the price of the stock is now $85 and no dividends are paid, and expects the price four years from now to be 4125 a share should the investor buy if he wants a 15 percent rate of return.
To determine whether the investor should buy the stock, we need to calculate the present value of the future expected price and see if it meets the investor's desired rate of return. Here are the steps to get the answer:
1. Determine the present value of the future stock price: We need to discount the future price back to the present using the investor's desired rate of return. The formula to calculate the present value (PV) of a future value (FV) is: PV = FV / (1 + r)^n, where r is the rate of return and n is the number of years.
PV = 4125 / (1 + 0.15)^4
PV = 4125 / (1.15)^4
PV ≈ 2408.93
2. Compare the present value with the current stock price: If the present value is greater than the current stock price ($85), it would be a good investment. However, if it is lower, it may not meet the investor's desired rate of return.
2408.93 > 85
Since the present value of the future price is greater than the current stock price, the investor should consider buying the stock if their goal is to achieve a 15% rate of return.
Please note that this calculation assumes no dividends are paid and only considers the future expected price and the investor's desired rate of return. Additional factors like the company's financials, market conditions, risk tolerance, and diversification should also be considered before making an investment decision.