Question

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

Year		Unit Sales
1			91,000
2			104,000
3			118,000
4			113,000
5			94,000

  
Production of the implants will require $1,700,000 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 $1,600,000 per year, variable production costs are $315 per unit, and the units are priced at $430 each. The equipment needed to begin production has an installed cost of $22,000,000. 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. Refer to Table 8.3.
  
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            %

Answer 1

First lets see the depreciation schedule based on the 7years MACRS :

Depreciation Schedule
Year	Opening Balance	Investment	Depreciation	Closing balance
-		187,00,000.00		187,00,000.00
1.00	187,00,000.00		26,72,230.00	160,27,770.00
2.00	160,27,770.00		45,79,630.00	114,48,140.00
3.00	114,48,140.00		32,70,630.00	81,77,510.00
4.00	81,77,510.00		23,35,630.00	58,41,880.00
5.00	58,41,880.00		16,69,910.00	41,71,970.00
6.00	41,71,970.00		16,68,040.00	25,03,930.00
7.00	25,03,930.00		16,69,910.00	8,34,020.00
8.00	8,34,020.00		8,34,020.00	-

• Opening balance = previous year's closing balance
• Closing balance = opening balance+investment-depreciation

Now lets calculate the cf for years 1 to 5

CF calculation
Year	Remarks	1.00	2.00	3.00	4.00	5.00
Sales units	Given	91000	104000	118000	113000	94000
Price	Given	430	430	430	430	430
Sales	Sales units*Price	39130000	44720000	50740000	48590000	40420000
VC per unit	Given	315	315	315	315	315
VC	Sales units*VC per unit	28665000	32760000	37170000	35595000	29610000
FC	Given	1600000	1600000	1600000	1600000	1600000
EBITDA	Sales-VC-FC	8865000	10360000	11970000	11395000	9210000
Depreciation	as per schedule	26,72,230.00	45,79,630.00	32,70,630.00	23,35,630.00	16,69,910.00
EBIT	EBITDA-Depreciation	6192770	5780370	8699370	9059370	7540090
Tax	0.30 x EBIT	1857831	1734111	2609811	2717811	2262027
NI	EBIT-Tax	4334939	4046259	6089559	6341559	5278063
Depreciation	Added back	2672230	4579630	3270630	2335630	1669910
CF		7007169	8625889	9360189	8677189	6947973
Additional WCINV		-4472000	-5074000	-4859000	-4042000	0
Salvage value	Recovered in the year					33,00,000.00
Tax savings on loss of sale	0.30x(4171970-3300000)					2,61,591.00
Wcinv Recovery	as per convention					20147000
Total CF	CF+Additional WCINV+Salvage value+Wcinv Recovery+Tax savings	2535169	3551889	4501189	4635189	30700162.5

Npw lets calculate the NPV:

Year	CF	Discount factor			Discounted CF
0	-1263,66,666.67	1/(1+0.17)^0	=	1	1*-126366666.666667	=	-126366667
1	2535169	1/(1+0.17)^1	=	0.854700855	0.854700854700855*2535169	=	2166811.111
2	3551889	1/(1+0.17)^2	=	0.730513551	0.730513551026372*3551889	=	2594703.046
3	4501189	1/(1+0.17)^3	=	0.624370556	0.624370556432796*4501189	=	2810409.881
4	4635189	1/(1+0.17)^4	=	0.533650048	0.533650048233159*4635189	=	2473568.833
5	30656564	1/(1+0.17)^5	=	0.456111152	0.456111152336034*30656564	=	13982800.73
					NPV	=	-102338373

NPV is negative at -102338373.1 this implie this project is not worth investing in

IRR is the rate at which NPV = 0, we can use goal seek in excel or can use trial and error method to calculate IRR. Using goal seek we get a negative IRR of -20.5639894% therefore this project doesnt have an IRR which implies the CF generated through this will never be able to recover the costs