Question

The Birdstrom Co. just recently paid a dividend of $2.00 per share. Stock market analysts expect that the growth rate for the dividend will be 40% in year 1, 30% in year 2, 20% in year 3, 15% in year 4, and 10% in year five. After the fifth year, the dividend will grow at a constant rate of 6%. If the required return for Birdstrom is 12%, calculate the current stock price and the expected dividend yield and capital gain in the first year if you buy the stock at the computed price

Answer 1

1)	The fair price of a stock is the PV of the expected dividends when discounted at the
	required rate of return. The dividends for the first five years have varying growth rates and the growth
	rate is constant from the 6th year at 6.0% per year. Hence, PVs of dividends have to be worked out separately for t1 to t5.
	However, the continuing value of dividends from t6 can be valued as a growing perpetuity having growth
	rate of 6.0% and then discounted to get the PV.
	Year	Expected Dividends	PVIF at 12%	PV at 12%
	1	2.8000	0.89286	$           2.50
	2	3.6400	0.79719	$           2.90		`
	3	4.3680	0.71178	$           3.11
	4	5.0232	0.63552	$           3.19
	5	5.5255	0.56743	$           3.14
	PV of expected dividends t1 to t5			$         14.84
	Terminal value of dividends = 5.5255*1.06/(0.12-0.06)=				$        97.62
	PV of terminal value = 97.62*0.56743 =			$         55.39
	Current stock price			$         70.23
2)	Expected stock price next year
	Year	Expected Dividends	PVIF at 12%	PV at 17.4%
	0	2.8000	0	$                -
	1	3.6400	0.89286	$           3.25
	2	4.3680	0.79719	$           3.48
	3	5.0232	0.71178	$           3.58
	4	5.5255	0.63552	$           3.51
	PV of expected dividends t1 to t4			$         13.82
	Terminal value of dividends = 5.5255*1.06/(0.12-0.06)=				$        97.62
	PV of terminal value = 97.62*0.63552 =			$         62.04
	Expected stock price next year			$         75.86
3)	Dividend yield = 2.8/70.23 =	3.99%
4)	Capital gains yield = 75.86/70.23-1 =	8.01%
5)	Total yield	12.00%