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XI = 1,

and the NPV is $106,000. Thus, projects A, B, and D should be accepted.

8.9 CAPITAL BUDGETING DECISIONS AND THE MODIFIED ACCELERATED COST

RECOVERY SYSTEM (MACRS)

Although the traditional depreciation methods still can be used for computing depreciation for book

purposes, 1981 saw a new way of computing depreciation deductions for tax purposes. The current rule

is called the Modified Accelerated Cost Recovery System (MACRS) rule, as enacted by Congress in 1981

and then modified somewhat in 1986 under the Tax Reform Act of 1986. This rule is characterized as

follows:

1. It abandons the concept of useful life and accelerates depreciation deductions by placing all

depreciable assets into one of eight age property classes. It calculates deductions, based on an allowable

percentage of the assetâ€™s original cost (see Tables 8-1 and 8-2).

With a shorter asset tax life than useful life, the company would be able to deduct depreciation more

quickly and save more in income taxes in the earlier years, thereby making an investment more

attractive. The rationale behind the system is that this way the government encourages the company to

invest in facilities and increase its productive capacity and efficiency. (Remember that the higher d, the

larger the tax shield (d)(t).)

2. Since the allowable percentages in Table 8-1add up to 100%, there is no need to consider the

salvage value of an asset in computing depreciation.

3. The company may elect the straight-line method. The straight-line convention must follow what

is called the half-year convention. This means that the company can deduct only half of the regular

straight-line depreciation amount in the first year. The reason for electing to use the MACRS optional

straight-line method is that some firms may prefer to stretch out depreciation deductions using the

straight-line method rather than to accelerate them. Those firms are the ones that just start out or have

little or no income and wish to show more income on their income statements.

EXAMPLE 8.19 Assume that a machine falls under a 3-year property class and costs $3,000 initially. The

straight-line option under MACRS differs from the traditional straight-line method in that under this method the

company would deduct only $500 depreciation in the first year and the fourth year ($3,000/3 years = $1,000;

$1,000/2= $500). The table below compares the straight-line with half-year convention with the MACRS.

Straight-line

(half-year) MACRS

Year Depreciation cost Deduction

MACRS O h

$ 999

33.3

1 $ 500 $3,000 X

3,000 x 1,335

44.5

2 1,ooo

3,000 x

3 14.8 444

1,(.)oo

3,000 X

500

4 222

7.4

$3,000 $3,000

EXAMPLE 8.20 A machine costs $lO,OOO. Annual cash inflows are expected to be $5,000. The machine will be

depreciated using the MACRS rule and will fall under the 3-year property class. The cost of capital after taxes is

213

CHAP. 81 CAPITAL BUDGETING (INCLUDING LEASING)

Table 8-1. Modified accelerated cost recovery system classification of assets

Property class

10- 15-year 20-year

7-year year

5-year

3-year

Year

5.0%

14.3% 10.0% 3.8%

20.0%

33.3%

1

18.0 7.2

9.5

32.0 24.5

2 44.5

14.4 8.6

17.5 6.7

19.2

14.8"

3

11.5 7.7 6.2

11.5" 12.5

4 7.4

9.2 6.9 5.7

11.5 8.9"

5

7.4 6.2 5.3

8.9

5.8

6

5.9"

8.9 6.6" 4.9

7

4.5"

6.6 5.9

4.5

8

5.9 4.5

6.5

9

6.5 5.9 4.5

10

5.9

3.3 4.5

11

5.9 4.5

12

5.9 4.5

13

5.9 4.5

14

5.9 4.5

15

3.0 4.4

16

4.4

17

18 4.4

19 4.4

20 4.4

21 2.2

I 100% 200% 100% 100% 100%

100%

=

Denotes the year of changeover to straight-line depreciation.

a

10%. The estimated life of the machine is 4 years. The salvage value of the machine at the end of the fourth year

is expected to be $1,200. The tax rate is 30%.

The formula for computation of after-tax cash inflows (S - E)(1 - t) + (d)(t) needs to be computed separately.

The NPV analysis can be performed as follows:

Present value Present

factor @ 10% value

Initial investment: $lO,OOO: $(10,o0O.00)

1.Ooo

(S - E)(1 - t):

$5,000 (1- 0.3) = $3,500 for 4 years 3.170(a) $ 11,095.00

L

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