Question

Halliford Corporation expects to have earnings this coming year of $ 2.84 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 46 % of its earnings. It will retain 17 % of its earnings from that point onward. Each​ year, retained earnings will be invested in new projects with an expected return of 20.62 % 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 8.1 %​, what price would you estimate for Halliford​ stock?

NB: Kindly mention the excel formulae separately if solving on excel.

Answer 1

Given	Expected Rate of Return			20.62%
	Cost of Capital			8.10%
Calculated	Growth rate after 5 Year (g)	g= ROE * Retention Rate	g= 20.62% * 0.17	3.51%

Year	0	1	2	3	4	5
Earnings $		2.84	3.43	4.13	4.52	4.95
Retention Ratio (Given)		1	1	0.46	0.46	0.17
Retained Earning $ (Earnings * Retention Ratio)		2.84	3.43	1.90	2.08	0.84
Returns $ (Expected rate of return * Retained Earnings)		0.59	0.71	0.39	0.43	0.17
Dividends $ (Earnings - Retained Earnings)		0	0	2.23	2.443	4.11
PV Of Dividends		-	-	1.77	1.79
					89.47
Total		-	-	1.77	91.26
Value of stock $	93.03

Step by step approach
1	Calculate the returns for the first year (Cell: E10)
2	Earnings for the first two years are retained(Cell: E8, F8)
3	As all earnings growth comes from the investment of retained earning so add these returns in earnings of the previous year to get next year earnings (F7=E7+E10)
4	Calculate returns for the subsequent years (Returns= Retained earnings * Expected rate of return)
5	Retention ratio for years 3 and 4 are 0.46. Calculate the retained earnings for year 3 &4. (Retained earnings = Earnings * Retention Ratio)
6	The retention ratio for year 5 is 0.17. Calculate the retained earnings for year 5. (Retained earnings = Earnings * Retention Ratio)
7	Calculate dividends for each year ( Dividends= Earnings - Retained earnings)
8	Calculate PV of dividends discounting with the cost of capital
9	Use constant dividend (Gordon model) for calculating PV of dividend after 5 years (P4 = D5 / (r-g))
10	Use of Dividend discount model to calculate the value of stock