund manager DianaTop hedge fund manager Diana Sauros believes that a
ID: 2731546 • Letter: T
Question
Top hedge fund manager DianaTop 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 $50. The stock will pay a dividend at year-end of $2. Assume that risk-free Treasury securities currently offer an interest rate of 2%.
Portfolio_______Average annual rate of return ____Average premium (extra return vs treasury bills)
Treasury bills--------------------3.9--------------------------
Treasury bonds---------------5.2--------------------1.3
Common stocks---------------11.5-------------------------7.6
A. what is the discount rate if the interest rate is 2%?
B. what price should she be willing to pay for the stock today? Assume now is the beginning of the year.
Hint:
1. the discount rate equals the expected return we require.
2. from chapter 7, we have P0= (p1+DIV1) / (1+r)
Explanation / Answer
a) Discount rate is calculated using the CAPM model.
rj = rf+ß(rm-rf)
rf = Risk free rate = 2%
ß = Beta of the stock = 1 (As stock follows the S&P)
rm = Average rate of return = 11.5%
2%+1(11.5%-2%) = 11.5%
So, the discount rate should be 11.5%.
b) Intrinsic value of the stock = (p1+DIV1) / (1+r)
=>($50 + $2) / (1.115) = $46.64