Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emu
ID: 2724355 • Letter: A
Question
Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows:
Production of the implants will require $1,690,000 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 $1,590,000 per year, variable production costs are $310 per unit, and the units are priced at $425 each. The equipment needed to begin production has an installed cost of $21,900,000. 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. AAI is in the 30 percent marginal tax bracket and has a required return on all its projects of 18 percent. MACRS schedule
What is the NPV of the project?
What is the IRR?
Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows:
Explanation / Answer
Initial Investment = $21,900,000 + $1,690,000 = $23,590,000
7 Years Schedule
Year
Basis
%
Depreciation Expense
Accumulated Depreciation
Ending Book Value
1
$21,900,000.00
14.286%
$3,128,634.00
$3,128,634.00
$18,771,366.00
2
$21,900,000.00
24.490%
$5,363,310.00
$8,491,944.00
$13,408,056.00
3
$21,900,000.00
17.493%
$3,830,967.00
$12,322,911.00
$9,577,089.00
4
$21,900,000.00
12.495%
$2,736,405.00
$15,059,316.00
$6,840,684.00
5
$21,900,000.00
8.925%
$1,954,575.00
$17,013,891.00
$4,886,109.00
Salvage Value of Machine = $21,900,000 x 20% = $4,380,000
After-tax salvage value = $4,380,000 – [($4,380,000 - $4,886,109) x 30%] = $4,531,832.70
(As selling value of machinery at the end of project is less than its book value, firm can claim a tax-deduction against this loss.)
Operating Cash Flows:
Year
1
2
3
4
5
Sales
$38,250,000.00
$43,775,000.00
$49,725,000.00
$47,600,000.00
$39,525,000.00
Less: Variable Cost
$27,900,000.00
$31,930,000.00
$36,270,000.00
$34,720,000.00
$28,830,000.00
Less: Fixed Cost
$1,590,000.00
$1,590,000.00
$1,590,000.00
$1,590,000.00
$1,590,000.00
Less: Depreciation
$3,128,634.00
$5,363,310.00
$3,830,967.00
$2,736,405.00
$1,954,575.00
EBT
$5,631,366.00
$4,891,690.00
$8,034,033.00
$8,553,595.00
$7,150,425.00
Less: Tax @ 30%
$1,689,409.80
$1,467,507.00
$2,410,209.90
$2,566,078.50
$2,145,127.50
Net Income
$3,941,956.20
$3,424,183.00
$5,623,823.10
$5,987,516.50
$5,005,297.50
Add: Depreciation
$3,128,634.00
$5,363,310.00
$3,830,967.00
$2,736,405.00
$1,954,575.00
Less: Change in NWC
$0.00
$948,458.33
$1,013,810.68
-$305,128.21
-$1,005,770.09
Add: Recovery of initial NWC
$0.00
$0.00
$0.00
$0.00
$1,690,000.00
Add: Salvage Value of Machine
$0.00
$0.00
$0.00
$0.00
$4,531,832.70
Operating Cash Flow
$7,070,590.20
$7,839,034.67
$8,440,979.42
$9,029,049.71
$14,187,475.29
Sales in a year = Number of units sold x sales price per unit
Variable Cost in a year = Number of units sold x variable cost per unit
Calculation of change in NWC = 15% x [(Sales in current year / Sales in previous year) – 1]
(In year one Change in NWC is 0 as it is the first year.)
NPV = -$23,590,000 + [($7,070,590.20)/(1.18)] + [($7,839,034.67)/(1.18)2] + [($8,440,979.42)/(1.18)3] + [($9,029,049.71)/(1.18)4] + [($14,187,475.29)/(1.18)5] = $4,027,898.51
IRR
0 = -$23,590,000 + [($7,070,590.20)/(IRR)] + [($7,839,034.67)/(IRR)2] + [($8,440,979.42)/(IRR)3] + [($9,029,049.71)/(IRR)4] + [($14,187,475.29)/(IRR)5] =24.54%
7 Years Schedule
Year
Basis
%
Depreciation Expense
Accumulated Depreciation
Ending Book Value
1
$21,900,000.00
14.286%
$3,128,634.00
$3,128,634.00
$18,771,366.00
2
$21,900,000.00
24.490%
$5,363,310.00
$8,491,944.00
$13,408,056.00
3
$21,900,000.00
17.493%
$3,830,967.00
$12,322,911.00
$9,577,089.00
4
$21,900,000.00
12.495%
$2,736,405.00
$15,059,316.00
$6,840,684.00
5
$21,900,000.00
8.925%
$1,954,575.00
$17,013,891.00
$4,886,109.00
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