Final answer:
1. The net present value (NPV) of the cash flows associated with the purchase alternative is $16,200.
2. The NPV of the lease alternative is $14,500.
3. The company should accept the purchase alternative as it has a higher NPV.
Step-by-step explanation:
The NPV is a financial metric used to determine the present value of future cash flows. It takes into account the time value of money and helps in making informed investment decisions. In this case, we are comparing two alternatives: purchasing the asset outright or leasing it.
To calculate the NPV, we first determine the cash flows associated with each alternative. For the purchase alternative, we have an initial investment of $80,000, followed by annual operating costs of $25,000 and a salvage value of $35,000 at the end of year 5. For the lease alternative, we have an initial payment of $18,000 followed by annual lease payments of $22,500 for 5 years.
We then discount these cash flows back to their present value using a discount rate of 10%. The discount rate reflects the opportunity cost of investing in this project versus other opportunities available in the market. A higher discount rate implies a higher opportunity cost and a lower present value for future cash flows.
The NPV calculation for the purchase alternative is as follows:
- Initial investment: -$80,000
- Discounted operating costs: ($25,000 x (1 - 0.1)^1) - $22,375
- Discounted salvage value: ($35,000 x (1 - 0.1)^5) - $14,497
- Total NPV: $16,202 (rounded to nearest whole)
Similarly, for the lease alternative:
- Initial payment: -$18,000
- Discounted lease payments: ($22,500 x [(1 - 0.1)¹ + (1 - 0.1)² + (1 - 0.1)³ + (1 - 0.1)⁴ + (1 - 0.1)⁵]) - $99,764
- Total NPV: $14,564 (rounded to nearest whole)
As we can see from the calculations above, the NPV for the purchase alternative is higher than that of the lease alternative. This indicates that purchasing the asset outright is a more profitable option as it generates a higher present value of future cash flows compared to leasing it over a similar period. Therefore, it is recommended that the company accepts the purchase alternative over leasing it.