Depreciation Methods

The Gruman Company purchased a machine for $ 220,000 on January 2, 2013. It made the following estimates:

Service life	5 years or 10,000 hours
Production	200,000 units
Residual value	$ 20,000

In 2013, Gruman uses the machine for 1,800 hours and produces 44,000 units. In 2014, Gruman uses the machine for 1,500 hours and produces 35,000 units. If required, round your final answer to the nearest dollar.

Required:

1. Compute the depreciation for 2013 and 2014 under each of the following methods:

a. Straight-line method 2013 $ ???? and 2014 $ ????

b. Sum-of-the-years'-digits method 2013 $ ???? and 2014 $ ????

c. Double-declining-balance method 2013 $ ???? and 2014 $ ????

d. Activity method based on hours worked 2013 $ ???? and 2014 $ ????

e. Activity method based on units of output 2013 $ ???? and 2014 $ ????

2. For each method, what is the book value of the machine at the end of 2013? At the end of 2014?

a. Straight-line method 2013 $ ???? and 2014 $ ????

b. Sum-of-the-years'-digits method 2013 $ ???? and 2014 $ ????

c. Double-declining-balance method 2013 $ ???? and 2014 $ ????

d. Activity method based on hours worked 2013 $ ???? and 2014 $ ????

e. Activity method based on units of output 2013 $ ???? and 2014 $ ????

3. If Gruman used a service life of 8 years or 15,000 hours and a residual value of $10,000, what would be the effect on the following under the straight-line, sum-of-the-years'-digits, and double-declining-balance depreciation methods?

Depreciation expense

a. Straight-line method 2013 $ ???? and 2014 $ ????

b. Sum-of-the-years'-digits method 2013 $ ???? and 2014 $ ????

c, Double-declining-balance method 2013 $ ???? and 2014 $ ????

Book value

a. Straight-line method 2013 $ ???? and 2014 $ ????

b. Sum-of-the-years'-digits method 2013 $ ???? and 2014 $ ????

c, Double-declining-balance method 2013 $ ???? and 2014 $ ????

Hints :

1. a. The straight-line method allocates an equal amount of an asset's cost to depreciation expense for each period of the asset's service life. Straight-line depreciation expense is calculated as follows:Straight-line depreciation = cost - estimated residual value / estimated service life

b. The sum-of-the-years'-digits method recognizes a declining depreciation expense each period by applying a decreasing fraction each year to the depreciable base of the asset. The denominator of the fraction is the sum of the years of the asset's service life. Therefore, for an asset with a 5-year life, the sum is 5 + 4 + 3 + 2 + 1 = 15. The numerator of the fraction is the number of years remaining in the asset's life as of the beginning of the year. Note that in this method, the depreciation base remains constant, while the fraction decreases each year.

c. The declining-balance methods recognize a declining depreciation expense amount each period by applying a constant rate to the book value of the asset at the beginning of each period. The declining balance depreciation rate is some multiple (m) of the straight-line rate:

The declining-balance depreciation rate = (m) x straight line rate

You should compute the depreciation expense for each period of an asset's life as follows: depreciation expense = The declining-balance depreciation rate x net book value at beginning period.

You should note two important points:

*The periodic depreciation declines because the book value is used and not the depreciation base.

** Because you should ignore the residual value in the calculation of depreciation expense, the application of the declining balance method can cause an asset's book value to be different from its residual value at the end of the asset's service life. Therefore, you should adjust depreciation expense toward the end of the asset's service life so that the book value will equal the residual value.

d. When the service life of the asset is affected primarily by the amount the asset is used and not by the passage of time, you should recognize depreciation expense using an activity method. You should usually measure activity, or usage, in terms of an input measure such as the number of hours worked or an output measure such as miles driven or units produced. To compute depreciation expense under the activity method, the depreciation rate is determined as follows: Depreciation rate = cost - residual value / estimated usage of the asset .

Next, depreciation expense is computed as follows:Depreciation rate = cost - residual value / estimated usage of the asset

e. When the service life of the asset is affected primarily by the amount the asset is used and not by the passage of time, you should recognize depreciation expense using an activity method. You should usually measure activity, or usage, in terms of an input measure such as the number of hours worked or an output measure such as miles driven or units produced. To compute depreciation expense under the activity method, the depreciation rate is determined as follows:

Depreciation rate = cost - residual value / estimated usage of the asset. Next, depreciation expense is computed as follows:Depreciation rate = cost - residual value / estimated usage of the asset

2. Book Value = Cost - Accumulated Depreciation

3. Depreciation

a. The straight-line method allocates an equal amount of an asset's cost to depreciation expense for each period of the asset's service life. Straight-line depreciation expense is calculated as follows: Straight-line depreciation = cost - estimated residual value / estimated service life

b. The sum-of-the-years'-digits method recognizes a declining depreciation expense each period by applying a decreasing fraction each year to the depreciable base of the asset. The denominator of the fraction is the sum of the years of the asset's service life. Therefore, for an asset with a 5-year life, the sum is 5 + 4 + 3 + 2 + 1 = 15. The numerator of the fraction is the number of years remaining in the asset's life as of the beginning of the year. Note that in this method, the depreciation base remains constant, while the fraction decreases each year.

c. The declining-balance methods recognize a declining depreciation expense amount each period by applying a constant rate to the book value of the asset at the beginning of each period. The declining balance depreciation rate is some multiple (m) of the straight-line rate:

The declining-balance depreciation rate = (m) x straight line rate

You should compute the depreciation expense for each period of an asset's life as follows: depreciation expense = The declining-balance depreciation rate x net book value at beginning period.

You should note two important points:

The periodic depreciation declines because the book value is used and not the depreciation base.

Because you should ignore the residual value in the calculation of depreciation expense, the application of the declining balance method can cause an asset's book value to be different from its residual value at the end of the asset's service life. Therefore, you should adjust depreciation expense toward the end of the asset's service life so that the book value will equal the residual value.

Book Value

Book Value = Cost - Accumulated Depreciation

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