Quick Guide to Depreciation  Part 2
Quick Guide to Depreciation  Part 2
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Sumoftheyears'digits depreciation
Equipment and vehicles often provide greater benefits when they are new than when they approach the end of their useful lives and more frequently require repairs. Using sumoftheyears'digits depreciation is one way for companies to assign a disproportionate share of depreciation expense to the first years of an asset's useful life. Under this method, depreciation expense is calculated using the following equation.
Calculating SumofYear'sDigits Depletion
The equation's denominator (the sum of the years' digits) can be found by adding each integer from one through the number of years in the asset's useful life (1 + 2 + 3…) or by substituting the number of years in the asset's useful life for x in the following equation.
The sum of the years' digits for an asset with a fiveyear useful life is 15.
Therefore, depreciation expense on the asset equals fivefifteenths of the depreciable cost during the first year, fourfifteenths during the second year, threefifteenths during the third year, twofifteenths during the fourth year, and onefifteenth during the last year.
The following table shows how the sumoftheyears'digits method allocates depreciation expense to the truck, which has a depreciable cost of $80,000 ($90,000 cost less $10,000 expected salvage value) and a useful life of five years.
SumoftheYears'Digits Depreciation  
Depreciable Cost 

Cost 
$90,000 

Year 1 
5/15 
× 
$80,000 
= 
$26,667 
$26,667 
63,333 
Year 2 
4/15 
× 
80,000 
= 
21,333 
48,000 
42,000 
Year 3 
3/15 
× 
80,000 
= 
16,000 
64,000 
26,000 
Year 4 
2/15 
× 
80,000 
= 
10,667 
74,667 
15,333 
Year 5 
1/15 
× 
80,000 
= 
5,333 
80,000 
10,000 
Decliningbalance depreciation
Decliningbalance depreciation provides another way for companies to shift a disproportionate amount of depreciation expense to the first years of an asset's useful life. Decliningbalance depreciation is found by multiplying an asset's net book value (not its depreciable cost) by some multiple of the straightline rate for the asset. The straightline rate is one divided by the number of years in the asset's useful life. Companies typically use twice (200%) the straightline rate, which is called the doubledecliningbalance rate, but rates of 125%, 150%, or 175% of the straightline rate are also used. Once the decliningbalance depreciation rate is determined, it stays the same for the asset's useful life.
Calculating DecliningBalance Depreciation
To illustrate doubledecliningbalance depreciation, consider the truck that has a cost of $90,000, an expected salvage value of $10,000, and a fiveyear useful life. The truck's net book value at acquisition is also $90,000 because no depreciation expense has been recorded yet. The straightline rate for an asset with a fiveyear useful life is 20% (1 ÷ 5 = 20%), so the doubledecliningbalance rate, which uses the 200% multiple, is 40% (20% x 200% = 40%). The following table shows how the doubledecliningbalance method allocates depreciation expense to the truck.
DoubleDecliningBalance Depreciation  
BeginningofYear Book Value 

Year 1 
40% 
× 
$90,000 
= 
$36,000 
$36,000 
$54,000 
Year 2 
40% 
× 
54,000 
= 
21,600 
57,600 
32,400 
Year 3 
40% 
× 
32,400 
= 
12,960 
70,560 
19,440 
Year 4 
40% 
× 
19,440 
= 
7,776 
78,336 
11,664 
At the end of an asset's useful life, the asset's net book value should equal its salvage value. Although 40% of $11,664 is $4,666, the truck depreciates only $1,664 during year five because net book value must never drop below salvage value. If the truck's salvage value were $5,000, depreciation expense during year five would have been $6,664. If the truck's salvage value were $20,000, then depreciation expense would have been limited to $12,400 during year three, and no depreciation expense would be recorded during year four or year five.
Comparing depreciation methods
All depreciation methods are designed to systematically allocate the depreciable cost of an asset to expense during the asset's useful life. Although total depreciation expense is the same no matter what depreciation method is used, the methods differ from each other in the specific assignment of depreciation expense to each year or accounting period, as shown in the following comparison of annual depreciation expense over five years using a truck's depreciable cost of $80,000.
Annual Depreciation Expense  
StraightLine Depreciation 
UnitsofActivity Depreciation 
SumoftheYears'Digits Depreciation 
DoubleDecliningBalance Depreciation 

