Question

Rearden Metals expects to have earnings this coming year of $2.50 per share. Rearden plans to retain all of its earnings for the next year. For the subsequent three years, the firm will retain 50% of its earnings. It will ten retain 25% of its earnings from that point onward. Each year, retained earnings will be invested in new projects with an expected return of 20% per year. Any earnings that are not retained will be paid out as dividends. Assume Rearden's shares outstanding remains constant and all earnings growth comes from the investment of retained earnings. If Rearden's equity cost of capital is 10%, then Rearden's stock price is closest to:

Answer 1

Statement showing price of stock

Year	EPS	Retain earning	Growth in earning (Retain earning*0.2)	Dividend (EPS-Retain earning)	PVIF @ 10%	Present value= Dividend*PVIF
1	2.5	2.5	0.50	0	0.909091	0
2	3	1.5	0.30	1.5	0.826446	1.24
3	3.3	1.65	0.33	1.7	0.751315	1.24
4	3.63	1.815	0.36	1.8	0.683013	1.24
5	3.99	1.00	0.20	2.99	0.620921	1.86
P5 (note1)				62.79	0.620921	38.99
			Price of stock			44.57

Note 1) first of all we need to find growth rate

Growth rate = Retention ratio*Return on asset

=25%*20%

=5%

Now we shall calculate price of stock at end of year 5

P5 = Dividend of year 6 /Cost of capital - growth rate

Dividend of year 6 = Dividend of year 5(1+growth rate)

=2.99(1+5%)

=2.99(1.05)

= 3.1395

Thus P5 = 3.1395/10%-5%

=3.1395/5%

=62.79$