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(2) Cash savings (annual):

Book

Cash

Income

Difference in cash operating costs:

$20,000

Old machine

17,000

New machine $3,000

$ 3,000

Depreciation expense (annual):

2,000

Old machine ($12,000/6 years)

3.OOo

New machine ($15,000/5 years)

1,000

Additional annual depreciation

Taxable savings $2,000

-800

Income tax on savings ($2,000 X 0.40)

Annual cash savings after income tax

Internal rate of return factor; $8,000/$2,200 = 3.636 years (about 11.5%).

MACRS and NPV Analysis. A machine costs $1,000 initially. Annual cash inflows are expected

8.27

to be $300. The machine will be depreciated using the MACRS rule and will fall in the 3-year

property class. No salvage value is anticipated. The cost of capital is 16 percent. The estimated

life of the machine is 5 years. The tax rate is 40 percent. Make a decision using NPV.

SOLUTION

16% PV

Amount of

Year(s) Having

Cash Flows Factor PV

Cash Flows

$0,000)

Now

Initial investment $1,000 1.OOo

Annual cash inflows:

$300

XO%

1-5 180 3.274 589

$180

Depreciation deductions:

Tax

MACRS

Shield

Depreciation

Year cost Y

O

333 133.20 133.20 114.82

$1,000 33.3 1 0.862

1

445 178.00 2 178.00 0.743 132.25

2 1,000 44.5

148 59.20 3 59.20 0.641 37.95

3 1,000 14.8

74

1,000 7.4 29.60 4 29.60 0.552 16.34

4

Net Present Value $(109.32)

We should not buy the machine, since the NPV of -$109.32 is negative.

MACRS and NPV Analysis. A firm is considering the purchase of an automatic machine for

8.28

$6,200. The machine has an installation cost of $800 and zero salvage value at the end of its

expected life of 5 years. Depreciation is by the straight-line method with the half-year convention.

The machine is considered a 5-year property. Expected cash savings before tax is $1,800per year

over the 5 years. The firm is in the 40 percent tax bracket. The firm has determined the cost of

capital (or minimum required rate of return) of 10 percent after taxes. Should the firm purchase

the machine? Use the NPV method.

243

CAPITAL BUDGETING (INCLUDING LEASING)

CHAP. 81

SOLUTION

Amount of

Year(s) Having 10%PV

Cash Flows Cash Flows Factor PV

Now $(7,000) $(7,000)

1.Ooo

Initial investmen t

Annual cash inflows:

$1,800

X 60%

4,094

3.791

1,080

1-5

$1,080

Depreciation deductions:

Tax

Shield

at 40%

Year Depreciation

$255

1 $280 0.909

$ 700 $280

1

2 463

560 0.826

2 1,400 560

0.751 421

3 560

3 1,400 560

382

4 560 0.683

4 1,400 560

348

5 560 0.621

5 1,400 560

0.564 158

6 280

6 700 280

Net Present Value $(879)

The firm should not buy the automatic machine since its NPV is negative.

MACRS and NPV Analysis. The Wessels Corporation is considering installing a new conveyor

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for materials handling in a warehouse. The conveyor will have an initial cost of $75,000 and an

installation cost of $5,000. Expected benefits of the conveyor are: ( a ) Annual labor cost will be

reduced by $16,500,and ( b )breakage and other damages from handling will be reduced by $400

per month. Some of the firmвЂ™s costs are expected to increase as follows: ( a ) Electricity cost will

rise by $100 per month, and ( b ) annual repair and maintenance of the conveyor will amount to

$900.

Assume the firm uses the MACRS rules for depreciation in the 5-year property class. No

salvage value will be recognized for tax purposes. The conveyor has an expected useful life of 8

years and a projected salvage value of $5,000. The tax rate is 40 percent.

1. Estimate future cash inflows for the proposed project.

2. Determine the projects NPV at 10 percent. Should the firm buy the conveyor?

SOLUTION

1 Annual cash inflow:

.

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