Question

Choose the right answer, showing your work:

The initial purchase cost of an equipment is 100 k$, the use life is 5 years, the salvage value of the equipment is 10 k$, what is the book value of the equipment at end of year 3 using sum-of-the-digits method?

(a) 28 k$

(b) 46 k$

(c) 54 k$

(b) 72 k$

Answer 1

Initial cost of equipment = $100,000

Salvage value of the equipment = $10,000

Depreciation base = Initial cost - Salvage value = $100,000 - $10,000 = $90,000

Following is the complete table -

Year	Depreciation base	Depreciation fraction	Depreciation expense
1	$90,000	5/15	[(5/15) * 90,000] = $30,000
2	$90,000	4/15	[(4/15) * 90,000] = $24,000
3	$90,000	3/15	[(3/15) * 90,000] = $18,000

Total depreciation in 3 years = $30,000 + $24,000 + $18,000 = $72,000

Calculate the book value at the end of Year 3 -

Book value = Initial cost - Total depreciation in 3 years

Book value = $100,000 - $72,000 = $28,000

The book value at the end of 3 year is $28,000.

Hence, the correct answer is the option (a).