Question

Halliford Corporation expects to have earnings this coming year of $3.000 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 50% of its earnings. It will retain 20% of its earnings from that point onward. Each​ year, retained earnings will be invested in new projects with an expected return of 25.0% 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 10.0%​, what price would you estimate for Halliford​ stock?

Answer 1

Halliford’s dividend forecast (g = retention rate × return on new investment)

Year	0	1	2	3	4	5	6
Earnings
1).EPS Growth Rate (vs. prior yr)			25%	25%	12.50%	12.50%	5%
2). EPS		$3.000	$3.75	$4.6875	$5.2734	$5.9326	$6.2292
Dividends
3). Retention Ratio		100%	100%	50%	50%	20%	20%
4). Dividend Payout Ratio		0%	0%	50%	50%	80%	80%

Dividends(2 x 4) $0 $0    $2.344 2.637 $4.746 $4.983

From year 5 on, dividends grow at constant rate of 5%. Therefore,

P(5) = D6 / (r - gC) = $4.983/ (10% - 5%) = $4.983 / 0.05 = $99.67

P(0) = [D3 / (1 + r)³] + [D4 / (1 + r)⁴] + [(D5 + P5) / (1 + r)⁵]

= [$2.344 / 1.1³] + [$2.637 / 1.1⁴] + [($4.746 + $99.67) / 1.1⁵]

= $1.76 + $1.80 + $64.83 = $68.39