Question

A proposed cost-saving device has an installed cost of $450,000.    The device will be used in a five-year project, but is classified as three-year MACRS property for tax purposes. The required initial net working capital investment is $30,000, the marginal tax rate is 35 percent, and the project discount rate is 12 percent.   The device has an estimated Year 5 salvage value of $75,000. What level of per year pretax cost savings do we require for this project to be profitable?

(Hint: To start, treat the per-year pretax cost savings as an unknown value, and then use the tax-shield approach to compute OCF directly. Solve for the breakeven level of cost savings, such that the NPV=0).

Answer 1

Solution: Investment in fixed assets + investment in NWC= Pretax cost savings*(1-t)* PVIFA(R%,n)+PV of dep tax shield +PV of salvage +PV of NWC Let the pretax cost savings be 'a' 450000+30000=a*(1-0.35)*3.6047762+126700.64+27662.06+17022.81 480000=2.34310453a +171385.51 2.34310453a=480000-171385.51 2.34310453a=308614.49 a=308614.49/2.34310453 _ a=131711.79

Working: Calculation of PV of depreciation tax shield MARCS Dep Depreciable cost Dep rate Dep x tax rate Tax shield on depreciation x discount factor at 12% 1 2 3 4 5 Total 450000 450000 450000 450000 0.3333 0.4445 0.1481 0.0741 149985.001 200025.00 66645.00 33345.00 0.350.350.350.35 52494.75 70008.75 23325.75 11670.75 0.89285714 0.79719388 0.71178025 0.63551808 0.56742686 3.60477620 46870.31 55810.55 16602.81 7416.97 126700.64 PV calculation of PV of after tax salvage Salvage x (1-tax rate) After tax salvage value X PVIF (12%,5) PV of after tax salvage 750001 65% 48750 0.56742686 27662.06 Calcualtion of PV of NWC recovered NWC X PVIF (12%,5) PV of NWC recovered 30000 0.56742686 17022.81