6 Suppose constant dividend growth model can be applied to v

6. Suppose constant dividend growth model can be applied to value the stock of XYZ Inc. You observe that their historical price earnings ratio is 5 times their price to book ratio. The rate at which their dividends grow is estimated to be 8% per year. They earn a return of 21.6% on the book value of their equity, work out the dollar amount of dividend that the firm is expected to pay at t-1 if its earnings per share at t-1 are expected to be $5.40.

Solution

Return Earned on Book Value of Equity = Return on Equity (ROE) = 21.6 %

ROE x Retention Ratio = Growth Rate

Growth Rate is constant and so is the return on equity. Assuming that retention ratio is also constant one can arrive at the following relationship.

[1-(DPS/EPS)] x ROE = Growth

[1-(DPS/5.4)] x 0.216 = 0.08

1-(DPS/5.4) = 0.37037

DPS = 0.62963 x 5.4 = $ 3.4 approximately.