McGaha Enterprises expects earnings and dividends to grow at a rate of 25% for the next 4 years, after the growth rate in earnings and dividends will fall 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 determine the expected dividend for each of the next four years using the dividend growth rate formula:
D1 = D0 × (1 + g)
D1 = $1.25 × (1 + 0.25) = $1.5625
D2 = $1.5625 × (1 + 0.25) = $1.9531
D3 = $1.9531 × (1 + 0.25) = $2.4414
D4 = $2.4414 × (1 + 0.25) = $3.0518

Next, we need to calculate the price of the stock at the end of year 4 using the constant growth formula:
P4 = D5 / (R - g)
Assuming the growth rate falls to zero after year 4, we can calculate the expected price of the stock at the end of year 4 as follows:
P4 = $3.0518 / (0.055 - 0) = $55.5796

Now we can use the dividend discount model to find the present value of the stock by discounting each of the expected dividends and the expected stock price back to the present:
P0 = D1 / (1 + R) + D2 / (1 + R)2 + D3 / (1 + R)3 + D4 / (1 + R)4 + P4 / (1 + R)4

Using the given inputs, we can solve for the present value of the stock:
P0 = $1.5625 / (1 + 0.08) + $1.9531 / (1 + 0.08)2 + $2.4414 / (1 + 0.08)3 + $3.0518 / (1 + 0.08)4 + $55.5796 / (1 + 0.08)4
P0 = $29.05

Therefore, the current price of the common stock is $29.05, which is closest to choice C).

McGaha Enterprises Expects Earnings and Dividends to Grow at a Rate