Chapter Five Appendix

1
Chapter Five Appendix

• DEPRECIATION METHODS

2
DEPRECIATION METHODS

• Straight-Line
• Sum-of-the-Years-Digits
• Double-Declining-Balance
• Modified Accelerated Cost Recovery System

3
EXAMPLE
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.
4
STRAIGHT-LINE METHOD
Under this method, an equal amount of
depreciation will be taken each period.
STEP 1 Compute the depreciable cost

SALVAGE VALUE
COST
DEPRECIABLE COST

36,000
40,000
4,000
5
STRAIGHT-LINE METHOD
STEP 2 Divide the depreciable cost by the
expected life of the asset.
Depreciation Expense per year
Depreciable Cost

Years of Life
7,200 per year
36,000

5 years
6
STRAIGHT-LINE METHOD
It is often convenient to use a depreciation rate
per year.
20 of the assets depreciable cost will be
recognized as Depreciation Expense each year.
100
Depreciation rate per year

Years of Life
100
20

5 years
7
STRAIGHT-LINE DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
36,000
Original Cost minus Salvage Value 40,000 -
4,000
8
STRAIGHT-LINE DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
36,000
20
100 / Years of Life 100 / 5 year life
9
STRAIGHT-LINE DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
7,200
36,000
20
Depreciable Cost x Depreciation Rate 36,000 x 20
10
STRAIGHT-LINE DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
7,200
7,200
36,000
20
Since this is the first year of the assets
life, only this years depreciation has
accumulated.
11
STRAIGHT-LINE DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
7,200
7,200
36,000
20
32,800
Book Value is Cost minus Accumulated
Depreciation. 40,000 - 7,200
12
STRAIGHT-LINE DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
7,200
7,200
36,000
20
32,800
36,000
2
Depreciable Cost does not change.
13
STRAIGHT-LINE DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
7,200
7,200
36,000
20
32,800
36,000
20
2
Depreciation Rate does not change.
14
STRAIGHT-LINE DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
7,200
7,200
36,000
20
32,800
7,200
36,000
20
2
Depreciation Expense remains the same each year.
15
STRAIGHT-LINE DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
7,200
7,200
36,000
20
32,800
14,400
36,000
20
7,200
2
Now two years of depreciation has
accumulated. 7,200 7,200
16
STRAIGHT-LINE DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
7,200
7,200
36,000
20
32,800
14,400
36,000
20
7,200
25,600
2
Cost - Accumulated Depreciation 40,000 - 14,400
17
STRAIGHT-LINE DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
7,200
7,200
36,000
20
32,800
14,400
36,000
20
7,200
25,600
2
Book Value declines over the life of the asset.
18
STRAIGHT-LINE DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
7,200
7,200
36,000
20
32,800
14,400
36,000
20
7,200
25,600
2
36,000
20
7,200
18,400
3
21,600
28,800
36,000
20
11,200
4
7,200
5
36,000
7,200
20
36,000
The entire Depreciable Cost has now
been recognized as Depreciation Expense.
19
STRAIGHT-LINE DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
7,200
7,200
36,000
20
32,800
14,400
36,000
20
7,200
25,600
2
36,000
20
7,200
18,400
3
21,600
28,800
36,000
20
11,200
4
7,200
4,000
5
36,000
7,200
20
36,000
Book Value has fallen to the Salvage Value.
20
SUM-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.

