Question

Red Corporation constructed a machine at a total cost of $64 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 11-year life using the straight-line method. The residual value is expected to be $3 million. At the beginning of 2024, Red decided to change to the sum-of-the-years'-digits method. Ignoring income taxes, what will be Red's depreciation expense for 2024? Note: Do not round intermediate calculations. Round final answer to 2 decimal places.

Answer 1

To calculate the depreciation expense for Red Corporation's machine for 2024, the sum-of-the-years'-digits method is applied, with the fourth year's fraction of total depreciable cost resulting in a depreciation expense of $13,555,555.56.

Step-by-step explanation:

The student has asked about calculating the depreciation expense for Red Corporation's machine for the year 2024, which requires a switch in depreciation methods.

To calculate this expense using the sum-of-the-years'-digits method, one must first determine the total depreciable cost of the machine, which is equal to the cost of the machine less its residual value ($61 million: $64 million - $3 million).

Over an 11-year life, the sum of the years' digits is calculated as 66 (the sum of numbers from 1 to 11). Since the machine has already been in service for 3 years, by 2024, it will be in its fourth year of service. The digits for these years must be subtracted from the total to find the remaining balance, and then the fraction for year 4 can be determined.

For the 4th year of service, this fraction is 8/36 (as there are eight years left and the sum of the years' digits is 66). The depreciation expense for 2024 is thus 8/36 of the total depreciable cost, which amounts to $13,555,555.56.