Final answer:
The net present value (NPV) can be calculated by finding the present value of the annual cash flows and the sale price at the end of the holding period, then subtracting the initial investment cost, all discounted at a given rate, which in this case is 10%.
Step-by-step explanation:
To determine the net present value (NPV) of an investment decision to purchase a property, we need to calculate the present value of both the annual cash flows and the sale price at the end of the holding period and then subtract the initial investment.
The formula for NPV is:
- NPV = (Present Value of Cash Flows) - (Initial Investment)
Since the cash flows are the same each year, we can use the annuity formula to calculate their present value:
PV of annual cash flows = Pmt * [(1 - (1 + r)^-n) / r]
where:
- Pmt = annual cash flow
- r = discount rate
- n = number of periods
The present value of the sale price is calculated by discounting it back to the present value:
PV of sale price = Future Value / (1 + r)^n
Using the provided figures and a discount rate of 10%:
- PV of annual cash flows = $10,000 * [(1 - (1 + 0.10)^-8) / 0.10]
- PV of sale price = $80,000 / (1 + 0.10)^8
Compute these values and subtract the initial investment of $90,000 to get the NPV. The final value will show whether the investment yields a positive or negative NPV, indicating its profitability.