An asset costs $10,000 and has a depreciable life of 10 years and a salvage value...

An asset costs $10,000 and has a depreciable life of 10 years and a salvage value of $3,000. Determine the book (asset) value at the end of the 9th year using each of the following methods of depreciation (a) double-declining-balance method (b) textbook-declining-balance method (Matheson formula), and (c) sum-of-years’ digits method.

Expert Solution

(a) Double Declining Balance method Depreciation = Beginning Book Value x 2 times straight line rate

Maximum Depreciation is such that ending book value doesnot fall below salvage value

YEAR	Beginning Book Value	Depreciation Sum of Digits@20%	Accumulated Depreciation	Ending Book Value
1	$ 10,000	$ 2,000	$ 2,000	$ 8,000
2	$ 8,000	$ 1,600	$ 3,600	$ 6,400
3	$ 6,400	$ 1,280	$ 4,880	$ 5,120
4	$ 5,120	$ 1,024	$ 5,904	$ 4,096
5	$ 4,096	$ 819	$ 6,723	$ 3,277
6	$ 3,277	$ 277	$ 7,000	$ 3,000
7	$ 3,000	$ -	$ 7,000	$ 3,000
8	$ 3,000	$ -	$ 7,000	$ 3,000
9	$ 3,000	$ -	$ 7,000	$ 3,000
10	$ 3,000	$ -	$ 7,000	$ 3,000

Book Value at end of 9th year = $3000

(b) Textbook Declining Balance Method = Beginning Book Value x Depreciation rate

YEAR	Beginning Book Value	Depreciation Sum of Digits @10%	Accumulated Depreciation	Ending Book Value
1	$ 10,000	$ 1,000	$ 1,000	$ 9,000
2	$ 9,000	$ 900	$ 1,900	$ 8,100
3	$ 8,100	$ 810	$ 2,710	$ 7,290
4	$ 7,290	$ 729	$ 3,439	$ 6,561
5	$ 6,561	$ 656	$ 4,095	$ 5,905
6	$ 5,905	$ 590	$ 4,686	$ 5,314
7	$ 5,314	$ 531	$ 5,217	$ 4,783
8	$ 4,783	$ 478	$ 5,695	$ 4,305
9	$ 4,305	$ 430	$ 6,126	$ 3,874
10	$ 3,874	$ 387	$ 6,513	$ 3,487

Book Value at end of 9th year = $3874

(c) Sum of Year's Digit Method = (Original Value - Salvage Value) / Sum of Years x Years remaining

YEAR	Beginning Book Value Depreciation Sum of Digits	Depreciation Sum of Digits	Accumulated Depreciation
1	$ 10,000	$ 1,273	$ 1,273	$ 8,727
2	$ 8,727	$ 1,145	$ 2,418	$ 7,582
3	$ 7,582	$ 1,018	$ 3,436	$ 6,564
4	$ 6,564	$ 891	$ 4,327	$ 5,673
5	$ 5,673	$ 764	$ 5,091	$ 4,909
6	$ 49,09	$ 636	$ 5,727	$ 4,273
7	$ 4,273	$ 509	$ 6,236	$ 3,764
8	$ 3, 764	$ 382	$ 6,618	$ 3,382
9	$ 3,382	$ 255	$ 6873	$ 3,127
10	$ 3,127	$ 127	$ 7,000	$ 3,000

Book Value at end of 9th year = $3127.

Rahul Sunny answered 8 months ago

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