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

As per CAPM

expected return = risk-free rate + beta * (Market risk premium)

Expected return% = 3 + 1.5 * (4.75)

Expected return% = 10.13

	Required rate=	10.13%
Year	Previous year dividend	Dividend growth rate	Dividend current year	Horizon value	Total Value	Discount factor	Discounted value
1	2.25	35.00%	3.0375		3.0375	1.1013	2.7581
2	3.0375	35.00%	4.100625		4.100625	1.21286169	3.38095
3	4.100625	35.00%	5.53584375		5.53584375	1.335724579	4.14445
4	5.53584375	35.00%	7.473389063	73.775	81.24838906	1.471033479	55.23218
	Long term growth rate (given)=	0.00%			Value of Stock =	Sum of discounted value =	65.52
Where
Current dividend =Previous year dividend*(1+growth rate)^corresponding year
Total value = Dividend + horizon value (only for last year)
Horizon value = Dividend Current year 4 *(1+long term growth rate)/( Required rate-long term growth rate)
Discount factor=(1+ Required rate)^corresponding period
Discounted value=total value/discount factor