Chapter 11, Problem 1P

1.

To determine

Calculate the depreciation expense of Company W for 2016 and 2017 under straight line method.

Explanation of Solution

Depreciation expense: Depreciation expense is a non-cash expense, which is recorded on the income statement reflecting the consumption of economic benefits of long-term asset on account of its wear and tear or obsolesces.

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.

Calculate the depreciation expense of Company W under straight line method as follows:

$\begin{array}{c}\text{Depreciation expenses}=\frac{\text{Acquisition cost – Residual value}}{\text{Useful life}}\\ =\frac{\text{\$700,000}-\text{\$50,000}}{\text{20 years}}\\ =\$32,500\text{ per year}\end{array}$

Conclusion

Therefore, the depreciation expense of Company W under straight line method is $22,500.

2.

To determine

Calculate the depreciation expense of Company W for 2016 and 2017 under activity method based on hours worked.

Explanation of Solution

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.

Calculate the depreciation expense of Company W for 2016 and 2017 under activity method based on hours worked as follows:

2016:

$\begin{array}{c}\text{Depreciation expense = }\left(\begin{array}{l}\text{Hours worked }\times \\ \text{Cost per hour}\end{array}\right)\\ =4,5\text{00 hours }\times \text{\$6}\text{.50 per hour (1)}\\ \text{=\$29,250}\end{array}$

2017:

$\begin{array}{c}\text{Depreciation expense = }\left(\begin{array}{l}\text{Hours worked }\times \\ \text{Cost per hour}\end{array}\right)\\ =5,5\text{00 hours }\times \text{\$6}\text{.50 per hour (1)}\\ \text{=\$35,750}\end{array}$

Working note (1):

Calculate the cost per hour.

$\begin{array}{c}\text{Cost per hour = }\frac{\text{Cost of equipment }-\text{Residual value}}{\text{Total estimated serivce hours}}\\ =\frac{\$700,000-\$50,000}{100,000\text{ hours}}\\ =\$6.50\end{array}$

3.

To determine

Calculate the depreciation expense of Company W for 2016 and 2017 under activity method based on units of output.

Explanation of Solution

Calculate the depreciation expense of Company W for 2016 and 2017 under activity method based on units of output as follows:

2016:

$\begin{array}{c}\text{Depreciation expense = }\left(\begin{array}{l}\text{Output units }\times \\ \text{Cost per unit}\end{array}\right)\\ =40,000\text{ units }\times \text{\$0}\text{.68 per unit (2)}\\ \text{=\$27,200}\end{array}$

2017:

$\begin{array}{c}\text{Depreciation expense = }\left(\begin{array}{l}\text{Output units }\times \\ \text{Cost per unit}\end{array}\right)\\ =60,000\text{ units }\times \text{\$0}\text{.68 per unit (2)}\\ \text{=\$40,800}\end{array}$

Working note (2):

Calculate the cost per unit.

$\begin{array}{c}\text{Cost per unit = }\frac{\text{Cost of equipment }-\text{Residual value}}{\text{Total out put units}}\\ =\frac{\$700,000-\$50,000}{950,000\text{ units}}\\ =\$0.68\text{ per unit}\end{array}$

4.

To determine

Calculate the depreciation expense of Company W for 2016 and 2017 under sum-of years’ digit method.

Explanation of Solution

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

Calculate the depreciation expense of Company W for 2016 and 2017 under sum-of years’ digit method as follows:

Year	Depreciable Base  ($) (3)		Depreciation rate per year		Depreciation expense ($)
2016	650,000	$\times$	$\frac{20}{210}$	=	61,905
2017	650,000	$\times$	$\frac{19}{210}$	=	58,810

Table (1)

Working note (3):

Calculate the depreciable base of asset.

$\begin{array}{c}\text{Depreciable base = Purchase price –Residual value }\\ \text{= \$700,000–\$50,000}\\ \text{=\$650,000}\end{array}$

Working note (4):

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

$\begin{array}{c}\text{Sum-of-the-digits = }\frac{\text{n}\times \left(\text{n}+1\right)}{2}\\ =\frac{20\times \left(20+1\right)}{2}\\ =\frac{20\times 21}{2}\\ =210\end{array}$

5.

To determine

Calculate the depreciation expense of Company W for 2016 and 2017 under the double-declining balance method.

Explanation of Solution

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

Calculate the depreciation expense of Company W for 2016 and 2017 under the double-declining balance method as follows:

2016:

$\begin{array}{c}\text{Depreciation expense}=\text{Aquisition cost of equipment}\times \text{Depreciation Rate }(5)\\ =\text{\$700,000}\times \frac{10}{100}\\ =\$70,000\end{array}$

2017:

$\begin{array}{c}\text{Depreciation expense}=\left[\begin{array}{l}\text{Aquisition cost of equipment}-\\ \text{Depreciation expense for 2016}\end{array}\right]\times \text{Depreciation Rate }(5)\\ =\left(\text{\$700,000}-\$70,000\right)\times \frac{10}{100}\\ =\$63,000\end{array}$

Working note (5):

Compute the depreciation rate:

Useful life = 20 years

$\begin{array}{c}\text{Depreciation rate}=\frac{\text{100\%}}{\text{20 years}}\times 2\\ =10\%\end{array}$

6.

To determine

Calculate the depreciation expense of Company W for 2016 and 2017 under the 150%-declining balance method.

