#### double declining balance

**Choosing a Method of Depreciation**

There are various ways to depreciate an asset and each company must determine which method to use. There are a number of items to consider when making this determination, including ease of calculation, the speed of cost recovery and predictability of the expense.

While all methods are fairly easy to calculate, the units-of-production method is based on usage of the asset and therefore requires usage to be tracked. This would be easy to calculate for a vehicle (mileage) but would be more difficult for a computer. I know I wouldn’t want to track exactly how many hours I used my computer each year, would you?

Most companies consider speed of cost recovery to be the most important consideration because how fast the cost is recovered affects many aspects of business. If the business paid cash for the asset, typically it would like to recover that cost as an expense as quickly as possible. However, if the company financed the asset over a longer period of time, the company may wish to match the cash expenditures of the loan payments to the expensing of the asset.

The speed of cost recovery also affects profit and taxes. A method like straight-line, where the depreciation is the same each year, will cause higher profit in the early years but lower profit in later years when compared to an accelerated method like double-declining balance. Double-declining balance generates a large amount of depreciation in early years of asset ownership, which lowers profit and lowers taxes. Later in the asset’s life, the amount of depreciation is lower than straight-line and causes higher profit and taxes. Some argue that an asset is more efficient when it is newer and generates more revenue, therefore accelerated methods, like double-declining balance, are the way to go. It could also be argued that units-of-production will most closely match revenue because it is based on the output of machinery, equipment and vehicles.

Being able to predict the amount of expense is important to some businesses for consistency in the financial statements. For some companies, that means using straight-line depreciation to evenly depreciate an asset. For some companies, that means using units-of-production to more closely match higher revenue with higher depreciation. Others argue that trying to match cash expenditures and expenses more closely is more consistent and therefore accelerated methods should be used for assets purchased with cash.

As you can see, there are no easy answers when deciding which method of depreciation to use. Luckily, the calculations are much easier than the decision making!

**Important Terminology**

Like most areas of accounting, there are a number of important terms to learn in order to correctly calculate depreciation. It is critical to know these terms and how to apply them to the calculations.

Most depreciation methods use **cost** in the calculation. Asset cost is the total cost of the asset, including costs to acquire, deliver, and get the asset ready to use. Both straight-line and units-of-production use cost in the calculation. Double-declining balance uses book value rather than cost. **Book value** is the cost of the asset less any accumulated depreciation on that asset. In the first year, book value is equal to cost because no depreciation has been recorded yet. As depreciation is recorded, the book value of the asset decreases. Book value can also be called **basis**.

When a company purchases an asset, the company typically has a plan to keep the asset for a certain period of time. At the end of that time, the company will usually sell the asset and use the proceeds toward the acquisition of a new asset. The amount the asset will probably be worth at the end of that time is called **salvage value**. Because there is value left at the end of the asset’s life, the company should only depreciate the asset so the book value at the end of the life equals the salvage value. Salvage value is not perfect, but it is an estimate at the time of purchase to help minimize gains or losses at the time of sale. Salvage value is used in all depreciation calculations, in one way or another, so that the asset is never depreciated below salvage value.

How long the asset will be useful is the last key to the calculation. **Useful life** is the period used to depreciate an asset. In most cases useful life is expressed as a measure of time, usually years. In the case of units-of-production, useful life is expressed in a unit of measure associated with the asset. For a vehicle, we typically use mileage when using units-of-production. For a copier, we might use number of copies we expect to be able to make over the life of the copier. For machinery, we could use the expected number of units that could be manufactured with the machine. Useful life has little connection to the actual life of an asset. The Internal Revenue Service has an extensive list of asset lives, which is used by most companies for depreciation purposes. For example, the useful life of a building used in business is 39 years. We all know of perfectly good buildings much older than that!

