## Modified Accelerated Cost Recovery System: the MACRS Depreciation method

MACRS Table

 Year 3-year 5-year 7-year 10-year 1 0.333 0.200 0.143 0.100 2 0.445 0.320 0.245 0.180 3 0.148 0.192 0.175 0.144 4 0.074 0.115 0.125 0.115 5 0.115 0.089 0.092 6 0.058 0.089 0.074 7 0.089 0.066 8 0.045 0.066 9 0.065 10 0.065 11 0.033

To calculate the depreciation for each year, simply (1) find the appropriate column for the period over which you will depreciate the asset, and (2) multiply the asset's cost (depreciable basis) times the numbers in the column.

#### Depreciation Methods for Different Purposes

Corporations are allowed to use one depreciation method for tax purposes and another depreciation method for financial statements (e.g., income statement and balance sheet).  It is in the companies' best interest to use an accelerated method for tax purposes, since this minimizes the firm's taxable income and therefore its taxes paid.  At the same time, the company wants to minimize its depreciation on its income statement since this results in a higher reported income (i.e., earnings per share).

MACRS is an accelerated depreciation method that is used primarily for tax purposes since its use minimizes the tax bill.  Corporations typically use straight line depreciation on their financial statements in order to maximize its reported income.

#### The MACRS Table - Where The Numbers Come From

The table above only shows values for 3, 5, 7, and 10-year depreciation periods.  There are longer periods in the complete table but they are omitted here for brevity.  Let's look at where the numbers in the table come from.

1.  An Accelerated Method

The numbers in the MACRS table above are based on the double declining balance depreciation method.  (The omitted columns, for depreciation periods over ten years, are based on 1 1/2 times declining balance, but we won't worry about that here.)  We will explain more about the double declining balance method below.

2.  The Half-Year Convention

How much depreciation should be allowed during the first year if one company buys an asset in January and another company purchases the same asset in December of the same year?  Should they both be allowed to claim a full year's depreciation?  Or should the second company be allowed to depreciate only 1/12 of a full year's amount since the asset was only used for one of the twelve months?

After a long and contentious debate, Congress finally agreed on a compromise:  no matter when the asset is purchased during the year, the company can claim a half-year's depreciation for the first year's write-off.  This is called the half-year convention. This results in the asset being depreciated over one extra year, e.g., 6 years for a 5-year depreciation period.  In essence, for an asset being depreciated over 5 years, the company gets one-half of a year's depreciation amount during the first year, four full years' depreciation, and then the remaining amount - a total of 6 years of write-offs, even though the selected depreciation period is 5 years.  For a 10-year depreciation period, you would get to claim a half-year's depreciation for the first year, nine years' depreciation, and the remaining amount during the eleventh year.

(Year 1)  Let's consider the first year's depreciation for a five-year depreciation period.  Since the straight line depreciation rate would be 20%, the double declining balance method would be twice that amount, or 40% (it is always double the straight-line rate.)  However, the half-year convention cuts this amount in half, or back to 20% of the asset's cost.

(Year 2) This means that, after the first year, 80% of the asset's cost remains to be depreciated in the future (i.e., 80% of the asset's cost is the declining balance after one year's depreciation has been claimed).  Using the double declining balance rate of 40% for the second year, we have 40% times 80%, or 32% of the asset's cost may be written off in the second year.

(Year 3) Since 52% of the asset's cost has been written off during the first two years, the remaining 48% remains to be depreciated in the future (i.e., 48% is the declining balance after one year's depreciation has been claimed).  Using the double declining balance rate of 40% for the third year, we have 40% times 48%, or 19.2% of the asset's cost may be written off in the third year.

In other words, as a percent of the asset's cost, the following amounts may be written off the first three years:  20%, 32%, and 19.2%.  Notice that these are the numbers shown on the first three rows of the 5-year column of the MACRS table (in decimal format).

 Year 5-year 1 0.200 2 0.320 3 0.192 4 0.115 5 0.115 6 0.058

So the MACRS table is based on the double declining balance depreciation method, with the allowable depreciation for the first year cut in half (due to the half-year convention).

3.  Switching to Straight Line Depreciation

The Internal Revenue Service (i.e., the U.S. government's tax collector) will allow companies to switch depreciation methods one time during the life of an asset.

At some point, it is to the company's advantage to switch from double declining balance to straight line depreciation at some point in the life of the asset.  In other words, if we take the remaining balance (declining balance) and divide it by the remaining number of years, at some point this will be larger than the amount of double declining balance depreciation for that year.  At that point, the company should switch from double declining balance to straight line depreciation.

The government has calculated the point at which it is to the company's advantage to switch to straight line and has built this switch into the MACRS table.  Notice that the numbers become constant near the bottom of the column.  (The last year's amount is simply the amount necessary to make the column total 100%.)

#### Summary

To summarize, the MACRS depreciation table is simply a table of values that is used for tax purposes.  The numbers in the table are multiplied times the cost of the asset.  The table assumes that the company will:

• use double declining balance depreciation,

• be allowed to claim only a half-year's depreciation during the year of the purchase, and

• switch to straight line depreciation when it is to its advantage to do so.