Depreciation methods Kristin is evaluating a capital budgeting project that shou

Question

Depreciation methods Kristin is evaluating a capital budgeting project that should last for 4 years. The project requires $550,000 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 10%, and its tax rate is 40%. a. What would the depreciation expense be each year under each method? Round your answers to the nearest cent. Year Scenario 1 (Straight-Line) Scenario 2 (MACRS) 1 $ $ 2 $ $ 3 $ $ 4 $ $ b. Which depreciation method would produce the higher NPV? -Select-Straight-LineMACRS How much higher would the NPV be under the preferred method? Round your answer to two decimal places. $

Explanation / Answer

a. Depreciation under straight line is $ 137,500 each year for 1st to 4th year.

          Depreciation based on MACRS accelerated method is:
          Depreciation rate x cost of project = depreciation charge
        Depreciation Year 1 =550000 x .33= 181500
        Depreciation Year 2= 550000 x .45= 247500
       Depreciation Year 3= 550000 x .15= 82500
      Depreciation Year 4 = 550000 x .07= 38500

b. MACRS depreciation will produce a higher NPV by $ 127816
        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 = 127816 x .40=51126.4 x 0.909090909= 46478.54
      Year 2 cash in due to tax shield = 127816 x .40= 51126.4 x 0.826446281= 42253.2231
    Year 3 cash in due to tax shield = 127816 x .40= 51126.4 x 0.751314801= 38412.021
   Year 4 cash in due to tax shield =127816 x .40= 51126.4 x 0.683013455= 34920.0191
   Total Present value of tax shield under straight line depreciation= 162063.809
   Year 0 cash out - 550,000 x 1. (Present value of $1 at year 0) = -550,000
   Net Present Value (straight line depreciation) ............ -387936.19


     Present value of tax shield of depreciation under MACRS:

    Year 1 cash in due to tax shield = 181500 x .40= 72600 x 0.909090909= 66000
   Year 2 cash in due to tax shield = 247500x .40= 99000 x 0.826446281= 81818.1818
    Year 3 cash in due to tax shield = 82500 x .40= 33000 x 0.751314801= 24793.3884
   Year 4 cash in due to tax shield = 38500 x .40 = 15400 x 0.683013455= 37846.018

Total Present value of cash in due to tax shield under MACRS= 210457.588
    Year 0 cash out = -5500000 x 1.0 (present value of 1 at year 0) = -550000
    NPV (MACRS depreciation.) =-339542.41

Difference in Net Present value between St line and MACRS depreciation is $ 48393.78
in favour of MACRS depreciation.
-5464108 minus -5336291= -48393.78

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/ 1.10 =0.826446281

Year 3=0.826446281/1.1=0.751314801

Year 4=0.751314801/1.1=0.683013455

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