Aria Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows:
Year Unit Sales
1 73,000
2 86,000
3 105,000
4 97,000
5 67,000
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?b. What is the IRR?

The net present value is the value that is operated on a series of cash flows at different times. It depends on the interval between the cash flow, and on the discount rates. It accounts for the time value.  

NPV is calculated as:

NPV =

 Initial investment = $16,500,000

Depreciation table:

R.Y.             Time               D.B.                   A.B.V.E.Y.  

1               14.29            $ 3,029,480               $ 18,170,520  

2             24.49             $ 5,191,880               $ 12,978,640  

3               17.49             $ 3,707,880               $ 9,270,760  

4                 12.49             $ 2,647,880               $ 6,622,880  

5                8.93              $ 1,893,160               $ 4,729,720  

6                8.92              $ 1,891,040              $ 2,838,680  

7                  8.93               $ 1,893,160                $ 945,520  

8                  4.46               $ 945,520                    $ 0

Book value at the end of 5 years  =  $4, 729, 720

After tax salvage value   =  

= $ 5, 128 ,916

Sales table:  

Year           Unit Sales  

1                   83,000  

2                  96,000  

3                 1,10,000  

4                  1,05,000  

5                   86,000

The calculation of the free cash flow of the project has been attached below.

1)  Using NPV formula

NPV = − $ 7 ,328 ,810.58

2)  IRR is the discount rate (R) when the NPV of the project will be equal to zero.

Solving the equation (1) for R we get:

R = 3.93%

So IRR of the project = 3.93%

Notes:

Recovery Year ----- R.Y.  

7-Year %----Time    

Depreciation Booked---D.B.

Asset Book Value at the end of Year-------A.B.V.E.Y

To know more about the calculation of the net present value, refer to the link below:

link

Solution:

NPV is calculated as:

NPV =

Initial investment = $16,500,000

Depreciation table:

Recovery Year    7-Year %    Depreciation Booked   Asset Book

                                                                                   Value at the end of Year

1                             14.29            $ 3,029,480               $ 18,170,520

2                            24.49             $ 5,191,880               $ 12,978,640

3                            17.49             $ 3,707,880               $ 9,270,760

4                            12.49             $ 2,647,880               $ 6,622,880

5                             8.93              $ 1,893,160               $ 4,729,720

6                             8.92              $ 1,891,040              $ 2,838,680

7                             8.93               $ 1,893,160                $ 945,520

8                            4.46               $ 945,520                    $ 0

Book value at the end of 5 years  =  $ 4 , 729 , 720

After tax salvage value   =  25 %  ∗  $ 21  , 200 , 000  −  ( 25 %  ∗ $  21,200,000) - $4,729,720 ) * 30%

=  $ 5, 128 ,916

Sales table:

Year           Unit Sales

1                   83,000

2                  96,000

3                 1,10,000

4                  1,05,000

5                   86,000

We calculate the free cash flow of the project : ( Check the attachment )

1)

Using NPV formula

NPV = − $ 7 , 328 , 810.58

2)

IRR is the discount rate (R) when the NPV of the project will be equal to zero.

Solving the equation (1) for R we get:

R = 3.93%

So IRR of the project = 3.93%