I am working on the following problem listed below. I have the solution to the p

Question

I am working on the following problem listed below. I have the solution to the problem, but i am confused onto why we use the fraction 1/4 and 3/4 for the year 2015.

E11-3 (Depreciation Computations—SYD, DDB—Partial Periods) Judds Company purchased a new plant asset on April 1, 2014, at a cost of $711,000. It was estimated to have a service life of 20 years and a salvage value of $60,000. Judds’ accounting period is the calendar year.

(a) Compute the depreciation for this asset for 2014 and 2015 using the sum-of-the-years’-digits method.

3/4 X 20/210 X ($711,000 – $60,000) = $46,500 for 2014

1/4 X 20/210 X ($711,000 – $60,000)

=

$15,500

+

3/4 X 19/210 X ($711,000 – $60,000)

=

44,175

for 2015 $59,675

1/4 X 20/210 X ($711,000 – $60,000)

=

$15,500

+

3/4 X 19/210 X ($711,000 – $60,000)

=

44,175

for 2015 $59,675

Explanation / Answer

The machine had been purchased on date 1st april 2014. Therefore the depreciation will be charged not for the full year 2014 but for the proportionate period in 2014 starting from 1st arpil to 31st Dec. This comes to 9 months. Expressed in fraction for the full year it can be written as 3/4 (i.e. 9/12).

Now in 2015, we have to charge depreciation on only 1/4th portion of the asset calculated using "SYD" of 20/210, because 3/4th portion of the same had been allowed in the previous year 2014. Therefore it comes to 1/4th of 20/210. Further, the remaining 3/4th year in 2015 will be charged using SYD of 19/210.

Thus, 2015 calculates depreciation in two parts:

1/4 X 20/210 X ($711,000 – $60,000) = 15500

+

3/4 X 19/210 X ($711,000 – $60,000) = 44175

                                                               59675

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