(Depreciation for Fractional Periods) On March 10, 2019, Lost World Company sells equipment that it purchased for \(192,000 on August 20, 2012. It was originally estimated that the equipment would have a life of 12 years and a salvage value of \)16,800 at the end of that time, and depreciation has been computed on that basis. The company uses the straight line method of depreciation.

Instructions

1. (a) Compute the depreciation charge on this equipment for 2012, for 2019, and the total charge for the period from 2013 to 2018, inclusive, under each of the six following assumptions with respect to partial periods.
   1. Depreciation is computed for the exact period of time during which the asset is owned. (Use 365 days for base and record depreciation through March 9, 2019.)
   2. Depreciation is computed for the full year on the January 1 balance in the asset account.
   3. Depreciation is computed for the full year on the December 31 balance in the asset account.
   4. Depreciation for one-half year is charged on plant assets acquired or disposed of during the year.
   5. Depreciation is computed on additions from the beginning of the month following acquisition and on disposals to the beginning of the month following disposal.
   6. Depreciation is computed for a full period on all assets in use for over one-half year, and no depreciation is charged on assets in use for less than one-half year. (Use 365 days for base.)
2. (b) Briefly evaluate the methods above, considering them from the point of view of basic accounting theory as well as simplicity of application.

In financial accounting, depreciation could be astrategy for spreading out the cost of tangible resources over their functional lives. Essentially, it is the disintegration of the value of an asset, which happens over time due to continuous use and abrasion of the asset.

Calculating annual depreciation charge

$\begin{array}{rcl}\text{Depreciation}& =& \frac{\text{Equipment}\text{cost}-\text{Salvage}\text{value}}{\text{Useful}\text{life}}\\ & =& \frac{\$192,000-\$16,800}{12}\\ & =& \$14,600\text{p.a.}\end{array}$

Calculating the total number of days

Total number of days since the asset was purchased on August 20, 2012:

$$\begin{gathered} \text{Total}\text{days}=\text{Sum}\text{of}\text{days} \\ =11+30+31+30+31 \\ =133\text{days} \end{gathered}$$

So, depreciation for 2012

$\begin{array}{rcl}\text{Depreciation}& =& \text{Depreciation} \text{per}\text{annum}\times \frac{\text{Total}\text{days}}{\text{Total}\text{days}\text{in}\text{a}\text{year}}\\ & =& \$14600\times \frac{133}{365}\\ & =& \$5,320\end{array}$

Depreciation from 2013 till 2018

$\begin{array}{rcl}\text{Depreciation}& =& \text{Number}\text{of}\text{year}\times \text{Depreciation}\text{per}\text{annum}\\ & =& 6\times \$14,600\\ & =& \$87,600\\ & & \end{array}$

Calculating the total number of days

Total number of days for 2019 from Jan.1, 2019, till March

$\begin{array}{rcl}\text{Total}\text{days}& =& \text{Sum}\text{of}\text{days}\\ & =& 31+28+10\\ & =& 69\text{days}\end{array}$

So, depreciation for 2019 is

$\begin{array}{rcl}\text{Depreciation}& =& \text{Depreciation}\text{per}\text{annum}\times \frac{\text{Total}\text{number}\text{of}\text{days}}{\text{Total}\text{days}\text{in}\text{a}\text{year}}\\ & =& \$14,600\times \frac{69}{365}\\ & =& \$2,760\end{array}$

Depreciation for 2012 shall be $0 since the asset has been purchased in the middle of the year 2012

Depreciation from 2013 till 2018 shall be:

$\begin{array}{rcl}\text{Depreciation}& =& \text{Number}\text{of}\text{year}\times \text{Depreciation}\text{per}\text{annum}\\ & =& 6\times \$14,600\\ & =& \$87,600\end{array}$

Depreciation for 2019 is $14,600 since the asset was sold in March, and the balance on January 1, 2019, was full asset value.

Depreciation for 2012 shall be $14,600 since the asset has been purchased in the middle of the year 2012.

