Question

Halliford Corporation expects to have earnings this coming year of $ 3.201 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 18 % of its earnings from that point onward. Each​ year, retained earnings will be invested in new projects with an expected return of 23.5 % 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 8.6 %​, what price would you estimate for Halliford​ stock?

Answer 1

Common stock value is given as the present value of all the expected cash flows from holding the stock. The expected cash flows from the common stock are the dividends to be received.

So to calculate the stock value, we will first calculate dividends to be received in future years. We can show the working in excel.

Years	Retention ratio	Payout ratio (100 - Retention ratio)	Return on Investment	Growth Rate (Retention ratio x Return on Investment)	Earnings per share	Dividend per share (Earnings per share x Payout ratio)
1	100%	0%	23.50%	23.50%	3.201	0
2	100%	0%	23.50%	23.50%	3.953	0
3	50%	50%	23.50%	11.75%	4.882	2.44
4	50%	50%	23.50%	11.75%	5.456	2.73
5	18%	82%	23.50%	4.23%	6.097	5.00

We can calculate earning per share by the following formula,

Current earnings = Previous earnings x (1 + Current year growth)

Now we know,

Cost of equity = 8.6%

The growth rate in year 5 = 4.23%

We can calculate the price of the share in year 4 by the Dividend Discount Model

Price of the stock in year 4 = Dividend for year 5 / (Cost of capital - Constant growth)
= 5/ (0.086 - 0.0423)

= $114.41

The current price of stock = Present value of all the expected dividends and present value of share price at Year 4.

Years	Dividends (a)	Discounting Factor (b ) = (1/1+r)^n	P.V. (c ) = (axb)
1	0	0.921	0
2	0	0.848	0
3	2.44	0.781	1.906
4	117.14	0.719	84.213
	SUM (PV)		$86.12

In year 4, we will discount the dividend($2.73) + value of the share in year 4($114.41)

Hence the price of Halliford​ stock is $86.12

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