Chapter 11, Problem 1E

Gruman Company purchased a machine for $220,000 on January 2, 2016. It made the following estimates:

In 2016, Gruman uses the machine for 1,800 hours and produces 44,000 units. In 2017, Gruman uses the machine for 1,500 hours and produces 35,000 units.

Required:

1. 1. Compute the depreciation expense for 2016 and 2017 under each of the following methods:
   1. a. straight-line
   2. b. sum-of-the-years’-digits (round to the nearest dollar)
   3. c. double-declining-balance
   4. d. activity method based on hours worked
   5. e. activity method based on units of output
2. 2. For each method, what is the book value of the machine at the end of 2016? At the end of 2017?
3. 3. Next Level 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 (a) depreciation expense and (b) book value under the straight-line, sum-of-the-years’digits, and double-declining-balance depreciation methods?

To determine

Compute the depreciation expense of Company G for 2016 and 2017 under the given depreciation method.

Explanation of Solution

Depreciation: Depreciation is a method of reducing the capitalized cost of long-lived operating assets or plant assets for the period the asset is used.

Straight-line depreciation method: The depreciation method which assumes that the consumption of economic benefits of long-term asset could be distributed equally throughout the useful life of the asset is referred to as straight-line method.

Activity method: In this method of depreciation, the amount of depreciation is charged based on the units of production or hours worked each year. When the usefulness of an asset is related to the production cost of a unit, this method is more appropriate to use.

Sum-of- the-years’ digits method: Sum-of-the years’ digits method determines the depreciation by multiplying the depreciable base and declining fraction.

Double-declining-balance method: The depreciation method which assumes that the consumption of economic benefits of long-term asset is high in the early years but gradually declines towards the end of its useful life is referred to as double-declining-balance method.

a. Straight line method:

2016:

$\begin{array}{c}\text{Depreciation expenses}=\frac{\text{Acquisition cost – Residual value}}{\text{Useful life}}\\ =\frac{\text{\$220,000}-\text{\$20,000}}{\text{5 years}}\\ =\$40,000\end{array}$

2017:

$\begin{array}{c}\text{Depreciation expenses}=\frac{\text{Acquisition cost – Residual value}}{\text{Useful life}}\\ =\frac{\text{\$220,000}-\text{\$20,000}}{\text{5 years}}\\ =\$40,000\end{array}$

b. Sum-of- the-years’ digits method:

Year	Depreciable Base  ($) (1)		Depreciation rate per year		Depreciation expense ($)
2016	200,000	$\times$	$\frac{5}{15}$	=	66,667
2017	200,000	$\times$	$\frac{4}{15}$	=	53,333

Table (1)

Working note (1):

Calculate the depreciable base of asset.

$\begin{array}{c}\text{Depreciable base = Purchase price –Residual value }\\ \text{= \$220,000–\$20,000}\\ \text{=\$200,000}\end{array}$

Working note (2):

Calculate the denominator of the fraction for sum-of-the-year’s digit.

$\begin{array}{c}\text{Sum-of-the-digits = }\frac{\text{n}\times \left(\text{n}+1\right)}{2}\\ =\frac{5\times \left(5+1\right)}{2}\\ =\frac{5\times 6}{2}\\ =15\end{array}$

c. Double-declining-balance method:

2016:

$\begin{array}{c}\text{Depreciation expense}=\text{Aquisition cost of equipment}\times \text{Depreciation Rate }(3)\\ =\text{\$220,000}\times \frac{40}{100}\\ =\$88,000\end{array}$

2017:

$\begin{array}{c}\text{Depreciation expense}=\left[\begin{array}{l}\text{Aquisition cost of equipment}-\\ \text{Depreciation expense for 2016}\end{array}\right]\times \text{Depreciation Rate }(3)\\ =\left(\text{\$220,000}-\$88,000\right)\times \frac{40}{100}\\ =\$52,800\end{array}$

Working note (3):

Compute the depreciation rate:

Useful life = 5 years

$\begin{array}{c}\text{Depreciation rate}=\frac{\text{100\%}}{\text{5 years}}\times 2\\ =40\%\end{array}$

d. Activity method (hours worked):

2016:

$\begin{array}{c}\text{Depreciation expense = }\left(\begin{array}{l}\text{Hours worked }\times \\ \text{Cost per hour}\end{array}\right)\\ =1,8\text{00 hours }\times \text{\$20 per hour (4)}\\ \text{=\$36,000}\end{array}$

2017:

$\begin{array}{c}\text{Depreciation expense = }\left(\begin{array}{l}\text{Hours worked }\times \\ \text{Cost per hour}\end{array}\right)\\ =1,5\text{00 hours }\times \text{\$20 per hour (4)}\\ \text{=\$30,000}\end{array}$

Working note (4):

Calculate the cost per hour.

$\begin{array}{c}\text{Cost per hour = }\frac{\text{Cost of equipment }-\text{Residual value}}{\text{Total estimated serivce hours}}\\ =\frac{\$220,000-\$20,000}{10,000\text{ hours}}\\ =\$20\text{ per hour}\end{array}$

e. Activity method (unit of output):

2016:

$\begin{array}{c}\text{Depreciation expense = }\left(\begin{array}{l}\text{Output units }\times \\ \text{Cost per unit}\end{array}\right)\\ =44,000\text{ units }\times \text{\$1 per unit (5)}\\ \text{=\$44,000}\end{array}$

2017:

$\begin{array}{c}\text{Depreciation expense = }\left(\begin{array}{l}\text{Output units }\times \\ \text{Cost per unit}\end{array}\right)\\ =35,000\text{ units }\times \text{\$1 per unit (5)}\\ \text{=\$35,000}\end{array}$

Working note (5):

Calculate the cost per unit.