Depreciation from 2013 till 2018 shall be:

$\begin{array}{rcl}\text{Depreciation}& =& \text{Number}\text{of}\text{year}\times \text{Depreciation}\text{per}\text{annum}\\ & =& 6\times \$14,600\\ & =& \$87,600\\ & & \end{array}$

Depreciation for 2019 is $ 0 since the asset has been sold in March.

Depreciation for 2012 shall be

$\begin{array}{rcl}\text{Depreciation}& =& \text{Annual}\text{depreciation}\times \frac{\text{Month}\text{in}\text{number}}{\text{Month}\text{in}\text{a}\text{year}}\\ & =& \$14,600\times \frac{6}{12}\\ & =& \$7,300\end{array}$

Note: the asset has been purchased in the middle of the year.

Depreciation from 2013 till 2018 shall be:

$\begin{array}{rcl}\text{Depreciation}& =& \text{Number}\text{of}\text{year}\times \text{Depreciation}\text{per}\text{annum}\\ & =& 6\times \$14,600\\ & =& \$87,600\\ & & \end{array}$

Depreciation for 2019 is:

localid="1651481195067" $\begin{array}{rcl}\text{Depriciation}& =& \text{Depreciation}\text{per}\text{annum}\times \frac{\text{Month}\text{in}\text{number}}{\text{Month}\text{in}\text{a}\text{year}}\\ & =& \$14,600\times \frac{6}{12}\\ & =& \$7,300\end{array}$

Note: The asset has been sold in March.

The depreciation charge for 2012

Calculating the total number of days

Total number of days from 1^st September 2012 to 31^st December 2012

$\begin{array}{rcl}\text{Total}\text{days}& =& \text{Sum}\text{of}\text{days}\\ & =& 30+31+30+31\\ & =& 122\text{days}\\ & & \end{array}$

So, depreciation for 2012:

$\begin{array}{rcl}\text{Depreciation}& =& \text{Depreciation}\text{per}\text{annum}\times \frac{\text{Total}\text{number}\text{of}\text{days}}{\text{Total}\text{days}\text{in}\text{a}\text{year}}\\ & =& \$14,600\times \frac{122}{365}\\ & =& \$4,880\end{array}$

Depreciation from 2013 till 2018 shall be:

$\begin{array}{rcl}\text{Depreciation}& =& \text{Number}\text{of}\text{year}\times \text{Depreciation}\text{per}\text{annum}\\ & =& 6\times \$14,600\\ & =& \$87,600\\ & & \end{array}$

Calculating the number of days

Total number of days from 2019 from January 1, 2019, till March 31, 2019

$\begin{array}{rcl}\text{Total}\text{days}& =& \text{Sum}\text{of}\text{days}\\ & =& 31+28+31\\ & =& 90\text{days}\end{array}$

So, depreciation for 2019 is:

$\begin{array}{rcl}\text{Depreciation}& =& \text{Depreciation}\text{per}\text{annum}\times \frac{\text{Total}\text{number}\text{of}\text{days}}{\text{Total}\text{days}\text{in}\text{a}\text{year}}\\ & =& \$14,600\times \frac{90}{365}\\ & =& \$3,600\end{array}$

Depreciation for 2012 shall be $0 since asset purchased in August and once used less than half of the year on 31^st December 2012

Depreciation from 2013 till 2018 shall be:

$$\begin{gathered} \text{Depreciation}=\text{Number}\text{of}\text{year}\times \text{Depreciation}\text{per}\text{annum} \\ =6\times \$14,600 \\ =\$87,600 \end{gathered}$$

Depreciation for 2019 is $0 since the asset has been sold in March.

The most accurate distribution of cost is given by methods 1 and 5 if it is assumed that a straight line is satisfactory. Reasonable accuracy is normally given by 2, 3, or 4. The simplest applications are 6, 2, 3, 4, 5, and 1, in about that order. Methods 2, 3, and 4 combine reasonable accuracy with the simplicity of application.