**Calculating Straight-line Depreciation**

Straight-line depreciation is the easiest of the three major depreciation methods. This method creates an equal amount of depreciation for each full year. Another perspective is to say that an equal percentage of the asset is depreciated each year. If an asset has a five year life, 20% of the depreciable value would be depreciated each year (100% / 5 years = 20% per year). As discussed earlier, a company cannot depreciate below salvage value; therefore, salvage value is subtracted from the cost of the asset. This depreciable basis is then spread out over the life of the asset to calculate annual depreciation. The formula for calculating straight-line depreciation is:

**Annual straight-line depreciation = (cost – salvage value) / life in years**

*Example #1: On January 1, 2013, Beans R’ Us purchases a van at a cost of $27,000. The company believes the van will have a useful life of five years or 250,000 miles. The salvage value is estimated to be $4,000. Calculate the annual depreciation, using straight-line depreciation, for the five years Beans R’ Us plans to own the vehicle and the journal entry to record the depreciation for 2013.*

Since we are using straight-line and the van was purchased on January 1, the depreciation will be the same amount each year. Plug the information given into the formula to calculate the annual depreciation.

($27,000 – $4,000) / 5 =$23,000 / 5 =**$4,600 per year**

Does this make sense?

At the end of the fifth year, the asset has been depreciated to the point where book value is equal to salvage value. The accumulated depreciation is equal to the depreciable value of the asset. If the company continues to keep the asset, there will be no additional depreciation, unless the company believes that the salvage value has changed.

#### Using Straight-line Depreciation with a short year

What if the asset as instead purchased on March 1? The depreciation for the first year would be less than $4,600 because the company only owned the van for 10 months. When this is the case, we must adjust the depreciation to reflect the short year. There are a few ways we could do this. We could calculate the monthly depreciation then multiply the monthly amount by the number of months the asset was owned. We could also use a ratio of the number of months owned to the number of months in the year. In this case, the ratio would be 10/12. Either way, you will get the same answer.

$4,600 * 10/12 = **$3,833** (rounded to the nearest whole dollar)

This would be the amount of depreciation for the first year. The remaining full years would still be $4,600. Because the van was purchased in March of 2013, we would need to depreciate in January and February of 2018 to record all of the depreciation. Although this is a five-year asset, in order to depreciate five full years, we need six years to do it.

* There are two months of deprecation remaining in 2018. $4,600 * 2/12 = $767 (rounded to the nearest whole dollar). You could also take the book value of $4,767 at the end of 2017 and subtract the salvage value of $4,000, which would also give you $767.

**Calculating Units-of-Production Depreciation**

Units-of-production is very similar to straight-line, but very rarely used. We are still looking at depreciable value and dividing that amount by the life of the asset. With units-of-production, we are not using years for the life. Instead we use a quantity of units. For vehicles, this quantity is typically mileage. It makes sense because the life of a vehicle is more closely tied to miles driven than age.

Using the depreciable value and units for the life, we can calculate a rate per unit that can then be applied to the actual usage for each year. Because depreciation is based on usage rather than life in years, partial year depreciation is not a factor in units-of-production. If the asset was acquired at any time other than the first of the year, actual activity would reflect that fact. The formula for calculating the rate is very similar to formula used in straight-line.

**Depreciation per unit = (cost – salvage value) / life in units**

Remember that an asset can never be depreciated below salvage value. This is critically important when using units-of-production because it is very easy to underestimate the life of an asset. If there is more activity than predicted, the company would just stop depreciating once the estimated life in units is reached.

*Example #2: On January 1, 2013, Beans R’ Us purchases a van at a cost of $27,000. The company believes the van will have a useful life of five years or 250,000 miles. The salvage value is estimated to be $4,000. The actual miles driven for the first five years are as follows:*

*Calculate annual depreciation using the units-of-production method for 2013 – 2017.*

The first step to solving a problem like this is to calculate the rate that the company will use to apply depreciation. Using the formula above we calculate the rate.

($27,000 – $4,000) / 250,000 = **$0.092 per mile**

This rate will be used for the life of the asset, unless the company believes that the life will be dramatically increased or decreased. Now that we have the rate, we can apply it to the actual activity for each year to calculate the annual depreciation. When calculating rates, label the rate! In the past, I have had students tell me that the depreciation is $0.092 per year because they did not label the rate and therefore did not apply it correctly. Get in the habit of labeling numbers you calculate.

