10. A firm has a dividend yield of 9%. What is the expected return, if a firm has a 45% payout ratio, a return on equity of 10%, and assuming dividends grow at a constant rate?

First, I solved for g = ROE x plowback

g = 0.45 x 0.1 = 0.045

Then, I used the DDM for constant growth formula: I/Yr = (Div1/PO) + g

0.09 + 0.045 = 0.135 or 13.5%

However, my professors solution is:

Expected Return (I/YR) = Dividend Yield (Div1/Po) + g = 9% + (55% x 10%) = 14.5%

I don't understand how he got 55% for payout instead of 45%?