21
SUM-OF-THE-YEARS-DIGITS
FORMULA
DEPRECIABLE COST
Remember, Depreciable Cost is Original Cost minus
Salvage Value.
22
SUM-OF-THE-YEARS-DIGITS
FORMULA
YEARS REMAINING
DEPRECIABLE COST
X
This is measured from the beginning of the year.
For example, to calculate the first years
depreciation. we would say there are 5 years
remaining.
23
SUM-OF-THE-YEARS-DIGITS
FORMULA
YEARS REMAINING
DEPRECIABLE COST
X
SUM-OF-THE-YEARS-DIGITS
5 YEAR LIFE 54321 OR 15 10 YEAR LIFE
10987654321 OR 55
24
SUM-OF-THE-YEARS-DIGITSDEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
36,000
Original Cost minus Salvage Value 40,000 -
4,000
25
SUM-OF-THE-YEARS-DIGITSDEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
5/15
36,000
Five years remaining divided by
sum-of-years-digits of 15 (54321)
26
SUM-OF-THE-YEARS-DIGITSDEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
5/15
12,000
36,000
36,000 X 5/15
27
SUM-OF-THE-YEARS-DIGITSDEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
5/15
12,000
36,000
Sum-of-the-years-digits method recognizes large
amounts of depreciation in the first year of the
assets life and smaller amounts each subsequent
year.
28
SUM-OF-THE-YEARS-DIGITSDEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
5/15
12,000
12,000
36,000
Only this first year of depreciation has
accumulated so far.
29
SUM-OF-THE-YEARS-DIGITSDEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
5/15
12,000
12,000
36,000
28,000
Original Cost minus Accumulated
Depreciation 40,000 - 12,000
30
SUM-OF-THE-YEARS-DIGITSDEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
5/15
12,000
12,000
36,000
28,000
2
36,000
Depreciable Cost does not change.
31
SUM-OF-THE-YEARS-DIGITSDEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
5/15
12,000
12,000
36,000
28,000
2
4/15
36,000
Now there are 4 years remaining.
32
SUM-OF-THE-YEARS-DIGITSDEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
5/15
12,000
12,000
36,000
28,000
2
4/15
9,600
36,000
Since the rate (fraction) is smaller, the
depreciation expense is also smaller in the 2nd
year.
33
SUM-OF-THE-YEARS-DIGITSDEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
5/15
12,000
12,000
36,000
28,000
2
4/15
9,600
21,600
36,000
There are now two years of depreciation
accumulated. 12,000 9,600
34
SUM-OF-THE-YEARS-DIGITSDEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
5/15
12,000
12,000
36,000
28,000
2
18,400
4/15
9,600
21,600
36,000
Book Value falls as the asset ages.
35
SUM-OF-THE-YEARS-DIGITSDEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
5/15
12,000
12,000
36,000
28,000
2
18,400
9,600
21,600
36,000
4/15
3
11,200
36,000
3/15
7,200
28,800
36,000
4,800
33,600
6,400
4
2/15
2/15
36,000
36,000
5
2,400
The entire depreciable cost has been recognized
as Depreciation Expense.
36
SUM-OF-THE-YEARS-DIGITSDEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
5/15
12,000
12,000
36,000
28,000
2
18,400
9,600
21,600
36,000
4/15
3
11,200
36,000
3/15
7,200
28,800
36,000
4,800
33,600
6,400
4
2/15
2/15
36,000
4,000
36,000
5
2,400
Book value now matches the Salvage Value.
37
DOUBLE-DECLINING-BALANCE

• 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 Sum-of-the-Years-Digits, larger
  amounts of depreciation are taken in the early
  years of the assets life.

