9.2 Depreciation Calculations

The C/Books Fixed Asset System calculates depreciation on each fixed asset using the depreciation method that was entered into Method field for the asset. The different depreciation methods are described below. An example asset is used to demonstrate each of the methods (excluding the Accelerated Recovery Method (acrs) and the Modified Accelerated Recovery Method (macrs) which use other example assets). The following table describes the example asset.

Purchase Cost: $325.00

Salvage Value: $ 25.00

Useful Life: 3 years

Periods in Year: 12

Percent: 200

Active: yes

The Purchase Cost, Useful Life, and Periods in Year parameters are used in all the methods of depreciation. Salvage Value is used with the straight line, declining balance, and the declining balance with switch to straight line methods. The declining balance and declining balance with switch to straight line methods use the Percent parameter.

This process does not depreciate an asset for an amount greater than the purchase cost minus the salvage value. Although the salvage value is not used in the double declining balance calculations, if there is a value greater than zero in the Salvage Value field, the asset is not depreciated past the value of the purchase cost less the salvage value.

Straight Line (sl)

The straight line depreciation method depreciates the asset by a constant amount every year. The yearly depreciation amount is calculated by first subtracting the salvage value from the purchase cost and then dividing the difference by the useful life of the asset. The yearly amount is then divided by the number of periods in the accounting year to get the depreciation amount for the period.

Using the straight line method, our example asset is depreciated every period as follows.

yearly amount = 325.00 - 25.00 / 3 = 100.00

period amount = 100.00 / 12 = 8.33

The yearly depreciation schedule would be as follows.

Year Depreciation Expense Accumulated Depreciation Book Value

At acquisition $325.00

1 $100.00 $100.00 $225.00

2 $100.00 $200.00 $125.00

3 $100.00 $300.00 $25.00

Declining Balance (ddb)

This is an accelerated method of depreciation that ignores the salvage value of the asset while calculating the yearly depreciation expense, but will not depreciate the asset below the salvage value. The yearly depreciation expense is calculated by multiplying a constant rate times the decreasing book value. (The book value is the purchase cost minus the accumulated depreciation.) The constant rate is the straight line rate (1 useful life) times the percent. The depreciation expense amount for a period is calculated by dividing the yearly depreciation expense amount by the number of periods in the accounting year.

The yearly depreciation expense amount is calculated for our example asset as follows.

straight line rate = 1 / 3 years = 0.333

constant rate = 0.333 x 2 = 0.667

yearly expense = 0.667 x book value

The yearly depreciation schedule for the first two years is displayed below.

Depreciation Accumulated Year Computations Expense Depreciation Book Value

At acquisition $325.00

1 0.667 x 325.00 216.78 216.78 108.22

2 0.667 x 108.22 72.18 288.96 36.04

The example asset has a salvage value of $25 which means that it cannot be depreciated below $25. The declining balance method depreciates this asset to $25 before the end of the third year. The yearly depreciation expense amount for the third year is initially calculated as:

yearly expense = 0.667 x 36.04 = 24.04

This amount is divided by 12 to get the period depreciation amount.

period expense = 24.04 / 12 = 2.00

The asset is depreciated each month by the period expense amount, $2.00, until its book value is equal to its salvage value of $25. The depreciation schedule for the third year is as follows:

Depreciation Accumulated Period Expense Depreciation Book Value

Start of year 3 288.96 36.04

1 2.00 290.96 34.04

2 2.00 292.96 32.04

3 2.00 294.96 30.04

4 2.00 296.96 28.04

5 2.00 298.96 26.04

6 1.04 300.00 25.00

Notice that the example asset is completely depreciated by the sixth period in the third year.

The period depreciation expense amount for the first two years is shown below:

Year Computation Depreciation Expense

1 216.78 / 12 18.07

2 72.18 / 12 6.02

Declining Balance with Switch to Straight Line (dbsl)

This method starts out depreciating the asset using the double declining balance method. It switches to the straight line method when the depreciation calculated using the straight line method is greater than it is using the declining balance method.

The following depreciation expense amounts for the example asset are taken from the two previous examples.

