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 =
COST
SALVAGE VALUE
DEPRECIABLE COST =
$36,000
$40,000
$4,000

5. Depreciation Expense per year
STRAIGHT-LINE METHOD
STEP #2: Divide the depreciable cost by the expected life of the asset.
Depreciable Cost
Depreciation Expense per year =
Years of Life
$7,200 per year
$36,000 =
5 years

6. 20% STRAIGHT-LINE METHOD = = 100% Years of Life 100% 5 years
It is often convenient to use a depreciation rate per year.
20% of the asset’s
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
$36,000
20%
$7,200
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
$36,000
20%
$7,200
$7,200
Since this is the first year of the
asset’s life, only this year’s
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
$36,000
20%
$7,200
$7,200
$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
$36,000
20%
$7,200
$7,200
$32,800 2
$36,000
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
$36,000
20%
$7,200
$7,200
$32,800 2
$36,000
20%
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
$36,000
20%
$7,200
$7,200
$32,800 2
$36,000
20%
$7,200
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
$36,000
20%
$7,200
$7,200
$32,800 2
$36,000
20%
$7,200
$14,400
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
$36,000
20%
$7,200
$7,200
$32,800 2
$36,000
20%
$7,200
$14,400
$25,600
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
$36,000
20%
$7,200
$7,200
$32,800 2
$36,000
20%
$7,200
$14,400
$25,600
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
$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
$36,000
20%
$7,200
$28,800
$11,200 5
$36,000
20%
$7,200
$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
$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
$36,000
20%
$7,200
$28,800
$11,200 5
$36,000
20%
$7,200
$36,000
$4,000
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 year’s 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 = OR 15
10 YEAR LIFE =
OR 55

24. SUM-OF-THE-YEARS’-DIGITS 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

25. SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year) x =
Year
Rate 1
$36,000
5/15
Five years remaining divided by
sum-of-years’-digits of 15
( )

26. SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year) x =
Year
Rate 1
$36,000
5/15
$12,000
$36,000 X 5/15

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

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

29. SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year) x =
Year
Rate 1
$36,000
5/15
$12,000
$12,000
$28,000
Original Cost minus Accumulated Depreciation
$40,000 - $12,000

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

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

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

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

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

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

36. SUM-OF-THE-YEARS’-DIGITS DEPRECIATION SCHEDULE
Accumulated Depreciation (end of year)
Depreciable Cost
Depreciation Expense
Book Value (end of year) x =
Year
Rate 1
$36,000
5/15
$12,000
$12,000
$28,000 2
$36,000
4/15
$9,600
$21,600
$18,400 3
$36,000
3/15
$7,200
$28,800
$11,200 4
$36,000
2/15
$4,800
$33,600
$6,400 5
$36,000
2/15
$2,400
$36,000
$4,000
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 asset’s life.

38. DOUBLE-DECLINING-BALANCE
FORMULA:
Book Value
Cost minus Accumulated Depreciation
equals Book Value.
For an asset’s first year depreciation,
Book Value equals Original Cost.

39. DOUBLE-DECLINING-BALANCE
FORMULA:
Book Value x 2
(Straight-Line Rate)
100% / Useful Life
For our example……
100%/5years = 20%

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

42. Double-Declining-Balance Depreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
Year
Rate 1
$40,000
40%
$16,000
Book Value x twice the Straight-Line Rate
$40,000 x 40%

43. Double-Declining-Balance Depreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
Year
Rate 1
$40,000
40%
$16,000
$16,000
First year’s depreciation is all
that has accumulated.

44. Double-Declining-Balance Depreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
Year
Rate 1
$40,000
40%
$16,000
$16,000
$24,000
Original Cost minus Accumulated Depreciation
$40,000 - $16,000

45. Double-Declining-Balance Depreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
Year
Rate 1
$40,000
40%
$16,000
$16,000
$24,000 2
$24,000
The Book Value at the end of one year
becomes the next year’s
beginning Book Value.

46. Double-Declining-Balance Depreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
Year
Rate 1
$40,000
40%
$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-Balance Depreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
Year
Rate 1
$40,000
40%
$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-Balance Depreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
Year
Rate 1
$40,000
40%
$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-Balance Depreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
Year
Rate 1
$40,000
40%
$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-Balance Depreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
Year
Rate 1
$40,000
40%
$16,000
$16,000
$24,000 2
$24,000
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
Book Value can fall only to the
amount of the Salvage Value.
$5,184 - $4,000 = $1,184 to go!!

51. Double-Declining-Balance Depreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
Year
Rate 1
$40,000
40%
$16,000
$16,000
$24,000 2
$24,000
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
Book Value x Rate = $2,073
This would be too much depreciation.
Can recognize only $1,184

52. Double-Declining-Balance Depreciation Schedule
Book Value (Beginning of Year)
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
Year
Rate 1
$40,000
40%
$16,000
$16,000
$24,000 2
$24,000
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
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 asset’s life.
Rates are then multiplied by the cost of the asset.
Abbreviated MACRS

54. The IRS would give this van a 6-year life and no salvage
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. MACRS Depreciation Schedule
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
Year
Cost
Rate 1
$40,000
IRS doesn’t allow a Salvage Value
for this asset.

56. MACRS Depreciation Schedule
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
Year
Cost
Rate 1
$40,000
20%
IRS sets the first year rate at 20%.

57. MACRS Depreciation Schedule
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
Year
Cost
Rate 1
$40,000
20%
$8,000
Cost x Rate
$40,000 x 20%

58. MACRS Depreciation Schedule
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
Year
Cost
Rate 1
$40,000
20%
$8,000
$8,000
$32,000
Cost - Accumulated Depreciation
$40,000 - $8,000

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

60. MACRS Depreciation Schedule
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
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.

61. MACRS Depreciation Schedule
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
Year
Cost
Rate
At the end of the
6 years, 100% of
the asset’s cost
will have been
recognized as
Depreciation Expense. 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%
100%

62. MACRS Depreciation Schedule
Accumulated Depreciation (end of year)
Depreciation Expense
Book Value (end of year) x =
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
100%
$40,000