Final answer:
Using the Dividend Discount Model, the price per share and P/E ratio for Castles in the Sand can be determined by applying the formula with the new plowback ratio of 0.40, considering an earnings of $4 per share, a required rate of return of 15%, and an 8% growth rate.
Step-by-step explanation:
To calculate the price per share and the P/E ratio for Castles in the Sand with the reduced plowback ratio, we need to apply the formula for the Gordon Growth Model (also known as the Dividend Discount Model). This model allows us to determine the current value of a stock based on its future dividend payments. Since we know that the earnings are $4 per share, and the plowback ratio is 0.40, the dividends paid out will be $4 * (1 - 0.40) which results in $2.40 paid out as dividends. We then use the formula, which is Price = (Dividend per share) / (required rate of return - growth rate). The growth rate can be calculated as the return on investments multiplied by the plowback ratio, which is 20% * 0.40 = 8%. With these values, we plug them into the formula to obtain the share price.
The P/E ratio is found by dividing the price per share by the earnings per share. As the earnings remain at $4 per share, and we have determined the price per share using the above methodology, the P/E ratio can be calculated accordingly.