(Error Analysis and Depreciation, SL and SYD) Mike Devereaux Company shows the following entries in its Equipment account for 2018. All amounts are based on historical cost.

Equipment
2018		2018
Jan 1	Balance 134,750	June 30	Cost of 23,000 equipment sold (purchased prior to 2018)
Aug. 10	Purchases 32,000
12	Freight on Equipment purchased 700
25	Installation costs 2,700
Nov. 10	Repairs 500

Instructions

1. Prepare any correcting entries necessary.
2. Assuming that depreciation is to be charged for a full year on the ending balance in the asset account, compute the proper depreciation charge for 2018 under each of the methods listed below. Assume an estimated life of 10 years, with no salvage value. The machinery included in the January 1, 2018, balance was purchased in 2016.
   
   a. Straight-line
   b. Sum-of-the-years’-digits.

Step by step solution

01

Meaning of Straight-Line Depreciation

Straight-line depreciation is the simplest way to assess depreciation over time.By allocating identical amounts to the asset's accounting periods over its useful life, it makes the asset's expense predictable along with smoothing net income.

02

(a) Preparing journal entries 

Date	Particular	Debit ($)	Credit ($)
	Maintenance and Repairs Expense	500
	Equipment		500

03

(b 1) Computing depreciation using the straight-line method

The proper ending balance in the asset account is:
January 1 balance	$134,750
Add New equipment:
Purchases $32,000
Freight 700
Installation 2,700	35,400
Less: Cost of equipment sold	23,000
December 31 balance	$147,150

Depreciation under straight line

$\begin{array}{rcl}\text{Depreciation}& =& \frac{\text{Cost}\text{of}\text{asset}\text{on}\text{december}31}{\text{Useful}\text{life}}\\ & =& \frac{\$147,150}{10}\\ & =& \$14,715\end{array}$

04

(b 2) Computing depreciation using the Sum-of-the-years’-digits method 

Calculating sum-of-years digits

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

Determining depreciation in 2018

For equipment purchased in 2016: $111,750 ($134,750-$23,000) of the cost of equipment purchased in 2016 is still on hand is	$16,255
For equipment purchased in 2018: 10/55 X $35,400	6,436
Total	$22,691

Working Notes:

Determining equipment cost

$\begin{array}{rcl}\text{Equipment}\text{on}\text{hand}& =& \text{Equipment}\text{cost}\times \frac{\text{Year}\text{of}\text{depreciation}\text{to}\text{be}\text{charged}}{\text{Sum}\text{of}\text{the}\text{yaers}\text{digit}}\\ & =& \$111,750\times \frac{8}{55}\\ & =& \$16,255\end{array}$

For equipment purchased in 2016: $111,750 of the cost of equipment purchased in 2016 is still on hand is	$16,255
For equipment purchased in 2018: 10/55 X $35,400	6,436
Total	$22,691

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