I have the answer sheet but need help seeing it worked out. Particularly for D3, D4, D5

A company currently has earnings (E₀) of $3.00 and a dividend (D₀) of $1.25. The firms current return on equity (ROE) is 40%. The firm will maintain the same dividend payout and ROE over the next two periods. Then it will transition in a linear reduction in years 3, 4, and 5 to a growth of 2%. The firm will then grow at 2% to perpetuity. The firms beta is presently 1.4, but this will transition to 1 over the same period. The risk-free rate is 4% and the market risk premium is 6%. ROE is expected to be 5% beginning in year 5 to perpetuity. What is the present value of this firms equity using a three-stage model with linear transition in years 3, 4, and 5?

in years 3, 4, and 5?

Model
Description/Year	0	1	2	3	4	5
Earnings Growth Rate						2.00%
EPS	$ 3.00
Dividend payout (DPS/EPS)			41.67%
Dividends per share (DPS)	$ 1.25
Cost of capital (Ke)						10.00%
Present value of cash flows

ANSWER SHEET:

Retention rate = (1-dividend payout) = [1-($1.25/$3.00)] = 58.33%

g = ROE x retention rate = 40% x (1-$1.25/$3.00) = 23.333%

Model
Description/Year	0	1	2	3	4	5
Earnings Growth Rate		23.33%	23.33%	16.22%	9.11%	2.00%
EPS	$3.00	$3.70	$4.56	$5.30	$5.79	$5.90
Dividend payout (DPS/EPS)		41.67%	41.67%	47.78%	53.89%	60.0%
Dividends per share (DPS)	$1.25	$1.54	$1.90	$2.53	$3.12	$3.54
Cost of capital (Ke)		12.40%	12.40%	11.60%	10.80%	10.00%
Present value of cash flows		$1.37	$1.51	$1.80	$2.00	$2.06
g = ROExb		0.2333333
k = rf+b(MRP)		12.400%
Dividend payout = 1-retention		60.0%
PV Divs 1-5		$8.73
P5 = D6/(k-g)		$45.15
PV P5		$26.28
Total value		$35.01