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.

I got 15.36 and I am not sure why It's not right.

Answer 1

Step-1, Calculation of the Required Rate of Return (Ke) using CAPM Approach

As per Capital Assets Pricing Model (CAPM), The Required Rate of Return (Ke) is calculated by using the following formula

Required Rate of Return (Ke) = Rf + [Beta x Market Risk Premium]

= 3.00% [ 1.50 x 4.75%]

= 3.00% + 7.125%

= 10.125%

Step-2, Dividend for the next 4 years

Dividend in Year 0 (D0) = $2.25

Dividend in Year 1 (D1) = $3.0375 [$2.25 x 135%]

Dividend in Year 2 (D2) = $4.1006 [$3.0375 x 135%]

Dividend in Year 3 (D3) = $5.5358 [$4.1006 x 135%]

Dividend in Year 4 (D4) = $7.4734 [$5.5358 x 135%]

Step-3, Share Price in Year 4

Dividend in Year 4(D4) = $7.4734

Dividend Growth Rate after Year 4 (g) = 0.00% per year

Required Rate of Return (Ke) = 10.125%

Share Price in Year 4 (P4) = D4(1 + g) / (Ke – g)

= $7.4734(1 + 0.00) / (0.10125 – 0.00)

= $7.4734 / 0.10125

= $73.81

Step-4, The intrinsic value of RRV’s common stock

As per Dividend Discount Model, Current Stock Price the aggregate of the Present Value of the future dividend payments and the present value the share price in year 4

Year	Cash flow	Present Value Factor (PVF) at 10.125%	Present Value of cash flows [Cash flows x PVF]
1	3.0375	0.90806	2.76
2	4.1006	0.82457	3.38
3	5.5358	0.74876	4.15
4	7.4734	0.67992	5.08
4	73.81	0.67992	50.19
TOTAL			65.55

Hence, the intrinsic value of RRV’s common stock is $65.55

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.