Question

Aylmer-in-You (AIY) Inc. projects unit sales for a new opera tenor emulation implant as follows: Year Unit Sales 1 98,000 2 112,000 3 122,000 4 142,000 5 87,000 Production of the implants will require $729,000 in net working capital to start and additional net working capital investments each year equal to 25% of the projected sales increase for the following year. (Because sales are expected to fall in Year 5, there is no NWC cash flow occurring for Year 4.) Total fixed costs are $174,000 per year, variable production costs are $320 per unit, and the units are priced at $360 each. The equipment needed to begin production has an installed cost of $7.0 million. Because the implants are intended for professional singers, this equipment is considered industrial machinery and thus falls into Class 8 for tax purposes (20%). In five years, this equipment can be sold for about 30% of its acquisition cost. AIY is in the 40% marginal tax bracket and has a required return on all its projects of 18%. Based on these preliminary project estimates, what is the NPV of the project? What is the IRR?

NPV $

IRR %

Answer 1

We first calculate the depreciation Year Beginning value Depreciation @20% 7,000,000.00 1,400,000.00 5,600,000.00 1,120,000.00 4,480,000.00 896,000.00 3,584,000.00 716,800.00 2,867,200.00 573,440.00 Ending value 5,600,000.00 4,480,000.00 3,584,000.00 2,867,200.00 2,293,760.00 Sale value 0.3*7000000 2,100,000.00 Since sale value is less than the book value so there would be no tax on salvage value Year 4 Year 5 Cash outflow Working capital Year 1 Year 2 Year 3 (7,000,000.00) (729,000.00) (1,260,000.00) (900,000.00) (1,800,000.00) Working capital is 25% of the next year increase Unit sales Sale price (360each) Variable cost (320) Fixed cost Depreciation 98,000 35,280,000 31,360,000 174,000 1,400,000 112,000 40,320,000 35,840,000 174,000 1,120,000 122,000 43,920,000 39,040,000 174,000 896,000 142,000 51,120,000 45,440,000 174,000 716,800 87,000 31,320,000 27,840,000 174,000 573,440 profit before tax Tax @ 40% Profit after tax depreciation working capital expenditure recovery of working capital Salvage value 2,346,000 938,400.0 1,407,600.0 1,400,000 (1,260,000.00) 3,186,000 1,274,400.0 1,911,600.0 1,120,000 (900,000.00) 3,810,000 1,524,000.0 2,286,000.0 896,000 (1,800,000.00) 4,789,200 1,915,680.0 2,873,520.0 716,800 2,732,560 1,093,024.0 1,639,536.0 573,440 add less add add 729,000 initial Working capital is recovered in the last year 2,100,000 Total cash flow (7,729,000.00) 1,547,600.00 2,131,600.00 1,382,000.00 3,590,320.00 5,041,976.00 use the excel formula to calculate the NPV @ 18% NPV @ 18% 10,276.51 IRR 18.05%