Question

Problem 7-05
Nonconstant Growth Valuation

A company currently pays a dividend of $3.5 per share (D₀ = $3.5). It is estimated that the company's dividend will grow at a rate of 19% per year for the next 2 years, and then at a constant rate of 5% thereafter. The company's stock has a beta of 1.2, the risk-free rate is 5%, and the market risk premium is 4%. What is your estimate of the stock's current price? Do not round intermediate calculations. Round your answer to the nearest cent.

$

Answer 1

Use the capital asset pricing model (CAPM) to find the required
return of the stock.
Under the Capital Asset pricing model
Rs = Rf + Beta*(Rm-Rf)
Rs is the required return on the stock
Beta	1.2
Rf is the risk-free rate that is 5%.
(Rm - Rf)	4%
where Rm is the expected return on the market.
Rs = .05 + 1.2*(.04)
Rs = .05 + .048
Rs = .098
The required return on the stock is 9.8%.

D0	3.5
For the first two years
g1	0.19
D1	4.165
D2	4.95635
After that
g2	0.05
D3	5.2041675
D4	5.464375875
Find the price of the stock in year 3
According to the dividend growth model.
P3 = D4/(R-g2)
where R is .098
P3	113.8411641
The value of the stock today = sum of present value of future cash flows.
Cash flow in year 3 (P3+D3)	119.0453316
Using R = .098
Year	1	2	3
Cash flow	4.165	4.95635	119.0453
Present value	3.79	4.11	89.93
sum of present values	97.83
The current price of the stock is $97.8