Year 1 
$16,000 
$22,000 
$26,667 
$36,000 
Year 2 
16,000 
14,000 
21,333 
21,600 
Year 3 
16,000 
18,000 
16,000 
12,960 
Year 4 
16,000 
16,000 
10,667 
7,776 
Year 5 
16,000 
10,000 
5,333 
1,664 
$80,000 
$80,000 
$80,000 
$80,000 
The sumoftheyears'digits and doubledecliningbalance methods are called accelerated depreciation methods because they allocate more depreciation expense to the first few years of an asset's life than to its later years.
Partialyear depreciation calculations. Partialyear depreciation expense calculations are necessary when depreciable assets are purchased, retired, or sold in the middle of an annual accounting period or when the company produces quarterly or monthly financial statements. The unitsofactivity method is unaffected by partialyear depreciation calculations because the perunit depreciation expense is simply multiplied by the number of units actually used during the period in question. For all other depreciation methods, however, annual depreciation expense is multiplied by a fraction that has the number of months the asset depreciates as its numerator and twelve as its denominator. Since depreciation expense calculations are estimates to begin with, rounding the time period to the nearest month is acceptable for financial reporting purposes.
Suppose the truck is purchased on July 26 and the company's annual accounting period ends on December 31. The company must record five months of depreciation expense on December 31 (AugustDecember).
Under the straightline method, the first full year's annual depreciation expense of $16,000 is multiplied by fivetwelfths to calculate depreciation expense for the truck's first five months of use. $16,000 of depreciation expense is assigned to the truck in each of the next four years, and seven months of depreciation expense is assigned to the truck in the following year.
StraightLine Depreciation 

Depreciable Cost 

Cost 
$90,000 

Year 1 (5 mo.) 
5/12 × 20% 
× 
$80,000 
= 
$ 6,667 
$ 6,667 
83,333 
Year 2 
20% 
× 
80,000 
= 
16,000 
22,667 
67,333 
Year 3 
20% 
× 
80,000 
= 
16,000 
38,667 
51,333 
Year 4 
20% 
× 
80,000 
= 
16,000 
54,667 
35,333 
Year 5 
20% 
× 
80,000 
= 
16,000 
70,667 
19,333 
Year 6 (7 mo.) 
7/12 × 20% 
× 
80,000 
= 
9,333 
80,000 
10,000 
Under the decliningbalance method, the first full year's annual depreciation expense of $36,000 is multiplied by fivetwelfths to calculate depreciation expense for the truck's first five months of use. In subsequent years, the truck's net book value is higher than it would have been if a full year's depreciation expense had been assigned during the first year, but the decliningbalance method's calculation of depreciation expense is otherwise unchanged.
DoubleDecliningBalance Depreciation  
BeginningofYear Book Value 

Year 1 (5 mo.) 
5/12 × 40% 
× 
$90,000 
= 
$15,000 
$15,000 
$75,000 
Year 2 
40% 
× 
75,000 
= 
30,000 
45,000 
45,000 
Year 3 
40% 
× 
45,000 
= 
18,000 
63,000 
27,000 
Year 4 
40% 
× 
27,000 
= 
10,800 
73,800 
16,200 
Year 5 
40% 
× 
16,200 
= 
6,200 * 
80,000 
10,000 
Year 6 (7 mo.) 
0 
80,000 
10,000 
Continuing from our previous article "Quick Guide to Depreciation  part 1"
Sumoftheyears'digits depreciation
Equipment and vehicles often provide greater benefits when they are new than when they approach the end of their useful lives and more frequently require repairs. Using sumoftheyears'digits depreciation is one way for companies to assign a disproportionate share of depreciation expense to the first years of an asset's useful life. Under this method, depreciation expense is calculated using the following equation.
Calculating SumofYear'sDigits Depletion
The equation's denominator (the sum of the years' digits) can be found by adding each integer from one through the number of years in the asset's useful life (1 + 2 + 3…) or by substituting the number of years in the asset's useful life for x in the following equation.
The sum of the years' digits for an asset with a fiveyear useful life is 15.
Therefore, depreciation expense on the asset equals fivefifteenths of the depreciable cost during the first year, fourfifteenths during the second year, threefifteenths during the third year, twofifteenths during the fourth year, and onefifteenth during the last year.
The following table shows how the sumoftheyears'digits method allocates depreciation expense to the truck, which has a depreciable cost of $80,000 ($90,000 cost less $10,000 expected salvage value) and a useful life of five years.
SumoftheYears'Digits Depreciation  
Depreciable Cost 

