Consider a project that requires investing $100,000 in an asset that is classified as a 3-year asset for tax purposes, even though its useful life is four years. If the investing company's marginal tax rate is 38 percent, the depreciation tax shield for the second year is closest to:

Question

Quizplus · Accepted Answer

The depreciation tax shield for the second year can be calculated using the double declining balance method for a 3-year asset. The depreciation rate is double the straight-line rate, which is 2/3 for a 3-year asset. In the second year, the depreciation expense is calculated on the remaining book value after the first year's depreciation. The first year's depreciation is 2/3 of 1/3 = 2/9 of $100,000, which is approximately $22,222. The remaining book value is $100,000 - $22,222 = $77,778. The second year's depreciation is again 2/9 of $77,778, which is approximately $17,283. The tax shield is the depreciation expense times the tax rate: $17,283 * 38% ≈ $6,567. However, this calculation does not match the provided options directly due to a mistake in the calculation process. The correct approach for the second year using MACRS for a 3-year asset would typically involve using the given percentage for the second year from the MACRS table, which is 32%. Thus, the depreciation expense is 32% of $100,000 = $32,000. The tax shield is then $32,000 * 38% = $12,160. The error in the explanation indicates a miscalculation or misunderstanding of the depreciation method or tax shield calculation. The correct answer should be based on the correct application of the MACRS depreciation method and the company's marginal tax rate to the initial investment. Given the options and the typical calculation method, none of the provided calculations accurately reflect the correct process for determining the depreciation tax shield for the second year based on the standard MACRS rates and the given tax rate. Therefore, a reevaluation of the calculation is necessary to align with the correct methodology.

Consider a Project That Requires Investing $100,000 in an Asset