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 find the expected dividends for the next four years using the formula:
Dn = D0(1+g)^n
D1 = $1.25(1+0.25) = $1.56
D2 = $1.56(1+0.25) = $1.95
D3 = $1.95(1+0.25) = $2.44
D4 = $2.44(1+0.25) = $3.05

Next, we need to find the present value of the expected dividends for the next four years using the formula:
PV = D / (1+r)^n
PV1 = $1.56 / (1+0.12)^1 = $1.39
PV2 = $1.95 / (1+0.12)^2 = $1.52
PV3 = $2.44 / (1+0.12)^3 = $1.68
PV4 = $3.05 / (1+0.12)^4 = $1.86

Then, we need to find the present value of the stock price at the end of year 4 using the formula:
P4 = D5 / (r - g)
P4 = $3.05 / (0.03 - 0) = $101.67

Next, we need to find the present value of all the cash flows using the formula:
P0 = PV1 + PV2 + PV3 + PV4 + P4 / (1+r)^4
P0 = $1.39 + $1.52 + $1.68 + $1.86 + $101.67 / (1+0.12)^4
P0 = $29.05
Therefore, the current price of the common stock is $29.05 (option C).