Question

On October 1, 2018, the Allegheny Corporation purchased machinery for $224,000. The estimated service life of the machinery is 10 years and the estimated residual value is $4,000. The machine is expected to produce 400,000 units during its life.

Required:
Calculate depreciation for 2018 and 2019 using each of the following methods. Partial-year depreciation is calculated based on the number of months the asset is in service.

1. Straight line.
2. Sum-of-the-years’-digits.
3. Double-declining balance.
4. One hundred fifty percent declining balance.
5. Units of production (units produced in 2018, 20,000; units produced in 2019, 35,000).

Answer 1

Date of purchase of machinery: 01.10.2018

Cost of the machinery $224,000.

The estimated service life 10 years

Estimated residual value $4,000

The machine is expected to produce 400,000 units during its life.

Calculation of Depreciation for 2018 and 2019

1. Under Straight Line Method

Depreciation = Original cost of asset – estimated residual value / Estimated Service life

Depreciation for 2018 (October 2018 to December 2018)- 3 months’ depreciation

=         224000 – 4000 / 10

                       =     220000/10 = $22000 per year

                        =     22000 x 3 months/12 months

                        =     $5,500

Depreciation for 2019 (January 2019 to December 2019)

=         224000 – 4000 /10

                       =     220000/10

                        =     $22000

2. Under Sum of years’ digits method

Depreciation

= Depreciable Amount x Un-depreciated useful life

                                              Some of the Years’ Digits

1. Depreciable Amount = Cost of the asset - Estimated Residual Value

                                         = 224,000 - 4,000

                                        = 220,000

1. Some of the years’ digits = n(n+1)/2

                                                = 10(10+1)/2 = 10(11)/2 = 110/2 = 55

1. Un-depreciated life means the service life remaining
   1. Service life remaining in the first year = 10 years (whole life)
   2. Service life remaining in the second year = 9 years (10-1)
   3. Service life remaining in the third year = 8 years(10-2) and so on.

Calculation of Depreciation under Some of the years’ Digit method

For 2018

Step 1: Calculate Depreciation for the whole year from (1^st October 2018 to 30^th September 2019)

            = Depreciable amount x undepreciated life / Some of the years’ digits

            = 220,000 x 10/55 = $40,000

Step 2: Calculate depreciation only for the year 2018, i.e., for the three months from Ist October 2018 to 31^st December 2018

= 40000 x 3 months/12 months

The depreciation for the year 2018 = $10,000

For 2019

Step 1: Split the 12 months of 2019 into two periods

1. The period between 01^st January 2019 to 30^th September 2019 (the first year balance period) (some of years’ digits = 10/55)
2. The period between 1^st October 2019 to 31^st December 2019( the second year first three months) (Some of years’ digits = 9/55)

Depreciation

For the period 1(1^st January 2019 to 30^th September 2019 = 9 months)

= 220,000 x 10/55 x 9months/12months = $30,000

For the period 2 (1^st October 2019 to 31^st December 2019)

= 220,000 x 9/55 x 3 months/12 months = $9,000

The total depreciation for 2019 = 30,000 + 9,000 = $39,000

(Reason: As per Some of years’ Digit method it calculates depreciation for the whole year, for example, 1^st year, 2^nd year and so on. An year is the period of 12 months from the date of purchase of the machinery. In this problem, the machinery is purchased on 1^st October 2018. The first year ends on 30^th September 2019. The second year begins on 1^st October 2019 and ends on 30^th September 2020 for the purpose of yearly depreciation under Some of the years’ digits method. But for accounting purpose every year ends on 31^st December. So the first year depreciation for the accounting year 2018 will be only for 3 months(October 2018 to December 2018). Because it is purchased on October 1, 2018. So the whole depreciation is calculated for one year from the date of purchase and we derive 3 months depreciation because accounting year ends on 31^st December.

The second year for calculating depreciation under some of years’ digits method is 1^st October 2019 to 30^th September 2020. For Accounting purpose the second year is 1^st January 2019 to 31^st December 2019. In this second year, some of years’ digit is 10/55 till 30^th September 2019 (first year) and 9/55 for 1^st October 2019 to 30^th September 2020. Hence the accounting year 2019 is split into two periods

1. Ist January 2019 to 30^th September 2019 (first year as per Some of years’ digit method) (10/55)
2. 1^st October 2019 to 31^st December 2019 (second year the first three months as per Some of years’ depreciation method) (9/55)

We can calculate depreciation under Some of years’ digits method by using the following table

Year	Depreciable amount	Useful remaining/some of years’ digits	depreciation	Accounting year	Depreciation for accounting year
1	220,000	10/55	40,000	2018	=40000x3/12 = 10,000
2	220,000	9/55	36,000	2019	=40000x9/12 = 30000 =36000x 3/12 = 9000 = 39000
3	220,000	8/55	32,000	2020
4	220,000	7/55	28,000	2021
5	220,000	6/55	24,000	2022
6	220,000	5/55	20,000	2023
7	220,000	4/55	16,000	2024
8	220,000	3/55	12,000	2025
9	220,000	2/55	8,000	2026
10	220,000	1/55	4,000	2027

3. Double Declining balance method

Depreciation =	Book value at the beginning of the period	X	percentage of depreciation under straight line method without considering the scrap value	X 2

Step 1: Calcluation of rate of depreciation (without

Yearly depreciation = original cost /estimated life = 224000/10 = 22,400

Rate of depreciation = depreciation/original cost x 100 = 22400/224000*100 = 10%

Step 2: Calculate Depreciation for the year 2018

= Book value at the beginning x % of depreciation x 2

= 224000 x 10/100 x 2 =$44,800

Step 3: Calculate Depreciation for the year 2019

Book value on 2019 = 224000-44800= 179200

Depreciation = 179200 x 10/100 x 2 =$35840