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Accelerated Depreciation

Author: Sophia

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1. Accelerated Depreciation

Accelerated depreciation should be used if we have assets that are used more heavily in their earlier years. These are assets that contribute more to production during their earlier years, and lose their functionality over time.

EXAMPLE

Vehicles, for example, are more heavily used in their earlier years. As the wear and tear starts to catch up with a vehicle, it loses its functionality over time.

A main benefit of accelerated depreciation is that there is a reduced time period for writing off that asset's cost, which helps to reduce taxes. This is due to the fact that In the earlier years of that asset's life, you're recording a higher level of depreciation, a greater expense, which will help reduce your taxes.

There are several methods of accelerated depreciation:

  • MACRS and ACRS
  • Sum of the year's digits
  • Units of production
  • Double declining balance

1a. MACRS and ACRS

MACRS stands for Modified Accelerated Cost Recovery System, and ACRS is Accelerated Cost Recovery System. These are used when reporting information to the IRS, so when doing your taxes, you need to use MACRS and ACRS as your depreciation method.

1b. Sum of the Year's Digits

Let's take a look at the formula to calculate depreciation using sum of the year's digits. We take the remaining life of the asset as of the beginning of the year and divide it by the sum of the years of the useful life.

formula to know
Sum of the Year's Digits
fraction numerator R e m a i n i n g space l i f e space left parenthesis b e g i n n i n g space o f space t h e space y e a r right parenthesis over denominator S u m space o f space t h e space y e a r s space o f space t h e space u s e f u l space l i f e end fraction

This means that if we have an asset with a five-year useful life, our denominator is going to be 5 + 4 + 3 + 2 + 1, or 15. This is how we would set up the calculation for sum of the year's digits--and where it gets its name.

1c. Units of Production

Another method, units of production, is beneficial for machinery. If you have machinery that is used in your production process, it might have a useful life expressed in hours. This could be the number of hours it can be in the production process or the number of units that it can produce.

The formula for units of production takes our depreciable base and multiplies it by the hours this year--the hours that the asset was used during the year--and divides it by the total estimated hours for that asset.

formula to know
Units of Production
fraction numerator D e p r e c i a b l e space b a s e space cross times space H o u r s space t h i s space y e a r over denominator T o t a l space e s t i m a t e d space h o u r s end fraction

Note, this formula can also be used for units. In this case, you would take the depreciable base, multiply it by units this year, and divide it by total estimated units.

1d. Double Declining Balance

Last, but certainly not least, is double declining balance, which is the most common accelerated depreciation method. One interesting thing about the double declining balance method is that it does not deduct the salvage value when computing the depreciable base.


2. Double Declining Balance Example

To further explain double declining balance, let's look at an example of calculating depreciation using the double declining balance method.

step by step
  1. The first step is to determine the straight line rate of depreciation for the year. In this case, we're going to take an asset with a total book value of $500,000 and a useful life of five years. Now, our straight line depreciation would be $100,000 per year, which is $500,000 divided by 5. We need to express that as a straight line depreciation percentage, which is 20% each year.

    This table for example facts has two columns. The items and entries in these columns are as follows:
Total book value $500,000
Useful value 5 years

Straight-line depreciation in dollars $100,000
Straight-line depreciation in percentage 20%
To calculate the straight-line depreciation percentage, 100,000 is divided by 500,000.
Double declining balance in percentage is blank.

  2. The next step is to multiply that straight line depreciation rate by 2, which gives us our double declining balance rate.

    This table for example facts has two columns. The items and entries in these columns are as follows:
Total book value $500,000
Useful value 5 years

Straight-line depreciation in dollars $100,000
Straight-line depreciation in percentage 20%
Double declining balance in percentage 40%

  3. Now that we have the rate for our double declining balance, we can start preparing our depreciation schedule. The depreciation schedule contains the following columns:
    • Year
    • Book value at the beginning of the year
    • Depreciation rate
    • Depreciation expense
    • Accumulated depreciation
    • Book value at the end of the year

    The table for example facts has two columns. The items and entries in these columns are as follows:
Total book value $500,000
Useful value 5 years

Straight-line depreciation in dollars $100,000
Straight-line depreciation in percentage 20%
Double declining balance in percentage 40%

Under this table is another table for double declining balance depreciation, which has six column headings, namely year, book value (beginning of year), depreciation rate, depreciation expense, accumulated depreciation, and book value (end of year).

  4. The fourth step is to take that double declining balance depreciation rate of 40% and apply it to our asset, in the "Depreciation Rate" column.

