(a) The risk-free rate of return is 8 percent, the required rate of return on th
ID: 2651403 • Letter: #
Question
(a) The risk-free rate of return is 8 percent, the required rate of return on the market, E[Rm] is 12 percent, and Stock X has a beta coefficient of 1.4. If the dividend expected during the coming year, D1, is $2.50 and g = 5%, at what price should Stock X sell?
(b) Now suppose the following events occur simultaneously:
(1)The Federal Reserve Board increases the money supply, causing the riskless rate to drop to 7 percent.
(2)Investors' risk aversion declines: this fact, combined with the decline in RF, causes RM to fall to 10 percent.
(3)Firm X has a change in management. The new group institutes policies that increase the growth rate to 6 percent. Also, the new management stabilizes sales and profits, and thus causes the beta coefficient to decline from 1.4 to 1.1.
After all these changes, what is Stock X's new equilibrium price? (Note: D1 goes to $2.52.)
Explanation / Answer
a)
As per CAPM
Required Rate of Return = risk-free rate of return + (E[Rm] - risk-free rate of return)*Beta
Required Rate of Return = 8 + (12-8)*1.4
Required Rate of Return = 13.60%
As per Dividend Discount Model
Price should Stock X sell = D1/(Required Rate of Return - g)
Price should Stock X sell = 2.50/(13.60%-5%)
Price should Stock X sell = $ 29.07
b) After all those changes mention in problem
As per CAPM
Required Rate of Return = risk-free rate of return + (E[Rm] - risk-free rate of return)*Beta
Required Rate of Return = 7 + (10-7)*1.1
Required Rate of Return = 10.30%
As per Dividend Discount Model
Stock X's new equilibrium price = D1/(Required Rate of Return - g)
Stock X's new equilibrium price = 2.52/(10.30%- 6%)
Stock X's new equilibrium price= $ 58.60
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