Question

Project Evaluation. Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows: Year Unit Sales 67.500 83.900 98,700 86,000 72,000 Production of the implants will require $1,500,000 in net working capital to start and additional networking capital investments each year equal to 15 percent of the projected sales increase for the following year. Total fixed costs are $1,950,000 per year, variable production costs are $230 per unit, and the units are priced at $355 each. The equipment needed to begin production has an installed cost of $18,500,000. 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. AAI is in the 35 percent marginal tax bracket and has a required return on all its projects of 15 percent. Based on these preliminary project estimates, what is the NPV of the project? What is the IRR?

Answer 1

Calculation of NPV and IRR
Particulars	Year	PVF@15%	Amount	PV	PVF @21%	PV
Cash outflows
Initial cost	0	1.000	$1,85,00,000.00	$1,85,00,000.00	1.000	$1,85,00,000.00
Net working capital	0	1.000	$15,00,000.00	$15,00,000.00	1.000	$15,00,000.00
Additional Working capital	1	0.870	$8,73,300.00	$7,59,391.30	0.826	$7,21,735.54
	2	0.756	$7,88,100.00	$5,95,916.82	0.683	$5,38,282.90
	3	0.658	$0.00	$0.00	0.564	$0.00
	4	0.572	$0.00	$0.00	0.467	$0.00
				$2,13,55,308.13		$2,12,60,018.44
Cash Inflows
Cash flows after tax	1	0.870	$52,52,875.00	$45,67,717.39	0.826	$43,41,219.01
	2	0.756	$65,85,375.00	$49,79,489.60	0.683	$44,97,899.73
	3	0.658	$77,87,875.00	$51,20,654.23	0.564	$43,96,052.41
	4	0.572	$67,56,000.00	$38,62,764.93	0.467	$31,51,723.86
	5	0.497	$56,18,500.00	$27,93,387.49	0.386	$21,66,174.97
terminal Value of asset	5	0.497	$37,00,000.00	$18,39,553.92	0.386	$14,26,510.17
Working capital recovered	5	0.497	$31,61,400.00	$15,71,774.53	0.386	$12,18,856.56
				$2,47,35,342.09		$2,11,98,436.71
			NPV	$33,80,033.96		-$61,581.73

Calculation of IRR: Lower Interest rate (NPV at lower interest rate/ (NPV at lower rate-NPV at higher rate)* (higher rate-lower rate)= 15+ (3380033/(3380033-(-61581))*6 = 20.89%

Working note: Calculation of cash flow after tax and additional working capital

Year	1	2	3	4	5
Unit Sales	67500	83900	98700	86000	72000
Sales (Selling price* unit sales)	$2,39,62,500.00	$2,97,84,500.00	$3,50,38,500.00	$3,05,30,000.00	$2,55,60,000.00
Less: Variable cost( VC per unit * unit sales)	$1,55,25,000.00	$1,92,97,000.00	$2,27,01,000.00	$1,97,80,000.00	$1,65,60,000.00
Less: Fixed cost	$19,50,000.00	$19,50,000.00	$19,50,000.00	$19,50,000.00	$19,50,000.00
Cash flow before tax	$64,87,500.00	$85,37,500.00	$1,03,87,500.00	$88,00,000.00	$70,50,000.00
Less: Depreciation on equipment	$29,60,000.00	$29,60,000.00	$29,60,000.00	$29,60,000.00	$29,60,000.00
Profit before tax	$35,27,500.00	$55,77,500.00	$74,27,500.00	$58,40,000.00	$40,90,000.00
Tax	$12,34,625.00	$19,52,125.00	$25,99,625.00	$20,44,000.00	$14,31,500.00
Cash flow after tax ( Cash flow before Tax- tax)	$52,52,875.00	$65,85,375.00	$77,87,875.00	$67,56,000.00	$56,18,500.00
Additional net WC (Increase in sales*15%)	873300	788100	0	0