ABC Company purchased an equipment on September 1, 2015 for $230,000. The salvage value of the equipment is $10,000 and the estimated useful life is 10 years. What is the book value of the equipment at December 31, 2016, if the company uses sum-of-years- digits method to record depreciation? W a. $154,000 b. $178,000 c. $190,000 d. $160,000?

Question

Answer

Solution:

Given,
Cost of equipment = $230,000
Salvage value = $10,000
Useful life = 10 years

Depreciation expense under sum-of-years-digits method is calculated as follows:

Step 1: Calculate the total number of years of useful life of the equipment.
Total useful life = 10 years

Step 2: Calculate the sum of the digits of the useful life.
Sum of the digits = 1+2+3+4+5+6+7+8+9+10 = 55

Step 3: Calculate the depreciation expense for each year.
Depreciation expense for year 1 = (10/55) x ($230,000 - $10,000) = $40,000
Depreciation expense for year 2 = (9/55) x ($230,000 - $10,000) = $35,273
Depreciation expense for year 3 = (8/55) x ($230,000 - $10,000) = $30,545
And so on, until year 10.

Step 4: Calculate the book value of the equipment at December 31, 2016.
Depreciation expense for 2015 = $40,000
Depreciation expense for 2016 = $35,273
Accumulated depreciation as of December 31, 2016 = $40,000 + $35,273 = $75,273
Book value as of December 31, 2016 = $230,000 - $75,273 = $154,727

Therefore, the book value of the equipment at December 31, 2016, if the company uses sum-of-years-digits method to record depreciation is $154,727.

Answer: a. $154,000

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