Your company is considering a machine which will cost $50,000 at Time 0 and which can be sold after 3 years for $10,000.$12,000 must be invested at Time 0 in inventories and receivables;these funds will be recovered when the operation is closed at the end of Year 3.The facility will produce sales revenues of $50,000/year for 3 years;variable operating costs (excluding depreciation)will be 40 percent of sales.No fixed costs will be incurred.Operating cash inflows will begin 1 year from today (at t = 1).By an act of Congress,the machine will have depreciation expenses of $40,000,$5,000,and $5,000 in Years 1,2,and 3,respectively.The company has a 40 percent tax rate,enough taxable income from other assets to enable it to get a tax refund on this project if the project's income is negative,and a 15 percent required rate of return.Inflation is zero.What is the project's NPV?
A) $7,673.71
B) $12,851.75
C) $17,436.84
D) $24,989.67
E) $32,784.25

Question

Quizplus · Accepted Answer

To calculate the project's NPV, we need to consider the initial investment, cash flows over the project's life, and the salvage value at the end of the project, taking into account depreciation and taxes.1. Initial investment: $50,000 for the machine + $12,000 for inventories and receivables = $62,000 at Time 0.2. Depreciation: $40,000 in Year 1, $5,000 in Year 2, and $5,000 in Year 3.3. Operating cash inflows: Sales revenues are $50,000/year for 3 years, with variable costs at 40% of sales, so operating costs are $20,000/year (40% of $50,000). This gives us a pre-tax income of $30,000/year ($50,000 - $20,000). After depreciation, taxable income varies each year.4. Taxes: With a 40% tax rate, the tax payment will depend on the taxable income each year, which is affected by depreciation.5. Salvage value: $10,000 at the end of Year 3, plus the recovery of the $12,000 invested in inventories and receivables.Calculating the after-tax cash flows for each year and discounting them back to the present value at a 15% discount rate, and then summing these with the initial investment and the discounted salvage value, gives us the NPV. The correct NPV, based on these calculations, is $7,673.71, which matches choice A. This calculation involves detailed steps including calculating the depreciation effect on taxable income, computing the tax savings, and then determining the net cash flows for each year before discounting them back to present value at the required rate of return.

Your Company Is Considering a Machine Which Will Cost $50,000