Question

Firm AAA's earnings and dividends are expected to grow by a rate of 0.04 a year. This growth will stop after year 4. In year 5 and later, it will pay out all earnings as dividends. Assume next year's dividend is 2, the cost of capital is 0.08, and next year's EPS is 12. What is AAA's stock price today? Round your answer to 2 decimal places.

Answer 1

Calculation of Earning per share and dividend
					Dividend (EPS * Dividend payout ratio)
Earnings first year			$12.0000	D1	$2.0000
Earnings 2 year ( 12. 00 + growth 4 %)			$12.4800	D2	$2.0800
Earnings 3 year (12.48 + growth 4%)			$12.9792	D3	$2.1632
Earnings 4 year (12.9792 + growth 4%)			$13.4984	D4	$2.2497
Earnings 5 year (13.4984 + growth 0)			$13.4984	D5	$13.4984	(100% paid)
Calculation of Present value of Equity at end of 5th Year
Thereafter growth is 0 and Dividend is paid $13.4984 forever.
So Present Value of Stock at end of year 4 (P4)) immediately after paying dividend shall be calculated by formula.
Cost of Capital (Ke) =		0.08
Growth rate =		0%
P4 = D5 /Ke-g
.        = 13.4984/ (0.08-0)
	$168.73
Calculation of Present Value of Stock by Dividend Discount model
Now, present value of stock shall be calculated by Dividend discount model
Dividend received upto 4 years and present value of stock received on 4h year end shall be discounted with cost of capital (ke) for relevant period.
Ke for 1-2 period =		13% or 0.13
ke for 3 to perpetuity = 10% or 0.10
Year		Cash flows	P.V.F.= 1/((1+i)^n)		Present value of cash flows
1	D1	$2.0000	1/((1+0.08)^1)	0.9259	$1.8519
2	D2	$2.0800	1/((1+0.08)^2)	0.8573	$1.7833
3	D3	$2.1632	1/((1+0.08)^3)	0.7938	$1.7172
4	D4	$2.2497	1/((1+0.08)^4)	0.7350	$1.6536
4	P4	$168.7296	1/((1+0.08)^4)	0.6806	$114.8345
	P0 (share price today)				$121.8405
So, AAA's stock price today is $121.84