Year Depreciation Expense sl ddb

1 100.00 216.78

2 100.00 72.18

3 100.00 24.04

The above table shows that the depreciation expense calculated using the straight line method is greater starting in the second year. The depreciation schedule is as follows.

Depreciation Accumulated Year Computations Expense Depreciation Book Value

At acquisition 325.00

1 0.667 x 325.00 216.78 216.78 108.22

2 0.333 x 300.00 100.00 316.78 8.22

As you can see, if the example asset is depreciated by the entire yearly depreciation expense amount for the second year, its book value falls below its salvage value of $25. This means that the asset is completely depreciated sometime during the second year. The depreciation expense amount for a period in the second year is $100.00 divided by 12 or $8.33. The following table shows the depreciation schedule for the second year.

Depreciation Accumulated Period Expense Depreciation Book Value

Start of year 3 288.96 36.04

1 2.00 290.96 34.04

2 2.00 292.96 32.04

3 2.00 294.96 30.04

4 2.00 296.96 28.04

5 2.00 298.96 26.04

6 1.04 300.00 25.00

7 8.33 275.09 49.91

8 8.33 283.42 41.58

9 8.33 291.75 33.25

10 8.25 300.00 25.00

The example asset is completely depreciated by period 10 of the second year.

Sum of years' digits (syd)

This method is calculated by first subtracting the salvage value from the purchase cost. The difference is then multiplied by a fractional amount that becomes smaller each year. The yearly fractional amounts have as their denominator the sum of the digits comprising the useful life. The specific year of life in inverse order is the value in the numerator. The example asset is depreciated as follows.

Denominator is: 1 / 2 / 3 = 6

Numerators are: 3, 2, 1

The yearly fractions are:

Year Fraction

1 3/6

2 2/6

3 1/6

The yearly depreciation schedule for the example asset is as follows.

Depreciation Accumulated Year Computations Expense Depreciation Book Value

At acquisition 325.00

1 300.00 x 3/6 150.00 150.00 175.00

2 300.00 x 2/6 100.00 250.00 75.00

3 300.00 x 1/6 50.00 300.00 25.00

The period depreciation expense amount for each year is the the yearly expense amount divided by the number of periods in the accounting year.

Year Period depreciation expense

1 150.00 / 12 = 12.50

2 100.00 / 12 = 8.33

3 50.00 / 12 = 4.17

Accelerated Cost Recovery System (acrs)

This method of depreciation is a creation of the IRS, and based strictly on a calendar year. In order to use this method, an asset must be placed in service after December 31, 1980 and before January 1, 1987.

Depreciation is calculated by subtracting the adjustment amount from the purchase cost and then multiplying that difference by a percentage. The percentage is taken from one of the standard IRS tables which is entered into the system through the menu selection ACRS Tables under the Select, Fixed Assets menu. The table used is specified on the second part of the Fixed Assets form in the field ACRS Method table. The percentage taken from the table depends on the the specific year being depreciated.

The example asset used to demonstrate acrs depreciation has the following characteristics.

Purchase Cost: $2,600.00

Useful Life: 5 years

Date of Service: 06/15/86

Adjustment: $100.00

ACRS Method table: 5-year

Periods in Year: 12

Active: yes

The 5-year table used in this example contains the percentages specified by the IRS for 5-year recovery property, and is shown below.

Year Percentage

1 15

2 22

3-5 2

The yearly depreciation expense amount is calculated as follows.

basis = 2,600.00 - 100.00 = 2,500.00

yearly expense = percentage x 2,500.00

The yearly depreciation schedule is shown below.

Depreciation Accumulated Year Computations Expense Depreciation Book Value

At acquisition 2,600.00

1 0.15 x 2,500.00 375.00 375.00 2,225.00

2 0.22 x 2,500.00 550.00 925.00 1,675.00

3 0.21 x 2,500.00 525.00 1,075.00 1,150.00

4 0.21 x 2,500.00 525.00 1,600.00 625.00

5 0.21 x 2,500.00 525.00 2,125.00 100.00

When using the acrs method of depreciation, the IRS considers all or any part of the first year as a full fiscal year. This means that, as in our example, since the asset's first period of depreciation begins in June, you may still take depreciation for the full fiscal year. However, you divide the full first fiscal year's depreciation by the remaining periods of the first fiscal year: seven.

