Question

A company currently pays a dividend of $2.25 per share (D0 = $2.25). It is estimated that the company's dividend will grow at a rate of 25% per year for the next 2 years, then at a constant rate of 6% thereafter. The company's stock has a beta of 1, the risk-free rate is 7%, 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

Answer-

Given

Dividend (D0) = $ 2.25
Growth rate = 25 % = 0.25
D1 = $ 2.25 x ( 1 + g)
D1 = $ 2.25 x ( 1 + 0.25)
D1 = $ 2.25 x 1.25 = $ 2.8125

D2 = $ 2.8125 x 1.25 = $ 3.5156

Cost of equity (r) = risk free rate + Beta x ( market risk premium)
Cost of equity (r) = 7 % + 1 x 6 % [ Beta = 1 ]
Cost of equity (r) = 13 % = 0.13
Constant growth rate (g1) = 6 % = 0.06

Value of stock (V0) = D1 / ( 1+r ) + D2 x ( 1+g1) / [ ( 1+r)2 x (r - g1) ]

V0 = $ 2.8125 / ( 1+0.13) + [ $ 3.5156 x (1+0.06) / {(1+0.13)2 x (0.13 - 0.06)}]

V0 = $ 2.8125 / ( 1.13) +[ $ 3.5156 x ( 1.06) / { (1.13)2 x (0.07)}]

V0 = $ 2.48894 + [ $ 3.7265 / ( 1.2769 x 0.07) ]

V0 = $ 2.48894 + [ $ 3.7265 / 0.08938 ]

V0 = $ 2.48894 + $ 41.693

V0 = $ 44.18194

Therefore the current stock price (V0) = $ 44.18194