The market price of a security is $44. Its expected rate of return is 7%. The ri
ID: 2757949 • Letter: T
Question
The market price of a security is $44. Its expected rate of return is 7%. The risk-free rate is 4%, and the market risk premium is 7%. What will the market price of the security be if its beta doubles (and all other variables remain unchanged)? Assume the stock is expected to pay a constant dividend in perpetuity. (Round your answer to 2 decimal places.)
The market price of a security is $44. Its expected rate of return is 7%. The risk-free rate is 4%, and the market risk premium is 7%. What will the market price of the security be if its beta doubles (and all other variables remain unchanged)? Assume the stock is expected to pay a constant dividend in perpetuity. (Round your answer to 2 decimal places.)
Explanation / Answer
When the beta of the security doubles, its risk premium will also double. The current risk premium rate is (7-4) = 3%. So, the new risk premium rate is 6%/ The new discount rate for the security will be 6+4 = 10%.
If the stocks pays a perpetual dividend, price is determined through following formula:
Price = Dividend/ Discount Rate
40 = Dividend/.07
Therefore, Dividend = 40*.07 = 2.80
As the new discount rate is 10%, the stock would be worth 2.80/.1 = 28 now. The increase in beta has lowered the stock price.
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