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College

Accounting

College

Accounting

Heintz & ParryHeintz & Parry2020thth Edition Edition

Appendix: Depreciation Methods

55ChapterChapter

Prepare a depreciation

schedule using the

straight-line method.

Depreciation MethodsDepreciation Methods

• Straight-line

• Sum-of-the-years’-digits

• Double-declining-balance

• Modified Accelerated Cost Recovery System

ExampleExample

For all illustrations in this appendix, we will assume that a delivery van was

purchased for $40,000. It has a five-year useful life and salvage value of $4,000.

Straight-line MethodStraight-line Method

Under this method, an equal amount of depreciation will be taken each period.

STEP #1: Compute the depreciable cost.

COSTSALVAGE

VALUE =DEPRECIABLE

$40,000 $4,000 = $36,000

STEP #2: Divide the depreciable cost by the expected life of the asset.

Depreciation Expense per Year=

Depreciable CostYears of Life

$36,0005 years = $7,200

per year

It is often convenient to use a depreciation rate per year.

Depreciation Rate per Year

Years of Life

100%5 years=20%

20% of the asset’s depreciable cost

will be recognized as Depreciation Expense each

Straight-line Depreciation ScheduleStraight-line Depreciation Schedule

YearDepreciable

Cost Rate

Depreciation Expense

Accumulated Depreciation (End of Year)

Book Value (End of Year)

1 $36,000

Original Cost – Salvage Value ($40,000 – $4,000)

YearDepreciable

Cost Rate

1 $36,000

100% ÷ Years of Life(100% ÷ 5-year life)

YearDepreciable

Cost Rate

1 $36,000

Depreciable Cost × Depreciation Rate($36,000 × 20%)

20% $7,200

YearDepreciable

Cost Rate

1 $36,000

Since this is the first year of the asset’s life, only this year’s depreciation has

accumulated.

20% $7,200 $7,200

YearDepreciable

Cost Rate

1 $36,000

Cost – Accumulated Depreciation ($40,000 – $7,200)

20% $7,200 $7,200 $32,800

YearDepreciable

Cost Rate

1 $36,000

Depreciable Cost does not change.

20% $7,200 $7,200 $32,800

2 $36,000

YearDepreciable

Cost Rate

1 $36,000

Depreciation Rate does not change.

20% $7,200 $7,200 $32,800

2 $36,000 20%

YearDepreciable

Cost Rate

1 $36,000

Depreciation Expense remains the same each year.

20% $7,200 $7,200 $32,800

2 $36,000 20% $7,200

YearDepreciable

Cost Rate

1 $36,000

Now two years of depreciation has accumulated.

($7,200 + $7,200)

20% $7,200 $7,200 $32,800

2 $36,000 20% $7,200 $14,400

YearDepreciable

Cost Rate

1 $36,000

Cost – Accumulated Depreciation($40,000 – $14,400)

20% $7,200 $7,200 $32,800

2 $36,000 20% $7,200 $14,400 $25,600

YearDepreciable

Cost Rate

1 $36,000

Book Value declines over the life of the asset.

20% $7,200 $7,200 $32,800

2 $36,000 20% $7,200 $14,400 $25,600

YearDepreciable

Cost Rate

1 $36,000 20%

$7,200 $7,200 $32,800

2 $36,000 20% $7,200 $14,400 $25,600

3 $36,000 20% $7,200 $21,600 $18,400

4 $28,800$36,000 20% $7,200 $11,200

5 $36,000 20% $7,200 $36,000

The entire Depreciable Cost has now been recognized as Depreciation Expense.

YearDepreciable

Cost Rate

1 $36,000 20%

$7,200 $7,200 $32,800

2 $36,000 20% $7,200 $14,400 $25,600

3 $36,000 20% $7,200 $21,600 $18,400

4 $28,800$36,000 20% $7,200 $11,200

5 $36,000 20% $7,200 $36,000

Book Value now matches the Salvage Value.

$4,000

schedule using the

sum-of-the-years’-

digits method.

Sum-of-the-years’-digitsSum-of-the-years’-digits

• Depreciation is determined by multiplying the depreciable cost by a schedule of fractions.

• The numerator (top) of the fraction for a specific year is the number of years of remaining useful life.

• The denominator (bottom) of the fraction is determined by adding the digits of the years of the estimated life of the asset.

FORMULA:

DEPRECIABLE COST

Remember, Depreciable Cost = Original Cost – Salvage Value.

