Nonconstant Growth Valuation
A company currently pays a dividend of $1.75 per share (D0 = $1.75). It is estimated that the company's dividend will grow at a rate of 18% per year for the next 2 years, and then at a constant rate of 5% thereafter. The company's stock has a beta of 2, the risk-free rate is 3%, and the market risk premium is 3%. What is your estimate of the stock's current price? Do not round intermediate calculations. Round your answer to the nearest cent.
Solution
For estimating the stock's current price, we have to compute the Cost of Capital.
Cost of capital (under CAPM Model) = Risk-free rate + (Beta X Risk Premium)
Here, Risk-free rate = 3%
Beta = 2
Risk Premium = 3%
Therefore, Cost of Capital (CAPM) = 3% + (2 X 3%) = 9%
Now, let us value stock's current price,
Dividend paid (D0) = $ 1.75 per share
Dividend will grow @ 18%, or 0.18 per $ for next 2 years, and then constant rate of 5%, or 0.05 per $ thereafter
Therefore, D1 = D0 X ( 1 + g) = $ [ 1.75 X (1 + 0.18) ] = $ 2.065
D2 = D1 X ( 1 + g) = $ [ 2.065 X (1 + 0.18) = $ 2.4367
D3 = D2 X (1+g) = $ [ 2.4367 X (1+0.05)] = $ 2.558535
Now, P2 = D3 / (Cost of Capital - g) = $ [ 2.558535 / (0.09 - 0.05)] = $ 63.96 (Approx)
Now, Current Market Price (P0) = [D1/(1+Cost of Capital)] + [(D2+P2)/(1+Cost of Capital)2]
=$ [2.065/(1+0.09)] + [(2.4367+63.96)/(1+0.09)2]
= $ (1.89 + 55.89)
= $ 57.78
Answer: Expected Current Market Price of the stock is $ 57.78.
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