Aria Acoustics, Inc., (AAI) projects unit sales for a new seven-octave voice emu
ID: 2801156 • Letter: A
Question
Aria Acoustics, Inc., (AAI) projects unit sales for a new seven-octave voice emulation implant as follows: Year Unit Sales 1 116,000 2 135,000 3 123,000 4 106,000 5 92,000 Production of the implants will require $1,660,000 in net working capital to start and additional net working capital investments each year equal to 15 percent of the projected sales increase for the following year. Total fixed costs are $1,510,000 per year, variable production costs are $241 per unit, and the units are priced at $361 each. The equipment needed to begin production has an installed cost of $31,000,000. Because the implants are intended for professional singers, this equipment is considered industrial machinery and thus qualifies as seven-year MACRS (MACRS Table) property. In five years, this equipment can be sold for about 20 percent of its acquisition cost. AAI is in the 35 percent marginal tax bracket and has a required return on all its projects of 18 percent. What is the NPV and IRR of the project?
Explanation / Answer
Tax rate 35% Year-1 Year-2 Year-3 Year-4 Year-5 Units 116,000 135,000 123,000 106,000 92,000 Sale @ 361 41,876,000 48,735,000 44,403,000 38,266,000 33,212,000 Less: Operating Cost @241 per unit 27,956,000 32,535,000 29,643,000 25,546,000 22,172,000 Contribution 13,920,000 16,200,000 14,760,000 12,720,000 11,040,000 Less: Fixed Cost 1,510,000 1,510,000 1,510,000 1,510,000 1,510,000 Less: Depreciation as per table given below 4,429,900 7,591,900 5,421,900 3,871,900 2,768,300 Profit before tax 7,980,100 7,098,100 7,828,100 7,338,100 6,761,700 Tax 2,793,035 2,484,335 2,739,835 2,568,335 2,366,595 Profit After Tax 5,187,065 4,613,765 5,088,265 4,769,765 4,395,105 Add Depreciation 4,429,900 7,591,900 5,421,900 3,871,900 2,768,300 Cash Profit After tax 9,616,965 12,205,665 10,510,165 8,641,665 7,163,405 Sale Increase YoY 6,859,000 (4,332,000) (6,137,000) (5,054,000) Working capital @ 15% of Sale increase (1,660,000) (1,028,850) 649,800 920,550 758,100 Total working capital increamental (360,400) Cost of macine 31,000,000 Depreciation for 5 years 24,083,900 WDV 6,916,100 Sale price-31,000,000*20% 6,200,000 Profit (716,100) Tax (250,635) Sale price after tax 6,450,635 Depreciation Year-1 Year-2 Year-3 Year-4 Year-5 Total Cost 31,000,000 31,000,000 31,000,000 31,000,000 31,000,000 Dep Rate 14.29% 24.49% 17.49% 12.49% 8.93% Deprecaition 4,429,900 7,591,900 5,421,900 3,871,900 2,768,300 24,083,900 Calculation of Annual Cash flow (1) Year Captial Working captial Operating cash Annual Cash flow 0 (31,000,000) (1,660,000) (32,660,000) 1 (1,028,850) 9,616,965 8,588,115 2 649,800 12,205,665 12,855,465 3 920,550 10,510,165 11,430,715 4 758,100 8,641,665 9,399,765 5 6,450,635 360,400 7,163,405 13,974,440 Calculation of NPV Year Annual Cash flow PV factor @ 18% Present values 0 (32,660,000) 1.000 (32,660,000) 1 8,588,115 0.847 7,278,064 2 12,855,465 0.718 9,232,595 3 11,430,715 0.609 6,957,086 4 9,399,765 0.516 4,848,294 5 13,974,440 0.437 6,108,357 Net Present Value 1,764,395 Calculation of IRR Year Total cash flow PV factor @ 20% Present values PV factor @ 25% Present values 0 (32,660,000) 1.000 (32,660,000) 1.000 (32,660,000) 1 8,588,115 0.833 7,156,763 0.800 6,870,492 2 12,855,465 0.694 8,927,406 0.640 8,227,498 3 11,430,715 0.579 6,614,997 0.512 5,852,526 4 9,399,765 0.482 4,533,066 0.410 3,850,144 5 13,974,440 0.402 5,616,014 0.328 4,579,144 188,246 (3,280,196) IRR =Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV) IRR =20%+5%*(188246/(188246+3280196)) 20.271%
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