Explanation of Solution

Calculate the depreciation expense of Company W for 2016 and 2017 under the 150%- declining balance method as follows:

2016:

$\begin{array}{c}\text{Depreciation expense}=\text{Aquisition cost of equipment}\times \text{Depreciation Rate }(6)\\ =\text{\$700,000}\times \frac{7.5}{100}\\ =\$52,500\end{array}$

2017:

$\begin{array}{c}\text{Depreciation expense}=\left[\begin{array}{l}\text{Aquisition cost of equipment}-\\ \text{Depreciation expense for 2016}\end{array}\right]\times \text{Depreciation Rate }(6)\\ =\left(\text{\$700,000}-\$52,500\right)\times \frac{7.5}{100}\\ =\$48,563\end{array}$

Working note (6):

Compute the depreciation rate:

Useful life = 20 years

$\begin{array}{c}\text{Depreciation rate}=\frac{\text{100\%}}{\text{20 years}}\times 1.5\\ =7.5\%\end{array}$

7.

To determine

Identify the effect of the depreciation expense under straight line, sum of the year’s digit, and declining balance methods, assume Company W used a service life of 16 years, 80,000 hours, or 75,000 units of output.

Explanation of Solution

Identify the effect of the depreciation expense under straight line, sum of the year’s digit, and declining balance methods, assume Company W used a service life of 16 years, 80,000 hours, or 75,000 units of output as follows:

Straight line method:

$\begin{array}{c}\text{Depreciation expenses}=\frac{\text{Acquisition cost – Residual value}}{\text{Useful life}}\\ =\frac{\text{\$700,000}-\text{\$50,000}}{\text{16 years}}\\ =\$40,625\text{ per year}\end{array}$

Activity method (hours worked):

2016:

$\begin{array}{c}\text{Depreciation expense = }\left(\begin{array}{l}\text{Hours worked }\times \\ \text{Cost per hour}\end{array}\right)\\ =4,5\text{00 hours }\times \text{\$8}\text{.125 per hour (7)}\\ \text{=\$36,563}\end{array}$

2017:

$\begin{array}{c}\text{Depreciation expense = }\left(\begin{array}{l}\text{Hours worked }\times \\ \text{Cost per hour}\end{array}\right)\\ =5,5\text{00 hours }\times \text{\$8}\text{.125 per hour (7)}\\ \text{=\$44,688}\end{array}$

Working note (7):

Calculate the cost per hour.

$\begin{array}{c}\text{Cost per hour = }\frac{\text{Cost of equipment }-\text{Residual value}}{\text{Total estimated serivce hours}}\\ =\frac{\$700,000-\$50,000}{80,000\text{ hours}}\\ =\$8.125\text{ per hour}\end{array}$

Activity method (unit of output):

2016:

$\begin{array}{c}\text{Depreciation expense = }\left(\begin{array}{l}\text{Output units }\times \\ \text{Cost per unit}\end{array}\right)\\ =40,000\text{ units }\times \text{\$0}\text{.87 per unit (8)}\\ \text{=\$34,800}\end{array}$

2017:

$\begin{array}{c}\text{Depreciation expense = }\left(\begin{array}{l}\text{Output units }\times \\ \text{Cost per unit}\end{array}\right)\\ =60,000\text{ units }\times \text{\$0}\text{.87 per unit (8)}\\ \text{=\$52,200}\end{array}$

Working note (8):

Calculate the cost per unit.

$\begin{array}{c}\text{Cost per unit = }\frac{\text{Cost of equipment }-\text{Residual value}}{\text{Total out put units}}\\ =\frac{\$700,000-\$50,000}{750,000\text{ units}}\\ =\$0.87\text{ per unit}\end{array}$

Sum-of- the-years’ digits method:

Year	Depreciable Base  ($) (3)		Depreciation rate per year		Depreciation expense ($)
2016	650,000	$\times$	$\frac{16}{136}$	=	76,471
2017	650,000	$\times$	$\frac{15}{136}$	=	71,691

Table (2)

Working note (9):

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

$\begin{array}{c}\text{Sum-of-the-digits = }\frac{\text{n}\times \left(\text{n}+1\right)}{2}\\ =\frac{16\times \left(16+1\right)}{2}\\ =\frac{16\times 17}{2}\\ =136\end{array}$

Double-declining-balance method:

2016:

$\begin{array}{c}\text{Depreciation expense}=\text{Aquisition cost of equipment}\times \text{Depreciation Rate }(10)\\ =\text{\$700,000}\times \frac{12.5}{100}\\ =\$87,500\end{array}$

2017:

$\begin{array}{c}\text{Depreciation expense}=\left[\begin{array}{l}\text{Aquisition cost of equipment}-\\ \text{Depreciation expense for 2016}\end{array}\right]\times \text{Depreciation Rate }(10)\\ =\left(\text{\$700,000}-\$87,500\right)\times \frac{12.5}{100}\\ =\$76,563\end{array}$

Working note (10):

Compute the depreciation rate:

Useful life = 16 years

$\begin{array}{c}\text{Depreciation rate}=\frac{\text{100\%}}{\text{16 years}}\times 2\\ =12.5\%\end{array}$

150%- declining balance method:

2016:

$\begin{array}{c}\text{Depreciation expense}=\text{Aquisition cost of equipment}\times \text{Depreciation Rate }(11)\\ =\text{\$700,000}\times \frac{9.375}{100}\\ =\$65,625\end{array}$

2017:

$\begin{array}{c}\text{Depreciation expense}=\left[\begin{array}{l}\text{Aquisition cost of equipment}-\\ \text{Depreciation expense for 2019}\end{array}\right]\times \text{Depreciation Rate }(11)\\ =\left(\text{\$700,000}-\$65,625\right)\times \frac{9.375}{100}\\ =\$59,473\end{array}$

Working note (11):

Compute the depreciation rate:

Useful life = 16 years

$\begin{array}{c}\text{Depreciation rate}=\frac{\text{100\%}}{\text{16 years}}\times 1.5\\ =9.375\%\end{array}$

When the service life of an asset decreases, the depreciation expense gets increased under straight line, sum of year’s digit, and declining balance method.