38
DOUBLE-DECLINING-BALANCE
FORMULA
Book Value
Cost minus Accumulated Depreciation equals Book
Value. For an assets first year
depreciation, Book Value equals Original Cost.
39
DOUBLE-DECLINING-BALANCE
FORMULA
Book Value
x
(Straight-Line Rate)
2
100 / Useful Life For our example 100/5years
20
40
Double-Declining-BalanceDepreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
40,000
Original Cost minus Accumulated Depr. 40,000 -
0
41
Double-Declining-BalanceDepreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
40
40,000
Twice the Straight-Line Rate 2 (100/5) or 2 x
20
42
Double-Declining-BalanceDepreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
40
40,000
16,000
Book Value x twice the Straight-Line Rate 40,000
x 40
43
Double-Declining-BalanceDepreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
40
40,000
16,000
16,000
First years depreciation is all that has
accumulated.
44
Double-Declining-BalanceDepreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
40
40,000
16,000
16,000
24,000
Original Cost minus Accumulated
Depreciation 40,000 - 16,000
45
Double-Declining-BalanceDepreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
40
40,000
16,000
16,000
24,000
2
24,000
The Book Value at the end of one year becomes
the next years beginning Book Value.
46
Double-Declining-BalanceDepreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
40
40,000
16,000
16,000
24,000
2
24,000
40
Rate will be the same every year. Always twice
the straight-line rate
47
Double-Declining-BalanceDepreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
40
40,000
16,000
16,000
24,000
2
24,000
40
9,600
Depreciation Expense will be smaller each year
because the book value is declining each year.
48
Double-Declining-BalanceDepreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
40
40,000
16,000
16,000
24,000
2
24,000
40
9,600
25,600
Two years depreciation has accumulated. 16,000
9,600
49
Double-Declining-BalanceDepreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
40
40,000
16,000
16,000
24,000
2
24,000
40
9,600
25,600
14,400
Original Cost - Acc. Depreciation 40,000 -
25,600
50
Double-Declining-BalanceDepreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
40
40,000
16,000
16,000
24,000
2
24,000
40
9,600
25,600
14,400
3
14,400
8,640
40
5,760
31,360
8,640
5,184
4
3,456
34,816
40
Book Value can fall only to the amount of the
Salvage Value. 5,184 - 4,000 1,184 to go!!
51
Double-Declining-BalanceDepreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
40
40,000
16,000
16,000
24,000
2
24,000
40
9,600
25,600
14,400
3
14,400
8,640
40
5,760
31,360
8,640
5,184
4
3,456
34,816
40
5
5,184
1,184
Book Value x Rate 2,073 This would be too much
depreciation. Can recognize only 1,184
52
Double-Declining-BalanceDepreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Year
Rate
1
40
40,000
16,000
16,000
24,000
2
24,000
40
9,600
25,600
14,400
3
14,400
8,640
40
5,760
31,360
8,640
5,184
4
3,456
34,816
40
4,000
5
5,184
1,184
36,000
Book Value has reached the Salvage Value.
53
MODIFIED ACCELERATED COST RECOVERY SYSTEM

• Used for Tax Purposes
• Internal Revenue Service classifies various
  assets according to useful life and sets
  depreciation rates for each year of the assets
  life.
• Rates are then multiplied by the cost of the
  asset.
• Abbreviated MACRS

54
MACRS 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 6-year life and no
salvage value.
55
MACRSDepreciation Schedule
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Cost
Year
Rate
1
40,000
IRS doesnt allow a Salvage Value for this asset.
56
MACRSDepreciation Schedule
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Cost
Year
Rate
1
20
40,000
IRS sets the first year rate at 20.
57
MACRSDepreciation Schedule
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Cost
Year
Rate
1
8,000
20
40,000
Cost x Rate 40,000 x 20
58
MACRSDepreciation Schedule
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Cost
Year
Rate
1
8,000
20
40,000
8,000
32,000
Cost - Accumulated Depreciation 40,000 - 8,000
59
MACRSDepreciation Schedule
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Cost
Year
Rate
1
8,000
20
40,000
8,000
32,000
2
40,000
32
IRS has a larger 2nd year rate.
60
MACRSDepreciation Schedule
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Cost
Year
Rate
1
8,000
20
40,000
8,000
32,000
12,800
20,800
19,200
2
40,000
32
3
40,000
19.20
Each year has a different rate.
61
MACRSDepreciation Schedule
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

At the end of the 6 years, 100 of the assets
cost will have been recognized as Depreciation
Expense.
Cost
Year
Rate
1
8,000
20
40,000
8,000
32,000
12,800
20,800
19,200
2
40,000
32
28,480
3
40,000
19.20
7,680
11,520
40,000
4,608
6,912
4
11.52
33,088
40,000
4,608
5
2,304
11.52
37,696
40,000
5.76
6
100
62
MACRSDepreciation Schedule
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year)
x

Cost
Year
Rate
1
8,000
20
40,000
8,000
32,000
12,800
20,800
19,200
2
40,000
32
28,480
3
40,000
19.20
7,680
11,520
40,000
4,608
6,912
4
11.52
33,088
40,000
4,608
5
2,304
11.52
37,696
40,000
40,000
5.76
0
6
2,304
100
40,000