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Suppose the company just paid dividend of $1. The dividends are expected to grow at 25%...

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Finance

Suppose the company just paid dividend of $1. The dividends areexpected to grow at 25% in Year 1 and 20% in Year 2, and 15% inYear 3. After that, the dividends will grow at a constant rate of5% forever. If the required rate of return is 10%, compute today'sprice of the stock.

Answer & Explanation Solved by verified expert
4.3 Ratings (627 Votes)

D(t+1) = D(t)*(1+g1)
D0 1
For the first year
g1 0.25
D1 1*(1+.25)
D1 1.25
For the second year
g2 0.2
D2 1.25*(1+.2)
D2 1.5
For the third year
g3 0.15
D3 1.5*(1+.15)
D3 1.725
For the fourth year
g4 0.05
D4 1.725*(1+.05)
D4 1.81125
According to the dividend growth model.
P4 = D5/(R-g4)
D5 1.81125*(1.05)
D5 1.9018125
R is the required rate of return that is 10%
P4 1.9018125/(.10 - .05)
P4 38.03625
Cash flow in year 4 D4+P4
Cash flow in year 4 39.8475
The price of the stock today = sum of present value of future cash flows.
Using R = .10
Year 1 2 3 4
Cash flow 1.25 1.5 1.725 39.8475
Present value 1.14 1.24 1.30 27.22
sum of present values 30.89
The price of the stock today is equal to $30.89.
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