Chapter 8, Problem 2PSB

To determine

Depreciation:

Depreciation is the amount of decrease in the value of an asset within a set time period due to wear and tear of that particular asset. It helps in readjusting the actual cost of the particular asset o which the depreciation is applied.

Double Declining Balance Method:

It is a method of depreciation in which the rate of depreciation is double the rate of straight line method of depreciation. The amount of depreciation applied to the asset declines every period because book value declines every period.

Straight Line Depreciation:

Straight line depreciation is one of the methods of depreciation in which fixed rate of depreciation is provided throughout the course of depreciation on a particular asset.

Units of Production Depreciation Method:

This is a method of depreciation where the depreciation is not applied as straight line and is calculated with respect to the units that a particular asset produces gives.

The amount of depreciation.

Explanation of Solution

Given,

Cost of machine is $324,000.

Salvage value is $30,000.

Formula to calculate Depreciable cost:

  $\text{Depreciable}\text{cost}=\text{Cost}\text{of}\text{machine}-\text{Salvage}\text{value}$

Substitute $257,000 as cost of machine and $20,000 as salvage value,

  $\begin{array}{c}\text{Depreciable}\text{cost}=\$324,000-\$30,000\\ =\$294,000\end{array}$

Total depreciable cost is $294,000.

Computation of depreciation amount:

Year	Straight line($)	Units of production($)	Double Declining Balance($)
1	58,800	71,120	128,750
2	58,800	64,080	64,375
3	58,800	63,400	32,188
4	58,800	68,720	12,187
5	58,800	26,680	11,990
Total	294,000	294,000	294,000

Working Notes:

Straight line method

Calculate Depreciation:

  $\begin{array}{c}\text{Depreciation}=\frac{\left(\text{Cost}\text{of}\text{the}\text{asset}-\text{Residual}\text{value}\right)}{\text{Useful}\text{life}}\\ =\frac{\$324,000-\$30,000}{5}\\ =\frac{\$294,000}{5}\\ =\$58,800\end{array}$

Depreciation that will be charged in the 4 years with respect to straight line method is $58,800.

Units of production method

Year 1

Calculate depreciation with respect to units of production:

  $\begin{array}{c}\text{Depreciation}\text{per}\text{unit}=\frac{\left(\text{Cost}\text{of}\text{the}\text{asset}-\text{Salvage}\text{value}\right)}{\text{Useful}\text{life}\text{in}\text{units}}\\ =\frac{\$324,000-\$30,000}{\$1,470,000\text{units}}\\ =\frac{\$294,000}{1,470,000}\\ =0.2\text{per}\text{unit}\end{array}$

Depreciation per unit is 0.2.

Computation of depreciation,

  $$

  $\begin{array}{c}\text{Depreciation}=\text{Total}\text{units}\text{produced}\text{in}1\text{st}\text{year}\times \text{Depreciation}\text{per}\text{unit}\\ =\$355,600\times 0.2\\ =\$71,120\end{array}$

Depreciation that will be charged in the first year is $71,120.

Year 2

Given,

Units produced are $320,400.

Depreciation per unit is 0.2 per unit.

Computation of Depreciation:

  $\begin{array}{c}\text{Depreciation}=\text{Total}\text{units}\text{produced}\text{in}\text{2nd}\text{year}\times \text{Depreciation}\text{per}\text{unit}\\ =\$320,400\times 0.2\\ =\$64,080\end{array}$

Depreciation that will be charged in the second year is $64,080.

Year 3

Depreciation per unit is 0.2 per unit.

Computation of Depreciation:

  $\begin{array}{c}\text{Depreciation}=\text{Total}\text{units}\text{produced}\text{in}3\text{rd}\text{year}\times \text{Depreciation}\text{per}\text{unit}\\ =\$317,000\times 0.2\\ =\$63,400\end{array}$

Depreciation that will be charged in the third year is $63,400.

Year 4

Depreciation per unit is 0.2 per unit.