Although we calculated the 2017 depreciation to be $3,956, that would drop the book value below $4,000 (the salvage value). Therefore, in the fifth year, the depreciation is limited to $2,484. Make sure to watch the accumulated depreciation and book value when doing these calculations so you do not over-depreciate the asset.

**Calculating Double Declining Balance**

Double declining balance is an accelerated method of depreciation. Companies use double declining balance when they want to quickly depreciate an asset. Those who use the method argue that the value of an asset falls quickly in the first few years and believe that the depreciation method selected should match. It can also be said that companies get more life out of an asset in the first few years of ownership.

The asset will depreciate much faster under this method than straight-line because we double the percentage that would be depreciated each year under straight-line. This does not mean we just calculate straight-line and double it. Instead, we calculate the straight-line percentage and double it. We then multiply that percentage by the book value of the asset. When using double declining balance, do not subtract salvage value when calculating depreciation. However, you must make sure to watch the book value as you do the calculations to ensure you do not depreciate the asset too much.

The formula for double declining balance is:

**Annual depreciation = Book value * 100% / life * 2**

**or**

**Annual depreciation = Book value * 200% / life**

When doing these calculations, calculate the percentage that should be used first. Once the percentage is calculated, it is the same for the rest of the asset’s life. For a five-year life, the percentage would always be 40% (200% / 5). For a four-year asset, the percentage is 50%. Many of the percentages are easy to calculate in your head.

*Example #3: On January 1, 2013, Beans R’ Us purchases a van at a cost of $27,000. The company believes the van will have a useful life of five years or 250,000 miles. The salvage value is estimated to be $4,000. Calculate annual depreciation, using double declining balance, assuming the company plans to keep the vehicle for five years.*

Since this asset has a five-year life, the percentage used is 40%. We will multiply the book value by this percentage. Book value in year one is $27,000 because no depreciation has been taken on the asset yet.

$27,000 * 40% = **$10,800**

As you can see, double declining balance results in a lot more depreciation than straight-line. It is more than twice straight-line because we did not subtract salvage.

When calculating the depreciation for 2014, use the book value of $16,200.

$16,200 * 40% = **$6,480**

For 2014, the amount of depreciation is significantly less than 2013 but still more than the annual depreciation under straight-line.

Keep running the calculations until you get close to salvage value.

We are only $1,832 from salvage. Calculate the depreciation for 2016.

$5,832 * 40% = **$2,332.80**

The annual depreciation for 2016 is more than the amount of remaining depreciation we are allowed to take on the asset. Therefore, we cannot take the full amount of depreciation calculated. Instead, we are limited to $1,832 in 2016. Since we have hit salvage value, there is no depreciation in 2017.

Because depreciation is accelerated, often the asset finishes depreciating before the end of its life. Make sure to watch book value!

#### Using Double Declining Balance with a short year

What if the asset was purchased June 1? If that is the case, use the same rules used for straight-line. Calculate the first year’s depreciation and then adjust it based on the number of months the company owned the asset. If the asset was purchased June 1, the company owned the asset for seven months in year 1.

$27,000 * .40 = $10,800 * 7/12 = **$6,300**

Once you calculate the first year’s depreciation, continue on as normal, depreciating the asset until book value is reached.

For 2017, the amount of depreciation calculated was $1,788.48 but we are limited to $471.20 because of the salvage value.

**Final Thoughts**

When completing depreciation calculations, know when to use salvage value in the calculation and always make sure to stop depreciating once you reach salvage value. For partial years, only depreciate for the months that the company owned the piece of equipment. Multiply the annual depreciation by the ratio of months owned to months in the year. This is not necessary for units-of-production since the calculation is based on units rather than time.

#### Related Videos

Straight-line depreciation

Double-declining balance depreciation

Partial year double declining balance depreciation

Units of production depreciation