FORMULA:

DEPRECIABLE COST ×

YEARS REMAINING

This is measured from the beginning of the year. For example, to calculate the first year’s depreciation…we would say there are 5 years

remaining.

FORMULA:

DEPRECIABLE COST

×YEARS

REMAINING

5-YEAR LIFE = 5 + 4 + 3 + 2 + 1 OR 15 10-YEAR LIFE =

10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 OR 55

SUM-OF-THE-YEARS’-DIGITS

Sum-of-the-years’-digits Depreciation ScheduleSum-of-the-years’-digits Depreciation Schedule

YearDepreciable

Cost Rate

1 $36,000

Original Cost – Salvage Value($40,000 – $4,000)

YearDepreciable

Cost Rate

1 $36,000

Original Cost – Salvage Value($40,000 – $4,000)

$36,000

Five years remaining divided by sum-of-years’-digits of 15

(5 + 4 + 3 + 2 + 1)

YearDepreciable

Cost Rate

$36,000

$36,000 × 5/15

5/15 $12,000

YearDepreciable

Cost Rate

$36,000

The sum-of-the-years’-digits method recognizeslarge amounts of depreciation in the first

year of the asset’s life and smaller amounts each subsequent year.

5/15 $12,000Year

Depreciable Cost Rate

$36,000

Only this first year of depreciation has accumulated so far.

5/15 $12,000 $12,000

YearDepreciable

Cost Rate

$36,000

Original Cost – Accumulated Depreciation($40,000 – $12,000)

5/15 $12,000 $12,000 $28,000

YearDepreciable

Cost Rate

$36,000

Depreciable Costdoes not change.

5/15 $12,000 $12,000 $28,000

2 $36,000

YearDepreciable

Cost Rate

$36,000

Now there are four years remaining.

5/15 $12,000 $12,000 $28,000

2 4/15$36,000

YearDepreciable

Cost Rate

$36,000

Since the rate (fraction) is smaller, the depreciation expense is also

smaller in the second year.

5/15 $12,000 $12,000 $28,000

2 4/15 $9,600$36,000

YearDepreciable

Cost Rate

$36,000

There are now two years of depreciation accumulated.

($12,000 + $9,600)

5/15 $12,000 $12,000 $28,000

2 $36,000 4/15 $9,600 $21,600

YearDepreciable

Cost Rate

$36,000

Book Value falls as the asset ages.

5/15 $12,000 $12,000 $28,000

2 4/15 $9,600 $21,600 $18,400$36,000

YearDepreciable

Cost Rate

5/15 $12,000 $12,000 $28,000

2 4/15 $9,600 $21,600 $18,400

3 3/15 $7,200 $28,800 $11,200

4 2/15 $4,800 $33,600 $6,400

5 2/15 $36,000

The entire depreciable cost has been recognized as Depreciation Expense.

$36,000

$36,000 $2,400

YearDepreciable

Cost Rate

$36,000 5/15 $12,000 $12,000 $28,000

2 4/15 $9,600 $21,600 $18,400

3 3/15 $7,200 $28,800 $11,200

4 2/15 $4,800 $33,600 $6,400

5 2/15

Book Value now matches the Salvage Value.

$4,000

$36,000

$36,000 $2,400 $36,000

YearDepreciable

Cost Rate

schedule using the

double-declining-

balance method.

Double-declining-balance MethodDouble-declining-balance Method

• The book value is multiplied by a fixed rate

Often double the straight-line rate

• Once the book value is reduced to the expected salvage value, no more depreciation may be recognized.

• Similar to the sum-of-the-years’-digits depreciation method, larger amounts of depreciation are taken in the early years of the asset’s life.

Double-declining-balance Method Double-declining-balance Method

FORMULA:

Book Value

Cost – Accumulated Depreciation = Book Value

For an asset’s first year depreciation,Book Value = Original Cost.

Double-declining-balance Method Double-declining-balance Method

FORMULA:

Book Value

× (Straight-Line Rate)2

100% ÷ Useful LifeFor our example……

100% ÷ 5 years = 20%

Double-declining-balance Depreciation ScheduleDouble-declining-balance Depreciation Schedule

Book Value (Beginning of

Year) Rate

1 $40,000

Original Cost – Accumulated Depreciation

($40,000 – $0)

Year) Rate

1 $40,000

Double the Straight-Line Rate 2 × (100% ÷ 5) or 2 × 20%

Year) Rate

1 $40,000

Book Value × Double the Straight-Line Rate

($40,000 × 40%)

40% $16,000

Year) Rate

1 $40,000

The first year’s depreciation is all that has accumulated.

