Question

Problem 10-36 Project Evaluation (L01] Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows: Year points Skipped Unit Sales 73,400 86,400 105,500 97,600 67,500 Production of the implants will require $1,600,000 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 $3,400,000 per year, variable production costs are $257 per unit, and the units are priced at $381 each. The equipment needed to begin production has an installed cost of $16,900,000. 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 14 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.) a. NPV b. IRR

Answer 1

Time line		0	1	2	3	4	5
Cost of new machine		-16900000
Initial working capital		-1600000
=Initial Investment outlay		-18500000
7 years MACR rate			14.29%	24.49%	17.49%	12.49%	8.93%	22.31%
Unit sales			73400	86400	105500	97600	67500
Profits	=no. of units sold * (sales price - variable cost)		9101600	10713600	13082000	12102400	8370000
Fixed cost			-3400000	-3400000	-3400000	-3400000	-3400000
-Depreciation	=Cost of machine*MACR%		-2415010	-4138810	-2955810	-2110810	-1509170	3770390	=Salvage Value
=Pretax cash flows			3286590	3174790	6726190	6591590	3460830
-taxes	=(Pretax cash flows)*(1-tax)		2563540.2	2476336.2	5246428.2	5141440.2	2699447.4
+Depreciation			2415010	4138810	2955810	2110810	1509170
=after tax operating cash flow			4978550.20	6615146.20	8202238.2	7252250.2	4208617.4
Working capital during the project	(N+1 sales-N sales)*0.15		-742950	-1091565	451485	1720215
reversal of working capital							1262815
+Proceeds from sale of equipment after tax	=selling price* ( 1 -tax rate)						2636400
+Tax shield on salvage book value	=Salvage value * tax rate						829485.8
=Terminal year after tax cash flows							4728700.8
Total Cash flow for the period		-18500000	4235600.20	5523581.20	8653723.200	8972465.2	8937318.2
Discount factor=	(1+discount rate)^corresponding period	1	1.14	1.2996	1.481544	1.6889602	1.9254146
Discounted CF=	Cashflow/discount factor	-18500000	3715438.772	4250216.374	5841016.669	5312419.7	4641763
a. NPV=	Sum of discounted CF=	5260854.52

Total Cash flow for the period		-18500000	4235600.20	5523581.20	8653723.200	8972465.2	8937318.2
Discount factor=	(1+discount rate)^corresponding period	1	1.237529012	1.531478056	1.895248525	2.345425	2.9025315
Discounted CF=	Cashflow/discount factor	-18500000	3422626.992	3606699.541	4566009.726	3825517.8	3079146
NPV=	Sum of discounted CF=	0.00
b. IRR is discount rate at which NPV = 0 =	23.75%