Final answer:
The correct book value of the asset at the end of the third year, using MACRS depreciation, is a. $108,000. This is calculated by subtracting the total depreciation over three years from the original cost of the asset.
Step-by-step explanation:
The question involves the calculation of the book value of an asset at the end of its third year using the Modified Accelerated Cost Recovery System (MACRS) method of depreciation. Under MACRS, different assets are assigned specific depreciation schedules. For a five-year asset, the corresponding MACRS percentages are 20%, 32%, 19.2%, 11.52%, and 11.52%, respectively for the first five years, with a final half-year of 5.76%. To find the book value at the end of the third year, we apply these rates to the asset's initial cost:
- Year 1 depreciation: $375,000 × 20% = $75,000
- Year 2 depreciation: $375,000 × 32% = $120,000
- Year 3 depreciation: $375,000 × 19.2% = $72,000
Summing up the depreciation amounts for the first three years: $75,000 + $120,000 + $72,000 = $267,000. The remaining book value at the end of the third year is the original cost minus the accumulated depreciation: $375,000 - $267,000 = $108,000.
Therefore, the correct answer is (a) $108,000, which is the book value of the asset at the end of the third year.