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

Step 1: Calculate the required rate of return (cost of equity)
R = Rf + beta*(Rm - Rf)
R = 3% + 1.20*(5.50%)
R = 9.6%

Step 2: Calculate the expected dividend for the next 4 years using the dividend growth model
D1 = D0*(1+g)^1
D2 = D0*(1+g)^2
D3 = D0*(1+g)^3
D4 = D0*(1+g)^4
where D0 = $1.25, g = 25%
D1 = 1.25*(1+0.25)^1 = $1.56
D2 = 1.56*(1+0.25)^2 = $1.95
D3 = 1.95*(1+0.25)^3 = $2.44
D4 = 2.44*(1+0.25)^4 = $3.05

Step 3: Calculate the price of the stock using the constant growth model
P4 = D4/(R-g)
where g = 0%, P4 is the price at the end of year 4 (when the high growth period ends)
P4 = 3.05/(0.096-0) = $31.77
PV = P4/(1+R)^4 = $21.53
D1 = $1.56, g = 25%, R = 9.6%-25% = -15.4% (assumes negative growth after year 4)
P0 = D1/(R-g) = $29.05 (rounded to two decimal places)

Therefore, the current price of the common stock is $29.05 (Option C).