Rentz RVs Inc. (RRV) is currently enjoying relatively high growth because of a surge in the demand for recreational vehicles. Management expects earnings and dividends to grow at a rate of 25% for the next 4 years, after which high gas prices 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. RRV's 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 = 3% + 1.20(5.50%) 
r = 9.6%

Next, we can use the dividend discount model (DDM) to calculate the current price of the stock:

P0 = D1/(r - g) 
D1 = D0(1 + g) = $1.25(1 + 0.25) = $1.5625 
g = 25% for the next 4 years, then 0% after 
Therefore, we can use the constant growth formula for the period after 4 years: 
P0 = $1.5625/(0.096 - 0.00) = $16.24 (4 years from now) 
To find the current price, we need to discount this future price back to the present: 
P0 = $16.24/(1 + 0.096)^4 = $11.43 
Therefore, the current price of the stock is $29.05 (rounded to two decimal places).