An asset was purchased for $120,000 on January 1, Year 1 and originally estimated to have a useful life of 10 years with a residual value of $10,000. At the beginning of the third year, it was determined that the remaining useful life of the asset was only 4 years with a residual value of $2,000. Compute the third-year depreciation expense using the revised amounts and straight-line method.

Question

An asset was purchased for $120,000 on January 1, Year 1 and originally estimated to have a useful life of 10 years with a residual value of $10,000. At the beginning of the third year, it was determined that the remaining useful life of the asset was only 4 years with a residual value of $2,000. Compute the third-year depreciation expense using the revised amounts and straight-line method.

BlackTom AI · Accepted Answer

Straight-line depreciation allocates cost minus residual value evenly over an asset’s useful life. Use: Annual depreciation = (Cost − Residual value) / Useful life. When estimates change, compute book value at the revision date, then spread the revised depreciable amount over the revised remaining life.

1) Relevant concepts
- Initial straight-line depreciation formula.
- Accumulated depreciation before the change equals annual depreciation × years already depreciated.
- Book value at revision = Cost − Accumulated depreciation.
- Revised annual depreciation = (Book value − Revised residual) / Revised remaining life.

2) Step-by-step reasoning and calculations
- Initial cost = $120,000; original residual = $10,000; original life = 10 years.
- Initial annual depreciation = (120,000 − 10,000) / 10 = 110,000 / 10 = $11,000 per year.
- Accumulated depreciation at beginning of Year 3 (after 2 years) = 2 × 11,000 = $22,000.
- Book value at that date = 120,000 − 22,000 = $98,000.
- Revised residual value = $2,000; revised remaining life = 4 years.
- Revised depreciable amount = Book value − Revised residual = 98,000 − 2,000 = $96,000.
- Revised annual depreciation = 96,000 / 4 = $24,000.

3) Intermediate steps shown above (annual original depreciation, accumulated depreciation, book value, revised depreciable base, division by remaining life).

4) Why this is correct
The third-year expense must be based on the asset’s book value at the start of Year 3 and the new estimates. Spreading $96,000 over the four remaining years yields $24,000 per year; that is the correct depreciation expense for Year 3 under the straight-line method after revision.

5) Why other options are incorrect
- $11,000: equals the original annual depreciation and ignores the revised shorter life and lower residual.
- $24,500: no correct intermediate leads to this; likely a calculation error (e.g., miscomputing book value or residual).
- $25,000: would result if one incorrectly used a $100,000 depreciable base divided by 4 (not applicable here).

6) Conclusion
The correct third-year depreciation expense is $24,000, which matches the provided answer.

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