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Sum-of-Years-Digits Depreciation

Lesson
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If you liked double-declining balance depreciation, you'll probably like its bigger brother even more.

In most cases it will depreciate even faster.then double-declining balance depreciation.

Here's how it works:

  1. Calculate the depreciable base: Take the initial item value and subtract its residual value
  2. Count the number of years of total depreciation. Add those numbers together. For instance, 5 years of depreciation would be 5+4+3+2+1=15.
  3. Starting with the first year, assign each the highest available number available from those listed above. For instance, the first year would be 5/15, the next would be 4/15 and so on.
  4. For each year, multiply the remaining depreciable base by the fraction above.
Question
Sierra inc., the ancient shirt designer, is examining some equipment that has been depreciated using the sum-of-years method.

Here are the relevant facts:

  • Its residual value is $4,421.

  • It was acquired for $51,100.

  • It has an expected lifespan of 5 years.

What is the total accumulated depreciation as of end of year number 2 when using the sum-of-years depreciation method?
Answer
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👉 Answer:

  • The total accumulated depreciation as of end of year number 2 is $28,007.40

👨‍🎓 Here's how we arrived at the answer:

  1. The first thing we need to do is figure out the sum of all of the years.
    1 + 2 + 3 + 4 + 5 = 15
  2. The math is a little complicated, so let's build a table. The fractional depreciation rate is calculated by taking the largest year number we haven't used yet and dividing it by the sum of all of the years (15).
    sum-of-years method
    YearDepreciation BaseFractional Depreciation RateDepreciationAccumulated DepreciationEnding Value
  3. Now let's fill in another year.
    sum-of-years method
    YearDepreciation BaseFractional Depreciation RateDepreciationAccumulated DepreciationEnding Value
    1 $46,679.00 5 / 15 $15,559.67 $15,559.67 $35,540.00
  4. Now let's fill in another year.
    sum-of-years method
    YearDepreciation BaseFractional Depreciation RateDepreciationAccumulated DepreciationEnding Value
    1 $46,679.00 5 / 15 $15,559.67 $15,559.67 $35,540.00
    2 $46,679.00 4 / 15 $12,447.73 $28,007.40 $23,092.00
  5. And here we can just read off the accumulated depreciation for year 2 from the table ($28,007.40).
    sum-of-years method
    YearDepreciation BaseFractional Depreciation RateDepreciationAccumulated DepreciationEnding Value
    1 $46,679.00 5 / 15 $15,559.67 $15,559.67 $35,540.00
    2 $46,679.00 4 / 15 $12,447.73 $28,007.40 $23,092.00
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