The next expected dividend for Stock P is $2.50, the current price of the stock is $32.50, and the firm is expected to grow at a constant rate of 4 percent per year forever. The risk free rate is 3 percent, the market risk premium is 5.5 percent, and the stock's beta is 1.2. Based on the given information, which of the following statements is correct?
A)An investor should buy this stock because its expected rate of return, 11.69 percent, is greater than its required rate of return, 9.6 percent.
B)An investor should not buy this stock because its expected rate of return, 9.6 percent, is greater than its required rate of return, 11.69 percent.
C)An investor should not buy this stock because its intrinsic value, $44.64, is greater than its current price of $32.50.
D)An investor should not buy this stock because its current price, $32.50, is not equal to its intrinsic value, $44.64.
E)An investor should be indifferent toward buying or selling the stock because its required rate of return is equal to its expected rate of return, 11.69 percent.

Question

Quizplus · Accepted Answer

To calculate the required rate of return, we use the capital asset pricing model (CAPM):

Required Rate of Return = Risk-Free Rate + Beta × (Market Risk Premium)
Required Rate of Return = 3% + 1.2 × 5.5%
Required Rate of Return = 9.6%

Using the constant growth dividend discount model, we can calculate the intrinsic value of the stock:

Intrinsic Value = Next Year's Dividend ÷ (Required Rate of Return − Growth Rate)
Intrinsic Value = $2.50 ÷ (9.6% − 4%)
Intrinsic Value = $44.64

Comparing the intrinsic value to the current price, we can see that the stock is undervalued. Additionally, the expected rate of return (11.69%) is higher than the required rate of return (9.6%), indicating that the stock is a good investment. Therefore, choice A is correct.

The Next Expected Dividend for Stock P Is $2