Question

Lemon crop currently has 5,000,000 shares. It will generate net income of $140,000,000 1 year from now and will pay out 30% of that income in dividends. The reinvested earnings will generate an annual return of 11%. Lemon crop will again pay out 30% of its earnings at year 2 and again will earn 11% on the new investment. At year 3 and every year thereafter, lemon will payout 90% of its earnings and will earn 8.4% on the reinvested earnings. If lemon's equity cost of capital is 8%, what is it share price?

Answer 1

first we will calculate growth rates for each year

growth = retention ratio*return on reinvested earnings

year	retention ratio	ROE	growth
1	70%	11	7.7
2	70%	11	7.7
3	10%	8.4	0.84

so for first 2 years growth will be 7.7% and from year 3 growth will be 0.84%

value of the firm is pv of cashflows

terminal value of cash flows can be calulated by using dividend discount model

= fcf3/(k-g)

fcf3= 14million +7.7% +0.84% =15.2046  million

k is cost of capital = 8%

g is growth = 0.84%

t.v= 15.2046/(0.08-0.0084) = 212.3547 million

year	cash flows	discount@8%	DCF
1	14.00	0.9259259259	12.96296296
2	14.08	0.8573388203	12.06875857
tv	212.35	0.793832241	168.5740074
		value	193.6057289

value of firm is 193.60 million

no of shares = 5 million

value per share = 193.60/5 = 38.72