Assume Gillette Corporation will pay an annual dividend of $ 0.62 one year from now. Analysts expect this dividend to grow at 11.4 % per year thereafter until the 44th year. Thereafter, growth will level off at 1.6 % per year. According to the dividend-discount model, what is the value of a share of Gillette stock if the firm's equity cost of capital is 7.9%?
Value per share = present value (PV) of the dividends for 44 years + PV of perpetual cash flow
PV of dividends for 44 years = D/(k-g)[1-((1+g)/(1+k))^n] where n = 44; k = 7.9%; g = 11.4%
0.62/(7.9%-11.4%)[1-((1+11.4%)/(1+7.9%))^44] = 54.45
Perpetual cash flow: D44 = D1*(1+g)^43 = 0.62*(1+11.4%)^43 = 64.34
Perpetual growth starts from the 45th year so D45 = D44*(1+G) = 64.34*(1+1.6%) = 65.37
Perpetual cash flow at t = 44 is D45/(k - G) where k = 7.9%
= 65.37/(7.9%-1.6%) = 1,037.55
PV of perpetual cash flow = 1,037.55/(1+7.9%)^44 = 36.56
Value per share = 54.45 + 36.56 = 91.02
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