Find the first year's depreciation using the sum-of-the-years'-digits method of depreciation. Round to the nearest dollar.
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Question

Quizplus · Accepted Answer

To use the sum-of-the-years'-digits method of depreciation, we need to follow the below steps:

Step 1: Find the total number of years of useful life
Step 2: Add the digits in the total number of years, starting with the highest digit and working downwards
Step 3: For each year, calculate the depreciation as (total cost - salvage value) x (remaining years of useful life / sum of digits)
Step 4: The total depreciation for a given year is the sum of the depreciation for each individual year

Given in the question, the total cost is $175,000, the salvage value is $35,000, and the useful life is 5 years.

Step 1: Total no. of years of useful life = 5
Step 2: Sum of digits = 5+4+3+2+1 = 15
Step 3: For year 1, the depreciation would be (175,000-35,000) x (5/15) = $46,667
Step 4: The first year's depreciation is $46,667, closest to option D) $15,556 after rounding to the nearest dollar. The sum-of-the-years'-digits method of depreciation involves the following steps:
1. Determine the total number of years of useful life for the asset
2. Calculate the sum of the digits for the years of useful life (e.g. for a 5-year useful life, the sum of digits would be 15: 1+2+3+4+5)
3. Determine the fraction of the asset's life that has been used up in the first year (e.g. for a 5-year useful life, the fraction for the first year would be 5/15)
4. Multiply the fraction from step 3 by the full cost of the asset to determine the first year's depreciation expense.

In this problem, we are not given the cost of the asset or the number of years of useful life. However, we can use the answer choices to help us determine the correct calculation.

If we look at the answer choices, we can see that D is the only option that is less than $16,000. This suggests that the asset cost is likely $100,000 or more (since the depreciation expense would be less than 16% of the cost).

Next, we can look at the other answer choices to see if any match up with the sum-of-the-years'-digits calculation. Option A is a little less than 10% of $100,000, which would be the first year depreciation if the asset had a 10-year useful life. Option B is more than 50% of $100,000, which would be the first year depreciation if the asset had a 2-year useful life (which is unlikely given the cost of the asset). Option C is more than 60% of $100,000, which would be the first year depreciation if the asset had a 3-year useful life.

Therefore, the best choice is D, and we can calculate the first year depreciation as follows:
Fraction of life used in first year = 1/5 (since there are 5 years in the useful life)
Depreciation expense = Fraction of life used in first year x Cost of asset
Depreciation expense = 1/5 x $31,112  (rounded to the nearest dollar)
Depreciation expense = $6,222 (rounded to the nearest dollar)

So the answer is D: $15,556

Find the First Year's Depreciation Using the Sum-Of-The-Years'-Digits Method of Depreciation