• Compute depreciation under accelerated methods

 

One of the most common accelerated methods of calculating depreciation is the double-declining-balance method (DDB). As the name implies, depreciation is calculated by doubling the straight-line rate and then applying that rate to the declining “value” of the asset.

For instance, in our last example, the straight-line rate for a 40-year asset would be 1/40 or 0.025, which is 2.5%. The double-declining-balance (DDB) rate would be 5%, but buildings are not often depreciated using accelerated methods, so let’s use a simple example: a small business owner comes to you and asks you to compare depreciating a $12,000 vehicle bought on Jan 1 with an estimated salvage value of $2,000 and a useful life of five years.

The straight-line computation would be $12,000 − $2,000 = depreciable value of $10,000. The depreciable value of $10,000 divided by 5 = $2,000 per year. The rate is ⅕, which is 0.20 or 20%. Since the asset was purchased at the beginning of January, there is no proration necessary. Depreciation under the straight-line method would look like this:

Under double-declining-balance (DDB), to compute periodic depreciation charges you begin by doubling the straight-line rate. In this case, the DDB rate would be 40% instead of 20%. Next, apply the DDB rate to the book value of the asset.

Book value is the original, historical cost minus accumulated depreciation (the depreciation taken so far). At the point where book value is equal to the salvage value, no more depreciation is taken.

For our client’s $12,000 vehicle, our calculation would look like this:

Less column	Cost	12,000	Percent and year
Less:	Depreciation	4,800	40% (YR 1)
Less column	Book Value	Single line7,200	Percent and year
Less:	Depreciation	2,880	40% (YR 2)
Less column	Book Value	Single line4,320	Percent and year
Less:	Depreciation	1,728	40% (YR 3)
Less column	Book Value	Single line2,592	Percent and year
Less:	Depreciation	592	40% (YR 4)
Less column	Book Value	Single line2,000Double line	Percent and year

 

Notice that we ignore the salvage value until the very end. Our year 4 (YR 4) depreciation expense would have been 40% of $2,592, except that would be $1036.80 which would have taken the ending book value down below $2,000. The ending book value, however, should always be equal to the salvage value (what we expect the asset to be worth when it is fully depreciated). So, in year 4, we only took $592 in depreciation, and then we are done.

In sum, we double the rate, and then apply that doubled rate to the DDB (book value).

Here are the two methods compared:

And graphically:

Straight-line depreciation, graphically, is a straight-line. Accelerated depreciation records a larger amount of depreciation in the early years, thus accelerating the allocation of cost to the periods. This method may make more sense if you look at it theoretically graphed against the repair and maintenance costs of the vehicle, which would be very small in the first years and larger in later years:

In addition, notice that graphing the declining balance (book value) leads both methods to the same ending book value:

The DDB book value drops faster because of the accelerated cost being recognized on the income statement (depreciation expense).

Let’s run this calculation now for the delivery vehicle on our fixed asset list:

Fixed Assets

As of 12/31/20X1
Spivey Company
Asset	Description	Date Purchased	Cost
1	Land	2/1/20X1	262,800
4	Land	10/1/20X1	120,000
Total Land			382,800
2	Building	7/1/20X1	490,000
5	Building	10/1/20X1	600,000
Total Buildings			1,090,000
3	Machine	7/1/20X1	162,000
6	Delivery Van	10/1/20X1	45,000
7	Machine	10/1/20X1	99,500
8	Office Furniture	10/1/20X1	70,000
9	Computer	10/1/20X1	5,500
Total Machinery and Equipment			382,000
Total PP&E			$ 1,854,800

This is going to be more complicated because we bought the rig on October 1st, so we will have to prorate the first year’s depreciation:

Less column	Cost	45,000	Percent and year
Less:	Depreciation	4,500	40% (YR 1 = 3/12)
Less column	Book Value	Single line40,500	Percent and year
Less:	Depreciation	16,200	40% (YR 2)
Less column	Book Value	Single line24,300	Percent and year
Less:	Depreciation	9,720	40% (YR 3)
Less column	Book Value	Single line14,580	Percent and year
Less:	Depreciation	5,832	40% (YR 4)
Less column	Book Value	Single line8,748	Percent and year
Less:	Depreciation	3,499	40% (YR 5)
Less column	Book Value	Single line5,249	Percent and year
Less:	Depreciation	249	40% (YR 6)
Less column	Book Value	Single line5,000Double line	Percent and year

 

There are six years because year one is a partial year, as is year six, which is simply the undepreciated amount left before the book value drops to salvage value.