# Straight-line depreciation

Straight-line depreciation is the simplest method of depreciation. We start with the purchase price of the asset. From this we subtract the scrap value and divide the remaining value by the number of years of useful life.

In Figure 4-9 it can be seen that the depreciation taken each year is the same, $4,500. Each year the accumulated depreciation increases by $4,500, and the book value of the equipment is reduced by the same $4,500. The $4,500 of depreciation is taken each year until the scrap value is reached. From this point on, if the asset is still owned by the company, depreciation expense is no longer taken. If the asset were sold before the end of its useful life, the difference between the selling price and the remaining depreciation would be taken as depreciation expense in that year.

Suppose the asset were sold at the end of year four for $20,000. At the end of year four, the remaining book value is $21,000. We would take the $1,000 of depreciation expense and clear the asset from our books. If the same asset were sold for $25,000, we would show a profit of $4,000. A depreciation expense of $21,000 would be taken, $25,000 would be added to the cash account, and $4,000 would be added to the equity account as profit on the machine.

Accelerated depreciation is used because it effectively reduces taxes on the company. Although the total amount of depreciation expense taken is the same as it is in straight-line depreciation, with the accelerated depreciation method, the depreciation taken in the earlier years is significantly greater than it is in the later years. Since larger amounts of depreciation mean that the depreciation expense is larger, the net profit before taxes is going to be smaller. The taxes are figured on the net profit before taxes, so the taxes will be lower as well. Now the total amount of tax the company pays over the years is going to be the same regardless of the depreciation method, but some of the taxes will be deferred to a

Figure 4-9: **Straight-line depreciation**

later time. Since the money we pay someone (the IRS in this example) later in time has less value, we will profit from accelerated depreciation.

This may all seem a bit strange, but it is a win-win situation all around. Companies like to accelerate their depreciation because it reduces their taxes in the early years of the equipment's life. The government likes this too because it encourages the company to sell the equipment before the end of its useful life and buy a new piece of equipment. The new piece of equipment not only makes the company more profitable and pays the government more taxes, it also makes profit for the equipment manufacturer, who in turn pays taxes on that money to the government as well.

# Sum of the years' digits

This is an accelerated depreciation method (see Figure 4-10). The depreciation for each year is calculated by first taking the digit of each year of the equipment's useful life and adding them together.

In our example the equipment has a useful life of eight years, so we add 1+2 + 3 + 4 + 5 + 6 + 7 + 8 = 36. The first year we take 8/36 of the allowable depreciation; in the second year we take 7/36 of the allowable depreciation; in the third year we take 6/36 of the allowable depreciation, and so on. Adding the numerator of the fractions we get 36/36. That is, we have taken all of the allowable depreciation.

Notice that in the sum of the years' digits depreciation method, we are still taking $36,000 depreciation just as we did using the straight-line method. Notice too that we still have $3,000 of scrap value. The only difference is that we have taken larger amounts of depreciation in the earlier years than we did in the later years.

Figure 4-10: **Sum of the years' digits**

# Double declining balances

This is another accelerated depreciation method. The first thing we do in this method is calculate the percentage of depreciation that would apply if we were using straight-line depreciation. In our example of straight-line depreciation we were taking straight-line depreciation over a period of eight years. That would be 12.5 percent each year. So, the double declining balances percentage is 25 percent. The depreciation expense for each year is taken by multiplying the remaining book value of the asset by 25 percent.

As can be seen in Figure 4-11, we start with a remaining book value of $39,000. This can be thought of as the remaining book value at the end of year zero, the time we purchased the asset. Multiplying $39,000 by 25 percent gives us the first year's depreciation of $9,750. This $9,750 is subtracted from $39,000 to give us $29,250, which is the book value at the end of year one. $29,250 is multiplied by 25 percent to get the next year's depreciation expense of $7,310.

Figure 4-11: **Double declining balances**

The calculation is continued until the last two years of the asset's life. For the last two years the scrap value is subtracted from the remaining book value and the difference is divided by two and used as the depreciation expense for both years.

The calculations for depreciation may seem a bit strange for engineers who are used to having things depend on natural laws of physics and other logical causes. Some accounting rules—including depreciation methods—are not subject to the laws of nature but are subject to ''generally accepted accounting practices.'' These are the rules of accounting that are agreed to by committees of qualified accountants. As long as everyone follows the same rules and the calculations for things like depreciation are carried out consistently, businesspeople, the IRS, and investors can all be confident that everyone is performing the same calculations in the same way.