Final answer:
To determine the NPV of the investment in the machine, the present value of future cash savings over the machine's 5-year life span is calculated using a 12% discount rate, and the initial investment is subtracted. The NPV was found to be negative at -$8,160.34, indicating that the investment is not financially viable for Kunkel Company.
Step-by-step explanation:
To determine the net present value (NPV) of the investment in the machine, we need to calculate the present value of the future cash flows that the machine is expected to generate and then subtract the initial cost of the machine.
The machine reduces operating costs by $8,000 per year and has a useful life of 5 years, with no salvage value at the end. We will use the company's required rate of return of 12% to discount these cash flows.
Calculate the present value (PV) of each year's cost savings using the formula: PV = Cash Flow / (1 + r)^n, where r is the discount rate and n is the year.
- Repeat this for all 5 years and sum the present values.
- Subtract the initial cost of the machine from the sum of discounted cash flows to get the NPV.
Let's do the calculation:
- Year 1: $8,000 / (1 + 0.12)¹ = $7,142.86
- Year 2: $8,000 / (1 + 0.12)² = $6,377.14
- Year 3: $8,000 / (1 + 0.12)³ = $5,692.80
- Year 4: $8,000 / (1 + 0.12)⁴ = $5,084.00
- Year 5: $8,000 / (1 + 0.12)⁵ = $4,542.86
The sum of the present values of the cash flows is $28,839.66.
The NPV of the investment is then $28,839.66 - $37,000 = -$8,160.34.
Since the NPV is negative, the investment is not financially viable under the company's required rate of return.