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

The required return per CAPM = 3%+1.5*5% =	10.50%
Price of the stock is the PV of the expected dividends.
The expected dividends are $2.8 per share for the 1st
year with 10% growth for the next 4 years.
After the 5th year it is perpetual growth rate in dividends.
So the PV of the dividends are to be calculated as two
streams.
1) PV of dividends t1 to t5:
Year	Expected dividend	PVIF at 10.5%	PV at 10.5%
1	$                 2.80	0.90498	$              2.53
2	$                 3.08	0.81898	$              2.52
3	$                 3.39	0.74116	$              2.51
4	$                 3.73	0.67073	$              2.50
5	$                 4.10	0.60700	$              2.49
Total PV of dividends of years t1 to t5			$           12.56
2) PV of continuing value of dividends = 43.40-12.56 =	$              30.84
Continuing value at t5 = 30.84/0.60700 =	$              50.81
Now 50.81 = 4.10*(1+g)/(0.105-g)
Solving for g:
(50.81/4.10)*(0.105-g) = 1+g
1.30123-12.39268*g = 1+g
0.30123 = 13.39268*g
g = 0.30123/13.39268 = 0.01083 = 2.25%
CHECK = 4.1*1.0225/(0.105-0.0225) = $50.82
Answer: Implied growth rate after the 5th year = 2.25%