40% $16,000 $16,000

Year) Rate

1 $40,000

($40,000 – $16,000)

40% $16,000 $16,000 $24,000

Year) Rate

1 $40,000

The Book Value at the end of one year becomes the next year’s beginning

Book Value.

40% $16,000 $16,000 $24,000

2 $24,000

Year) Rate

1 $40,000

The rate will be the same every year (always double the straight-line rate).

40% $16,000 $16,000 $24,000

2 $24,000 40%

Year) Rate

1 $40,000

Depreciation Expense will be smaller each year because the book value

is declining each year.

40% $16,000 $16,000 $24,000

2 $24,000 40% $9,600

Year) Rate

1 $40,000

Two years’ depreciation has accumulated…

($16,000 + $9,600)

40% $16,000 $16,000 $24,000

2 $24,000 40% $9,600 $25,600

Year) Rate

1 $40,000

($40,000 – $25,600)

40% $16,000 $16,000 $24,000

2 $24,000 40% $9,600 $25,600 $14,400

Year) Rate

1 $40,000

$16,000 $16,000 $24,000

2 $24,000

Book Value can fall only to the amount of the Salvage Value. ($5,184 – $4,000 =

$1,184 to go!!)

40% $9,600 $25,600 $14,400

3 $14,400 40% $5,760 $31,360 $8,640

4 $8,640 40% $3,456 $34,816 $5,184

Year) RateDepreciation

Expense

1 $40,000

$16,000 $16,000 $24,000

2 $24,000

Book Value × Rate = $2,074. This would be too much depreciation. We can only

recognize $1,184.

40% $9,600 $25,600 $14,400

3 $14,400 40% $5,760 $31,360 $8,640

4 $8,640 40% $3,456 $34,816 $5,184

5 $5,184 $1,184

Year) Rate

1 $40,000

$16,000 $16,000 $24,000

2 $24,000

Book Value has reached the Salvage Value.

40% $9,600 $25,600 $14,400

3 $14,400 40% $5,760 $31,360 $8,640

4 $8,640 40% $3,456 $34,816 $5,184

5 $5,184 $1,184 $36,000 $4,000

schedule for tax purposes

using the modified

accelerated cost recovery

system.

Modified Accelerated Cost Recovery System Modified Accelerated Cost Recovery System

• Used for tax purposes

• The Internal Revenue Service (IRS) classifies various assets according to useful life and sets depreciation rates for each year of the asset’s life

• These rates are then multiplied by the cost of the asset

• Abbreviation: MACRS

MACRS ExampleMACRS Example

A delivery van was purchased for $40,000. It has a five-year useful life

and salvage value of $4,000.

The IRS would give this van a six-year life and no salvage value.

MACRS Depreciation ScheduleMACRS Depreciation Schedule

Year Cost RateDepreciation

Expense

1 $40,000

The IRS doesn’t allow a salvage value for this asset.

Expense

1 $40,000

The IRS sets the first-year rate at 20%.

Expense

1 $40,000

Cost × Rate ($40,000 × 20%)

20% $8,000

Expense

1 $40,000

Cost – Accumulated Depreciation($40,000 – $8,000)

20% $8,000 $8,000 $32,000

Year Cost Rate

1 $40,000

The IRS has a larger second-year rate.

20% $8,000 $8,000 $32,000

2 $40,000 32%

Year Cost Rate

1 $40,000

20% $8,000 $8,000 $32,000

2 $40,000 32% $12,800 $20,800 $19,200

3 $40,000 19.20%

Each year has a different rate.

Year Cost Rate

1 $40,000

20% $8,000 $8,000 $32,000

2 $40,000 32% $12,800 $20,800 $19,200

3 $40,000 19.20% $7,680 $28,480 $11,520

4 $40,000 11.52% $4,608 $33,088 $6,912

5 $40,000 11.52% $4,608 $37,696 $2,304

6 $40,000 5.76%

At the end of the 6 years, 100% of the asset’s cost will have been recognized

as Depreciation Expense.

Year Cost Rate

1 $40,000

20% $8,000 $8,000 $32,000

2 $40,000 32% $12,800 $20,800 $19,200

3 $40,000 19.20% $7,680 $28,480 $11,520

4 $40,000 11.52% $4,608 $33,088 $6,912

5 $40,000 11.52% $4,608 $37,696 $2,304

6 $40,000 5.76%

$2,304 $40,000 $0

$40,000

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