Final answer:
The target stock price in five years is calculated using the Dividend Discount Model, accounting for expected dividend growth and applying the benchmark PE ratio along with the estimated payout ratio. The present stock price is the discounted value of estimated future dividends and the terminal stock price using the required rate of return. Exact calculations require detailed future earnings data.
Step-by-step explanation:
To calculate the target stock price in five years for a company that just paid a dividend of $1.45 with dividends expected to grow at 15 percent over the next five years, we use the Gordon Growth Model (also called the Dividend Discount Model). First, we calculate the dividends for each of the next five years by growing the initial dividend by 15 percent each year. Then, we estimate the terminal stock price in five years using the given benchmark PE ratio and the estimated payout ratio. Finally, to find the stock price today, we discount these future dividends and the terminal stock price back to the present using the required return of 12.5 percent. To provide a numerical example, if after five years of growth the dividend is expected to be, say, $2.94 (just an example), and the earnings at that time are such that the 45 percent payout ratio results in this dividend, then the total earnings would be $2.94 / 45% = $6.53. Using the benchmark PE ratio of 27, we would multiply the earnings of $6.53 by 27 to get the terminal stock price five years from now. The present value of all future dividends plus this terminal stock price gives us the value of the stock today. However, the calculation requires detailed financial analysis and cannot be done without specific data on the future earnings.