Chapter 11, Problem 11.2E

(1)

To determine

Depreciation:

Depreciation refers to the reduction in the monetary value of a fixed asset due to its wear and tear or obsolescence. It is a method of distributing the cost of the fixed assets over its estimated useful life. The following is the formula to calculate the depreciation.

$\text{Depreciation cost = }\frac{\text{Cost of the asset-Salvage value}}{\text{Estimated useful life of the asset}}$

To calculate: The depreciation for 2016 and 2017 using straight line method.

Explanation of Solution

Corporation A purchased machinery for $115,000. The estimated service life of the machinery is 10 years and the estimated residual value is $5,000.

Calculate depreciation using straight line method

Straight line method:

Under the straight-line method of depreciation, the same amount of depreciation is allocated every year over the estimated useful life of an asset.

$\text{Depreciation expense = }\frac{\text{Cost of the asset-Salvage value}}{\text{Estimated useful life of the asset}}$

$\begin{array}{c}\text{Depreciation}\text{expense = }\frac{\left(\$115,000-\$5,000\right)}{10\text{years}}\\ =\frac{\$110,000}{10}\\ =\$11,000\end{array}$

Hence, depreciation for 2016 and 2017 is $11,000.

(2)

To determine

To calculate: The depreciation for 2016 and 2017 using Sum-of-the-years’-digits method.

Explanation of Solution

Corporation A purchased machinery for $115,000. The estimated service life of the machinery is 10 years and the estimated residual value is $5,000.

Sum-of- the-years’ digits (SYD) method:

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

$\begin{array}{c}\text{Depreciation}\text{expense}\text{=}\{\begin{array}{l}\text{Cost of the asset }\times \left(\begin{array}{l}\text{Number of years of}\\ \text{estimated life remaining }\\ \text{at the beginning of the year}\end{array}\right)\begin{array}{l}\text{÷}\text{SYD}\hfill \end{array}\\ \end{array}\\ \text{SYD}\text{=}\frac{\text{n}\left(\text{n+1}\right)}{\text{2}}\end{array}$

Where n is estimated life time of the asset.

$\begin{array}{c}SYD=\frac{n\left(n+1\right)}{2}\\ =\frac{10\left(10+1\right)}{2}\\ =55\end{array}$

Calculate depreciation for 2016 and 2017 using Sum-of-the-years’-digits method.

For 2016:

$\begin{array}{c}\text{Depreciation}\text{expense}=\frac{\left(\$15,000-\$5,000\right)\times 10}{55}\\ =\frac{\$110,000\times 10}{55}\\ =\$20,000\end{array}$

For 2017:

$\begin{array}{c}\text{Depreciation}\text{expense}=\frac{\left(\$15,000-\$5,000\right)\times 9}{55}\\ =\frac{\$110,000\times 9}{55}\\ =\$18,000\end{array}$

Hence, a depreciation expense for 2016 is $20,000 and for 2017 is $18,000.

(3)

To determine

To calculate: The depreciation expenses for 2016 and 2017 using double declining balance method.

Explanation of Solution

Corporation A purchased machinery for $115,000. The estimated service life of the machinery is 10 years and the estimated residual value is $5,000.

Double declining balance (DDB) method:

In this method of depreciation, the depreciation is calculated by multiply beginning of year book value, not depreciable base, by an annual rate that is a multiple of the straight line rate.

$\text{Depreciation expense}\text{=}\left(\begin{array}{l}\text{Begining}\text{value}\\ \text{of}\text{the}\text{asset}\end{array}\right)\text{×}\left(\begin{array}{l}\text{Straight}\text{line}\text{rate}\\ \text{of}\text{depreciation }\times \text{ 2}\end{array}\right)$

Calculate depreciation expense for 2016 and 2017.

For 2016:

$\begin{array}{c}\text{Depreciation expense = \$115,000}\times \left(\frac{1}{10}\right)\times 2\\ =\$23,000\end{array}$

For 2017:

$\begin{array}{c}\text{Depreciation expense = }\left(\text{\$115,000}-\$23,000\right)\times \left(\frac{1}{10}\right)\times 2\\ =\$92,000\times \left(\frac{2}{10}\right)\\ =\$18,400\end{array}$

Hence, a depreciation expense for 2016 is $23,000 and for 2017 is $18,400.

(4)

To determine

To calculate: The depreciation expense for 2016 and 2017 using One hundred fifty percent declining balance.

Explanation of Solution

Corporation A purchased machinery for $115,000. The estimated service life of the machinery is 10 years and the estimated residual value is $5,000.

One hundred fifty percent declining balance:

In this method of depreciation, the depreciation is calculated by multiply beginning of year book value, not depreciable base, by an annual rate that is a 150% or 1.5 of the straight line rate.

$\text{Depreciation expense}\text{=}\left(\begin{array}{l}\text{Begining}\text{value}\\ \text{of}\text{the}\text{asset}\end{array}\right)\text{×}\left(\begin{array}{l}\text{Straight}\text{line}\text{rate}\\ \text{of}\text{depreciation }\times \text{ 1}\text{.5}\end{array}\right)$

Calculate depreciation for 2016 and 2017.

For 2016:

$\begin{array}{c}\text{Depreciation expense = \$115,000}\times \left(\frac{1}{10}\right)\times 1.5\\ =\$17,250\end{array}$

For 2017:

$\begin{array}{c}\text{Depreciation expense = }\left(\text{\$115,000}-\$17,250\right)\times \left(\frac{1}{10}\right)\times 1.5\\ =\$97,750\times \left(\frac{1}{10}\right)\times 1.5\\ =\$14,663\end{array}$

Hence, a depreciation expense for 2018 is $17,250 and for 2019 is $14,663.

(5)

To determine

To calculate: The depreciation expense for 2016 and 2017 using Units of production method.

Explanation of Solution

Corporation A purchased machinery for $115,000. The estimated service life of the machinery is 10 years and the estimated residual value is $5,000. The machine is expected to produce 220,000 units during its life. During 2016, units produced were 10,000 and during 2019, units produced were 25,000.

Units of production method:

The units’ of-production method is an activity-based method that calculates a depletion or depreciation or amortization rate per measure of activity and then multiplies this rate by actual activity to determine periodic cost allocation.

$\text{Depreciation expense = }\frac{\text{Cost of the asset - Residual value}}{\text{Expected}\text{production}}\times \left(\begin{array}{l}\text{Number}\text{of}\text{measures}\\ \text{produced}\text{in}\text{that}\text{period}\end{array}\right)$

Calculate depreciation expense for 2016 and 2017:

For 2016:

$\begin{array}{c}\text{Depreciation expense = }\frac{\text{\$115,000 }-\text{ \$5,000}}{220,000\text{ units}}\times \left(10,000\text{units}\right)\\ =\frac{\$110,000}{220,000}\times 10,000\\ =\frac{1}{2}\times 10,000\\ =\$5,000\end{array}$

For 2017:

$\begin{array}{c}\text{Depreciation expense = }\frac{\text{\$115,000 }-\text{ \$5,000}}{220,000\text{ units}}\times \left(25,000\text{units}\right)\\ =\frac{\$110,000}{220,000}\times 25,000\\ =\frac{1}{2}\times 25,000\\ =\$12,500\end{array}$

Hence, a depreciation expense for 2016 is $5,000 and for 2017 is $12,500.