Question

Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows Year 2 4 Unit Sales 73,000 86,000 105,000 97,000 67,000 5 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 (MACRS schedule). 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. a. What is the NPV of the project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the IRR? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a. NPV b. IRR

Answer 1

Tax rate		21%
	Year-0	Year-1	Year-2	Year-3	Year-4	Year-5
Units		73,000	86,000	105,000	97,000	67,000
Sale Price		375	375	375	375	375
variable cost		255	255	255	255	255
Sale		27,375,000	32,250,000	39,375,000	36,375,000	25,125,000
Less: Operating Cost		18,615,000	21,930,000	26,775,000	24,735,000	17,085,000
Contribution		8,760,000	10,320,000	12,600,000	11,640,000	8,040,000
Less: Fixed Cost		3,200,000	3,200,000	3,200,000	3,200,000	3,200,000
Less: Depreciation as per table given below		2,357,850	4,040,850	2,885,850	2,060,850	1,473,450
Profit before tax		3,202,150	3,079,150	6,514,150	6,379,150	3,366,550
Tax		672,452	646,622	1,367,972	1,339,622	706,976
Profit After Tax		2,529,699	2,432,529	5,146,179	5,039,529	2,659,575
Add Depreciation		2,357,850	4,040,850	2,885,850	2,060,850	1,473,450
Cash Profit After tax		4,887,549	6,473,379	8,032,029	7,100,379	4,133,025
Cost of macine			16,500,000
Depreciation			12,818,850
WDV			3,681,150
Sale price			3,300,000
Profit/(Loss)			(381,150)
Tax			(80,042)
Sale price after tax			3,380,042
Depreciation		Year-1	Year-2	Year-3	Year-4	Year-5	Total
Cost		16,500,000	16,500,000	16,500,000	16,500,000	16,500,000
Dep Rate		14.29%	24.49%	17.49%	12.49%	8.93%
Deprecaition		2,357,850	4,040,850	2,885,850	2,060,850	1,473,450	12,818,850
Calculation of NPV
						18.00%
Year		Captial	Working captial	Operating cash	Annual Cash flow	PV factor	Present values
0		(16,500,000)	(1,500,000)		(18,000,000)	1.000	(18,000,000)
1			(731,250)	4,887,549	4,156,299	0.847	3,522,287
2			(1,068,750)	6,473,379	5,404,629	0.718	3,881,520
3			450,000	8,032,029	8,482,029	0.609	5,162,424
4			1,687,500	7,100,379	8,787,879	0.516	4,532,690
5		3,380,042	1,162,500	4,133,025	8,675,566	0.437	3,792,170
					Net Present Value		2,891,091
Calculation of IRR
			23.00%		24.00%
Year		Total cash flow	PV factor @ 23%	Present values	PV factor @ 24%	Present values
0		(18,000,000)	1.000	(18,000,000)	1.000	(18,000,000)
1		4,156,299	0.813	3,379,104	0.806	3,351,854
2		5,404,629	0.661	3,572,363	0.650	3,514,977
3		8,482,029	0.537	4,558,106	0.524	4,448,716
4		8,787,879	0.437	3,839,402	0.423	3,717,041
5		8,675,566	0.355	3,081,572	0.341	2,959,303
				430,547		(8,110)
		IRR	=Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
		IRR	'=23%+ (24%-23%)*(430547./(430547.-(-8110.2)
			23.98%