Question

Depreciation Methods

Gruman Company purchased a machine for $198,000 on January 2, 2016. It made the following estimates:

Service Life	5 years or 10,000 hours
Production	180,000 units
Residual value	$18,000

In 2016, Gruman uses the machine for 1,700 hours and produces 45,000 units. In 2017, Gruman uses the machine for 1,400 hours and produces 30,000 units. If required, round your final answers to the nearest dollar.

Required:

1. Compute the depreciation for 2016 and 2017 under each of the following methods:

Straight-line method

2016	$
2017	$

Sum-of-the-years'-digits method

2016	$
2017	$

Double-declining-balance method

2016	$
2017	$

Activity method based on hours worked

2016	$
2017	$

Activity method based on units of output

2016	$
2017	$

2. For each method, what is the book value of the machine at the end of 2016? At the end of 2017?

Straight-line method

2016	$
2017	$

Sum-of-the-years'-digits method

2016	$
2017	$

Double-declining-balance method

2016	$
2017	$

Activity method based on hours worked

2016	$
2017	$

Activity method based on units of output

2016	$
2017	$

3. If Gruman used a service life of 8 years or 15,000 hours and a residual value of $9,000, what would be the effect on the following under the straight-line, sum-of-the-years'-digits, and double-declining-balance depreciation methods?

Depreciation expense

Straight-line method

2016	$
2017	$

Sum-of-the-years'-digits method

2016	$
2017	$

Double-declining-balance method

2016	$
2017	$

Book value

Straight-line method

2016	$
2017	$

Sum-of-the-years'-digits method

2016	$
2017	$

Double-declining-balance method

2016	$
2017	$

Answer 1

1. A) Depreciation under Straight Line Method

   Under Staight Line Method Cost of Asset is written off equally during it's useful.         

    Hence depreciation for each useful life will be equal.

      Depreciation = (Purchase Cost of Machine - Salvage Vale) / Service Life

      Depreciation = (198000 - 18000) / 5

                              = 180000 / 5 = 36000 $/ Year

     Depreciation for 2016 = 36000 $

    Depreciation for 2017 = 36000 $

B) Depreciation under Sum of Years Digit Method

This method takes assets expected life and adds together the digits of each year. Then each years digit is diveded by this sum to determine percentage by which the Asset shoud be depeciated each year starting with the highest number in Year 1.

Sum of Useful Life = 5+4+3+2+1 = 15

Depreciation percentage for 2016 = 5/15 * 100 = 33.33 %

Depreciation percentage for 2017 = 4/15 * 100 = 26.67 %

Depreciation for 2016 = (198000 - 18000) * 33.33 %

                                        = 180000 * 33.33 % = 60000 $

Depreciation for 2017 = (198000 - 18000) * 26.67 %

                                        = 180000 * 26.67 % = 48000 $

C) Depreciation under Double Declining balance method

Under this method Asset depreciated twice at the rate which is depreciated under Straight Line Method and each years depreciation is deducted from book value to calculate depreciation in the following year. Depreciation is calculated till it reaches it's Salvage Value

Depreciation = 2 * Cost of Asset * Depreciation Rate OR

                            2 * Cost of Asset / Service Life

Rate of Depreciation = 1 / Service Life * 100

                                       = 1 / 5 * 100 = 20 %

Depreciation for 2016 = 2 * 198000 * 20 %

                                        = 396000 * 20 % = 79200 $

Depreciation for 2017 = (198000 - 79200) * 2 * 20%

                                       = 118800 * 2 * 20 % = 47520 $

D)    Activity method based on Hours Worked

   Under this method Depreciation is calaculated based on hours worked each year to Total useful working hours of Machine.

Depreciation = Hours worked / Total Useful Hours * Cost of Asset

Depreciation for 2016 = 1700 / 10000 * (198000 -18000)           

                                        = 180000 * 1700 /10000

                                       = 30600 $

Depreciation for 2017 = 1400 / 10000 * (198000 -18000)      

=180000 * 1400 /10000

   = 25200 $

E) Activity method based on Units of Output

Under this method Depreciation is calaculated based on Units produced each year to Total Units Capacity.

Depreciation = Cost of Asset * Units Produced / Total Units Capacity

Depreciation for 2016 = (198000 -18000) * 45000 /180000

                                        = 180000 * 45000 /180000 = 45000 $

Depreciation for 2016 = (198000 -18000) * 30000 / 180000

                                        = 180000 * 30000 / 180000 = 30000 $

2) A. Book Value under Straight Line Method

Year	Cost / WDV (A)	Depreciation(B)	Book Value (A - B)
2016	180000	36000	144000
2017	144000	36000	108000

B. Book Value under Sum of Years Digit Method

Year	Cost / WDV (A)	Depreciation(B)	Book Value (A - B)
2016	180000	60000	120000
2017	120000	48000	72000

C. Book Value under Double Declining balance method

Year	Cost / WDV (A)	Depreciation(B)	Book Value (A - B)
2016	198000	79200	118800
2017	118800	47520	71280

D. Book Value under Activity method based on Hours Worked

Year	Cost / WDV (A)	Depreciation(B)	Book Value (A - B)
2016	180000	30600	149400
2017	149400	25200	124200

E. Book Value under Activity method based on Units of Output

Year	Cost / WDV (A)	Depreciation(B)	Book Value (A - B)
2016	180000	45000	135000
2017	135000	30000	105000

3) Effects of Changes

Service Life = 8 Years / 15000 Hours

Residual Value = 9000 $

A) Depreciation under Straight Line Method

   Depreciation = 198000 - 9000 / 8

                           = 189000 / 8 = 23625 $ (for every year)

B) Depreciation under Sum of Years Digit Method

Sum of Useful Life = 8+7+6+5+4+3+2+1 = 36

Depreciation percentage for 2016 = 8 / 36 * 100 = 22.22 %

Depreciation percentage for 2017 = 7 / 36 * 100 = 19.44 %

Depreciation for 2016 = 189000 * 22.22 % = 42000 $

Depreciation for 2017 = 189000 * 19.44 % = 36750 $

C) Depreciation under Double Declining balance method

Rate of Depreciation = 1 / Service Life * 100

                                       =1/8 *100 = 12.5 %

Depreciation for 2016 = 2 * 198000 * 12.5 %

                                        = 396000 * 12.5 % = 49500 $

Depreciation for 2017 = (198000 - 49500) * 2 * 12.5%

                                       = 148500 * 2 * 12.5 % = 37125 $

D) Book Value under Straight Line Method

Year	Cost / WDV (A)	Depreciation(B)	Book Value (A - B)
2016	189000	23625	165375
2017	165375	23625	141750

E) Book Value under Sum of Years Digit Method

Year	Cost / WDV (A)	Depreciation(B)	Book Value (A - B)
2016	189000	42000	147000
2017	147000	36750	110250

F) Book Value under Double Declining balance method

Year	Cost / WDV (A)	Depreciation(B)	Book Value (A - B)
2016	198000	49500	148500
2017	148500	37125	111375

• Change in Capacity in Hours only effects calaculation of Depreciation under Activity method based on Hours Worked