Question

Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows: Year points -NM Unit Sales 73,000 86,000 105,000 97,000 67,000 Skipped eBook Print References Production of the implants will require $1,500,000 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 $3,200,000 per year, variable production costs are $255 per unit, and the units are priced at $375 each. The equipment needed to begin production has an installed cost of $16,500,000. Because the implants are intended for professional singers, this equipment is considered industrial machinery and thus qualifies as seven-year MACRS property (MACRS schedule). In five years, this equipment can be sold for about 20 percent of its acquisition cost. The tax rate is 21 percent tax and the required return is 18 percent. 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. IRRI 이

Answer 1

a

Time line		0	1	2	3	4	5
Cost of new machine		-16500000
Initial working capital		-1500000
=Initial Investment outlay		-18000000
7 years MACR rate			14.29%	24.49%	17.49%	12.49%	8.93%	22.31%
Unit sales			73000	86000	105000	97000	67000
Profits	=no. of units sold * (sales price - variable cost)		8760000	10320000	12600000	11640000	8040000
Fixed cost			-3200000	-3200000	-3200000	-3200000	-3200000
-Depreciation	=Cost of machine*MACR%		-2357850	-4040850	-2885850	-2060850	-1473450	3681150	=Salvage Value
=Pretax cash flows			3202150	3079150	6514150	6379150	3366550
-taxes	=(Pretax cash flows)*(1-tax)		2529698.5	2432528.5	5146178.5	5039528.5	2659574.5
+Depreciation			2357850	4040850	2885850	2060850	1473450
=after tax operating cash flow			4887548.5	6473378.5	8032028.5	7100378.5	4133024.5
Working capital during the project	(N+1 sales-N sales)*0.15		-731250	-1068750	450000	1687500
reversal of working capital							1162500
+Proceeds from sale of equipment after tax	=selling price* ( 1 -tax rate)						2607000
+Tax shield on salvage book value	=Salvage value * tax rate						773041.5
=Terminal year after tax cash flows							4542541.5
Total Cash flow for the period		-18000000	4156298.5	5404628.5	8482028.5	8787878.5	8675566
Discount factor=	(1+discount rate)^corresponding period	1	1.18	1.3924	1.643032	1.9387778	2.2877578
Discounted CF=	Cashflow/discount factor	-18000000	3522286.864	3881520.037	5162424.408	4532690	3792169.9
NPV=	Sum of discounted CF=	2891091.13

b

Total Cash flow for the period		-18000000	4156298.5	5404628.5	8482028.5	8787878.5	8675566
Discount factor=	(1+discount rate)^corresponding period	1	1.239811711	1.537133079	1.905755594	2.3627781	2.9294
Discounted CF=	Cashflow/discount factor	-18000000	3352362.671	3516044.624	4450743.069	3719299.1	2961550.5
NPV=	Sum of discounted CF=	0.00
IRR is discount rate at which NPV = 0 =	24.00%