Chapter 9, Problem 7PB

a)

To determine

Calculate the amount of depreciation expense that Incorporation H should expect to recognize under each of the following depreciation methods in the first and second years of the truck’s useful life.

1. Straight-line.

2. Double-declining-balance.

3. Units-of-output (based on miles).

Explanation of Solution

1. Straight-line Depreciation: Under the straight-line method of depreciation, the same amount of depreciation is allocated every year over the estimated useful life of an asset. The formula to calculate the depreciation cost of the asset using the residual value is shown as below:

$\text{Depreciation = }\frac{\left(\text{Cost of the asset}-\text{Residual value}\right)}{\text{Estimated useful life of the asset}}$

Truck cost is $24,000, expected residual value is $6,000 and estimated useful life is 6 years.

Calculate the amount of depreciation expense under Straight-line depreciation method in the first and second years of the truck’s useful life:

$\begin{array}{c}\text{Depreciation = }\frac{\left(\text{Cost of the asset}-\text{Residual value}\right)}{\text{Estimated useful life of the asset}}\\ =\frac{\left(\$24,000-\$6,000\right)}{6\text{years}}\\ =\$3,000\end{array}$

The annual depreciation of the truck is $3,000.

Therefore, the amount of depreciation expense for the first and second years is $3,000 each.

2. 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.

$\text{Depreciation = }\left(\text{Cost}-\text{accumulated depreciation}\right)\times \frac{2}{\text{Useful Life}}$

Calculate depreciation expense for first year under Double-declining-balance method:

Truck cost is $24,000, expected residual value is $6,000 and estimated useful life is 6 years.

$\begin{array}{c}\text{Depreciation = }\left(\text{Cost}-\text{accumulated depreciation}\right)\times \frac{2}{\text{Useful Life}}\\ =\left(\$24,000-\$0\right)\times \frac{2}{6\text{years}}\\ =\$8,000\end{array}$

Therefore, depreciation expense for first year under double declining method is $8,000.

Calculate depreciation expense for second year under Double-declining-balance method:

Truck cost is $24,000, expected residual value is $6,000 and estimated useful life is 6 years. Accumulated depreciation is $8,000 (first year depreciation).

$\begin{array}{c}\text{Depreciation = }\left(\text{Cost}-\text{accumulated depreciation}\right)\times \frac{2}{\text{Useful Life}}\\ =\left(\$24,000-\$8,000\right)\times \frac{2}{6\text{years}}\\ =\$5,333\end{array}$

Therefore, depreciation expense for second year under double declining method is $5,333.

3. Unit-of-output Method: Under this method of depreciation, the depreciation expense is calculated on the basis of output in a year. This method is suitable when a company has fluctuating productive rate. The formula to calculate the depreciation expense under this method is as follows:

$\text{Depreciation = }\frac{\text{Cost}-\text{Residual value}}{\text{Estimated output of useful life}}\times \text{Actual output}$

Compute the first year depreciation of the truck:

Truck cost is $24,000, expected residual value is $6,000 and estimated useful life is 6 years.

$\begin{array}{c}\text{Depreciation = }\frac{\text{Cost}-\text{Residual value}}{\text{Estimated output of useful life}}\times \text{Actual output}\\ \text{=}\frac{\left(\$24,000-\$6,000\right)}{15,000+\left(20,000\times 2\right)+\left(12,000\times 3\right)\text{miles}}\times 15,000\text{miles}\\ \text{=}\frac{\$18,000}{91,000\text{miles}}\times 15,000\text{miles}\\ \text{=}\$2\text{,967}\end{array}$

Hence, depreciation expense for the first year under units of output method is $2,967.

Compute the second year depreciation of the truck:

$\begin{array}{c}\text{Depreciation = }\frac{\text{Cost}-\text{Residual value}}{\text{Estimated output of useful life}}\times \text{Actual output}\\ \text{=}\frac{\left(\$24,000-\$6,000\right)}{15,000+\left(20,000\times 2\right)+\left(12,000\times 3\right)\text{miles}}\times 20,000\text{miles}\\ \text{=}\frac{\$18,000}{91,000\text{miles}}\times 20,000\text{miles}\\ \text{=}\$3\text{,956}\end{array}$

Hence, depreciation expense for the second year under units of output method is $3,956.

b)

To determine

Prepare the plant assets section of the balance sheet at the end of the second year of the asset’s useful life under the units of output method.

Explanation of Solution

Balance Sheet: Balance Sheet is one of the financial statements which summarize the assets, the liabilities, and the Shareholder’s equity of a company at a given date. It is also known as the statement of financial status of the business.

Prepare the plant assets section of the balance sheet at the end of the second year of the asset’s useful life under the units of output method:

Incorporation H
Balance sheet
As on second year end
Assets:
Truck	$24,000
Less: Accumulated depreciation (1)	($6,923)	$17,077

Table (1)

Accumulated depreciation: The total amount of depreciation expense deducted, from the time asset acquired till date, as reported in the account as on a particular date, is referred to as accumulated depreciation

Therefore, the accumulated depreciation at the end of second year is $6,923 $\left(\$2,967\text{first}\text{year}\text{depreciation}+\$3,956\text{second year depreciation}\right)$ (1)

c)

To determine

Identify the method of depreciation, in which it is not possible to ascertain the actual amount of depreciation expense prior to the end of each year. Explain the causes for this uncertainty.

Explanation of Solution

The unit of output method is the method of depreciation, in which it is not possible to ascertain the actual amount of depreciation expense prior to the end of each year. The reason for such uncertainty is, to calculate the depreciation expense amount actual output (estimated number of miles driven) is used. Hence, the depreciation expense is not determined until the period ends.