If you had purchased the asset in October, you would divide the first full year's depreciation by 3, the number of remaining periods in the first year. You take credit for a full year of depreciation whether you acquire the asset in period 1 or period 12, using the percentage allowable by the IRS. After the first year's depreciation, each subsequent year is divided into 12 equal periods and depreciation is taken on a full year's basis, period by period. Remember you must enter the IRS percentage tables through the Enter ACRS Tables form which is accessed from the menu selection ACRS Tables under the Select, Fixed Assets menu.

Now, back to our example. The asset was acquired in June and we wish to start depreciation in that period, leaving seven periods left for the first year. In the first year, the period depreciation amount is 53.57, i.e. 375.00 (the full year's depreciation) divided by the remaining 7 periods of the first year. The period depreciation amount for the second year is 45.83 (550.00 divided by 12.)

Annual Number of Period Depreciation Year Amount Periods Calculations

1986 375.00 7 375.00 / 7 = 53.57

1987 550.00 12 550.00 / 12 = 45.83

1988 525.00 12 525.00 / 12 = 43.75

1989 525.00 12 525.00 / 12 = 43.75

1990 525.00 12 525.00 / 12 = 43.75

Alternate Accelerated Recovery Method

Assets placed in service after December 31, 1980 and before January 1, 1987 may be depreciated using the alternate acrs method. This method uses a modified version of the straight line method to calculate depreciation. Like the acrs method, depreciation is calculated by subtracting the adjustment amount from the purchase cost and then multi-plying that difference by a percentage. The percentage is determined by dividing 100 by the useful life of the asset.

In some cases you must also apply the half-year convention. When you apply the half-year convention, only a half year of depreciation is taken for the first year the asset is placed in service regardless of when in the tax year the asset was placed in service. For each of the remaining years of the useful life of the asset you take a full year's depreciation. If you retain the asset for the entire useful life of the asset, a half year of depreciation can be taken for the year following the last year of useful life.

The following example asset is the same one used to demonstrate the acrs method except instead of specifying an ACRS Method table, the straight line method is used by entering yes in the ACRS Method sl field. The half-year convention is applied by entering yes in the convention field Half-year. The following describes the example asset.

Useful Life: 5 years

Date of Service: 06/15/86

Purchase Cost: $2,600.00

Adjustment: $100.00

Half-year yes

ACRS Method sl: yes

The yearly depreciation expense is calculated as shown.

basis = 2,600.00 - 100.00 = 2,500.00

percentage = 100 / 5 = 20%

yearly expense = 0.20 x 2,500.00 = 500.00

half-year convention = 500.00 / 2 = 250.00

The table below shows the yearly depreciation schedule.

Depreciation Accumulated Year Computations Expense Depreciation Book Value

At acquisition 2,600.00

1 0.20 x 2,500.00 / 2 250.00 250.00 2,350.00

2 0.20 x 2,500.00 500.00 750.00 1,850.00

3 0.20 x 2,500.00 500.00 1,250.00 1,350.00

4 0.20 x 2,500.00 500.00 1,750.00 850.00

5 0.20 x 2,500.00 500.00 2,250.00 350.00

6 0.20 x 2,500.00 / 2 250.00 2,500.00 100.00

As with the standard acrs method, the IRS considers all or any part of the first year as a full fiscal year, so depreciation is taken for the full fiscal year even though the asset's first period of depreciation begins in June. The depreciation amount for the first year is divided by 7, the number of periods remaining in the first year, to get the depreciation for each period. The depreciation amount for each subsequent year is divided by 12 to get the period depreciation. The period depreciation schedule is shown below.

