Question

Simpkins Corporation does not pay any dividends because it is expanding rapidly and needs to retain all of its earnings. However, investors expect Simpkins to begin paying dividends, with the first dividend of $1.50 coming 3 years from today. The dividend should grow rapidly - at a rate of 75% per year - during Years 4 and 5. After Year 5, the company should grow at a constant rate of 5% per year. If the required return on the stock is 15%, what is the value of the stock today (assume the market is in equilibrium with the required return equal to the expected return)? Round your answer to the nearest cent. Do not round your intermediate computations. $ ________

Answer 1

First Dividend at the end of Year 3 = D3 = $ 1.5, Initial Growth Rate for Year 4 and Year 5 = 75 % and Growth Rate post Year 5 = 5 %

Required Rate of Return = 15 %

D4 = 1.5 x 1.75 = $ 2.625 and D5 = D4 x 1.75 = 2.625 x 1.75 = $ 4.59375

D6 = D5 x 1.05 = 4.59375 x 1.05 = $ 4.823438

Horizon Value of Perpetual Dividends at the end of Year 5 = HV = 4.823438 / (0.15 - 0.05) = $ 48.23438

Current Stock Price = PV of D3, D4, D5 and HV = 1.5 / 1.15 + 2.625 / (1.15)^(2) + 4.59375 / (1.15)^(3) + 48.23438 / (1.15)^(3) = $ 28.75204 ~ $ 28.75