Computation of Depreciation:

  $\begin{array}{c}\text{Depreciation}=\text{Total}\text{units}\text{produced}\text{in}4\text{th}\text{year}\times \text{Depreciation}\text{per}\text{unit}\\ =\$343,600\times 0.2\\ =\$68,720\end{array}$

Depreciation charged in the 4^th year is $68,720.

Year 5

Depreciation per unit is 0.2 per unit.

Computation of Depreciation:

  $\begin{array}{c}\text{Depreciation}=\text{Total}\text{units}\text{produced}\text{in}4\text{th}\text{year}\times \text{Depreciation}\text{per}\text{unit}\\ =\$138,500\times 0.2\\ =\$27,700\end{array}$

But the depreciation will be charged $26,680 only as depreciation can’t be charged on the salvage value of the asset.

Double Declining Balance method

Computation of Depreciation rate:

  $\begin{array}{c}\text{Double}\text{declining}\text{depreciation}\text{rate}=\frac{100\%}{\text{Useful}\text{years}}\times 2\\ =\frac{100\%}{5}\times 2\\ 40\%\end{array}$

Double declining depreciation rate is 40%.

Year 1

Computation of depreciation in the first year:

  $\begin{array}{c}\text{Depreciation}=\text{Cost}\text{of}\text{the}\text{machine}\times \text{Depreciation}\text{rate}\\ =\$324,000\times 40\%\\ =\$129,600.\end{array}$

Depreciation that will be charged in the first year is $129,600.

Year 2

Computation of book value in year 2:

  $\begin{array}{c}\text{Book}\text{value}=\text{Cost}\text{of}\text{the}\text{asset}-\text{Depreciation}\\ =\$324,000-\$129,600\\ =\$194,400\end{array}$

Book value at the beginning of the second year is $194,400.

Computation of depreciation in the second year:

  $\begin{array}{c}\text{Depreciation}=\text{Cost}\text{of}\text{the}\text{machine}\times \text{Depreciation}\text{rate}\\ =\$194,400\times 40\%\\ =\$77,760.\end{array}$

Depreciation that will be charged in the second year is $77,760.

Year 3

Book value of the asset in the year 2 is $194,400.

Computation of book value in year 3:

  $\begin{array}{c}\text{Book}\text{value}=\text{Cost}\text{of}\text{the}\text{asset}-\text{Depreciation}\\ =\$194,400-\$77,760\\ =\$116,640\end{array}$

Book value at the beginning of the third year is $116,640.

Computation of depreciation in the third year:

  $\begin{array}{c}\text{Depreciation}=\text{Cost}\text{of}\text{the}\text{machine}\times \text{Depreciation}\text{rate}\\ =\$116,640\times 40\%\\ =\$46,656\end{array}$

Depreciation that will be charged in the third year is $46,656.

Year 4

Book value of the asset in the year 3 is $116,640.

Computation of book value in year 4:

  $\begin{array}{c}\text{Book}\text{value}=\text{Cost}\text{of}\text{the}\text{asset}-\text{Depreciation}\\ =\$116,640-\$46,656\\ =\$69,984\end{array}$

Computation of depreciation in the 4^th year:

  $\begin{array}{c}\text{Depreciation}=\text{Cost}\text{of}\text{the}\text{machine}\times \text{Depreciation}\text{rate}\\ =\$69,984\times 40\%\\ =\$27,994\end{array}$

Depreciation that will be charged in the 5^th year is $27,994.

Year 5

Book value of the asset in the year 4 is $69,984.

Computation of book value in year 5:

  $\begin{array}{c}\text{Book}\text{value}=\text{Cost}\text{of}\text{the}\text{asset}-\text{Depreciation}\\ =\$69,984-\$27,994\\ =\$41,990\end{array}$

Computation of depreciation in the 5^th year:

  $\begin{array}{c}\text{Depreciation}=\text{Cost}\text{of}\text{the}\text{machine}\times \text{Depreciation}\text{rate}\\ =\$41,990\times 40\%\\ =\$16,796\end{array}$

But the depreciation charged will only be 11,990 as the depreciation can’t be charged from the salvage value of the asset.