Question

25 Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows: Year points FNM to Unit Sales 75,800 88,800 108,500 101,200 68,700 Skipped eBook Print References Production of the implants will require $2,200,000 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 $4,600,000 per year, variable production costs are $269 per unit, and the units are priced at $417 each. The equipment needed to begin production has an installed cost of $19,300,000. 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 24 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

a

Time line		0	1	2	3	4	5
Cost of new machine		-19300000
Initial working capital		-2200000
=Initial Investment outlay		-21500000
7 years MACR rate			14.29%	24.49%	17.49%	12.49%	8.93%	22.31%
Unit sales			75800	88800	108500	101200	68700
Profits	=no. of units sold * (sales price - variable cost)		11218400	13142400	16058000	14977600	10167600
Fixed cost			-4600000	-4600000	-4600000	-4600000	-4600000
-Depreciation	=Cost of machine*MACR%		-2757970	-4726570	-3375570	-2410570	-1723490	4305830	=Salvage Value
=Pretax cash flows			3860430	3815830	8082430	7967030	3844110
-taxes	=(Pretax cash flows)*(1-tax)		2933926.8	2900030.8	6142646.8	6054942.8	2921523.6
+Depreciation			2757970	4726570	3375570	2410570	1723490
=after tax operating cash flow			5691896.8	7626600.8	9518216.8	8465512.8	4645013.6
Working capital during the project	(N+1 sales-N sales)*0.15		-813150	-1232235	456615	2032875
reversal of working capital							1755895
+Proceeds from sale of equipment after tax	=selling price* ( 1 -tax rate)						2933600
+Tax shield on salvage book value	=Salvage value * tax rate						1033399.2
=Terminal year after tax cash flows							5722894.2
Total Cash flow for the period		-21500000	4878746.8	6394365.8	9974831.8	10498388	10367908
Discount factor=	(1+discount rate)^corresponding period	1	1.14	1.2996	1.481544	1.6889602	1.9254146
Discounted CF=	Cashflow/discount factor	-21500000	4279602.456	4920256.848	6732727.344	6215888.4	5384766.4
NPV=	Sum of discounted CF=	6033241.44

b

Total Cash flow for the period		-21500000	4878746.8	6394365.8	9974831.8	10498388	10367908
Discount factor=	(1+discount rate)^corresponding period	1	1.236153025	1.528074301	1.888933669	2.3350111	2.886431
Discounted CF=	Cashflow/discount factor	-21500000	3946717.52	4184590.892	5280668.117	4496076.2	3591947.2
NPV=	Sum of discounted CF=	0.00
IRR is discount rate at which NPV = 0 =	24.00%