cost of retained earning question

[annexguy]

An analyst gathered following info. about a company and the market:
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Current market price per share of common stock $28
most recent dividend per share paid on common stock(D0) $2.0
expected dividend payout rate 40%
expected ROE 15%
Beta for common stock 1.3
expected rate of return on market portfolio 13%
risk-free rate of return 4%
Using discounted cash flow(DCF) approach, the cost of retained earnings for the company is closest to
A 13.6% B. 15.7% C. 16.1% D 16.8%
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answer is D. the expected return is sum of expected dividend yield plus expected growth (1-40%)*15%=9%. expected dividend yield is $2.18/$28=7.8%, sum is 16.8%.
anyone can explain where the $2.18 (D1) from?
my calculation of D1 is : 2*(1+15%*40%)=2.12

 

[Char-Lee]

you used payout rate to calculate D1 not retention rate (1-payout ratio)… it should be 2*(1+(0.15*(1-0.40)))=2.18

 

[supersharpshooter]

My reasoning is this:
Expected growth is (1-Dividend payout rate)*ROE = 0.6*0.15 = 0.09
Dividends are expected to grow at 9% which is $0.18 on top of the current $2 dividend. Therefore the next dividend is expected to be $2.18.
2.18/28 + 0.09 =~ 0.1679 =~ 16.8%
edit: beaten by Char-Lee

 

[annexguy]

thank you.
my brain jammed after a long day.