Question

Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows: Year AM Unit Sales 78,000 91,000 105,000 100,000 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. 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? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) NPV What is the IRR? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) IRR $ 21.75

Answer 1

solution: Calculation of NPV units sales x sale price Total sales Less : variable cost (units sales * VC per unit) Les : fixed cost Less : depreciation ** EBT Less : Tax at 30% EAT Add : depreciation OCF Inital cost working capital changes after tax sale value* total cash flow x discount factor at 17% PV NPV (sum of PV) 5 78000 91000 105000 100000 81000 365 365 365 365 365 28470000 33215000 38325000 36500000 29565000 -19500000 -22750000 -26250000 -25000000 -20250000 -1470000 - 1470000 - 1470000 -1470000 -1470000 -2958030 -5069430 -3620430 -2585430 -1848510 4541970 3925570 6984570 7444570 5996490 - 1,362,591.00 - 1,177,671.00 - 2,095,371.00 - 2,233,371.00 - 1,798,947.00 3,179,379.00 2,747,899.00 4,889,199.00 5,211,199.00 4,197,543.00 2.958.030.00 5,069,430.00 3,620,430.00 2,585,430.00 1,848,510.00 1 6,137,409.00 7,817,329.00 8,509,629.00 7,796,629.00 6,046,053.00 - 20,700,000.00 |- 1,570,000.00 - 474,500.00 511,000.00 182,500.00 693,500.00 1,679,500.00 3,558,951.00 1-22,270,000.00 5,662,909.00 7,306,329.00 8,692,129.00 8,490,129.00 11,284,504.00 1.00000 0.85470 0.73051 0.62437 0.53365 0.45611 - 22,270,000.00 4,840,093.16 5,337,372.34 5,427,109.42 4,530,757.75 5,146,988.12 3,012,320.80 workings: **depreciation Cost x de preciation rate depreciation 20,700,000.00 0.1429 2,958,030.00 20,700,000.00 0.2449 5,069,430.00 20,700,000.00 0.1749 3,620,430.00 20,700,000.00 0.1249 2,585,430.00 5 total 20,700,000.00 0.0893 1,848,510.00 16081830 after tax sale value* cost accumulated depreciation book value after 5 years Sale value = 15%* 20700000 Loss on sale Tax shield on Loss= 1513170*30% after tax sale value 20700000 16081830 4618170 3105000 1513170 453951 3558951 discount factor formula = 1/(1+r)^n

Part b: IRR using trial and error method year cash flow 0 - 22,270,000.00 1 5,662,909.00 2 7,306,329.00 3 8,692,129.00 4 8,490,129.00 5 11,284,504.00 discount factor at 20% PV at 20% discount factor at 22% PV at 22% C=a*b e=a*d 1.00000 -22,270,000.00 1.00000 - 22,270,000.00 0.83333 4,719,090.83 0.81967 4,641,728.69 0.69444 5,073,839.58 0.67186 4,908,847.76 0.57870 5,030,167.25 0.55071 4,786,815.31 0.48225 4,094,390.91 0.45140 3,832,436.49 0.40188 4,534,989.07 0.37000 4,175,258.04 1, 182,477.65 NPV 75,086.28 NPV By interpolation: IRR = 20+(1182477.65*2/(1182477.65-75086.28)) 22.14%