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1.AAI, Inc., forecasts unit sales for a potential new product as follows:Year Units of Output95,000107,000110,000The initial investment in Net Working Capital (NWC) is $1,500,000. At the end of the project, theinvestment in NWC is expected to be fully recovered. Total fixed costs are $1,750,000 each year,variable costs are $280 per unit, and the units are sold at $330 each. The new equipment is expected tocost S4,400,000 and will be depreciated using the 3-year MACRS depreciation schedules (relevantdepreciation rates are 33% in year 1, 45% in year 2, 15% in year 3 and 7% in year 4). At the end ofthree years the equipment can be sold for $100,000. If the new project is taken, there will be a negativeeffect on the firm's existing products - cash flow from the firm's existing products will decrease by88,000 on a post-tax basis in years 1, 2, and 3. The tax rate s 40% and AAI Inc's cost ofcapital is 12%Compute the (i) payback period, (ii) NPV, (iii) IRR, and (iv) profitability index of the project.

Question
1.
AAI, Inc., forecasts unit sales for a potential new product as follows:
Year Units of Output
95,000
107,000
110,000
The initial investment in Net Working Capital (NWC) is $1,500,000. At the end of the project, the
investment in NWC is expected to be fully recovered. Total fixed costs are $1,750,000 each year,
variable costs are $280 per unit, and the units are sold at $330 each. The new equipment is expected to
cost S4,400,000 and will be depreciated using the 3-year MACRS depreciation schedules (relevant
depreciation rates are 33% in year 1, 45% in year 2, 15% in year 3 and 7% in year 4). At the end of
three years the equipment can be sold for $100,000. If the new project is taken, there will be a negative
effect on the firm's existing products - cash flow from the firm's existing products will decrease by
88,000 on a post-tax basis in years 1, 2, and 3. The tax rate s 40% and AAI Inc's cost ofcapital is 12%
Compute the (i) payback period, (ii) NPV, (iii) IRR, and (iv) profitability index of the project.
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1. AAI, Inc., forecasts unit sales for a potential new product as follows: Year Units of Output 95,000 107,000 110,000 The initial investment in Net Working Capital (NWC) is $1,500,000. At the end of the project, the investment in NWC is expected to be fully recovered. Total fixed costs are $1,750,000 each year, variable costs are $280 per unit, and the units are sold at $330 each. The new equipment is expected to cost S4,400,000 and will be depreciated using the 3-year MACRS depreciation schedules (relevant depreciation rates are 33% in year 1, 45% in year 2, 15% in year 3 and 7% in year 4). At the end of three years the equipment can be sold for $100,000. If the new project is taken, there will be a negative effect on the firm's existing products - cash flow from the firm's existing products will decrease by 88,000 on a post-tax basis in years 1, 2, and 3. The tax rate s 40% and AAI Inc's cost ofcapital is 12% Compute the (i) payback period, (ii) NPV, (iii) IRR, and (iv) profitability index of the project.

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check_circleAnswer
Step 1

Please see the table below. Since all the steps are sequential, I have converted the same into a tabular form.

Please be guided by the sign [+] / [-] against each variable in the first column.This will help you understand whether a particular variable has been added or subtracted.  

Please be guided by the second column called "Linkage". This will help you understand the mathematics behind each row.

All the four subparts have been solved at appropriate place in the table itself.

Step 2

Year, N

Linkage

0

1

2

3

Purchase cost of new equipment

A

4,400,000

   

Investment in working capital

B

1,500,000

   

Total Initial Investment

C = A + B

5,900,000

   
      

Depreciation schedule

D

 

33%

45%

15%

Depreciation

E = D x A

 

1,452,000

1,980,000

660,000

Accumulated Depreciation

F = Sum of E

 

1,452,000

3,432,000

4,092,000

Tax Basis (Asset balance)

G = A - F

4,400,000

2,948,000

968,000

308,000

      

Units of Output

H

 

95,000

107,000

110,000

Sale Price per unit

I

 

330

330

330

Variable cost per unit

J

 

280

280

280

      

Annual Operating Cash flows

     

Revenue

K = H x I

 

31,350,000

35,310,000

36,300,000

[-] Variable Costs

L = H x J

 

26,600,000

29,960,000

30,800,000

[-] Fixed Costs

M

 

1,750,000

1,750,000

1,750,000

[-] Depreciation

E (as above)

 

1,452,000

1,980,000

660,000

EBIT

N = K-L-M-E

 

1,548,000

1,620,000

3,090,000

[-] Taxes

O = 40% x N

 

619,200

648,000

1,236,000

NOPAT

P =N - O

 

928,800

972,000

1,854,000

[-] Post tax reduction in existing cash flows

P'

 

88,000

88,000

88,000

Annual Operating Cash flows

Q = P + E - P'

 

2,292,800

2,864,000

2,426,000

      

Sale value of the machine

R

   

100,000

Gain / (Loss) on sale

S = R - G

   

(208,000)

Tax on gain / loss

T = S x 40%

   

(83,200)

      

Terminal Cash flows

     

Post tax salvage value

U = R - T

   

183,200

Release of working capital

B (as above)

   

1,500,000

Terminal Cash flows

V = U + B

   

1,683,200

      

Net Cash flows

W = -C + Q + V

(5,900,000)

2,292,800

2,864,000

4,109,200

Cumulative cash flows

Sum of W

(5,900,000)

(3,607,200)

(743,200)

3,366,000

      

Part (i) Payback Period

 

2.18

=2+743,200/4,109200

 
      

Cost of Capital

X

12%

   

Discount Factor

Y = (1 + X)-N

1.0000

0.8929

0.7972

0.7118

PV of cash flow

Z = W x Y

(5,900,000)

2,047,143

2,283,163

2,924,847

Part (ii) NPV

AA = Sum of Z

1,355,154

   
      

Part (iii) IRR

 

24%

=IRR(-5900000,2292800,2864000,4109200)

      

Part (iv) Profitability Index

(AA + C) / C

1.23

   
...

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