Cost 
$90,000 

Year 1 
5/15 
× 
$80,000 
= 
$26,667 
$26,667 
63,333 
Year 2 
4/15 
× 
80,000 
= 
21,333 
48,000 
42,000 
Year 3 
3/15 
× 
80,000 
= 
16,000 
64,000 
26,000 
Year 4 
2/15 
× 
80,000 
= 
10,667 
74,667 
15,333 
Year 5 
1/15 
× 
80,000 
= 
5,333 
80,000 
10,000 
Decliningbalance depreciation
Decliningbalance depreciation provides another way for companies to shift a disproportionate amount of depreciation expense to the first years of an asset's useful life. Decliningbalance depreciation is found by multiplying an asset's net book value (not its depreciable cost) by some multiple of the straightline rate for the asset. The straightline rate is one divided by the number of years in the asset's useful life. Companies typically use twice (200%) the straightline rate, which is called the doubledecliningbalance rate, but rates of 125%, 150%, or 175% of the straightline rate are also used. Once the decliningbalance depreciation rate is determined, it stays the same for the asset's useful life.
Calculating DecliningBalance Depreciation
To illustrate doubledecliningbalance depreciation, consider the truck that has a cost of $90,000, an expected salvage value of $10,000, and a fiveyear useful life. The truck's net book value at acquisition is also $90,000 because no depreciation expense has been recorded yet. The straightline rate for an asset with a fiveyear useful life is 20% (1 ÷ 5 = 20%), so the doubledecliningbalance rate, which uses the 200% multiple, is 40% (20% x 200% = 40%). The following table shows how the doubledecliningbalance method allocates depreciation expense to the truck.
DoubleDecliningBalance Depreciation  
BeginningofYear Book Value 

Year 1 
40% 
× 
$90,000 
= 
$36,000 
$36,000 
$54,000 
Year 2 
40% 
× 
54,000 
= 
21,600 
57,600 
32,400 
Year 3 
40% 
× 
32,400 
= 
12,960 
70,560 
19,440 
Year 4 
40% 
× 
19,440 
= 
7,776 
78,336 
11,664 
At the end of an asset's useful life, the asset's net book value should equal its salvage value. Although 40% of $11,664 is $4,666, the truck depreciates only $1,664 during year five because net book value must never drop below salvage value. If the truck's salvage value were $5,000, depreciation expense during year five would have been $6,664. If the truck's salvage value were $20,000, then depreciation expense would have been limited to $12,400 during year three, and no depreciation expense would be recorded during year four or year five.
Comparing depreciation methods
All depreciation methods are designed to systematically allocate the depreciable cost of an asset to expense during the asset's useful life. Although total depreciation expense is the same no matter what depreciation method is used, the methods differ from each other in the specific assignment of depreciation expense to each year or accounting period, as shown in the following comparison of annual depreciation expense over five years using a truck's depreciable cost of $80,000.
Annual Depreciation Expense  
StraightLine Depreciation 
UnitsofActivity Depreciation 
SumoftheYears'Digits Depreciation 
DoubleDecliningBalance Depreciation 

Year 1 
$16,000 
$22,000 
$26,667 
$36,000 
Year 2 
16,000 
14,000 
21,333 
21,600 
Year 3 
16,000 
18,000 
16,000 
12,960 
Year 4 
16,000 
16,000 
10,667 
7,776 
Year 5 
16,000 
10,000 
5,333 
1,664 
$80,000 
$80,000 
$80,000 
$80,000 
The sumoftheyears'digits and doubledecliningbalance methods are called accelerated depreciation methods because they allocate more depreciation expense to the first few years of an asset's life than to its later years.
Partialyear depreciation calculations. Partialyear depreciation expense calculations are necessary when depreciable assets are purchased, retired, or sold in the middle of an annual accounting period or when the company produces quarterly or monthly financial statements. The unitsofactivity method is unaffected by partialyear depreciation calculations because the perunit depreciation expense is simply multiplied by the number of units actually used during the period in question. For all other depreciation methods, however, annual depreciation expense is multiplied by a fraction that has the number of months the asset depreciates as its numerator and twelve as its denominator. Since depreciation expense calculations are estimates to begin with, rounding the time period to the nearest month is acceptable for financial reporting purposes.
Suppose the truck is purchased on July 26 and the company's annual accounting period ends on December 31. The company must record five months of depreciation expense on December 31 (AugustDecember).
Under the straightline method, the first full year's annual depreciation expense of $16,000 is multiplied by fivetwelfths to calculate depreciation expense for the truck's first five months of use. $16,000 of depreciation expense is assigned to the truck in each of the next four years, and seven months of depreciation expense is assigned to the truck in the following year.
StraightLine Depreciation 

