Question

1. You expect that Bean Enterprises will have earnings per share of $2 for the coming year. Bean plans to retain all of its earnings for the next three years. For the subsequent two years, the firm plans on retaining 50% of its earnings. It will then retain only 25% of its earnings from that point forward. Retained earnings will be invested in projects with an expected return of 20% per year. If Bean's equity cost of capital is 10%, what is the price of a share of Bean's stock?

Hint: use g=ROE*retention ratio to calculate growth rate

Answer 1

Price of share is calculated as follows,

Price of share = PV of Dividend + PV of Terminal value

PV of Dividend and Terminal value is calculated as,

Year	EPS	ROE	Retention ratio	g = ROE x Retention ratio	Payout ratio	Dividend = EPS x Payout ratio	Terminal value	PV factor @ 10%	PV @ 10%
1	2.00	20%	100%	20%	-	-		0.91	-
2	2.40	20%	100%	20%	-	-		0.83	-
3	2.88	20%	100%	20%	-	-		0.75	-
4	3.46	20%	50%	10%	50%	1.73		0.68	1.18
5	3.80	20%	50%	10%	50%	1.90		0.62	1.18
6	4.18	20%	25%	5%	75%	3.14	62.73	0.62	38.95
Price of share	41.31

Note:

1) Here, Earning gets increased each year by g of previous year.

2) Terminal value is calculated as,

Terminal value = Dividend /(Re - g)

Terminal value = 3.14 /(.1 - 0.05)

Terminal value =62.73