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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
Howard corp., the ever-maligned shirt importer, is examining some equipment that has been depreciated using the sum-of-years method.

Here's what you know:

  • It will last for 5 years.
  • Its residual value is $777.
  • It was purchased for $70,300.
What is the total accumulated depreciation as of end of year number 5 when using the sum-of-years depreciation method?
Answer
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👉 Answer:

  • The total accumulated depreciation as of end of year number 5 is $69,523.00

👩‍🎓 Here are the steps to figure it out:

  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 $69,523.00 5 / 15 $23,174.33 $23,174.33 $47,125.00
  4. Now let's fill in another year.
    sum-of-years method
    YearDepreciation BaseFractional Depreciation RateDepreciationAccumulated DepreciationEnding Value
    1 $69,523.00 5 / 15 $23,174.33 $23,174.33 $47,125.00
    2 $69,523.00 4 / 15 $18,539.47 $41,713.80 $28,586.00
  5. Now let's fill in another year.
    sum-of-years method
    YearDepreciation BaseFractional Depreciation RateDepreciationAccumulated DepreciationEnding Value
    1 $69,523.00 5 / 15 $23,174.33 $23,174.33 $47,125.00
    2 $69,523.00 4 / 15 $18,539.47 $41,713.80 $28,586.00
    3 $69,523.00 3 / 15 $13,904.60 $55,618.40 $14,681.00
  6. Now let's fill in another year.
    sum-of-years method
    YearDepreciation BaseFractional Depreciation RateDepreciationAccumulated DepreciationEnding Value
    1 $69,523.00 5 / 15 $23,174.33 $23,174.33 $47,125.00
    2 $69,523.00 4 / 15 $18,539.47 $41,713.80 $28,586.00
    3 $69,523.00 3 / 15 $13,904.60 $55,618.40 $14,681.00
    4 $69,523.00 2 / 15 $9,269.73 $64,888.13 $5,411.00
  7. Now let's fill in another year.
    sum-of-years method
    YearDepreciation BaseFractional Depreciation RateDepreciationAccumulated DepreciationEnding Value
    1 $69,523.00 5 / 15 $23,174.33 $23,174.33 $47,125.00
    2 $69,523.00 4 / 15 $18,539.47 $41,713.80 $28,586.00
    3 $69,523.00 3 / 15 $13,904.60 $55,618.40 $14,681.00
    4 $69,523.00 2 / 15 $9,269.73 $64,888.13 $5,411.00
    5 $69,523.00 1 / 15 $4,634.87 $69,523.00 $777.00
  8. And here we can just read off the accumulated depreciation for year 5 from the table ($69,523.00).
    sum-of-years method
    YearDepreciation BaseFractional Depreciation RateDepreciationAccumulated DepreciationEnding Value
    1 $69,523.00 5 / 15 $23,174.33 $23,174.33 $47,125.00
    2 $69,523.00 4 / 15 $18,539.47 $41,713.80 $28,586.00
    3 $69,523.00 3 / 15 $13,904.60 $55,618.40 $14,681.00
    4 $69,523.00 2 / 15 $9,269.73 $64,888.13 $5,411.00
    5 $69,523.00 1 / 15 $4,634.87 $69,523.00 $777.00
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