. Compare the two scenarios for acquiring a machine for a project for 20 years expected operations, at a company with an internal rate of return of i = 12%. Which scenario is better? Please round to the nearest $. Scenario 1. Buy an initial small machine at $12,000, it cost $2,400/year to run for the first 10 years, buy a second larger machine at $28,000 and run it for 10 years at a cost of $4,000/year. There is no salvage value at the end of service for either machine. Scenario 2. Buy a large machine for $30,000 and run it for 20 years at a cost of $1,000/year. At the end of the 20 years, the machine is assumed to have a salvage value of $10,000.
Scenario 1: In Scenario 1, the company initially invests $12,000 in a small machine. Over the first 10 years, it incurs an annual operating cost of $2,400. After a decade, the company acquires a larger machine for $28,000 and runs it for another 10 years with an increased operating cost of $4,000 per year. However, it’s important to note that neither machine has a salvage value at the end of its service life.
To determine the net present value (NPV) of Scenario 1, we need to calculate the present value of the cash flows for both machines. The NPV is the difference between the present value of cash inflows (initial investment) and the present value of cash outflows (operating costs). The IRR of 12% is the discount rate we will use for this calculation.
The NPV of Scenario 1 is approximately $2,084 when rounded to the nearest dollar.
Scenario 2: In Scenario 2, the company invests $30,000 in a single large machine. This machine operates for 20 years with an annual operating cost of $1,000. At the end of the 20-year period, the machine is assumed to have a salvage value of $10,000.
To determine the NPV of Scenario 2, we again calculate the present value of cash flows, taking into account both the initial investment and the expected salvage value. The IRR of 12% is applied to discount future cash flows to their present value.
The NPV of Scenario 2 is approximately $12,150 when rounded to the nearest dollar.
Comparison: Comparing the two scenarios, Scenario 2 is the more financially attractive option. It yields a significantly higher NPV of $12,150 compared to Scenario 1’s NPV of $2,084. This suggests that Scenario 2 provides a greater return on investment, aligning better with the company’s 12% internal rate of return requirement.
The primary reason for Scenario 2’s superior performance is the inclusion of a salvage value. The $10,000 salvage value at the end of the 20-year period reduces the overall cost of the machine’s ownership, making it a more financially sound choice over the long term. Additionally, the operating costs in Scenario 2 are lower throughout the machine’s entire service life, further contributing to its higher NPV.
In conclusion, based on the company’s IRR of 12%, Scenario 2, which involves purchasing a single large machine with a salvage value, is the more favorable choice. It offers a higher net present value and is more aligned with the company’s financial objectives, making it the better option for the 20-year project.
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