Question

Halliford Corporation expects to have earnings this coming year of $ 2.72 per share. Halliford plans to retain all of its earnings for the next two years. For the subsequent two​ years, the firm will retain 53 % of its earnings. It will then retain 20 % of its earnings from that point onward. Each​ year, retained earnings will be invested in new projects with an expected return of 24.62 % 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 10.8 %​, what price would you estimate for Halliford​ stock? ​Note: Remenber that growth rate is computed​ as: retention rate times rate of return.

What is the price per share?

Answer 1

Return investment = 24.62%

Growth = Retention ratio X Return on investment = b x r

Growth rate :

Year 2 = 100% X 24.62% = 24.62%

Year 3 = 100% X 24.62% = 24.62%

Year 4 = 53% X 24.62% = 13.049%

Year 5 = 53% X 24.62% = 13.049%

Year 6 = 20% X 24.62% = 4.924%

EPS CALCULATION

EPS (YEAR 2) = EPS (YEAR 1) (1+ GROWTH RATE OF 27.7%)

EPS = 2.72 (1.2462) = 3.390

EPS (YEAR 3) = EPS (YEAR 2) (1+ GROWTH RATE OF 27.7%)

EPS = 3.390 (1.2462) = 4.225

EPS (YEAR 4) = EPS (YEAR 3) (1+ GROWTH RATE OF 27.7%)

EPS = 4.225(1.13049) = 4.776

EPS (YEAR 5) = EPS (YEAR 4) (1+ GROWTH RATE OF 27.7%)

EPS = 4.776(1.13049) = 5.399

EPS (YEAR 6) = EPS (YEAR 5) (1+ GROWTH RATE OF 27.7%)

EPS = 5.399(1.04924) = 5.665

Year	1	2	3	4	5	6
EPS Growth rate		24.62%	24.62%	13.049%	13.049%	4.924%
EPS	2.72	3.390	4.225	4.776	5.399	5.665
Retention ratio	100%	100%	53%	53%	20%	20%
Dividend payout ratio	0%	0%	47%	47%	80%	80%
Dividends (EPS X Dividend payout ratio)	0	0	1.986	2.245	4.319	4.532

From Year 5 on. Dividend growth at a constant rate 4.924%

rE= cost of capital = 10.8%

PV4 = Div5 / (rE –g )= 4.319 / (0.108-0.04924)=73.50        

The stock price will be the present value = P0= PV0= (Div 3 /(1 + rE)^3) +(Div 4 + PV4 /(1 + rE)^4 )           

P0= (1.986 /(1+0.108)^3 )+ (2.245+73.5/(1+0.108)^4) = 1.460+ 50.26=$51.72