An investment generates $10,000 per year for 25 years. If you can earn 10 percent on other investments, what is the current value of this investment? If its current price is $120,000, should you buy it?
Current value equals $-114,699.21. No because the price is higher than the value.
To calculate the current value of the investment, we need to determine the present value of the future cash flows. The formula for calculating present value is:
PV = CF / (1 + r)^n
Where:
PV = Present Value
CF = Cash Flow in each period
r = Rate of Return
n = Number of periods
In this case, the cash flow is $10,000 per year for 25 years, and the rate of return is 10 percent.
Let's calculate the present value of each cash flow:
PV = $10,000 / (1 + 0.10)^1 + $10,000 / (1 + 0.10)^2 + ... + $10,000 / (1 + 0.10)^25
Now, we can use a present value of annuity formula to calculate the present value efficiently:
PV = CF * [(1 - (1 + r)^-n) / r]
PV = $10,000 * [(1 - (1 + 0.10)^-25) / 0.10]
After calculating this equation, the present value of the investment is approximately $139,020.74.
Now, let's compare the current price of the investment ($120,000) with its present value ($139,020.74). Since the present value is higher than the current price, it suggests that the investment is undervalued. In this scenario, buying the investment would likely be a good decision, as it is priced lower than its expected value. However, we should also take into consideration other factors like the investment's risk profile, potential future cash flows, and our own investment goals and risk tolerance before making a final decision.