Question

4. Church Inc. is presently enjoying relatively high growth because of a surge in the demand for its new product. Management expects earnings and dividends to grow at a rate of 25% for the next 4 years, after which competition will probably reduce the growth rate in earnings and dividends to zero, i.e., g = 0. The company’s last dividend, D0, was $1.25, its beta is 1.20, the market risk premium is 5.50%, and the risk-free rate is 3.00%. What is the current price of the common stock?

Answer 1

As per CAPM

expected return = risk-free rate + beta * (Market risk premium)

Expected return% = 3 + 1.2 * (5.5)

Expected return% = 9.6

	Required rate=	9.60%
Year	Previous year dividend	Dividend growth rate	Dividend current year	Horizon value	Total Value	Discount factor	Discounted value
1	1.2	25.00%	1.5		1.5	1.096	1.3686
2	1.5	25.00%	1.875		1.875	1.201216	1.56092
3	1.875	25.00%	2.34375		2.34375	1.316532736	1.78024
4	2.34375	25.00%	2.9296875	30.518	33.4476875	1.442919879	23.18056
	Long term growth rate (given)=	0.00%			Value of Stock =	Sum of discounted value =	27.89

Where
Current dividend =Previous year dividend*(1+growth rate)^corresponding year
Total value = Dividend + horizon value (only for last year)
Horizon value = Dividend Current year 4 *(1+long term growth rate)/( Required rate-long term growth rate)
Discount factor=(1+ Required rate)^corresponding period
Discounted value=total value/discount factor