Question

Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows:

Year	Unit Sales
1	73,000
2	86,000
3	105,000
4	97,000
5	67,000

Production of the implants will require $1,500,000 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 $3,200,000 per year, variable production costs are $255 per unit, and the units are priced at $375 each. The equipment needed to begin production has an installed cost of $16,500,000. 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 20 percent of its acquisition cost. The tax rate is 21 percent tax and the required return is 18 percent. MACRS SCHEDULE: Year 1- 14,29% Year 2- 24,49% Year 3- 17,49% Year 4- 12,49% Year 5- 8,93% Year 6- 8,92% Year 7- 8,93% Year 8- 4,46%

a.	What is the NPV of the project?
b.	What is the IRR?

Answer 1

Answer 1
Calculation of NPV of project
Year	0	1	2	3	4	5
Investment in equipment	-$16,500,000
Increase in net working capital	-$1,500,000	-$731,250	-$1,068,750
Operating cash flow		$4,887,549	$6,473,379	$8,032,029	$7,100,379	$4,133,025
Recovery of net working capital						$3,300,000
After tax sale value of equipment						$3,380,042
Net Cash flow	-$18,000,000	$4,156,299	$5,404,629	$8,032,029	$7,100,379	$10,813,066
x Discount Factor @ 18%	1	0.847457627	0.71818443	0.608630873	0.515788875	0.437109216
Present Values	-$18,000,000	$3,522,287	$3,881,520	$4,888,541	$3,662,296	$4,726,491
NPV of project	$2,681,134
Answer 2
Calculation of IRR of project
Year	Cash flow
0	-$18,000,000
1	$4,156,299
2	$5,404,629
3	$8,032,029
4	$7,100,379
5	$10,813,066
IRR of project	23.47%
Working 1
Calculation of operating cash flow for the project over 5 years
Year	1	2	3	4	5
Sales Units	73000	86000	105000	97000	67000
x Selling price per unit	$375.00	$375.00	$375.00	$375.00	$375.00
Sales	$27,375,000.00	$32,250,000.00	$39,375,000.00	$36,375,000.00	$25,125,000.00
Less : Variable cost ($255 per unit)	$18,615,000.00	$21,930,000.00	$26,775,000.00	$24,735,000.00	$17,085,000.00
Contribution Margin	$8,760,000.00	$10,320,000.00	$12,600,000.00	$11,640,000.00	$8,040,000.00
Less : Fixed cost	$3,200,000.00	$3,200,000.00	$3,200,000.00	$3,200,000.00	$3,200,000.00
Less : Depreciation	$2,357,850.00	$4,040,850.00	$2,885,850.00	$2,060,850.00	$1,473,450.00
Profit before tax	$3,202,150.00	$3,079,150.00	$6,514,150.00	$6,379,150.00	$3,366,550.00
Less : Tax @ 21%	$672,451.50	$646,621.50	$1,367,971.50	$1,339,621.50	$706,975.50
Add : Depreciation	$2,357,850.00	$4,040,850.00	$2,885,850.00	$2,060,850.00	$1,473,450.00
Operating Cash flow	$4,887,549	$6,473,379	$8,032,029	$7,100,379	$4,133,025
Working 2
Calculation of depreciation using seven-year MACRS property
Year	Depreciable value	Depreciation rates	Depreciation
1	$16,500,000.00	14.29%	$2,357,850.00
2	$16,500,000.00	24.49%	$4,040,850.00
3	$16,500,000.00	17.49%	$2,885,850.00
4	$16,500,000.00	12.49%	$2,060,850.00
5	$16,500,000.00	8.93%	$1,473,450.00
Calculation of additional net working Capital requirement
Year	1	2	3	4	5
Sales	$27,375,000.00	$32,250,000.00	$39,375,000.00	$36,375,000.00	$25,125,000.00
Projected Sales Increase		$4,875,000.00	$7,125,000.00
Additional net working capital [15% of sales increase in following year]	$731,250.00	$1,068,750.00
Working
Calculation of after tax sale value of equipment
Sale value [20% of $16,500,000]	$3,300,000.00
Less : Book value of equipment [$1,65,00,000 - $1,28,18,850]	$3,681,150.00
Loss on sale of equipment	-$381,150.00
Tax benefit @ 21% of loss	$80,041.50
After tax sale value [Sale value + Tax benefit]	$3,380,041.50