Sum-of-Years-Digits Depreciation
Lesson:
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:
- Calculate the depreciable base: Take the initial item value and subtract its residual value
- 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.
- 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.
- For each year, multiply the remaining depreciable base by the fraction above.
Ultra Biz, the mysterious violin manufacturer, is examining some equipment that has been depreciated using the sum-of-years method.
This is what you've been told:
- It was acquired for $76,800.
- Its residual value is $3,089.
- It has an expected lifespan of 5 years.
What is the value of the item as of end of year number 3 when using the sum-of-years depreciation method?
Answer:
- The value as of end of year number 3 is $17,831.00
Explanation:
- The first thing we need to do is figure out the sum of all of the years.
1 + 2 + 3 + 4 + 5 = 15 - 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 Year Depreciation Base Fractional Depreciation Rate Depreciation Accumulated Depreciation Ending Value - Now let's fill in another year.
sum-of-years method Year Depreciation Base Fractional Depreciation Rate Depreciation Accumulated Depreciation Ending Value 1 $73,711.00 5 / 15 $24,570.33 $24,570.33 $52,229.00 - Now let's fill in another year.
sum-of-years method Year Depreciation Base Fractional Depreciation Rate Depreciation Accumulated Depreciation Ending Value 1 $73,711.00 5 / 15 $24,570.33 $24,570.33 $52,229.00 2 $73,711.00 4 / 15 $19,656.27 $44,226.60 $32,573.00 - Now let's fill in another year.
sum-of-years method Year Depreciation Base Fractional Depreciation Rate Depreciation Accumulated Depreciation Ending Value 1 $73,711.00 5 / 15 $24,570.33 $24,570.33 $52,229.00 2 $73,711.00 4 / 15 $19,656.27 $44,226.60 $32,573.00 3 $73,711.00 3 / 15 $14,742.20 $58,968.80 $17,831.00 - And here we can just read off the ending item value for year 3 from the table ($17,831.00).
sum-of-years method Year Depreciation Base Fractional Depreciation Rate Depreciation Accumulated Depreciation Ending Value 1 $73,711.00 5 / 15 $24,570.33 $24,570.33 $52,229.00 2 $73,711.00 4 / 15 $19,656.27 $44,226.60 $32,573.00 3 $73,711.00 3 / 15 $14,742.20 $58,968.80 $17,831.00