Castles in the Sand generates a ROE of 22.3 percent and maintains a payout ratio of 0.6 . Its earnings this coming year will be $ 3.79 per share. Investors expect a return of 15.76 percent on the stock. What is the stocks P/E ratio?

Use the payout rate and the expected earnings for the coming year to determine the expected dividend payout one year hence.
Use the ROE and the payout rate to determine the expected dividend growth rate.
Note the appropriate discount rate as given in the problem, as the investors' required return.


With these three numbers in hand you have all the necessary ingredients to determine the current stock price using the Gordon (or "constant") growth model. Given the setup of this particular problem, this model will be given in your text.

Finally, from the stock price as determined, along with the given earnings for the coming year, you've got the P/E ratio.