Annual Number of Period Depreciation Year Amount Periods Calculations

1986 250.00 7 250.00 / 7 = 35.71

1987 500.00 12 500.00 / 12 = 41.67

1988 500.00 12 500.00 / 12 = 41.67

1989 500.00 12 500.00 / 12 = 41.67

1990 500.00 12 500.00 / 12 = 41.67

1991 250.00 12 250.00 / 12 = 20.83

ACRS Method with Limits

The IRS places annual dollar limits on the depreciation that can be taken on some types of assets that are depreciated using the ACRS method. These limits must be entered into the system through the menu choice Depreciation Limits under the Select, Fixed Assets menu. The limits to be applied to a particular asset are specified by entering the limit table code in the Limit Table field on the second part of the asset form.

The annual depreciation is calculated as described above using either the standard acrs method or the alternate acrs method. A comparison is made with the limit, and the asset is depreciated by the lower amount.

The following asset will be used to demonstrate an acrs asset with limits.

Purchase Cost: $25,000

Date of Service: 03/03/86

Useful Life: 3 years

Method: acrs

Adjustment: $0.00

ACRS Method table: 3-year recovery

Limit Table: 3-year

The acrs percentages entered for the 3-year recovery table are shown below.

Year Percent

1 25

2 38

3 37

The limits on depreciation are as follows.

Year Limit

1 3,200.00

2-3 4,800.00

The depreciation schedule is shown below.

Computed Depreciation Accumulated Year Depreciation Limit Expense Depreciation Book Value

At acquisition 25,000.00

1 6,250.00 3,200.00 3,200.00 3,200.00 21,800.00

2 9,500.00 4,800.00 4,800.00 4,800.00 17,000.00

3 9,500.00 4,800.00 4,800.00 4,800.00 12,200.00

Early Disposition of ACRS Property

If an asset, that is being depreciated using either of the acrs methods, is disposed of before the end of its useful life, the IRS generally will not allow depreciation for the year in which the asset is disposed. Assets covered by this rule usually are 3-year, 5-year, or 10-year properties.

On the other hand, the IRS does allow depreciation to be taken in the year of disposition for other types of properties such as 15-year, 18-year, or 19-year properties. In these cases depreciation is based on the number of months the asset was in use. Sometimes a full-month or a mid-month convention must also be applied to the depreciation amount.

If a full-month convention is applied, no depreciation is allowed for the month in which the asset is disposed. If a mid-month convention is applied, a half a month's depreciation is taken for the month in which the asset was disposed regardless of when in the month the disposition took place.

The following example asset demonstrates the early disposition of a 15-year property using the full-month convention.

Date of Service: 04/02/84

Useful Life: 15 years

Purchase Cost: $98,000.00

Method: acrs

Date of Disposal: 06/11/87

ACRS Method table: 15-year

Deduction in year of

disposition: yes

Full-month Convention: yes

The acrs percentages for 15-year property are shown below.

Year Percent

1 10

2 11

3 9

4 8

5 7

6-9 6

10-15 5

16 1

Depreciation Accumulated Year Computations Expense Depreciation Book Value

At acquisition 98,000.00

1 0.10 x 98,000.00 9,800.00 9,800.00 88,200.00

2 0.11 x 98,000.00 10,780.00 20,580.00 77,420.00

3 0.09 x 98,000.00 8,820.00 29,400.00 68,600.00

4 0.08 x 98,000.00 x 5/12 3,266.67 32,666.67 65,333.33

Since the asset was disposed of in the sixth month of 1987, the depreciation for 1987 is pro-rated for the first five months of 1987.

Modified Accelerated Cost Recovery System (macrs)

In 1987 the IRS replaced the Accelerated Cost Recovery method with the Modified Accelerated Cost Recovery method (macrs). This method can only be used on assets placed in service after December 31, 1986. Under macrs, depreciation is calculated by using either the straight line method or the declining balance with switch to straight line method and by applying one of three different conventions: half-year, mid-month, or mid-quarter.

The rate used in the declining balance method is calculated by dividing the specified declining balance percentage by the useful life of the asset. The straight line rate is calculated by dividing the number 100 by the number of years remaining in the useful life of the asset.

The IRS has various rules for determining which convention should be applied. The rules for applying the half-year convention or the mid-month convention are generally based on the type of asset being depreciated. The application of the mid-quarter convention depends on the relative cost of the assets placed in service in the last quarter of the year in relation to the total cost of assets placed in service during the year.

