Question

Restful RVs Inc. (RRV) is presently 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 35% 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 paid dividend, D0, was $2.25. RRV’s beta is 1.50, the market risk premium is 4.75%, and the risk-free rate is 3.00%. What is the intrinsic value of RRV’s common stock? Enter your answer rounded to two decimal places. Do not enter $ or comma in the answer box. For example, if your answer is $12,300.456 then enter as 12300.46 in the answer box.

Answer 1

Required rate of return = Risk free rate + beta * market risk premium
= 3% + 1.50 * 4.75%
= 3% + 7.125%
= 10.125%

D0 = $2.25
D1 = $2.25 * (1 + 35%) = $3.0375
D2 = $3.0375 * (1 + 35%) = $4.100625
D3 = $4.100625 * (1 + 35%) = $5.53584375
D4 = $5.53584375 * (1 + 35%) = $7.473389063
D5 = $7.473389063

P4 = D5 / (ke - g)
= $7.473389063 / (0.10125 - 0)
= $73.81125

Intrinsic value = (D1 / (1+r)^1) + (D2 / (1+r)^2) + (D3 / (1+r)^3) + (D4 / (1+r)^4) + (P4 / (1+r)^4)

= ($3.0375 / 1.10125^1) + ($4.100625 / 1.10125^2) + ($5.53584375 / 1.10125^3) + ($7.473389063 / 1.10125^4) + ($73.81125 / 1.10125^4)

= $2.7582 + $3.3813 + $4.1450 + $5.0813 + $50.1856

= $65.55

Intrinsic value = $65.55