Question

a particular piece of equipment for your production process. An​ equipment-leasing company has offered to lease the equipment to you for $10,100 per year if you sign a guaranteed​ five-year lease​ (the lease is paid at the end of each​ year). The company would also maintain the equipment for you as part of the lease.​ Alternatively, you could buy and maintain the equipment yourself. The cash flows from doing so are listed below​ (the equipment has an economic life of five​ years). If your discount rate is 7.3%​, what should you​ do? Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 −$39,500 −$2,000 −$2,000 −$2,000 −$2,000 −$2,000 Question content area bottom Part 1 The net present value of the leasing alternative is ​$enter your response here. ​(Round to the nearest​ dollar.)

Answer 1

To decide between leasing or buying, calculate the net present value (NPV) for both options using the discount rate of 7.3%. The lease payments are annuitized, while the buy option includes an initial cost and annual maintenance. Compare the NPVs to determine the most cost-effective option.

Step-by-step explanation:

To determine whether to lease or buy equipment, we need to calculate the net present value (NPV) of both options, using the provided discount rate of 7.3%. The leasing option involves payments of $10,100 per year for five years, while the buying option involves an initial cost of $39,500 followed by annual maintenance costs of $2,000 for five years.

To calculate the NPV for the leasing option:

1. Identify the annual lease payment: $10,100.
2. Because these payments are annual and the same amount over the lease term, we can use the formula for the present value of an annuity:
3. The formula is PV = Pmt × ((1 - (1 + r)^(-n)) / r), where Pmt is the annual payment, r is the discount rate, and n is the number of periods.
4. Plug in the numbers: PV = $10,100 × ((1 - (1 + 0.073)^(-5)) / 0.073).
5. Perform the calculation.
6. The NPV of leasing the equipment is the present value we just calculated.

Similarly, to calculate the NPV for the buying option, we would:

1. Identify the initial investment and subsequent maintenance costs.
2. Use the NPV formula for a series of different cash flows.
3. Discount the initial investment and each maintenance cost back to their present value using the discount rate and sum them up.

After finding the NPV for both options, we can compare them to decide which option is more cost-effective.