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An answer of $6,112 results from using the gross asset cost less the salvage value to calculate the depreciation. However, under MACRS, the depreciation rate is applied to the gross asset cost, not the depreciable base.
Although this question involves replacing one asset with another asset, we are not given information that would enable us to do an incremental analysis of the difference (if any) between the depreciation on the new asset versus the depreciation on the old asset. Thus, we will analyze this as if it were a new asset purchase, not a replacement of an existing asset. Since depreciation under MACRS is applied to the gross purchase price of the asset ($400,000) and the fourth year's depreciation will be 7% of $400,000, the fourth year's depreciation will be $28,000. Crane's tax rate is 40%, so the depreciation tax shield is $28,000 × .40, or $11,200. Since the question asks for the present value of the depreciation tax shield for the fourth year, we will discount it using .59 from the table (the PV of $1 at 14% for 4 years). $11,200 × .59 = $6,608, which is the present value of the depreciation tax shield for the fourth year of MACRS depreciation.
An answer of $16,520 results from discounting the fourth year's depreciation amount to year 0. The question asks for the present value of the fourth year's depreciation tax shield, not the present value of the fourth year's depreciation.
An answer of $0 results from failing to recognize that under MACRS, the "half-year convention" is normally used. Under the half-year convention, one-half of one year's depreciation is taken in the first year the asset is placed in service. For an asset with a three-year life, one year's depreciation would then be taken in each of years 2 and 3; and one-half of one year's depreciation would be taken in year 4. Thus, the present value of the depreciation tax shield for the fourth year could not be zero because the depreciation in year 4 would not be zero.