Question

On January 1, 2015, a machine was purchased for $94,500. The machine has an estimated salvage value of $6,300 and an estimated useful life of 5 years. The machine can operate for 105,000 hours before it needs to be replaced. The company closed its books on December 31 and operates the machine as follows: 2015, 21,000 hrs; 2016, 26,250 hrs; 2017, 15,750 hrs; 2018, 31,500 hrs; and 2019, 10,500 hrs. Compute the annual depreciation charges over the machine’s life assuming a December 31 year-end for each of the following depreciation methods. (Round answers to 0 decimal places, e.g. 45,892.)

Assume a fiscal year-end of September 30. Compute the annual depreciation charges over the asset’s life applying each of the following methods. (Round answers to 0 decimal places, e.g. 45,892.)

Year		Straight-line Method		Sum-of-the-years'-digits method		Double-declining-balance method
2015		$		$		$
2016
2017
2018
2019
2020

Answer 1

Computing depreciation when year-end is December 31

Straight-line method
Cost of machine	94500
Less: Salvage value	6300
	88200
Useful life	5 years
Depreciation per year (88200/5)	17,640

Sum of the years' digits method

Depreciation Expense	Remaining useful life of the asset x depreciable cost
	Sum of the years' digits

Year	Depreciation base	Remaining life	Depreciation fraction	Depreciation rate	Depreciation expense
1	88,200	5	5/15	33%	29,400
2	88,200	4	4/15	27%	23,520
3	88,200	3	3/15	20%	17,640
4	88,200	2	2/15	13%	11,760
5	88,200	1	1/15	7%	5,880
					88,200

Double declining balance method

Useful life	5 years
Depreciation rate	1/5
	20%
Double declining balance formula	= 2 x normal depreciation rate
	=2 x 20%
	40%

Year	Beginning value	Depreciation	Ending book value
2015	94,500	37,800	56,700
2016	56,700	22,680	34,020
2017	34,020	13,608	20,412
2018	20,412	8,165	12,247
2019	12,247	5,947	6,300

2019 depreciation is adjusted keeping in mind the residual value of 6300.

Summary

Year	Straight line method	Sum of the years' digits method	Double declining balance method
2015	$         17,640	$          29,400	$           37,800
2016	$         17,640	$          23,520	$           22,680
2017	$         17,640	$          17,640	$           13,608
2018	$         17,640	$          11,760	$             8,165
2019	$         17,640	$             5,880	$             5,947
2020	$                  -	$                    -	$                    -

Computing depreciation when year-end is September 30

Straight line method
Year	Depreciable amount	Rate	Depreciation expense
2015	88,200	10% (20%*6/12)	8,820
2016	88,200	20%	17,640
2017	88,200	20%	17,640
2018	88,200	20%	17,640
2019	88,200	20%	17,640
2020	88,200	10%(20%*6/12)	8,820
Total			88,200

Sum of the years' digits method
Year	Depreciation base	Depreciation fraction	Depreciation fraction	Depreciation expense
2015	88,200	6/12*5/15	16.67%	14,700
2016	88,200	[(6/12*5/15)+(6/12*4/15)]	30.00%	26,460
2017	88,200	[(6/12*4/15)+(6/12*3/15)]	23.33%	20,580
2018	88,200	[(6/12*3/15)+(6/12*2/15)]	16.67%	14,700
2019	88,200	[(6/12*2/15)+(6/12*1/15)]	10.00%	8,820
2020	88,200	6/12*1/15	3.33%	2,940
				88,200

Double declining balance method
Year	Beginning value	Depreciation rate	Depreciation	Ending book value
2015	94,500	20% (40%*6/12)	18,900	75,600
2016	75,600	40%	30,240	45,360
2017	45,360	40%	18,144	27,216
2018	27,216	40%	10,886	16,330
2019	16,330	40%	6,532	9,798
2020	9,798	20% (40%*6/12)	3,498	6,300
			88,200

Summary

Year	Straight line method	Sum of the years' digits method	Double declining balance method
2015	$           8,820	$          14,700	$           18,900
2016	$         17,640	$          26,460	$           30,240
2017	$         17,640	$          20,580	$           18,144
2018	$         17,640	$          14,700	$           10,886
2019	$         17,640	$             8,820	$             6,532
2020	$           8,820	$             2,940	$             3,498