Question

On January 1, 2017, a machine was purchased for $90,000. The machine has an estimated residual value of $6,000 and an estimated useful life of 5 years. The machine can operate for 100,000 hours before it needs to be replaced. The company closed its books on December 31 and operates the machine as follow; 2017, 20,000 hours; 2018, 25,000 hours; 2019, 15,000 hours; 2020, 30,000 hours; and 2021, 10,000 hours.

((((((((((((((Instructions))))))))))))))))

A) Compute the annual depreciation charges over the machine’s life assuming a December 31 year-end for each of the following depreciation methods.

1- Straight-line method

2- Activity Method

3- Sum-of-the-years-digits method

4- Double-declining-balance method

B) Assume a fiscal year-end of September 30. Compute the annual depreciation charges over the asset’s life applying each of the following methods.

1- Straight-line method

2- Sum-of-the-years-digits method

3- Double-declining-balance method

Answer 1

A. Assuming a December 31 year-end

1- Straight-line method

Date	Depn. Amt.	Carrying/Book value
1	2=(90000-6000)/5=16800	3=Prev.3-Current 2
Jan 1 2017		90000
31-Dec-17	16800	73200
31-Dec-18	16800	56400
31-Dec-19	16800	39600
31-Dec-20	16800	22800
31-Dec-21	16800	6000
Total	84000

2- Activity Method
Date	Depn. Amt.
1	2	3	4=prev.4-curr.3
Jan 1 2017			90000
31-Dec-17	20000/100000*84000=	16800	73200
31-Dec-18	25000/100000*84000=	21000	52200
31-Dec-19	15000/100000*84000=	12600	39600
31-Dec-20	30000/100000*84000=	25200	14400
31-Dec-21	10000/100000*84000=	8400	6000
		84000

3- Sum-of-the-years-digits method
Date	Depn. Amt.
1	2	3	4=prev.4-curr.3
Jan 1 2017			90000
31-Dec-17	5/15*84000=	28000	62000
31-Dec-18	4/15*84000=	22400	39600
31-Dec-19	3/15*84000=	16800	22800
31-Dec-20	2/15*84000=	11200	11600
31-Dec-21	1/15*84000=	5600	6000
		84000

4- Double-declining-balance method

Depn. Rate under DDB= Twice that of SLM rate on declining balance, each yr.---till salvag e is reached

ie. 1/5 yrs.*2= 40% on declining balance

Date	Depn. Amt.
1	2=Prev 3*40%	3=prev.3-current 2
Jan 1 2017		90000
31-Dec-17	36000	54000
31-Dec-18	21600	32400
31-Dec-19	12960	19440
31-Dec-20	7776	11664
31-Dec-21	4666	6998
Total	83002

B) Assume a fiscal year-end of September 30

1- Straight-line method

Date	Depn. Amt.	Carrying/Book value
1	2=(90000-6000)/5=16800	3=Prev.3-Current 2
Jan 1 2017		90000
30-Sep-17	12600	77400	16800/12*9=
30-Sep-18	16800	60600
30-Sep-19	16800	43800
30-Sep-20	16800	27000
30-Sep-21	16800	10200
31-Dec-21	4200	6000	16800/12*3=
Total	84000

	3- Sum-of-the-years-digits method
Date	Depn. Amt.
1	2	3	4=prev.4-curr.3
Jan 1 2017			90000
30-Sep-17	5/15*84000*9/12=	21000	69000
30-Sep-18	(5/15*84000*3/12)+(4/15*84000*9/12)=	23800	45200
30-Sep-19	(4/15*84000*3/12)+(3/15*84000*9/12)=	18200	27000
30-Sep-20	(3/15*84000*3/12)+(2/15*84000*9/12)=	12600	14400
30-Sep-21	(2/15*84000*3/12)+(1/15*84000*9/12)=	7000	7400
31-Dec-21	1/15*84000*3/12=	1400	6000
Total		84000

4- Double-declining-balance method

Depn. Rate under DDB= Twice that of SLM rate on declining balance, each yr.---till salvag e is reached

ie. 1/5 yrs.*2= 40% on declining balance

Date	Depn. Amt.
1	2=Prev 3*40%	3=prev.3-current 2
Jan 1 2017		90000
30-Sep-17	27000	63000	90000*40%*9/12
30-Sep-18	25200	37800
30-Sep-19	15120	22680
30-Sep-20	9072	13608
30-Sep-21	5443	8165
31-Dec-21	817	7348	8165*40%*3/12
Total	82652