     The table for example facts has two columns. The items and entries in these columns are as follows:
Total book value $500,000
Useful value 5 years

Straight-line depreciation in dollars $100,000
Straight-line depreciation in percentage 20%
Double declining balance in percentage 40%

Under this table is another table for double declining balance depreciation, which has six columns with entries as follows: Year 1
Book value (beginning of year) $500,000
Depreciation rate 40%
Depreciation expense $200,000
Accumulated depreciation $200,000
Book value (end of year) $300,000

In the example, the asset value or the book value at the beginning of the year, $500,000, is multiplied by 0.40, which equals $200,000, the depreciation expense. The depreciation expense of $200,000 is subtracted from the asset value or the book value at the beginning of the year, $500,000, which equals $300,000, the book value at the end of the year.

    We apply it to the initial value, and in the subsequent years, we apply that double declining balance rate to the carrying value at the beginning of the year.

    Ω The table for example facts has two columns. The items and entries in these columns are as follows:
Total book value $500,000
Useful value 5 years

Straight-line depreciation in dollars $100,000
Straight-line depreciation in percentage 20%
Double declining balance in percentage 40%

Under this table is another table for double declining balance depreciation, which has six columns with entries as follows: Year 1
Book value (beginning of year) $500,000
Depreciation rate 40%
Depreciation expense $200,000
Accumulated depreciation $200,000
Book value (end of year) $300,000

Year 2
Book value (beginning of year) $300,000
Depreciation rate 40%
Depreciation expense $120,000
Accumulated depreciation $320,000
Book value (end of year) $180,000

Year 3
Book value (beginning of year) $180,000
Depreciation rate 40%
Depreciation expense $72,000
Accumulated depreciation $392,000
Book value (end of year) $108,000

Year 4
Book value (beginning of year) $108,000
Depreciation rate 40%
Depreciation expense 43,200
Accumulated depreciation $435,200
Book value (end of year) $64,800

Year 5
Book value (beginning of year) $64,800
Depreciation rate 40%
Depreciation expense $43,200
Accumulated depreciation $461,120
Book value (end of year) $38,880

    As you can see at the beginning of the year in year two, our book value is the same book value that we ended the first year with.

    We would complete this process for all five years. You can see that at the end of year five, we have a book value of $38,880.


3. Depreciation Calculation Comparison

We have one final visual representation to examine. Here we have the same example facts as before, only now we've added production life for our units of production method, as well as the production hours over the course of the life of this example asset.

We're going to look at the comparison of these three depreciation methods--double declining balance, sum of the year's digits, and units of production.

The table for example facts has two columns. The items and entries in these columns are as follows:
Total book value $500,000
Useful value 5 years

Straight-line depreciation in dollars $100,000
Straight-line depreciation in percentage 20%
Double declining balance in percentage 40%

The production hours is shown in two columns as follows:
Year 1 5,000 hours
Year 2 10,000 hours
Year 3 12,500 hours
Year 4 10,000 hours
Year 5 7,500 hours

Under this table, a line graph shows three depreciation methods, namely, double declining balance, sum of the year’s digits, and units of production. The x-axis is labeled “Year” and lists all the numbers from 0 to 5. The y-axis is labeled “Depreciation Expense,” ranging from $0 to $250,000, in increments of $50,000. There are three lines on the graph labeled “Double Declining Balance,” “Sum of the year’s digits,” and “Units of production.” In the graph, the Double Declining Balance line begins at $200,000 in Year 1; declines to $120,000 in Year 2; and then trails off to $520,000 in Year 3, $490,000 in Year 4, and $27,000 in Year 5. In the graph, the “Sum of the year’s digits” line begins at $170,000 in Year 1 and systematically declines to $140,000 in Year 2, $100,000 in Year 3, $70,000 in Year 4, and $28,000 in Year 5. In the graph, the Double Declining Balance line begins at $50,000 in Year 1, rises to $100,000 in Year 2, continues to rise steadily to $125,000 in Year 3, and then starts to decline steadily to $100,000 in Year 4 and $75,000 in Year 5. All data are approximate.

You'll see with that double declining balance, in the early years the depreciation is greater and then starts to taper off towards the end of that asset's useful life.

In sum of the year's digits, it's a very linear, downward sloping line, because it's systematically decreasing over time.

Lastly, units of production is based entirely on the amount of production, so the trajectory of depreciation depends on the production over time. There might be spikes in depreciation, and then as that asset starts to age, its productivity decreases.

summary
Today we learned in depth about accelerated depreciation, which should be used when we have assets that are used more heavily in their earlier years. We explored the different methods of accelerated depreciation: MACRS and ACRS, sum of the year's digits, units of production, and the most common method, double declining balance. We focused specifically on double declining balance by looking at an example of calculating depreciation using the double declining balance method. Lastly, we used our example's information to perform a depreciation calculation comparison, comparing the three depreciation methods.

Source: Adapted from Sophia instructor Evan McLaughlin.