Question

Metatrend's stock will generate earnings of $3 per share this year. The discount rate for the stock is 15%, and the rate of return on reinvested earnings also is 15% a. Find both the growth rate of dividends and the price of the stock if the company reinvests the following fraction of its earnings in the form: (0) 0%, (m) 40%, (i) 60% (Do not round intermediate calculations. Enter the growth rates as a whole percent.) 0% Reinvestment of Earnings 40% 0% 60% Growth rate of dividends Stock price b. Redo part (a) now assuming that the rate of return on reinvested earnings is 20% What is the present value of growth opportunities (PVGO) for each reinvestment rate? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Reinvestment of Earnings 0% 40% 60 % PVGO

Answer 1

(a) Return on Reinvested Earnings = RR = 15%, Cost of Capital = 15 % and Current Dividend = $ 3

(i) Reinvestment Fraction = F = 0%

Growth = F x RR = 0 x 15 = 0%

Stock Price = 3 / 0.15 = $ 20

(ii) Reinvestment Fraction = F = 40%

Growth = 0.4 x 15 = 6%

Stock Price = [3 x 1.06 / (0.15-0.06)] = $ 35.33

(iii) Reinvestment Fraction = F = 60%

Growth = F x RR = 0.6 x 15 = 9%

Stock Price = [(3 x 1.09) / (0.15-0.09)] = $ 54.5

(b) PVGO = Normal Stock Price with Dividend Growth - No Growth Stock Price (Stock Price at 0% Growth)

(i) Reinvestment Fraction = 0 % RR = 20%

Growth = 0 x 20 = 0 %

Stock Price = 3/0.15 = $ 20

(ii) Reinvestment Fraction = 40%

Growth = 0.4 x 20 = 8%

Stock Price = [(3 x 1.08) / (0.15-0.08)] = $ 46.286

PVGO = 46.286 - 20 = $ 26.286

(iii) Reinvestment Fraction = 60%

Growth = 0.6 x 20 = 12 %

Stock Price = [(3 x 1.12) / (0.15-0.12)] = $ 112

PVGO = 112 - 20 = $ 92