Chapter 11, Problem 11.5P

To determine

Depreciation:

It refers to the reduction in the monetary value of fixed tangible assets over its useful life due to its wear and tear or, obsolescence. In other words, it is the method of distributing the cost of tangible fixed assets over its estimated useful life.

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:

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

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:

It is an accelerated method of depreciation under which the depreciation declines in each successive year until the value of asset becomes zero. Under this method, the book value (original cost less accumulated depreciation) of the long-term asset is decreased by a fixed rate. It is double the rate of the straight-line depreciation. Use the following formula to determine the annual depreciation:

$\text{Depreciation = Purchase price × }\frac{\text{2}}{\text{Useful}\text{life}}$

Amortization:

It is the process of allocating the value of an intangible asset over its definite useful life.

To determine: The missing amounts in fixed assets and depreciation schedule of Corporation T.

Explanation of Solution

1. Cost of Land A:

Asset	Fair value ($)	Percent of  total fair value (%)	Initial valuation ($)
Land A	72,000	8%	65,000
Building  A	828,000	92%	747,500
Total	900,000	100.0%	812,500

Table (1)

Thus, the cost of land A is $65,000.

Note:

$\text{Percent of total fair value = }\frac{\text{Fair value of land / building}}{\text{Total}\text{fair}\text{value}}$

$\text{Initital valuation = Percent of total fair value }\times \text{ Cash paid for the property}$

2. Cost of Building A:

Refer 1 for calculation of cost of building. Hence, the cost of land is $747,500.

3. Estimated useful life of Building:

$\begin{array}{c}\text{Depreciation = }\frac{\text{Cost of the Asset }-\text{ Residual value}}{\text{Estimated Useful Life of the Asset}}\\ \$14,000=\frac{\text{\$747,500 – \$47,500}}{\text{Estimated Useful Life of the Asset}}\\ \begin{array}{l}\text{Estimated Useful}\\ \text{ Life of the Asset}\end{array}\}=\frac{\text{\$747,500 – \$47,500}}{\$14,000}\\ =50\text{years}\end{array}$

Thus, the estimated useful life is 50 years.

4. The amount of depreciation (Building A) for the year 2016:

Corporation T used the straight line method for cost allocation. So, depreciation is same as prior year. Thus, the depreciation on building is $14,000.

5. Cost of land B:

$\begin{array}{c}\text{Cost of land B =}\left(\begin{array}{l}\left(\text{Number of shares }\times \text{ Price per share}\right)\\ +\text{Demolition of old building}\end{array}\right)\\ =\left(3,000\text{shares}\times \$25\text{per}\text{share}\right)+\$10,400\\ =\$85,400\end{array}$

Thus, the cost of land B is $85,400.

6. The amount of depreciation (Building B) for the year 2016:

Building B is under construction, hence there is no depreciation value before the use of building.

7. Cost of donated equipment:

The fair value of donated equipment is equal to the cost of donated equipment. Therefore, the cost of donated equipment is $16,000.

8. The amount of depreciation (Equipment) for the year 2015:

The company uses 150% declining balance method. Therefore, depreciation is determined as follows:

$\begin{array}{c}\text{Depreciation = Cost of equipment }\times \text{ Depreciation rate (1)}\\ \text{= \$16,000}\times \text{15\%}\\ \text{=\$2,400}\end{array}$

Thus, the depreciation is $2,400.

Working note:

Calculate the depreciation rate

$\begin{array}{c}150\%\text{declining balance method = 1}\text{.5 }\times \text{ Straight-line rate }\left(\text{10\%}\right)\\ =\text{}1.5\times 10\%\\ =15\%\end{array}$ (1)

9. The amount of depreciation (Equipment) for the year 2016:

The company uses 150% declining balance method. Therefore, depreciation is determined as follows:

$\begin{array}{c}\text{Depreciation = }\left(\text{Cost of equipment–Depreciation for 2017}\right)\times \text{ Depreciation rate (1)}\\ =\left(\$16,000–\$2,400\right)\times 15\%\\ =\$2,040\end{array}$

Thus, the depreciation is $2,040.

10. Cost of Machine A:

$\begin{array}{c}\text{Cost of Mahcine A = Total cost – Normal repairs }\\ \text{= \$110,000 – \$11,000}\\ \text{=\$99,000}\end{array}$

Thus, the cost of Machine A is $99,000.

11. The amount of depreciation (Machine A) for the year 2015:

The company uses declining balance method. Therefore, depreciation is determined as follows:

$\begin{array}{c}\text{Depreciation = Depreciable base (3) }\times \frac{\text{Estimated useful life }}{\text{Sum-of-years'}\text{digits (2)}}\\ =\$94,000\times \frac{10}{55}\\ =\$17,000\end{array}$

Thus, the depreciation is $17,000.

Working note:

1. Calculate the sum-of-the-digits

$\begin{array}{c}\text{Sum-of-the-digits = }\frac{\text{n}\times \left(\text{n}+1\right)}{2}\\ =\frac{10\times \left(10+1\right)}{2}\\ =\frac{10\times 11}{2}\\ =55\end{array}$ (2)

2. Calculate the amount of depreciation base

$\begin{array}{c}\text{Depreciable base = Purchase price –Residual value }\\ =\$99,000–\$5,500\\ =\$94,000\end{array}$ (3)

12. The amount of depreciation (Machine B) for the year ended 2016:

The company uses declining balance method. Therefore, depreciation is determined as follows:

$\begin{array}{c}\text{Depreciation = }\left[\begin{array}{l}\left(\text{Depreciable base (4) –Depreciation for 2017}\right)\\ \times \frac{\text{Estimated remaining life }}{\text{Sum-of-years'}\text{digits (5) }}\times \frac{4}{12}\end{array}\right]\\ =\$94,000\times \frac{9}{55}\times \frac{4}{12}\\ =\$5,100\end{array}$

Hence, the amount of depreciation (Machine B) for the year ended 2016 is $5,100.

Working note:

1. Calculate the sum-of-the-digits

$\begin{array}{c}\text{Sum-of-the-digits = }\frac{\text{n}\times \left(\text{n}+1\right)}{2}\\ =\frac{10\times \left(10+1\right)}{2}\\ =\frac{10\times 11}{2}\\ =55\end{array}$ (4)

2. Calculate the amount of depreciation base

$\begin{array}{c}\text{Depreciable base = Purchase price –Residual value }\\ \text{= \$99,000–\$5,500}\\ \text{=\$94,000}\end{array}$ (5)

13. Cost of Machine B:

$\begin{array}{c}\text{Present value annuity due = Annuity amount }\times \text{Present value of an annuity due of \$1 }\\ =\$4,000\times \text{ 7}\text{.71008}\\ =\$30,840\end{array}$

Note: PV factor (Present value of an annuity due of $1: n = 11, i =8%) is taken from the table value (Table 6 in Appendix from textbook).

Hence, the cost of Machine B is $30,840.

14. The amount of depreciation for Machine B –Straight line method:

$\begin{array}{c}\text{Depreciation = }\frac{\text{Cost of the Asset }-\text{ Residual value}}{\text{Estimated Useful Life of the Asset}}\\ =\frac{\text{\$30,840 – \$0}}{\text{15 years}}\\ =\$2,056\end{array}$

Thus, the depreciation is $2,056.