Question

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

Year		Unit Sales
1			76,400
2			89,400
3			109,250
4			102,100
5			69,000

Production of the implants will require $2,350,000 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 $4,900,000 per year, variable production costs are $272 per unit, and the units are priced at $426 each. The equipment needed to begin production has an installed cost of $19,900,000. 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 22 percent the required return is 17 percent. MACRS schedule

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.)

  

Answer 1

NPV Calculation

	Year	0	1	2	3	4	5
	Sales Unit		76400	89400	109250	102100	69000
							Amount in $
PV of Cash Outflows	Sales income @ 426 per unit		32,546,400	38,084,400	46,540,500	43,494,600	29,394,000
	Equipment Salvage value						3,980,000
	Total	-	32,546,400	38,084,400	46,540,500	43,494,600	33,374,000
PV of Cash Outflows	Net working capital to start	2,350,000
	Equipment cost	19,900,000
	Fixed Cost		4,900,000	4,900,000	4,900,000	4,900,000	4,900,000
	Variable cost @ 272 per unit		20,780,800	24,316,800	29,716,000	27,771,200	18,768,000
	Additional WC investment @ 15% of projected sale increase of next year		830,700	1,268,415	-	-	-
	Total	22,250,000	26,511,500	30,485,215	34,616,000	32,671,200	23,668,000
	Net cashflow before depreciation & tax	(22,250,000)	6,034,900	7,599,185	11,924,500	10,823,400	9,706,000
	Depreciation	-	3,184,000	3,184,000	3,184,000	3,184,000	3,184,000
	Net cashflow after depreciation before tax	(22,250,000)	2,850,900	4,415,185	8,740,500	7,639,400	6,522,000
	Tax @ 22%	(4,895,000)	627,198	971,341	1,922,910	1,680,668	1,434,840
	Net cashflow after tax	(17,355,000)	2,223,702	3,443,844	6,817,590	5,958,732	5,087,160
	PV Factor	1	0.854701	0.730514	0.624371	0.533650	0.456111
	PV of Net cash flows	(17,355,000)	1,900,600	2,515,775	4,256,702	3,179,878	2,320,310
	NPV of Project						(3,181,735)

Hence NPV of Project is negative i.e. $ 3,181,735

IRR : it to determine which discount rate makes the present value of future after-tax cash flows equal the initial cost of the capital investment i.e. NPV is zero.

Hence IRR will be 9.73%

	Year	0	1	2	3	4	5
	Net cashflow after tax	(17,355,000)	2,223,702	3,443,844	6,817,590	5,958,732	5,087,160
	PV Factor @ 9.73%	1	0.911353	0.830541	0.756895	0.689780	0.628615
	PV of Net cash flows	(17,355,000)	2,026,577	2,860,254	5,160,201	4,110,212	3,197,756
	NPV of Project						0