$\begin{array}{c}\text{Cost per unit = }\frac{\text{Cost of equipment }-\text{Residual value}}{\text{Total out put units}}\\ =\frac{\$220,000-\$20,000}{200,000\text{ units}}\\ =\$1\text{ per unit}\end{array}$

To determine

Calculate the book value of the machine at the end of 2016 and 2017 under each depreciation method.

Explanation of Solution

Calculate the book value of the machine at the end of 2016 and 2017 under each depreciation method as follows:

Year	Book Value (A)	Depreciation (B)	Ending Book Value $\left(\text{A}-\text{B}\right)$
a. Straight-line Method
2016	$220,000	$40,000	$180,000
2017	$180,000	$40,000	$140,000
b. Sum-of-the-years’-digits
2016	$220,000	$66,667	$153,333
2017	$153,333	$53,333	$100,000
c. Double-declining-balance
2016	$220,000	$88,000	$132,000
2017	$132,000	$52,800	$79,200
d. Activity based method on hours worked
2016	$220,000	$36,000	$184,000
2017	$184,000	$30,000	$154,000
e. Activity based method on units of output
2016	$220,000	$44,000	$176,000
2017	$176,000	$35,000	$141,000

Table (2)

Note: Ending book value for 2016 is considered as the beginning book value for 2017.

To determine

Identify the effect of (a) the depreciation expense and (b) book value under the straight line, sum of the year’s digit, and double-declining balance method, assume that Company G used a service life of 8 years, or 15,000 hours and residual value of $10,000.

Explanation of Solution

(a) Identify the effect of the depreciation expense under the straight line, sum of the year’s digit, and double-declining balance method as follows:

Straight line method:

2016:

$\begin{array}{c}\text{Depreciation expenses}=\frac{\text{Acquisition cost – Residual value}}{\text{Useful life}}\\ =\frac{\text{\$220,000}-\text{\$10,000}}{\text{8 years}}\\ =\$26,250\end{array}$

2017:

$\begin{array}{c}\text{Depreciation expenses}=\frac{\text{Acquisition cost – Residual value}}{\text{Useful life}}\\ =\frac{\text{\$220,000}-\text{\$10,000}}{\text{5 years}}\\ =\$26,250\end{array}$

Sum-of- the-years’ digits method:

Year	Depreciable Base  ($) (6)		Depreciation rate per year		Depreciation expense ($)
2016	210,000	$\times$	$\frac{8}{36}$	=	46,667
2017	210,000	$\times$	$\frac{7}{36}$	=	40,833

Table (3)

Working note (6):

Calculate the depreciable base of asset.

$\begin{array}{c}\text{Depreciable base = Purchase price –Residual value }\\ \text{= \$220,000–\$10,000}\\ \text{=\$210,000}\end{array}$

Working note (7):

Calculate the denominator of the fraction for sum-of-the-year’s digit.

$\begin{array}{c}\text{Sum-of-the-digits = }\frac{\text{n}\times \left(\text{n}+1\right)}{2}\\ =\frac{8\times \left(8+1\right)}{2}\\ =\frac{8\times 9}{2}\\ =36\end{array}$

Double-declining-balance method:

2016:

$\begin{array}{c}\text{Depreciation expense}=\text{Aquisition cost of equipment}\times \text{Depreciation Rate }(8)\\ =\text{\$220,000}\times \frac{25}{100}\\ =\$55,000\end{array}$

2017:

$\begin{array}{c}\text{Depreciation expense}=\left[\begin{array}{l}\text{Aquisition cost of equipment}-\\ \text{Depreciation expense for 2019}\end{array}\right]\times \text{Depreciation Rate }(8)\\ =\left(\text{\$220,000}-\$55,000\right)\times \frac{25}{100}\\ =\$41,250\end{array}$

Working note (8):

Compute the depreciation rate:

Useful life = 5 years

$\begin{array}{c}\text{Depreciation rate}=\frac{\text{100\%}}{\text{8 years}}\times 2\\ =25\%\end{array}$

b) Identify the effect of the book value under the straight line, sum of the year’s digit, and double-declining balance method as follows:

Year	Book Value (A)	Depreciation (B)	Ending Book Value $\left(\text{A}-\text{B}\right)$
Straight-line Method
2016	$220,000	$26,250	$193,750
2017	$193,750	$26,250	$167,500
Sum-of-the-years’-digits
2016	$220,000	$46,667	$173,333
2017	$173,333	$40,833	$132,500
Double-declining-balance
2016	$220,000	$55,000	$165,000
2017	$165,000	$41,250	$123,750

Table (4)

Note: Ending book value for 2016 is considered as the beginning book value for 2017.

When the service life of an asset increases, the depreciation expense gets decreased under straight line, sum of year’s digit, and double-declining balance method, and this decreased depreciation expense increases the ending book value of machinery.