Question

Grominet is expected to pay an annual dividend of $2.8 one year from now. Analysts also expect this dividend to grow at 10% per year thereafter until the fifth year. After then, growth has not been forecasted by analysts, but it is expected to be lower. Assume that the risk free rate of return is 3%, that the beta of Grominet is 1.5 and the market risk premium is 5%. What is the expected growth rate after year 5 implied by a stock price of $43.40?

Answer 1

D0 = $2.80

Growth rate for first 5 years is 10%

D1 = $2.800 * 1.10 = $3.080
D2 = $3.080 * 1.10 = $3.388
D3 = $3.388 * 1.10 = $3.727
D4 = $3.727 * 1.10 = $4.099
D5 = $4.099 * 1.10 = $4.509

Cost of Capital, r = Risk-free Rate + Beta * Market Risk Premium
Cost of Capital, r = 3% + 1.50 * 5%
Cost of Capital, r = 10.50%

P0 = $3.080/1.105 + $3.388/1.105^2 + $3.727/1.105^3 + $4.099/1.105^4 + $4.509/1.105^5 + P5/1.105^5
$43.40 = $13.811 + P5*0.6070
P5 * 0.6070 = $29.589
P5 = $48.746

Let constant growth rate be g%

P5 = D5*(1+g) / (r - g)
$48.746 = $4.509 * (1 + g) / (0.105 - g)
10.811 = (1 + g) / (0.105 - g)
1.135 - 10.811*g = 1 + g
0.135 = 11.811*g
g = 0.0114
g = 1.14%

So, expected growth rate is 1.14%