Depreciable Cost 

Cost 
$90,000 

Year 1 (5 mo.) 
5/12 × 20% 
× 
$80,000 
= 
$ 6,667 
$ 6,667 
83,333 
Year 2 
20% 
× 
80,000 
= 
16,000 
22,667 
67,333 
Year 3 
20% 
× 
80,000 
= 
16,000 
38,667 
51,333 
Year 4 
20% 
× 
80,000 
= 
16,000 
54,667 
35,333 
Year 5 
20% 
× 
80,000 
= 
16,000 
70,667 
19,333 
Year 6 (7 mo.) 
7/12 × 20% 
× 
80,000 
= 
9,333 
80,000 
10,000 
Under the decliningbalance method, the first full year's annual depreciation expense of $36,000 is multiplied by fivetwelfths to calculate depreciation expense for the truck's first five months of use. In subsequent years, the truck's net book value is higher than it would have been if a full year's depreciation expense had been assigned during the first year, but the decliningbalance method's calculation of depreciation expense is otherwise unchanged.
DoubleDecliningBalance Depreciation  
BeginningofYear Book Value 

Year 1 (5 mo.) 
5/12 × 40% 
× 
$90,000 
= 
$15,000 
$15,000 
$75,000 
Year 2 
40% 
× 
75,000 
= 
30,000 
45,000 
45,000 
Year 3 
40% 
× 
45,000 
= 
18,000 
63,000 
27,000 
Year 4 
40% 
× 
27,000 
= 
10,800 
73,800 
16,200 
Year 5 
40% 
× 
16,200 
= 
6,200 * 
80,000 
10,000 
Year 6 (7 mo.) 
0 
80,000 
10,000 
Under the sumoftheyears'digits method, the first full year's annual depreciation expense of $26,667 is multiplied by fivetwelfths to calculate depreciation expense for the truck's first five months of use. During the second year, depreciation expense is calculated in two steps. The remaining seventwelfths of the first full year's annual depreciation expense of $26,667 is added to fivetwelfths of the second full year's annual depreciation expense of $21,333. This twostep calculation continues until the truck's final year of use, at which time depreciation expense is calculated by multiplying the last full year's annual depreciation expense of $5,333 by seventwelfths.
Revising depreciation estimates. Depreciation expense calculations depend upon estimates of an asset's useful life and expected salvage value. As time passes, a number of factors may cause these estimates to change. For example, after recording three years of depreciation expense on the truck, suppose the company decides the truck should be useful until it is seven rather than five years old and that its salvage value will be $14,000 instead of $10,000. Prior financial statements are not changed when useful life or salvage value estimates change, but subsequent depreciation expense calculations must be based upon the new estimates of the truck's useful life and depreciable cost.
Under the straightline method, depreciation expense for years four through seven is calculated according to the following equation.
Revising StraightLine Depreciation
Assume that the company purchased the truck at the beginning of an annual accounting period. The previous table shows how depreciation expense was calculated during the truck's first three years of use. The truck's net book value of $42,000 at the end of year three is reduced by the new, $14,000 estimate of salvage value to produce a revised depreciable cost of $28,000. The revised depreciable cost is divided by the four years now estimated to remain in the truck's useful life, yielding annual depreciation expense of $7,000.
Similar revisions are made for each of the other depreciation methods. The asset's net book value when the revision is made along with new estimates of salvage value and useful life—measured in years or units—are used to calculate depreciation expense in subsequent years.
use one depreciation method for financial reporting purposes and a different method for income tax purposes. Tax laws are complex and tend to change, at least slightly, from year to year. Therefore, this book does not attempt to explain specific income tax depreciation methods, but it is important to understand why most companies choose different income tax and financial reporting depreciation methods.
For financial reporting purposes, companies often select a depreciation method that apportions an asset's depreciable cost to expense in accordance with the matching principle. For income tax purposes, companies usually select a depreciation method that reduces or postpones taxable income and, therefore, tax payments. In the United States, straightline depreciation is the method companies most frequently use for financial reporting purposes, and a special type of accelerated depreciation designed for income tax returns is the method they most frequently use for income tax purposes.
For more information regarding this article, please refer to:
http://www.cliffsnotes.com/study_guide/DepreciationofOperatingAssets.topicArticleId21081,articleId21076.html
You can find the guide of other depreciation method in our previous article "Quick Guide to Depreciation  part 1"