Deitz J.E., Southam J.L. Contemporary Business Mathematics for Colleges

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The straight-line (SL) method of determining depreciation is the easiest method. It

distributes depreciation evenly over the useful life of an asset, assigning equal amounts

to designated units (miles, number of items made, etc.) or periods (usually months or

years). It is based on the assumption that wear and obsolescence occur evenly over the

life of the property. The three factors used to compute depreciation by the straight-line

method are

1. The original cost, which includes the price paid for an item and any freight charges

and expenses for installation. Cost includes anything necessary to get the asset to

where it is to be used and in a condition to be used.

2. The estimated service life, which is the length of time the buyer expects to be able to

use an asset. The estimated service life may be stated in terms of years or months that

normally may be expected during the life of the asset.

3. The estimated scrap value (SV), which is the amount the owner of an asset expects to

receive upon disposing of it at the end of its estimated service life.

The basic formula for computing the amount of depreciation under the straight-line

method is

(Original cost 2 Scrap value) 4 Estimated service life in periods of time

5 Depreciation amount for one unit or period

Depreciation is the decrease in the value of assets owned by a business, such as automo-

biles, buildings, and computers. Depreciation is caused by wear or by obsolescence

(becoming out-of-date). In the toy manufacturing industry, some dies and tools last

only 1 or 2 years because of changing fads. An automobile will wear out after a number

of years or miles of use. Buildings lose value as wood, electrical wiring, and fixtures

deteriorate and as design characteristics and owners’ needs change. A business computer

frequently becomes obsolete in 3 to 5 years.

In business, depreciation is figured on almost all physical assets owned and in use.

Depreciation is deducted from gross profits as an expense. In this chapter, we present five

common methods of calculating depreciation: the straight-line, units-of-production,

declining-balance, sum-of-the-years-digits, and Modified Accelerated Cost Recovery

System methods.

364 Part 5 Business Applications

Computing Depreciation with the

Straight-Line Method

Learning Objective

Compute depreciation using the

straight-line method.

18.1 When an asset is purchased,

some sales and other business taxes

are subject to interpretation.When

possible,some companies will expense

these costs immediately.In other cases,

all taxes paid will become part of the

original cost of the depreciable asset.

EXAMPLE A

An office computer costing $12,500 has an estimated life of 5 years and an estimated

scrap value of $900. What is the annual depreciation amount?

$12,500 cost 2 $900 SV 5 $11,600 estimated total depreciation

$11,600 4 5 estimated total years 5 $2,320 annual depreciation

The units-of-production method of determining depreciation distributes depreciation

based on how much the asset is used. It is usually expressed in miles driven, hours used,

tons hauled, or units produced. Calculation is like that used in the straight-line method

except that miles, hours, tons, or units are used rather than months or years. The basic

formula for computing the amount of depreciation under the units-of-production

method is

(Original cost 2 Scrap value) 4 Estimated life in service units

5 Depreciation amount for one unit

Example B shows depreciation of an asset based on the number of hours it is used.

First you must find the hourly depreciation and then multiply it by the number of hours

operated during a particular month or year.

Chapter 18 Depreciation 365

Computing Depreciation with the

Units-of-Production Method

Example C shows depreciation in terms of the number of units that it will produce

during its lifetime: Divide the number of units into the estimated total depreciation

amount to get the depreciation per unit.

EXAMPLE B

A machine costing $10,000 has an estimated life of 60,000 hours of operation and an

estimated scrap value of $400. If it was operated for 2,800 hours during the first year,

how much depreciation expense will be shown for the first year?

$10,000 cost 2 $400 SV 5 $9,600 estimated total depreciation

$9,600 4 60,000 estimated total hours 5 $0.16 hourly depreciation

2,800 hours operated 3 $0.16 5 $448 first year’s depreciation.

BOOK VALUE

The book value of an asset is the original cost minus the accumulated depreciation, or

the total of all depreciation to that time.

EXAMPLE C

A press that costs $145,000 will produce an estimated 3,500,000 units in its life and has

an estimated scrap value of $5,000. If it produced 235,000 units this year, how much

depreciation will be shown for the year?

$145,000 cost 2 $5,000 SV 5 $140,000 estimated total depreciation

$140,000 4 3,500,000 estimated total units 5 $0.04 depreciation per unit

235,000 units produced 3 $0.04 5 $9,400 first year’s depreciation

Compute depreciation using the

units-of-production method.

Learning Objective

EXAMPLE D

At the end of the first year, the book value of the press in example C would be

$145,000 cost 2 $9,400 accumulated depreciation 5 $135,600

The book value can be determined at any time in the life of an asset.

366 Part 5 Business Applications

EXAMPLE E

At the end of the third year, the book value of the computer in example A would be

computed as follows:

$2,320 annual depreciation 3 3 years 5 $6,960 accumulated depreciation

$12,500 cost 2 $6,960 5 $5,540.

