Church Inc.is presently enjoying relatively high growth because of a surge in the demand for its new product.Management expects earnings and dividends to grow at a rate of 25% for the next 4 years,after which competition will probably reduce the growth rate in earnings and dividends to zero,i.e.,g = 0.The company's last dividend,D₀,was $1.25,its beta is 1.20,the market risk premium is 5.50%,and the risk-free rate is 3.00%.What is the current price of the common stock?

Question

Quizplus · Accepted Answer

First, we need to calculate the required rate of return using the Capital Asset Pricing Model (CAPM):
r = Rf + β(Rm - Rf)
r = 0.03 + 1.20(0.055)
r = 0.03 + 0.066
r = 0.096 or 9.6%
Next, we can use the dividend discount model to calculate the current stock price:
P0 = D1 / (r - g)
where D1 is the dividend for next year and g is the expected growth rate for the first four years.
D1 = D0(1 + g) = $1.25(1 + 0.25) = $1.56
g = 0.25 for the first four years and 0 after that
P0 = $1.56 / (0.096 - 0.25)
P0 = $29.05
Therefore, the current price of the common stock is $29.05. Option C is the correct answer.