Business Mathematics: Depreciation - Double Declining Balance Method

The double declining balance method produces the highest amount of depreciation in the earlier years. It does not recognize salvage or scrap value. Instead, the book value of the asset remaining at the end of the depreciation period becomes the salvage or scrap value. Under this method, the straight-line rate is doubled and applied to the declining book balance each year.

Many companies prefer the double declining balance method because of the greater “write-off’ in the earlier years, a time when the asset contributes most to the business and when the expenditure was actually made. The procedure is to apply a fixed rate to the declining book value of the asset each year. As the book value declines, the depreciation becomes smaller.

Example
A $17,000 asset is to be depreciated over 5 years. The double declining balance rate is thus 40%/yr from

The yearly depreciation and book value are shown in the following table.

The $1,322 book value at the end of the fifth year becomes the scrap value. If, however, a scrap value of $2,000 had been determined, the depreciation for the fifth year would be adjusted from $881 to $204 ($2,204 - $2,000).
The date of purchase should also be considered. In the previous example, we assumed that the equipment was purchased at the beginning of the year, which is usually not a common occurrence. Therefore, a change in the computation for the first partial year of service is needed if we determine that the equipment was purchased later in the year.

Example
If the equipment in Example 5 had been purchased and put to use at the end of the ninth month of the fiscal year, the pro rata portion of the first full year’s depreciation would be

The method of computation for the remaining years would not be affected (although the amounts would change). Thus, the depreciation for the second year would be
40% ($17,000 - $1,700) = $6,120
and the book value at the end of the second year would be
$9,180 = [$17,000 - ($1,700 + $6,120)]

Solved Problems

4.31   On January 1, Morgan Company purchased office furniture for $1,000. The furniture has an estimated useful life of 10 years, and its salvage value is $100. Using the double declining balance method of depreciation, what is the depreciation at the end of the first year?
 

Solution

Note that the salvage value is not considered when determining depreciation with this method.

4.32   Equipment was bought on January 5 for $25,000. It has an estimated useful life of 40 years and a trade-in value of $5,000. Using the double declining balance method, determine the book value at the end of the third year.
 

Solution

Note that in calculating the depreciation for years 2 and 3, we use the preceding year’s book value as the cost in each case. We can state this in mathematical terms as follows:
 

[Cost (from previous yr) — depreciation (from previous yr)] × depreciation rate = depreciation
or more simply,
Book value X depreciation rate = depreciation

4.33   Using the double declining balance method of depreciation, determine the book value at the end of the first year on an item that was bought on April 8 for $60,000 and that has a salvage value of $8,000 and an estimated useful life of 50 years.
 

Solution

End of first-year depreciation:

Book value at end of first year:


4.34   Using the double declining balance method, determine the accumulated depreciation at the end of the second year for a bulldozer that cost $6,000. The bulldozer’s estimated useful life is 20 years, and its trade-in value is $500. It was bought on November 27.
 

Solution

End of first-year depreciation:

Depreciation for second year:

Accumulated depreciation at end of second year:
$50 + $595 = $645
* See Prob. 4.32.

4.35   Using the double declining balance method of depreciation, prepare a depreciation schedule for the first 5 years on a piece of machinery that cost $80,000, has a trade-in value of $5,000 and an estimated life of 25 years.
 

Solution



4.36   Using the double declining balance method of depreciation, prepare a depreciation schedule to the end of the third year for the March 29 purchase of 20 typewriters at a cost of $600 each by Starr Office Management, Inc. The typewriters have an estimated useful life of 5 years and a trade-in value of $100 each.
 

Solution

End of first-year depreciation:



4.37   If machinery that cost $60,000 and has a trade-in value of $5,000 was put into use on January 1, what is the book value at the end of the fifth year, if said machinery has an estimated useful life of 25 years?
 

Solution

Book value at end of fifth year:


4.38   Wilson Vending Company bought machines costing a total of $27,000. The machines have an estimated trade-in value of $7,000 and a life expectancy of 8 years. Using the double declining balance method, what is the accumulated depreciation at the end of the fourth year?
 

Solution


4.39  A conveyor with an estimated useful life of 20 years and a salvage value of $700 was purchased for $7,000. Using the double declining balance method of depreciation, determine the book value at the end of the third year.
 

Solution

Book value at end of third year:


4.40   Using the double declining balance method of depreciation, find the book value to the nearest dollar at the end of the second year for the following:

Solution
(a)
100%/estimated life × 2 = depreciation rate
100%/25 yr × 2 = 8%/yr

Depreciation at end of year 2:

Book value at end of year 2:

* Note that, as before, the original cost less the depreciation for the first year (i.e., the book value) becomes the cost of the item at the beginning of the second year.
(b)

Depreciation at end of year 1:

Depreciation at end of year 2:

Book value at end of year 2:

Depreciation at end of year 1:

Depreciation at end of year 2:

Book value at end of year 2:


4.41  By preparing a depreciation schedule based on the double declining balance method of depreciation, determine the accumulated depreciation at the end of 5 years on 25 tables purchased at $150 each by Mohawk Restaurant. Their estimated useful life is 16 years, and they have no salvage value. The date of purchase was January 1. (Round the depreciation to the nearest dollar.)
 

Solution


4.42   Using the double declining balance method, prepare a depreciation schedule for a truck costing $8,800 purchased on January 1. The truck has an estimated useful life of 5 years and a salvage value of $1,000. (Round the depreciation to the nearest dollar.)
 

Solution

When an item has a salvage value, the depreciation for the final year of useful life is calculated as follows (see also Example 5):

Cost (at beginning of final year) - salvage value = depreciation $1,141 - $1,000 = $141

4.43   McGuire Enterprises purchased a copy machine on December 21 for $5,200. The copier has an estimated useful life of 8 years and a salvage value of $500. Using the double declining balance method of depreciation, find the book value at the end of the second year.
 

Solution

* December 21 to December 31 of the year in which copier was bought is not counted.

4.44   Using the double declining balance method, prepare a depreciation schedule for an item bought on September 1 for $12,000. It has a trade-in value of $1,000 and an estimated useful life of 4 years.
 

Solution

Since the item has a salvage value and year 4 is the last year of this item’s useful life, the depreciation for year 4 is calculated as follows (see Example 5):
Cost (at beginning of final year) - salvage value = depreciation $2,500 - $1,000 = $1,500

4.45   Using the double declining balance method, what is the accumulated depreciation at the end of 4 years for a piece of equipment bought on January 1 for $6,100, if the equipment has an estimated useful life of 10 years and a salvage value of $570? (Round the depreciation to the nearest dollar.)
 

Solution