irwin, incorporated constructed a machine at a total cost of $68 million. construction was completed at the…

irwin, incorporated constructed a machine at a total cost of $68 million. construction was completed at the end of 2020 and the machine was placed in service at the beginning of 2021. the machine was being depreciated over a 10 - year life using the sum - of - the - years’ - digits method. the residual value is expected to be $2 million. at the beginning of 2024, irwin decided to change to the straight - line method.\n\nignoring income taxes, prepare the journal entry relating to the machine for 2024.\nnote: if no entry is required for a transaction/event, select \no journal entry required\ in the first account field. do not round intermediate calculations. enter your answers in millions rounded to 1 decimal place (i.e., 5,500,000 should be entered as 5.5).

irwin, incorporated constructed a machine at a total cost of $68 million. construction was completed at the end of 2020 and the machine was placed in service at the beginning of 2021. the machine was being depreciated over a 10 - year life using the sum - of - the - years’ - digits method. the residual value is expected to be $2 million. at the beginning of 2024, irwin decided to change to the straight - line method.\n\nignoring income taxes, prepare the journal entry relating to the machine for 2024.\nnote: if no entry is required for a transaction/event, select \no journal entry required\ in the first account field. do not round intermediate calculations. enter your answers in millions rounded to 1 decimal place (i.e., 5,500,000 should be entered as 5.5).

Answer

Explanation:

Step1: Calculate sum - of - years' digits

The sum of the years' digits for a 10 - year asset is $\sum_{n = 1}^{10}n=\frac{10\times(10 + 1)}{2}=55$.

Step2: Calculate annual depreciation under sum - of - years' digits method for first 3 years

The depreciable base is $68 - 2=66$ million. The depreciation for 2021: $\text{Depreciation}{2021}=\frac{10}{55}\times66 = 12$ million. The depreciation for 2022: $\text{Depreciation}{2022}=\frac{9}{55}\times66 = 10.8$ million. The depreciation for 2023: $\text{Depreciation}_{2023}=\frac{8}{55}\times66 = 9.6$ million. The accumulated depreciation at the beginning of 2024 is $12+10.8 + 9.6=32.4$ million. The book - value at the beginning of 2024 is $68-32.4 = 35.6$ million.

Step3: Calculate annual depreciation under straight - line method from 2024

The remaining useful life is $10-(2024 - 2021)=7$ years. The new annual depreciation is $\frac{35.6 - 2}{7}=\frac{33.6}{7}=4.8$ million.

The journal entry for 2024:

Account Title Debit (in millions) Credit (in millions)
Depreciation Expense 4.8 Accumulated Depreciation - Machine

Answer:

Account Title Debit (in millions) Credit (in millions)
Depreciation Expense 4.8 Accumulated Depreciation - Machine