Question

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 22% 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? Do not round intermediate calculations.

Answer 1

The current price of the common stock is $26.57

Step-by-step explanation:

Using the SML equation, we can calculate the required rate of return on the company's stock.

r = 3% + 1.2 * 5.5%

r = 9.6%

The stock price of the company can be determined using the two stage growth model.

P0 = D1 / (1+r) + D2 / (1+r)² + ... + (D / r) / (1+r)^n

Here, as the stock becomes a zero growth stock after 4 years, we will replace terminal value with price formula of zero growth stock and discount it.

Thus,

P0 = 1.25(1+0.22) / (1+0.096) + 1.25(1+0.22)² / (1+0.096)² + 1.25(1+0.22)³/(1+0.096)³ + 1.25(1+0.22)^4 / (1+0.096)^4 + (1.25(1+0.22)^4/0.096) / (1+0.096)^4

PO = $26.57