## The Tax Environment

To illustrate some of the various methods of depreciation, let's first consider straight-line depreciation. If the fuily installed acquisition cost of a five-year property class asset is g I 0,000, annual depreciation charges using straight-line depreciation would be g10,000/5, or 92,000. (For tax purposes, expected salvage value does not affect depreciation charges.) Declining-balance depreciation, on the other hand, calls for an annual charge that is a "fured percentage" of the asset's net book value (acquisition cost minus accumulated depreciation) at the beginning of the year to which the depreciation charge applies. For example, when using the rlouble-declining-balance (DDB) method, we compute a rate by dividing I by the number of years of depreciable life for the asset. Then we double that rate. (Other decliningbalance methods use other multiples.) Under the declining-balance methods the general formula for determining the depreciation charge in any period is

m(1/n)NBV

where m is the multiple, n is the depreciable life of the asset, and NBV is the asset's net book value at the start ofthe year. For a \$10,000 asset, with a five-year life, the depreciation charge in the first year using the DDB method would be

2(1/5)\$10,000 = \$4,000

For our example,2(1/5) determines the "fi-xed percentage," or 40 percent, that is applied against the declining net book value each year. The depreciation charge in the second year is based on the depreciated net book value of 96,000. We arrive at the \$6,000 by subtracting the first year's depreciation charge, \$4,000, from the asset's original acquisition cost. The depreciation charge in the second year would be

2(1/5)\$6,000 = \$2,400

The third year's charge would be

2(1/5)\$3,600 = \$1,440

arid so on.

Modified Acceterated cost Recovery System. For the 3-,5-,7-, and 10-year property classes, the double declining balance (also called 200o/o declining balance) depreciation method is used. This method then switches to straight-line depreciation for the remaining undepreciated book value in the first year that the straight-line method yields an equal or greater deduction than the declining-balance method. Assets in the 15- and 20-year classes are depreciated using the 150 percent declining balance method, again switching to straight-line at the optimal time. The straight-line method must be used for all real estate.

Normally, the half-year convention must be applied to all declining-balance methods. This calls for a halfyear ofdepreciation in the year an asset is acquired, regardless ofthe date of purchase. There is also a halfyear ofdepreciation in the year an asset is sold or retired from service. If property is held for longer than its recovery period, a half year of depreciation is allowed for the year following the end of the recovery period. Thus 5-year property class assets held for 6 years or longer have depreciation spread over 6 years. To illustrate for the 5-year 200 percent property class, assume that an asset costing \$10,000 is acquired in February. For our example, the declining-balance formula yields 2(1/5) = 40o/o as the flxed percentage annual depreciation. However, in the first year the half-year convention is employed, so first-year depreciation is 20 percent, or 92,000. In the fourth year it is favorable to switch to straight-line depreciation.

At the beginning ofthe fourth year, the net book value at the end ofthe third year is divided by ihe remaining life to get straight-line depreciation. The remaining life is 2.5 years, owing to the half-year convention in the sixth year. Finally, in the sixth year the remaining balance is \$576, or one-half the yearly straight-line amount.