"An investor is proposing to buy shares in XYZ company. XYZ company is expected to an annual dividend of $2.50 per share. The current share price is $50.00. If the investor requires an annual rate of return of10%, what must the share price be in 1 yr?.
The investor wants to make 5 dollars per share in the first year, he makes 2.50 from dividend, so needs the stock to appreciate by 2.50 or have a price of 52.50. That return assumes he sells it.
To determine the share price in 1 year, we need to calculate the future value of the dividend payment and the future value of the initial investment. Here's what we need to do step by step:
1. Calculate the future value of the annual dividend payments:
Future Value = Dividend Payment / (Required Rate of Return - Dividend Growth Rate)
In this case, the dividend payment is $2.50 and the required rate of return is 10%. Since we don't have information about the dividend growth rate, we'll assume it to be zero for simplicity.
Future Value = $2.50 / (0.10 - 0) = $25.00
2. Calculate the future value of the initial investment:
Future Value = Initial Investment * (1 + Required Rate of Return)
In this case, the initial investment is the current share price, which is $50.00, and the required rate of return is 10%.
Future Value = $50.00 * (1 + 0.10) = $55.00
3. Add the future values of the dividend payments and the initial investment to get the future share price:
Future Share Price = Future Value of Dividend Payments + Future Value of Initial Investment
Future Share Price = $25.00 + $55.00 = $80.00
Therefore, the share price in 1 year, based on the given information, would be $80.00.