MACRS is generally double declining balance for the first half of of the asset's life, and then reverts to straight-line for the remainder of the asset's life. Thus, for example, for 7 year property using the half year convention, the first year depreciation is 2/7 *1/2 (or .1429). The double-declining method represents a depreciation rate of double the rate of straight line; as we are applying the half-year convention, you must cut that rate in to represent that we only take depreciation for half of the year in the first year of the asset's life. Then, in the second year, the depreciation represents a double-declining balance fraction of the adjusted basis; however, the tables represent it as a multiple of the original cost. This will probably be much clearer with an example:
For 7-year property costing $100,000 using the half-year method, the first year of depreciation would be $100,000 * (2/7) * (1/2), or 14,290. This is where the MACRS number of .1429 comes from. MACRS then computes the second year of depreciation based on the new adjusted basis of the property of $85,710 ($100,000-$14,290). Thus, for the second year, we take $85,710 * (2/7), or about 24,489 of depreciation expense. Thus, the rate of depreciation for the second year is about .2449 * $100,000 (the original cost). This is where the .2449 comes from in the MACRS table. This process is repeated for the third and fourth year–(you can verify by plugging the numbers). In the 5th-8th year however, we revert to a straight-line basis on the assumption that the property has 3.5 years of life remaining. We go halfway into the 8th year to make up for only taking a half year of depreciation in the first year. Thus, continuing with the $100,000, 7 year property example, at the beginning of the 5th year the adjusted basis of this property would be $31,240 (Cost minus accumulated depreciation to date). $31,240/3.5 years remaining=$8,926 of depreciation in Years 5, 6, and 7 (Note these correlate to the numbers in the MACRS tables for these years.). As we are only allowed half a year of depreciation in year 8, we take $8.926/2, or $4,463 of depreciation expense. The property has now been fully depreciated over the 7-year life.
The process is the same for other property as well, just substitute (2/7) with (2/5) for 5-year property, etc.. For property using the mid-quarter convention, just note that instead of depreciating by 1/2 in the first year you multiply by the appropriate ratio for the quarter the property was placed in service. Also note that this is only the process for personal property; real property is depreciated using the straight-line method. Hope this is clear! It is a confusing system!
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