You have been asked whether you firm should go ahead with a project to manufacto

Question

You have been asked whether you firm should go ahead with a project to manufactory and sell socks. You have hired a consultant who conducted a marketing study. She estimates the first year sales should be $1 million then sales should grow by 15% per year for the next three year after that. She was paid $50,000 for her report. The cost of the equipment to manufacture the socks is $200,000. Your company will depreciate the equipment using a 3-year MACRS depreciation schedule. The equipment will be sold at the end of 4 years and the projected sale price is $50,000. Your marketing department has told you than the cost of sales is 85% (Includes Cost of Goods sold and GSA) and that the project will require an investment in working capital of 10% of sales (assume it is needed at the beginning of the year and you recover it at the end of the project). You accounting department has told you that the tax rate is 40% and that the proper discount rate for the project is 12.00%. What is the NPV of the project?

What are the IRR and MIRR of the project? Should the firm take the project? Why?

Explanation / Answer

Initial Investment: $200,000 + $50,000 = $250,000

After-tax salvage value of equipment = $50,000 x (1-tax rate) = $30,000

3 Year Depreciation Schedule

Year

Basis

%

Depreciation Expense

Accumulated Depreciation

Ending Book Value

1

$200,000.00

33.333%

$66,666.68

$66,666.68

$133,333.32

2

$200,000.00

44.444%

$88,888.90

$155,555.58

$44,444.42

3

$200,000.00

14.815%

$29,630.40

$185,185.98

$14,814.02

4

$200,000.00

7.407%

$14,814.02

$200,000.00

$0.00

Year

1

2

3

4

Sales

$1,000,000.00

$1,150,000.00

$1,322,500.00

$1,520,875.00

Less: COGS

$850,000.00

$977,500.00

$1,124,125.00

$1,292,743.75

Less: Depreciation

$66,666.68

$88,888.90

$29,630.40

$14,814.02

EBT

$83,333.32

$83,611.10

$168,744.60

$213,317.23

Less: Tax @ 40%

$33,333.33

$33,444.44

$67,497.84

$85,326.89

Net Income

$49,999.99

$50,166.66

$101,246.76

$127,990.34

Less: Working Capital

$100,000.00

$115,000.00

$132,250.00

$152,087.50

Add: Depreciation

$66,666.68

$88,888.90

$29,630.40

$14,814.02

Add: Salvage Value of Equipment

$0.00

$0.00

$0.00

$30,000.00

Operating Cash Flow

$16,666.67

$24,055.56

-$1,372.84

$20,716.86

NPV = {$16,666.67/(1+.12)1} + {$24,055.56/(1+.12)2} + {-$1,372.84/(1+.05)3} + {$20,716.86/(1+.05)4} - $250,000 = -$203,753.32

IRR:

0 = -$250,000 + [($16,666.67)/(IRR)] + [($24,055.56)/(IRR)2] + [(-$1,372.84)/(IRR)3] + [($20,716.86)/(IRR)4] = -40.15%

MIRR:
Time 4 Cash flow:
$16,666.67*(1.12)3 + $24,055.56*(1.12)2 -$1,372.84 + $20,716.86 = $75,420.81

So, the MIRR:

0 = -$250,000 +[($75,420.81)/(1+MIRR)4]
$250,000 = [($75,420.81)/(1+MIRR)4]
(1+MIRR)4 = $75,420.81/$250,000
MIRR = ($75,420.81/$250,000)1/4
MIRR = (0.301683238)1/4 – 1 = -0.2589 or -25.89%

Since the NPV, IRR and MIRR are negative, firm should not take the project as it will result in losses.

3 Year Depreciation Schedule

Year

Basis

%

Depreciation Expense

Accumulated Depreciation

Ending Book Value

1

$200,000.00

33.333%

$66,666.68

$66,666.68

$133,333.32

2

$200,000.00

44.444%

$88,888.90

$155,555.58

$44,444.42

3

$200,000.00

14.815%

$29,630.40

$185,185.98

$14,814.02

4

$200,000.00

7.407%

$14,814.02

$200,000.00

$0.00

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