Kristin is evaluating a capital budgeting project that should last for 4 years.

Question

Kristin is evaluating a capital budgeting project that should last for 4 years. The project requires $350,000 of equipment. She is unsure what depreciation method to use in her analysis, straight-line or the 3-year MACRS accelerated method. Under straight-line depreciation, the cost of the equipment would be depreciated evenly over its 4-year life. The applicable MACRS depreciation rates are 33%, 45%, 15%, and 7%. The company’s WACC is 10%, and its tax rate is 40%.

a) What is the NPV of the depreciation tax shield using straight-line depreciation?

b) What is the NPV of the depreciation tax shield using MACRS?

The Chang Company is considering the purchase of a new machine to replace an obsolete one. The machine being used for the operation has a book value and a market value of zero. However, the machine is in good working order and will last at least another 5 years. The proposed replacement machine will perform the operation so much more efficiently that Chang’s engineers estimate that it will produce after-taxcash flows (labor savings and depreciation) of $13,100 per year. The new machine will cost $39,300 delivered and installed, and its economic life is estimated to be 5 years. It has zero salvage value. The firm’s WACC is 11.20%, and its marginal tax rate is 40%. Calculate the NPV of the replacement analysis?

Explanation / Answer

a) Depreciation for each year = $350,000/4= $87,500. Tax sheild for each year= $87,500 * 40%= $35,000. NPV of Tax sheild= $35000/(1.1)+$35000/(1.1)^2+$35000/(1.1)^3+$35000/(1.1)^4= 31,818.18+28,925.6+26,296.0+23,905.5= $110,945

b)Depreciation for year 1 = $350,000*33%= $115,500. Depreciation for year 2 = $350,000*45%= $157,500.

Depreciation for year 3 = $350,000*15%= $52,500.Depreciation for year 4 = $350,000*7%= $24,500.

Tax sheild for year 1 = $115000 * 40%= $46200. Tax sheild for year 2 = $157500 * 40%= $63000. Tax sheild for year 3 = $52500 * 40%= $21000, Tax sheild for year 4 = $24500 * 40%= 9800

$NPV of Tax sheild= $46000/(1.1)+$63000/(1.1)^2+$21000/(1.1)^3+$9800/(1.1)^4= 42000+52066.12+15777.61+6693.53= $116537.3 (Answer)

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