On January 1, Oakdale Appliances bought a new delivery truck for $48,000. Oakdale’s

accountant estimated a truck life of 200,000 miles and a scrap (trade-in) value of $4,000. In

the first year, the truck was driven 38,000 miles; in the second year, it was driven 46,000 miles.

Compute the depreciation and book value for the first 2 years.

$48,000 cost 2 $4,000 SV 5 $44,000 estimated total depreciation

$44,000 4 200,000 miles 5 $0.22 depreciation per mile

Year 1: 38,000 miles 3 $0.22 per mile 5 $8,360 depreciation

$48,000 cost 2 $8,360 5 $39,640 book value

Year 2: 46,000 miles 3 $0.22 per mile 5 $10,120 depreciation

$39,640 year 1 book value 2 $10,120 5 $29,520 new book value

$48,000 cost 2 ($8,360 1 $10,120) accumulated depreciation 5 $29,520 book value

✔

CONCEPT CHECK 18.1

Computing Depreciation with the

Declining-Balance Method

Learning Objective

Compute depreciation using the

declining-balance method.

The declining-balance (DB) method is based on the theory that depreciation is greatest

in the first year and less in each succeeding year.

to Compute Depreciation, Using the DB Method

1. Divide 100% by the estimated years of useful life to determine the basic

depreciation rate.

2. Multiply the basic depreciation rate by 2 (double-declining-balance) or

by 1.5 (150%-declining-balance) to determine the declining-balance

depreciation rate.

3. Multiply the declining-balance depreciation rate by the book value of the

asset at the beginning of the year to determine the depreciation amount

for that year. (For the first year, the book value at the beginning of the

year equals the asset cost. Do not subtract the scrap value.)

STEPS

Step 3 is repeated each year, using the new (declined) book value (last year’s

beginning book value minus last year’s depreciation amount). The same rate is used each

year. The declining-balance rate continues to apply until the scrap value is reached. The

item may not be depreciated below its scrap value.

Chapter 18 Depreciation 367

EXAMPLE F

Use the declining-balance method with an annual double-declining balance to depreci-

ate the office computer in example A.

100% 4 5 years 5 20%

20% 3 2 5 40% annual double-declining-balance rate.

Beginning

Year Book Value Rate Depreciation

1 $12,500 3 40% 5 $5,000

2 $12,500 2 $5,000 5 7,500 340% 5 3,000

3 7,500 2 3,000 5 4,500 340% 5 1,800

4 4,500 2 1,800 5 2,700 340% 5 1,080

5 2,700 2 1,080 5 1,620 340% 5 648

6 1,620 2 648 5 972 340% 5 388.80 $72*

*As book value ($972) is larger than estimated scrap value ($900), there is some depreciation in the sixth year.

However, the calculated depreciation ($388.80) is greater than book value minus scrap value ($972 2 $900 5 $72).

Thus, depreciation is limited to the smaller amount, $72.

STEP 3

STEP 2

STEP 1

On January 1, Oakdale Appliances bought a new delivery truck for $60,000. Oakdale’s

accountant estimated a truck life of 4 years and a scrap value of $6,000. Compute the

depreciation for the first 2 years using the 150%-declining-balance method.

$60,000 cost

100% 4 4 years 5 25%

25% 3 1.5 5 37.5% annual 150%-declining-balance rate

Year 1: $60,000 3 37.5% 5 $22,500 depreciation

$60,000 2 $22,500 5 $37,500 book value

Year 2: $37,500 3 37.5% 5 $14,062.50 depreciation

✔

CONCEPT CHECK 18.2

368 Part 5 Business Applications

Learning Objective

Compute depreciation using the

sum-of-the-years-digits method.

Computing Depreciation with the

Sum-of-the-Years-Digits Method

The sum-of-the-years-digits (SYD) method also is used to compute a greater

depreciation amount in the earlier years of an asset’s life. The book value decreases

more slowly than under the declining-balance method. This method’s name comes

from the calculation done in Step 1.

18.2 Most companies use basic

computer programs to compute

monthly and annual depreciation

figures,thus simplifying application of

the sum-of-the-years-digits method to

assets with many years of use.

to Compute Depreciation Using the SYD method

1. Compute the sum of all the year’s digits in the estimated life of the asset.

Use this shortcut formula:

where n 5 number of years in the estimated life.

2. Determine the current year’s depreciation fraction by using this

formula: Estimated years of life remaining at the beginning of the

current year 4 Sum of all digits from Step 1.

3. Multiply the total depreciation amount (Cost 2 SV) of the asset by the

depreciation fraction from Step 2 to determine depreciation for the

current year.

