cost of retained earning question

An analyst gathered following info. about a company and the market: ---------------------------------------------------------------------------- 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% ------------------------------------------------------------------------- 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

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

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

thank you. my brain jammed after a long day.