Question

1. The company accountant is uncertain which of three depreciation methods the firm should use for welding equipment that costs $200,000, and has a zero salvage value at the end of a 10-year depreciable life. Compute the depreciation schedule for the welding equipment using the methods listed:
   1. Straight line
   2. Double declining balance
   3. Sum-of-years’ –digits

      Based on your analysis, which depreciation method is most profitable for the firm?

Answer 1

(a) Straight-line (SLM) method

SL annual depreciation = Cost / Useful life = 200,000 / 10 = 20,000

SLM depreciation schedule as follows.

SLM
Year	Beginning-of-year Book Value ($)	Annual Depreciation ($)	Accumulated Depreciation ($)	End-of-Year Book Value ($)
1	2,00,000	20,000	20,000	1,80,000
2	1,80,000	20,000	40,000	1,60,000
3	1,60,000	20,000	60,000	1,40,000
4	1,40,000	20,000	80,000	1,20,000
5	1,20,000	20,000	1,00,000	1,00,000
6	1,00,000	20,000	1,20,000	80,000
7	80,000	20,000	1,40,000	60,000
8	60,000	20,000	1,60,000	40,000
9	40,000	20,000	1,80,000	20,000
10	20,000	20,000	2,00,000	0
TOTAL		2,00,000

(b) DDB method

Straight line depreciation rate = 1 / Useful life = 1/10 = 0.1

DDB depreciation rate = 2 x SLM rate = 2 x 0.1 = 0.2

Depreciation schedule as follows.

DDB
Year	Beginning-of-year Book Value ($)	Depreciation Rate	Annual Depreciation ($)	Accumulated Depreciation ($)	End-of-Year Book Value ($)
1	2,00,000	0.20	40,000	40,000	1,60,000
2	1,60,000	0.20	32,000	72,000	1,28,000
3	1,28,000	0.20	25,600	97,600	1,02,400
4	1,02,400	0.20	20,480	1,18,080	81,920
5	81,920	0.20	16,384	1,34,464	65,536
6	65,536	0.20	13,107	1,47,571	52,429
7	52,429	0.20	10,486	1,58,057	41,943
8	41,943	0.20	8,389	1,66,446	33,554
9	33,554	0.20	6,711	1,73,156	26,844
10	26,844	0.20	5,369	1,78,525	21,475
TOTAL			1,78,525

(c) SOYD method

Sum-of-years-digit (SOYD) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

Annual depreciation in year N = Cost x (Number of years remaining at beginning of year N / SOYD)

= 200,000 x (Number of years remaining at beginning of year N / 55)

Depreciation schedule as follows.

SOYD
Year	Net Cost ($)	Depreciation Rate	Annual Depreciation ($)	Accumulated Depreciation ($)	End-of-Year Book Value ($)
1	2,00,000	10/55	36,364	36,364	1,63,636
2	2,00,000	9/55	32,727	69,091	1,30,909
3	2,00,000	8/55	29,091	98,182	1,01,818
4	2,00,000	7/55	25,455	1,23,636	76,364
5	2,00,000	6/55	21,818	1,45,455	54,545
6	2,00,000	5/55	18,182	1,63,636	36,364
7	2,00,000	4/55	14,545	1,78,182	21,818
8	2,00,000	3/55	10,909	1,89,091	10,909
9	2,00,000	2/55	7,273	1,96,364	3,636
10	2,00,000	1/55	3,636	2,00,000	0
TOTAL			2,00,000

(d)

The lower the total depreciation over project life, the higher the net profit of the project over its lifetime. Since DDB method has lowest total depreciation over project life, this method leads to highest profitability.