Note that each year a new depreciation fraction from Step 2 is determined

and Step 3 is repeated.The sum of all digits in Step 1 and the total

depreciation amount in Step 3 are the same every year.

(n 1 1) 3 n

STEPS

EXAMPLE G

Under the sum-of-the-years-digits method, the office computer in example A would be

depreciated as follows:

(or 1 1 2 1 3 1 4 1 5 5 15)

Depreciation

Year Fraction Total Amount Depreciation

1 3 $11,600 5 $ 3,866.67

2 3 11,600 5 3,093.33

3 3 11,600 5 2,320.00

4 3 11,600 5 1,546.67

5 3 11,600 5  773.33

Total depreciation $11,600.00

STEP 3STEP 2

(5 1 1) 3 5

5 15

STEP 1

Businesses use the depreciation methods previously described for financial reporting.

However, federal tax laws regulate how depreciation must be taken for income tax pur-

poses. The IRS requires that the Modified Accelerated Cost Recovery System (MACRS)

be used for depreciation of property purchased and put into service after 1986. MACRS

“recovers” the entire cost of depreciable property over the allowable period. No scrap

value is permitted.

For common business assets, MACRS provides depreciation periods of 3, 5, 7, 10, 15,

and 20 years. Examples of assets from each of these categories are as follows:

3 years: Property with a life of 4 years or less—some types of equipment used

for research and development, some machine tools, some tractors, and

racehorses more than 2 years old when placed in service

5 years: Property with a life of 4 to 10 years—computers, automobiles and taxis,

office machines, certain telephone equipment, and trucks and buses

7 years: Property with a life of 10 to 15 years—office furniture and fixtures, some

agricultural and horticultural structures, and commercial airplanes

10 years: Property with a life of 16 to 19 years—tugboats, vessels, and barges

15 years: Property with a life of 20 to 24 years—this category usually contains

certain municipal, public utility, and telephone distribution plants

20 years: Property with a life of 25 or more years—farm buildings and certain

municipal infrastructure items such as sewers

Figure 18-1 shows IRS annual percentages used to compute depreciation by MACRS.

Chapter 18 Depreciation 369

On January 1, Oakdale Appliances bought a new delivery truck for $48,000. Oakdale’s

accountant estimated a truck life of 4 years and a scrap value of $4,000. Compute the

depreciation for the first 2 years using the sum-of-the-years-digits method.

$48,000 cost 2 $4,000 SV 5 $44,000 to be depreciated

(or 1 1 2 1 3 1 4 5 10)

Year 1: 3 $44,000 5 $17,600 depreciation

Year 2: 3 $44,000 5 $13,200 depreciation

(4 1 1) 3 4

5 10

✔

CONCEPT CHECK 18.3

Computing Depreciation with the Modified

Accelerated Cost Recovery System

Compute depreciation for income

tax purposes using the Modified

Accelerated Cost Recovery System

(MACRS).

Learning Objective

18.3 Some businesses compute

depreciation for their assets twice:

once for business purposes,using one

of the first three methods previously

explained,and once for tax purposes,

using MACRS.Doing so is perfectly

legal so long as the business always

reports annual depreciation for IRS tax

purposes on the basis of MACRS.

370 Part 5 Business Applications

18.4 Current-year MACRS

depreciation tables are published

annually by the IRS and will usually

be mailed in response to a phone

request to a local IRS office.The IRS

provides a number of tables for

MACRS,such as the one shown in

Figure 18-1.The computations

provided in the examples illustrate

the correct mathematical

procedures.Be sure to consult

current tax law for appropriate

tables,rates for other assets,and

additional rules,such as maximum

annual depreciation amounts for

luxury automobiles.

Appropriate Percentage

3-Year 5-Year 7-Year 10-Year 15-Year 20-Year

Year Class Class Class Class Class Class

1 33.33 20.00 14.29 10.00 5.00 3.750

2 44.45 32.00 24.49 18.00 9.50 7.219

3 14.81 19.20 17.49 14.40 8.55 6.677

4 7.41 11.52 12.49 11.52 7.70 6.177

5 11.52 8.93 9.22 6.93 5.713

6 5.76 8.92 7.37 6.23 5.285

7 8.93 6.55 5.90 4.888

8 4.46 6.55 5.90 4.522

9 6.56 5.91 4.462

10 6.55 5.90 4.461

11 3.28 5.91 4.462

12 5.90 4.461

13 5.91 4.462

14 5.90 4.461

15 5.91 4.462

16 2.95 4.461

17 4.462

18 4.461

19 4.462

20 4.461

21 2.231

Note: The MACRS percentage for the first year is applicable to a partial or

full year.

Figure 18-1 MACRS Depreciation Schedule

EXAMPLE H

Use the MACRS Depreciation Schedule shown in Figure 18-1 to depreciate the office

computer in example A for tax purposes.

