Depreciation, Amortization, Depletion

Definition: The allocation of the cost of an asset over its useful life.

Depreciation can be calculated using a variety of methods. The most common method for financial reporting purposes is the Straight-line method or the Unit-of-Production (output) method (this is a variation of the straight-line method)

Sometimes companies use one of the accelerated methods for financial reporting purposes, but generally accelerated depreciation methods are used for tax purposes only. At the current time, tax law requires companies to use the Modified Accelerated Cost Recovery System (MACRS). This method is not further discussed here (tax law changes frequently). Two commonly used accelerated depreciation methods are the declining balance method and the sum-of-the-years-digits method. These methods are discussed below. The important thing to remember is that depreciation expense for tax purposes is frequently calculated using a different method than for financial reporting purposes. This is acceptable, since it is recognized that the objectives of financial reporting are different than the objectives of tax reporting:

 Objective of financial reporting Objective of tax reporting Fairly present the financial position (results of operation) of the firm Minimize taxes Complying with tax law

Illustration of Various Depreciation Methods

Basic data:

 Cost of equipment \$50,000 Estimated salvage value \$ 5,000 Estimated useful life 10 years Or 100,000 units

Straight-Line Depreciation is calculated using the following equation:

(cost-estimated salvage value)/estimated useful life (in years or perhaps months). This method results in equal depreciation expense for each accounting period:

 (50,000 - 5,000)/10 = \$4,500 depreciation expense per year

Depreciation under the Unit of production (output) method is calculated using the following equation:

(cost-estimated salvage value)/estimated useful life (in total number of units). This method results in equal depreciation expense per unit produced. To determine depreciation expense for each accounting unit, the number of units produced must be known:

 (50,000 - 5,000)/100,000 = \$.45 depreciation expense per unit

Determination of depreciation expense for each year:

 Number of units produced Depreciation expense for the year Year 1 6,000 6,000 * .45 = \$2,700 Year 2 9,000 9,000 * .45 = \$4,050 Year 3 12,000 12,000 * .45 = \$5,400 Total for three years 27,000 \$12,150

Accelerated Depreciation Methods

1. Double Declining Balance method (DDB)

2. Sum-of-the-years-digits method (SYD)

Under both of these methods depreciation expense will start out higher than straight line and will decline over time. Different formulas are used to calculate depreciation expense under each of them and generally SYD will have a "gentler slope" than DDB. In other words, SYD depreciation expense will not be as high as DDB depreciation at the beginning of an asset's life and will decline more gradually. MACRS is a variation of DDB. I have no idea what the purpose of SYD is, other than to torture accounting students.

 Formula for DDB Formula for SYD Book-value * 2/useful life (cost-salvage value) * remaining life/SYD SYD: Add up the digits of the years of useful life: Book value: Cost - accumulated depreciation This is the declining balance (as accumulated depreciation increases, book-value becomes smaller) If the useful life is ten years: 1+2+3+4+5+6+7+8+9+10 = 55 OR: use the following formula: n(n+1)/2: where n = number of years: 10(10 + 1)/2 = 55

Using the data above:

 DDB SYD Year 1 50,000 *2/10 10,000 45,000 * 10/55 8,182 Year 2 40,000 *2/10 8,000 45,000 * 9/55 7,364 Year 3 32,000 *2/10 6,400 45,000 * 8/55 6,545 Year 4 25,600 *2/10 5,120 45,000 * 7/55 5,727 Year 5 20,480 * 2/10 4,096 45,000 * 6/55 4,909 Year 6 16,384 *2/10 3,276 45,000 * 5/55 3,273

And so on and so on. Note that under DDB the final year's depreciation expense needs to be "forced" to arrive at the correct salvage value. For the complete example for all 10 years under all methods, see the Excel file depreciation.

Notice the more gradual decline in the depreciation expense under SYD compared to DDB.