Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emu

Question

Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows: Year Unit Sales 1 78,000 2 91,000 3 105,000 4 100,000 5 81,000 Production of the implants will require $1,570,000 in net working capital to start and additional net working capital investments each year equal to 10 percent of the projected sales increase for the following year. Total fixed costs are $1,470,000 per year, variable production costs are $250 per unit, and the units are priced at $365 each. The equipment needed to begin production has an installed cost of $20,700,000. Because the implants are intended for professional singers, this equipment is considered industrial machinery and thus qualifies as seven-year MACRS property. In five years, this equipment can be sold for about 15 percent of its acquisition cost. AAIcost. AAI is in the 30 percent marginal tax bracket and has a required return on all its projects of 17 percent. MACRS schedule What is the NPV of the project? What is the IRR? Please show all calculations and formulas

Explanation / Answer

IRR : rate of return at which NPV = 0

Time line 0 1 2 3 4 5 Cost of new machine -20700000 +Working capital -1570000 =Initial Investment outlay -22270000 7 yr MACR% 14.29% 24.49% 17.49% 12.49% 8.93% 22.3100% Unit sales 78000 91000 105000 100000 81000 Profits =no. of units sold * (sales price - variable cost) 8970000 10465000 12075000 11500000 9315000 -fixed cost -1470000 -1470000 -1470000 -1470000 -1470000 -Depreciation =Cost of machine*MACR% -2958030 -5069430 -3620430 -2585430 -1848510 -4618170 =salvage book value -Working capital =10% of ( next year revenues - current revenues) -474500 -511000 0 0 0 =Pretax cash flows 4145470 3505570 7089570 7544570 6077490 -taxes =(Pretax cash flows)*(1-tax) 2901829 2453899 4962699 5281199 4254243 +Depreciation 2958030 5069430 3620430 2585430 1848510 =after tax operating cash flow 5859859 7523329 8583129 7866629 6102753 reversal of working capital 2555500 +Proceeds from sales after tax =0.15*acquisition cost* ( 1 -tax rate) 2173500 +Tax shield on salvage book value =book value * tax rate 1385451 "=Terminal year after tax cash flows 6114451 Total Cash flow for the period -22270000 5859859 7523329 8583129 7866629 12217204 Discount factor= (1+discount rate)^corresponding period 1 1.17 1.3689 1.601613 1.8738872 2.192448 Required rate 17% Discounted CF= Cashflow/discount factor -22270000 5008426.5 5495893.78 5359053 4198026.9 5572403 NPV= Sum of discounted CF= 3363803.25

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