All three of these conventions are applied to the first year of depreciation as well as to the depreciation for the year the asset is disposed, if it is disposed before the end of its useful life.

When the half-year convention is applied, a half year of depreciation is taken for the first year the asset is placed in service regardless of what month the asset was placed in service. A full year's depreciation is taken each year for the remainder of the useful life of the asset. If the asset is disposed before the end of its useful life, a half year of depreciation is taken for the year of disposal regardless of the month in which the asset was disposed. If the asset is kept for the asset's entire useful life, a half year of depreciation is taken in the year following the last year of its useful life.

If the mid-month convention is applied, the asset is considered to have been placed in service in the middle of the month and a half a month's depreciation is calculated for the month the asset is placed in service. If an asset is disposed before the end of its useful life, it is considered to have been disposed in the middle of the month and half a month's depreciation is calculated for the month in which the asset is disposed.

When the mid-quarter convention is applied, depreciation is calculated as if the asset was placed in service or disposed at the mid-point of the quarter. For example, if an asset is placed in service January 1, 1987, depreciation would be calculated as if the asset had been placed in service in the middle of February, the midpoint of the first quarter.

The following examples demonstrate various ways of calculating depreciation under the MACRS method. In the first example, the asset is depreciated using the declining balance with switch to straight line and the half-year convention is applied.

The following parameters are entered for the example asset.

Useful Life: 7 years

Purchase Cost: $11,000.00

Adjustment: $1,000.00

Percent: 200

Method: macrs

MACRS Method ddb: yes

Half-year Convention: yes

The declining balance (ddb) and straight line (sl) rates are calculated as follows.

ddb rate = percent / useful life

sl rate = 100 / remaining useful life

The table below shows the declining balance and straight line rates for the 7-year example asset.

Declining Balance Straight Line Year Calculation Rate Calculation Rate

1 200 / 7 28.57% 100 / 7.0 14.28%

2 200 / 7 28.57% 100 / 6.5 15.38%

3 200 / 7 28.57% 100 / 5.5 18.18%

4 200 / 7 28.57% 100 / 4.5 22.28%

5 200 / 7 28.57% 100 / 3.5 28.57%

6 200 / 7 28.57% 100 / 2.5 40.00%

7 200 / 7 28.57% 100 / 1.5 66.67%

8 200 / 7 28.57% 100 / 0.5 200.00%

As a result of the application of the half-year convention, the remaining useful life used in the straight line rate calculation for the second year of depreciation, decreases by only a half year because only a half year of depreciation is taken in the first year. This leaves a half year of depreciation at the end of the useful life of the asset which is taken in the eighth year.

The basis for depreciation is calculated as follows.

basis = Purchase Cost - Adjustment

basis = 11,000.00 - 1,000.00 = 10,000.00

The table below shows the depreciation schedule.

Depreciation Accumulated Year Computations Expense Depreciation Book Value

At acquisition 11,000.00

1 0.2857 x 10,000.00 / 2 1,428.50 1,428.50 8,571.50

2 0.2857 x 8,571.50 2,448.88 3,877.38 6,122.62

3 0.2857 x 6,122.62 1,749.23 5,626.61 4,373.39

4 0.2857 x 4,373.39 1,249.48 6,876.09 3,123.91

5 0.2857 x 3,123.91 892.50 7,768.59 2,231.41

6 0.40 x 2,231.41 892.56 8,661.15 1,338.85

7 0.6667 x 1,338.85 892.61 9,553.76 446.24

8 2.000 x 446.24 / 2 446.24 10,000.00 0.00

In the next example, an asset is depreciated using the straight line method with the mid-month convention. The following parameters are entered for the example asset.

Useful Life: 30 years

Purchase Cost: $100,000.00

Date of Service: 10/08/87

Date of Disposal: 06/01/93

Method: macrs

MACRS Method sl: yes

Mid-Month Convention: yes

In the first year, depreciation is calculated for 2.5 months, half of October and all of November and December. The asset is disposed before the end of its useful life in June of the sixth year. Depreciation for the disposal year is calculated for months January through May and half of June, 5.5 months. The table below shows the depreciation schedule for this asset.

