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 40 percent and the appropriate cost of capital for this project is 10 percent, the present value of the depreciation tax shields is closest to:

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The present value of the depreciation tax shields can be calculated using the Modified Accelerated Cost Recovery System (MACRS) rates for a 3-year asset and the company's marginal tax rate. The MACRS rates for the first three years are 33.33%, 44.45%, and 14.81%, respectively, and there's a half-year convention which effectively spreads the depreciation over four years. The depreciation tax shield for each year is the depreciation expense multiplied by the tax rate. The present value of these tax shields is then calculated by discounting them at the project's cost of capital (10%). The calculation is as follows:Year 1: $100,000 * 33.33% * 40% = $13,332; PV = $13,332 / (1 + 0.10)^1Year 2: $100,000 * 44.45% * 40% = $17,780; PV = $17,780 / (1 + 0.10)^2Year 3: $100,000 * 14.81% * 40% = $5,924; PV = $5,924 / (1 + 0.10)^3Year 4: $100,000 * 7.41% * 40% = $2,964; PV = $2,964 / (1 + 0.10)^4Adding the present values of these tax shields gives a total close to $33,289, which is option C.

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