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ID: 2613349 • Letter: N

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Note: You must keep all decimal places to correctly solve this problem.

Nonconstant Growth Valuation

A company currently pays a dividend of $2 per share (D0 = $2). It is estimated that the company's dividend will grow at a rate of 16% per year for the next 2 years, then at a constant rate of 8% thereafter. The company's stock has a beta of 1.25, the risk-free rate is 5%, and the market risk premium is 6%. What is your estimate of the stock's current price? Round your answer to the nearest cent.

Nonconstant Growth Valuation

Explanation / Answer

Current Dividend D0 = $2
Growth rate of Dividend for 2 years g1 = 16%
Period of dividend growth at 16% t = 2 years
Constant growth rate after 2 years g2 = 8%
risk-free rate rf = 5%
Market Risk Premium = 6%
Stock Beta = 1.25

Market Risk Premium = Expected Rate of Return on Stock - Risk-free rate

6% = Expected Rate of Return on Stock - 5%

Expected Rate of Return on Stock r = 6% + 5% = 11%

Dividend for year 1 D1 = D0*(1+g1) = 2 * (1+0.16) = 2*1.16 = $ 2.32
Dividend for year 2 D2 = D1*(1+g1) = 2.32 * 1.16 = 2.6912
Dividend for year 3 D3 = D2* (1+g2) = 2.6912*1.08 = 2.906496

Current stock price P can be calculated using the formula

P = D1/(1+r) + D2/(1+r)^2 + (D3/(r-g2))/(1+r)^2

Substituting the values

P = 2.32/(1+0.11) + 2.6912/(1+0.11)^2 + (2.906496/0.11-0.08)/(1+0.11)^2

= (2.32/1.11) + 2.6912/(1.11)^2 + (2.906496/0.03)/(1.11)^2

= 2.0901 + 2.6912/1.2321 + 96.8832/1.2321 = 2.0901 + 2.1842 + 78.6326

P = 82.9069 or $ 82.91

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