Natchez, Inc.is considering the purchase of a new machine costing $200,000.The company will incur $5,000 per year in cash operating expenses but it will allow the company to earn an additional $100,000 per year in revenues.Natchez expects the machine to provide future benefits for 3 years and salvage value at the end of the 3-year period to be $10,000.The company uses straight-line depreciation method.The income tax rate is 30%.If the required rate of return is 10%, how much is the net present value of this project?

Question

Quizplus · Accepted Answer

1. First, we need to calculate the annual cash inflows as follows:
Annual cash inflows = Revenues - Operating expenses
Annual cash inflows = $100,000 - $5,000
Annual cash inflows = $95,000

2. Next, we need to calculate the annual depreciation expense:
Depreciation expense = (Cost of machine - Salvage value) / Useful life
Depreciation expense = ($200,000 - $10,000) / 3
Depreciation expense = $63,333.33

3. We can now calculate the annual taxable income as follows:
Annual taxable income = Annual cash inflows - Depreciation expense
Annual taxable income = $95,000 - $63,333.33
Annual taxable income = $31,666.67

4. We can now calculate the annual tax expense as follows:
Annual tax expense = Annual taxable income x Tax rate
Annual tax expense = $31,666.67 x 30%
Annual tax expense = $9,500

5. We can now calculate the net annual cash flows as follows:
Net annual cash flows = Annual cash inflows - Cash operating expenses - Tax expense
Net annual cash flows = $95,000 - $5,000 - $9,500
Net annual cash flows = $80,500

6. We can now calculate the present value of each year's net cash flow using the formula:
PV = FV / (1 + r)^n
where PV is the present value, FV is the future value, r is the required rate of return, and n is the number of years.

Year 1: PV = $80,500 / (1 + 10%)^1 = $73,181.82
Year 2: PV = $80,500 / (1 + 10%)^2 = $66,528.11
Year 3: PV = ($80,500 + $10,000) / (1 + 10%)^3 = $76,308.46

7. Finally, we can calculate the net present value of the project by summing the present values of each year's net cash flow and subtracting the initial investment:
NPV = PV1 + PV2 + PV3 - Initial investment
NPV = $73,181.82 + $66,528.11 + $76,308.46 - $200,000
NPV = $20,018.39

Therefore, the net present value of the project is $20,018.39, which is closest to answer choice A ($20,143).