Question

Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows: Year Unit Sales 1 77,000 2 90,000 3 104,000 4 99,000 5 80,000 Production of the implants will require $1,560,000 in net working capital to start and additional net working capital investments each year equal to 20 percent of the projected sales increase for the following year. Total fixed costs are $1,460,000 per year, variable production costs are $245 per unit, and the units are priced at $360 each. The equipment needed to begin production has an installed cost of $20,600,000. 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 25 percent of its acquisition cost. AAI is in the 30 percent marginal tax bracket and has a required return on all its projects of 19 percent. (MACRS schedule) What is the NPV of the project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) NPV $ What is the IRR? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

IRR $

Answer 1

Depreciation schedule as per MACRS 7 year is as follows:

Year	Depreciation rate	Depreciation	Book Value at the end of the year
1.00	14.29%	$ 29,43,740.00	$   176,56,260.00
2.00	24.49%	$ 50,44,940.00	$   126,11,320.00
3.00	17.49%	$ 36,02,940.00	$     90,08,380.00
4.00	12.49%	$ 25,72,940.00	$     64,35,440.00
5.00	8.93%	$ 18,39,580.00	$     45,95,860.00
6.00	8.92%	$ 18,37,520.00	$     27,58,340.00
7.00	8.93%	$ 18,39,580.00	$        9,18,760.00
8.00	4.46%	$    9,18,760.00	$                           -

NPV is calculated below:

Particulars	Remark	0	1	2	3	4	5
Units Sold	Given		77000	90000	104000	99000	80000
SP	Given		360	360	360	360	360
Sales	SP x Units		$ 277,20,000.00	$ 324,00,000.00	$ 374,40,000.00	$ 356,40,000.00	$ 288,00,000.00
VC per unit	Given		$                245.00	$                245.00	$                245.00	$                245.00	$                245.00
Total VC	VC per unit x Units		$ 188,65,000.00	$ 220,50,000.00	$ 254,80,000.00	$ 242,55,000.00	$ 196,00,000.00
Fixed cost	Given		$    14,60,000.00	$    14,60,000.00	$    14,60,000.00	$    14,60,000.00	$    14,60,000.00
EBITDA	Sales-Total VC-Fixed Cost		$    73,95,000.00	$    88,90,000.00	$ 105,00,000.00	$    99,25,000.00	$    77,40,000.00
Depreciation	MACRS		$    29,43,740.00	$    50,44,940.00	$    36,02,940.00	$    25,72,940.00	$    18,39,580.00
EBT	EBITDA-Depreciation		$    44,51,260.00	$    38,45,060.00	$    68,97,060.00	$    73,52,060.00	$    59,00,420.00
Tax	0.30% x EBT		$    13,35,378.00	$    11,53,518.00	$    20,69,118.00	$    22,05,618.00	$    17,70,126.00
EAT	EBT-Tax		$    31,15,882.00	$    26,91,542.00	$    48,27,942.00	$    51,46,442.00	$    41,30,294.00
Depreciation	Added back as non cash		$    29,43,740.00	$    50,44,940.00	$    36,02,940.00	$    25,72,940.00	$    18,39,580.00
OCF	EAT+Depreciation		$    60,59,622.00	$    77,36,482.00	$    84,30,882.00	$    77,19,382.00	$    59,69,874.00
FCINV	Given	$ -206,00,000.00
WCINV		$    -15,60,000.00	$    -9,36,000.00	$ -10,08,000.00	$      3,60,000.00	$    13,68,000.00	$    17,76,000.00
Salvage							$    51,50,000.00
Tax on profit on salvage value							$    -1,66,242.00
FCF	OCF+FCINV+WCINV+Salvage+Tax	$ -221,60,000.00	$    51,23,622.00	$    67,28,482.00	$    87,90,882.00	$    90,87,382.00	$ 127,29,632.00
Discount factor Formula	at 19 %	1/1.19^0	1/1.19^1	1/1.19^2	1/1.19^3	1/1.19^4	1/1.19^5
Discount factor	Calculated using above formula	1	0.840336134	0.706164819	0.593415814	0.498668751	0.419049371
DCF	FCF x Discount Factor	$ -221,60,000.00	$    43,05,564.71	$    47,51,417.27	$    52,16,648.40	$    45,31,593.44	$    53,34,344.28
NPV = sum of all DCF	$                        19,79,568.10

• WCINV is calculated on increase in sales. The year the sales is projected to increase, there will be an outflow and the year it is projected to decrease, there will be a recover. And the entire outflow not recovered till year 5 will be recovered at the end of year 5
• Out flows are negative, inflows are positive
• As the book value at the end of year 5 was  $45,95,860.00 and the salvage value was 0.25 x  $206,00,000.00 = $51,50,000.00, the profit =  $5,54,140.00 which will be taxed at 30%
• NPV is positive, the project should be invested in
• IRR is the rate where NPV = 0 and can be calculated using a financial calculator or excel's goal seek, it comes to 22.39% rounded to 2 decimal places:
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