Question

Nonconstant Dividend Growth Valuation A company currently pays a dividend of $1.8 per share (DO = $1.8). It is estimated that the company's dividend will grow at a rate of 22% per year for the next 2 years, and then at a constant rate of 7% thereafter. The company's stock has a beta of 1.1, the risk- free rate is 9%, and the market risk premium is 5.5%. What is your estimate of the stock's current price? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

1). According to the CAPM,

Required Return = Risk-free Rate + [Beta * Market Risk Premium]

= 9% + [1.1 * 5.5%] = 9% + 6.05% = 15.05%

D1 = D0 * (1 + g1) = $1.8 * (1 + 0.22) = $2.20

D2 = D1 * (1 + g1) = $2.20 * (1 + 0.22) = $2.68

D3 = D2 * (1 + gC) = $2.68 * (1 + 0.07) = $2.87

P2 = D3 / (r - gC) = $2.87 / (0.1505 - 0.07) = $2.87 / 0.0805 = $35.61

P0 = [D1 / (1 + r)] + [(D2 + P2) / (1 + r)²]

= [$2.20 / (1 + 0.1505)] + [($2.68 + $35.61) / (1 + 0.1505)²]

= $1.91 + $28.93 = $30.84

2-a). P1 = P0 * (1 + g) = $21 * (1 + 0.09) = $22.89

2-b). r = [{D0 * (1 + g)} / P0] + g

= [{$1.80 * (1 + 0.09)} / $21] + 0.09

= 0.0934 + 0.09 = 0.1834, or 18.34%