Depreciation Accumulated Year Computations Expense Depreciation Book Value

At acquisition 11,000.00

1 100,000.0 / 30 x 2.5 / 12 694.44 694.44 99,305.56

2 99,305.56 / 29.79 3,333.52 3,877.38 95,972.04

3 95,972.04 / 28.79 3,333.52 7,210.90 92,638.52

4 92,638.52 / 27.79 3,333.52 10,544.42 89,305.00

5 89,305.00 / 26.79 3,333.52 13,877.94 85,971.48

6 85,971.48 / 25.79 3,333.52 17,211.46 82,637.96

7 82,637.96 / 24.79 x 5.5 / 12 1,527.86 18,739.32 81,110.10

The next example asset demonstrates MACRS depreciation with the mid-quarter convention.

Useful Life: 5 years

Purchase Cost: $5,000.00

Date of Service: 09/07/87

Method: macrs

MACRS Method ddb: yes

Mid-quarter Convention: yes

The declining balance (ddb) rate is calculated as follows.

ddb rate = percent / useful life

ddb rate = 200 / 5 = 40%

Starting in the fourth year depreciation is calculated using the straight line rate. The straight line (sl) rates for the fourth in fifth years are calculated as follows.

sl rate = 100 / remaining useful life

sl rate - 4th year = 100 / 2 = 50%

sl rate - 5th year = 100 / 1 = 100%

The asset is placed in service in the third quarter of the 1987. Depreciation is calculated as of the middle of the third quarter (i.e. depreciation is calculated for 4 and a half months for 1987).

Depreciation Accumulated Year Computations Expense Depreciation Book Value

At acquisition 11,000.00

1 0.40 x 5,000.00 x 4.5 / 12 750.00 750.00 4,250.00

2 0.40 x 4,250.00 1,700.00 2,450.00 2,550.00

3 0.40 x 2,550.00 1,020.00 3,470.00 1,530.00

4 0.50 x 1,530.00 765.00 4,235.00 765.00

5 1.00 x 765.00 765.00 5,000.00 0.00

MACRS Method with Limits

The IRS places limits on the annual depreciation for certain kinds of assets depreciated using the macrs method. Tables describing these limits must be entered into the system through the menu choice Depreciation Limits under the Select, Fixed Assets menu. A limits table consists of a code identifying the table, a description of the table, and the limits on depreciation for each year.

The table below shows a limits table for an asset with a useful life of 5 years.

Year Limit

1 2,560.00

2-3 4,100.00

3 2,450.00

4-5 1,475.00

The following example asset demonstrates the depreciation with limits applied from the table above.

Useful Life: 5 years

Purchase Cost: $15,000.00

Date of Service: 05/04/87

Method: macrs

Percent: 200

Adjustment: $0.00

MACRS Method ddb: yes

Half-year Convention: yes

Limit Table: 5-year recovery

The basis for depreciation is

basis = purchase cost - adjustment

basis = 15,000.00 - 0.00 = 15,000.00

The declining balance (ddb) rate used the first 3 years is computed as follows.

ddb rate = percent / 100 / useful life

ddb rate = 200 / 5 = 40%

The straight line (sl) rates for years 4 and 5 are:

sl rate = 100 / remaining useful life

sl rate - 4th year = 100 / 2 = 50%

sl rate - 5th year = 100 / 1 = 100%

The half-year convention is applied to the depreciation calculated for the year the asset was placed in service, the first year of depreciation.

depreciation = 0.40 x 15,000 / 2 = 3,000.00

The following table shows how the depreciation is calculated when limits are applied.

Computed Depreciation Accumulated Year Depreciation Limit Expense Depreciation Book Value

At acquisition 15,000.00

1 3,000.00 2,560.00 2,560.00 2,560.00 12,440.00

2 4,976.00 4,100.00 4,100.00 6,660.00 8,340.00

3 3,336.00 2,450.00 2,450.00 9,110.00 5,890.00

4 2,945.00 1,475.00 1,475.00 10,585.00 4,415.00

5 4,415.00 1,475.00 1,475.00 12,060.00 2,940.00