Question

An asset with a fixed investment cost of $100,000 is depreciated over a 7-year period, and it is expected to have a $5,000 salvage value at the end of the 7 years. Using the SOYD method, find the book value in year 4. a) Between $28,700 and $29,000 Ob) Between $35,200 and $35,500 O c) Between $45,200 and $45,500 d) Between $38,700 and $40,000 e) Between $25,200 and $25,500 f) None of the answers are correct

Answer 1

Correct answer is (f)

See the calcution:

SYD formula is = n(n+1)/2

Where n= estimated useful life

Here useful life is 7,

Then   SYD= 7(7+1)/2

                   =7*8/2=7*4

                    =28

This formula yields the sum of each year of the estimated useful life:

1+ 2+ 3 + 4+ 5+ 6 + 7 = 28

Fixed investment cost is $100,000. It has a useful life of 7 years and a salvage value of $5,000.This means the depreciable value of the asset is $100,000 minus $5,000, or $95,000. The sum-of-digits depreciation schedule is as follows in table

Year	Remainig estimated useful life at beginning of Year	SYD	Applicable%	Annual Depriciation
1	7	7/28	25%	23750
2	6	6/28	21.43%	20357.14
3	5	5/28	17.86%	16964.29
4	4	4/28	14.29%	13571.43
5	3	3/28	10.71%	10178.57
6	2	2/28	7.14%	6785.71
7	1	1/28	3.57%	3392.86
Total	28		100%	95000

Book value in year four is 13571.43, and we don’t have this value in given any option so correct answer is (f) None of the answer correct