Kristin is evaluating a capital budgeting project that should last for 4 years.
ID: 2634451 • Letter: K
Question
Kristin is evaluating a capital budgeting project that should last for 4 years. The project requires $375,000 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 (ignore the half-year convention for the straight-line method). The applicable MACRS depreciation rates are 33%, 45%, 15%, and 7%. The company's WACC is 12%, and its tax rate is 35%.
Year Scenario 1(Straight-Line) Scenario 2
(MACRS) 1 $?? _________ $?? _______ 2 $?? _________ $?? ________ 3 $?? _________ $?? ________ 4 $?? _________ $?? _________
Explanation / Answer
Depreciation under straight line is $ 93750 each year for 1st to 4 year.
Depreciation based on MACRS acceleted method is:
Depreciation rate x cost of project = depreciation charge
Depreciation Year 1 =$375,000 x .33= 123750
Depreciation Year 2= $375,000 x .45= 168750
Depreciation Year 3= $375,000 x .15= 56250
Depreciation Year 4 = $375,000 x .07= 26250
b. MACRS depreciation will produce a higher NPV by $ 5242
Present value of tax shield under straight line depreciation is
Depreciation x .4 ( tax rate) = Tax Shield x Present Value Factor of 1 at year n = present value
Year 1 cash in due to tax shield = $ 93750 x .35 = 32812.5 x 0.909090909= 29830
Year 2 cash in due to tax shield = $ 93750 x .35 = 32812.5 x 0.826446281= 27118
Year 3 cash in due to tax shield = $ 93750 x .35 = 32812.5 x 0.751314801= 24653
Year 4 cash in due to tax shield = $ 93750 x .35 = 32812.5 x 0.683013455= 22411
Total Present value of tax shield under straight line depreciation= 104012
Year 0 cash out - $375,000 x 1. ( present value of $1 at year 0) = -$375,000
Net Present Value (straight line depreciation) ............ -270988
Present value of tax shield of depreciation under MACRS:
Year 1 cash in due to tax shield = 123750 x .35= 43312.5 x 0.909090909= 39375
Year 2 cash in due to tax shield = 168750 x .35= 59062.5 x 0.826446281= 48812
Year 3 cash in due to tax shield = 56250 x ..35= 19687.5 x 0.751314801= 14792
Year 4 cash in due to tax shield = 26250 x .35 = 9187.5 x 0.683013455= 6275
Total Present value of cash in due to tax shield under MACRS= 109254
Year 0 cash out = -8000000 x 1.0 ( present value of 1 at year 0) = -$375,000
NPV ( MACRS depreciation.) =-265746
Difference in Net Present value between St line and MACRS depreciation is $ 5242
in favor of MACRS depreciation.
-270988 minus -265746= -5242
Depreciation is a tax deductible expense. With depreciation, you save on paying income tax.
So, the tax saving is a cash inflow.
If Depreciation is not tax deductible, then you would have to pay higher income tax.
Present value factor of $1 at 10%
Year 0 =1
Year 1 = 1/1.1= 0.909090909
Year 2 = 0.909090909 divided by 1.10 =0.826446281
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