Final answer:
Using the sum-of-the-years'-digits method, the depreciation for Cutter Enterprises' equipment for 2025 is $10,640, and the book value on December 31, 2025, is $24,060, which corresponds to Option D.
Step-by-step explanation:
To calculate the depreciation using the sum-of-the-years'-digits method for Cutter Enterprises' equipment purchased for $48,000 on January 1, 2024, with an expected life of five years and a residual value of $8,100, we must first identify the sum of the years' digits. Since the useful life of the equipment is 5 years, the sum is calculated as 5 + 4 + 3 + 2 + 1 = 15.
The depreciable base is the cost of the equipment minus the residual value: $48,000 - $8,100 = $39,900. For each year, the depreciation expense will be a fraction of the depreciable base, with the numerator being the remaining years' digit and the denominator the sum of the years' digits.
For 2025, which is the second year of the depreciation schedule, the fraction is 4/15. The depreciation expense for 2025, hence, would be $39,900 * (4/15), which is $10,640.
The book value at the end of 2025 is the original cost minus the accumulated depreciation over the two years. For 2024, the depreciation would have used the fraction 5/15, so the total depreciation over these two years would be ($39,900 * (5/15) + $39,900 * (4/15)).
The book value at the end of 2025 would thus be $48,000 - ($39,900 * (5/15) + $39,900 * (4/15)) = $24,060.
Therefore, the correct answer is Option D: $10,640 and $24,060, respectively.