Question

A company currently pays a dividend of $3.25 per share (D0 = $3.25). It is estimated that the company's dividend will grow at a rate of 25% per year for the next 2 years, and then at a constant rate of 7% thereafter. The company's stock has a beta of 1.75, the risk-free rate is 4%, and the market risk premium is 6%. What is your estimate of the stock's current price? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Working : Cost of equity = Rf + Beta * ( Rm - Rf)

Here,

Rf (risk free rate) = 4% or 0.04

Rm - Rf (Market risk premium) = 6% or 0.06

Beta = 1.75

Now,

Cost of equity = 0.04 + (1.75 * 0.06)

Cost of equity = 0.04 + 0.105

Cost of equity (ke) = 0.145 or 14.5%

Calculation of stock price = (D1 / (1 + ke)^1) + (D2 / (1 + ke)^2) + ((D3 / (ke - g)) * (1/(1 + ke)^2))

Here,

g (growth rate) = 25% or 0.25 for 1st 2 year & 7% or 0.07 thereafter

D1 (expected dividend at year 1) = D0 + g = $3.25 + 25% = $4.06

D2 (expected dividend at year 2) = D1 + g = $4.06 + 25% = $5.075

D3 (expected dividend at year 3) = D2 + g = $5.075 + 7% = $5.43

Ke (cost of equity) = 0.145

Now put the values into formula,

Stock price = ($4.06 / (1 + 0.145)^1) + ($5.075 / (1 + 0.145)^2) + (($5.43 / (0.145 - 0.07)) * (1 / (1 + 0.145)^2))

Stock price = ($4.06 / 1.145) + ($5.075 / 1.311) + (($5.43 / 0.075) * (1 / 1.311))

Stock price = $3.55 + $3.87 + ($72.40 * 0.7628)

Stock price = $3.55 + $3.87 + $55.23

Stock price = $62.65