Question

Halliford Corporation expects to have earnings this coming year of

$ 3.385$3.385

per share. Halliford plans to retain all of its earnings for the next two years.​ Then, for the subsequent two​ years, the firm will retain

45 %45%

of its earnings. It will retain

19 %19%

of its earnings from that point onward. Each​ year, retained earnings will be invested in new projects with an expected return of

19.4 %19.4%

per year. Any earnings that are not retained will be paid out as dividends. Assume​ Halliford's share count remains constant and all earnings growth comes from the investment of retained earnings. If​ Halliford's equity cost of capital is

10.5 %10.5%​,

what price would you estimate for Halliford​ stock?

Answer 1

ROE=	19.40%	Required rate=	10.50%	Long term ret. Rate=	19.00%
Year	EPS previous year	Retention ratio	Growth rate	EPS current year	Dividend current year	Terminal value	Total Value	Discount factor	Discounted value
1	0	100.00%	19.400%	3.385	0		0	1.105	0
2	3.385	100.00%	19.400%	4.04169	0		0	1.221025	0
3	4.04169	45.00%	8.730%	4.394529537	2.416991245		2.416991245	1.349233	1.791382
4	4.394529537	45.00%	8.730%	4.778171966	2.627994581	39.98917613	42.61717071	1.490902	28.58482
	Long term growth rate =	=ROE*long term ret. Rate=	3.686%				Value of stock =	Sum of discounted values=	30.38

Where

Growth rate = ROE*retention rate for corresponding year

EPS curr. Year = EPS previous year*(1+growth rate) if not given

Dividend current year = EPS current year*(1-retention ratio)

Terminal value = Dividend Current year 4 *(1+long term growth rate)/( Required rate-long term growth rate)

Total value = Dividend + horizon value (only for last year)

Discount factor=(1+ Required rate)^corresponding period

Discounted value=total value/discount factor