Asset depreciation answers the question, “How much does the asset cost per period?” To answer that question, you need to: know the cost of the asset, estimate the number of periods in the asset’s useful life, project any salvage value the asset will have at the end of its useful life, and choose a depreciation method. For example, suppose your business purchases a delivery truck for $10,000, uses it for five years, and then sells it for $2,000. Using the simplest depreciation method, straight-line depreciation, you calculate the cost of the truck over the five years as the $10,000 original cost less the $2,000 salvage value for a result of $8,000. Now divide the $8,000 by the five years of useful life. The result—$1,600—is the depreciation expense.
Straight-line depreciation is the most popular method because it’s easy to apply and intuitive. The other methods—declining balance, sum-of-the-years’-digits, annuity/sinking fund, and activity—simply allocate the asset cost over the asset’s useful life in different ways.
The declining balance depreciation method expenses more of the cost of the asset in the early periods of an asset’s estimated life than in the later periods. It does so using the following formula:
(Declining Balance Percentage)*(Net Book Value)/(Estimated Life)
For example, suppose you want to recalculate the first year’s depreciation expense for the delivery truck using 200% declining balance depreciation. The declining balance percentage is 200%. The net book value, because no depreciation has occurred, is $10,000. The estimated life is five years. Accordingly, you calculate the first year’s depreciation expense as:
The declining balance percentage is always greater than 100%. Accordingly, the formula accelerates the depreciation of an asset. Often, federal and state income tax laws determine usage of the declining balance depreciation method. Tax laws allow declining balance depreciation for many types of assets and specify a variety of declining balance percentages to be used, including 125, 150, 175, and 200%, depending on which year you acquire and begin using an asset. Generally, the tax law in effect when you buy and begin using an asset determines the types of assets for which you can use the declining balance method, as well as the declining balance percentage.
The sum-of-the-years’-digits depreciation method, like the declining balance method, also expenses more of the cost of an asset in the early periods of an asset’s estimated life than in the later periods. It does so using the following formula:
(Periods Left in Estimated Life)/(Sum of the Periods? Digits)*(Original Cost-Salvage Value)
For example, suppose you want to recalculate the first year’s depreciation expense for the delivery truck using the sum-of-the-years’-digits method. The periods left in the estimated life, because the asset is still new, is five years. The sum of the periods’ (or years’) digits is 1+2+3+4+5, or 15. The original cost less the salvage value is $10,000–$2,000, or $8,000. Accordingly, you calculate the first year’s depreciation expense as:
Because the fraction becomes smaller in each succeeding period, the amount of depreciation expensed each year becomes smaller.
The annuity and sinking fund depreciation methods are mechanically identical, so this book supplies the same starter workbook for both. Both of these methods expense less of the cost of an asset in the early periods of an asset’s life than in the later periods, so they are roughly the opposite of the declining balance and sum-of-the-years’-digits methods in this regard. The annuity and sinking fund methods also include in their depreciation expenses a specified return on the investment. Generally, the annuity and sinking fund methods violate the Generally Accepted Accounting Principles (GAAP). (Generally Accepted Accounting Principles are the rules and methods that certified public accountants, with help from business and the government, develop and use for financial accounting. Usually, when people refer to Generally Accepted Accounting Principles, they mean the pronouncements of the Financial Accounting Standards Board, an independent professional group.) Because they are contrary to GAAP and because they are complex, these methods are rarely used in practice except in heavily regulated industries such as public utilities in which governmental rate-setting agencies often specify returns on investment. The annuity and sinking fund depreciation methods use the following formula to calculate depreciation expenses:
(Original Cost?(Present Value of the Salvage Value))/(Present Value Factor of an Ordinary Annuity for n Periods at i%)
where n equals the estimated life, and i equals the specified return on investment.
For example, suppose you want to recalculate the first year’s depreciation expense for the delivery truck using the annuity or sinking fund method. Also suppose that you are assured a 10% return on assets by a state regulatory agency. The 10% is the specified return on investment. The original cost is $10,000. The estimated life is five years. The present value of the salvage value is calculated as follows: For each year in the asset’s estimated life, the $2,000 salvage value is divided by the sum of 1 plus the specified return on investment, or (1+10%)^5, or $1,241.84.
You can then calculate the present value of an ordinary ($1) annuity for 5 periods using a 10% discount rate using the PV function as follows:
for a result of 3.7908. Accordingly, you calculate the depreciation expense as:
This depreciation amount also includes assumed investment revenue of 10% on the asset cost of $10,000, or $1,000, meaning the actual amount of the asset being expensed in this period is $2,310.37 minus $1,000 or $1,310.37. In other words, the depreciated value of the truck after one year under this method is $8,689.63.
As the net book value of the asset becomes smaller over its useful life, the assumed investment revenue becomes smaller. Consequently, the $2,310.37 of depreciation represents less assumed investment revenue and more actual asset being expensed. The assumed investment revenue amounts to the assumed return on assets allowed by the regulatory agency.
The activity method depreciates an asset as it’s used, instead of as time passes, by calibrating the estimated life of an asset in units of use. It does so by using the following formula:
(Period Units of Use/Estimated Life in Units of Use)*(Original Cost-Salvage Value)
For example, suppose you want to recalculate the first year’s depreciation expense for the delivery truck using the activity depreciation method. If a delivery truck lasts for 100,000 miles and you anticipate driving the truck 30,000 miles the first year, you calculate the first year’s depreciation expense as:
In general, financial accounting standards and the tax laws guide you in determining asset cost, useful life, and salvage value and in selecting a depreciation method. Accordingly, if you’re building a depreciation schedule to use for tax accounting, your best resources are the publications of the Internal Revenue Service and your tax adviser. Alternatively, if you’re building a depreciation schedule to use for financial accounting, your best resources are the publications of the Financial Accounting Standards Board and your certified public accountant.
Note: Be consistent in the financial measurement periods you use in depreciating assets. If you’re building a monthly forecast, calculate depreciation expenses on a monthly basis and enter the useful life in months. Alternatively, if you’re building a quarterly or yearly forecast, calculate your depreciation expenses on a quarterly or yearly basis and enter the estimated life of an asset in quarters or years.