Depreciation Beginning Current Ending

Year Rate (%) Cost (Rounded) Book Value Depreciation Book Value

1 20.00 3$12,500 5 $2,500 $12,500 2 $2,500 5 $10,000

2 32.00 3 12,500 5 4,000 10,000 2 4,000 5 6,000

3 19.20 3 12,500 5 2,400 6,000 2 2,400 5 3,600

4 11.52 3 12,500 5 1,440 3,600 2 1,440 5 2,160

5 11.52 3 12,500 5 1,440 2,160 2 1,440 5 720

6 5.76 3 12,500 5 720 720 2 720 5 0

Frequently, businesses are faced with the need to compute depreciation for only part of

the year. Partial-year depreciation can be computed with any of the methods described

in this chapter.

With the straight-line method, compute the depreciation amount for a partial year by

dividing the annual depreciation amount by 12 and then multiplying that result by the

number of months of use.

With the units-of-production method, simply multiply the number of units (miles or

hours) used by the per-unit amount.

With the declining-balance method, find the current year’s annual depreciation and

then divide by 12; multiply that result by the number of months of use.

With the sum-of-the-years-digits method, first consider the overlapping years. To

find the annual depreciation for the first partial year, divide by 12 and multiply the result

by the number of months of use. From then on, every year will include the remaining

fraction of the prior year’s depreciation and the partial-year depreciation for the

remainder of the current year.

MACRS tables automatically consider partial-year depreciation for the first and last

years regardless of the date the item was placed in service.

Chapter 18 Depreciation 371

On April 10, Oakdale Appliances bought a new delivery truck for $48,000. Compute the depreciation for the first

year and for the second year using the MACRS table (5-year class).

MACRS depreciation first year: $48,000 3 20.00% 5 $9,600 (MACRS percentage for the first year is applicable to

a partial or full year.)

MACRS depreciation second year: $48,000 3 32.00% 5 $15,360

✔

CONCEPT CHECK 18.4

Computing Partial-Year Depreciation

Compute partial-year depreciation

using the five different primary

depreciation methods covered.

Learning Objective

EXAMPLE I

Office furniture costing $18,000 and put in use on May 1 is expected to have a useful

life of 10 years. Its estimated resale value is $1,500. Using each of the four appropriate

methods, compute the depreciation expense for May 1 through December 31 of the

first tax year and all 12 months of the second year.

Method Year Calculation (rounded to the nearest dollar)

SL 1st ($18,000 2 $1,500) 4 10 35$1,100

2nd ($18,000 2 $1,500) 4 10 5 $1,650

DB (200%) 1st

2nd ($18,000 2 $2,400) 3 20% 5 $3,120

100%

b 3 2 3 $18,000 3

5 $2,400

Method Year Calculation (rounded to the nearest dollar)

SYD 1st

2nd

$2,800

MACRS 1st $18,000 3 14.29% 5 $2,572.20

(7-year class) 2nd $18,000 3 24.49% 5 $4,408.20

($18,000 2 $1,500) 3

5 $1,800

($18,000 2 $1,500) 3

5 $1,000

($18,000 2 $1,500) 3

5 $2,000

(10 1 1) 3 10

5 55

372 Part 5 Business Applications

In October, Oakdale Appliances bought a new mid-size van for $34,000. It had an estimated

scrap value of $4,000 and a useful life of 5 years. Compute the depreciation expense for the

3 months of the first year and for the full second year, using the 150%-declining-balance

and the sum-of-the-years-digits methods.

$34,000 cost 2 $4,000 scrap value 5 $30,000 to be depreciated

Declining Balance

100% 4 5 years 3 1.5 5 30%

30% 3 $34,000 5 $10,200

Year 1: $10,200 35$2,550 (3 months)

Year 2: ($34,000 2 $2,550) 3 30% 5 $9,435 (full year)

Sum of the Years Digits

(or 1 1 2 1 3 1 4 1 5 5 15)

Year 1: $10,000 35$2,500 (3 months)

Year 2: (9 months)

(3 months)

$7,500 1 $2,000 5 $9,500 in year 2

COMPLETE ASSIGNMENTS 18.1 AND 18.2.

$8,000 3

5 $2,000

3 $30,000 5 $8,000

$10,000 3

5 $7,500

3 $30,000 5 $10,000

(5 1 1) 3 5

5 15

✔

CONCEPT CHECK 18.5

Chapter 18 Depreciation 373

accumulated depreciation

basic depreciation rate

book value

declining-balance (DB) method

declining-balance depreciation

rate

depreciation

double-declining-balance

estimated service life

Modified Accelerated Cost

Recovery System (MACRS)

obsolescence

150%-declining-balance

original cost

scrap value (SV)

straight-line (SL) method

sum-of-the-years-digits (SYD)

method

units-of-production method

Chapter Terms for Review