Question

Currently, your firm plans on depreciating an upcoming project’s PPE from an initial value of $800k to a final book value of $100k over a 10 year period. You’ve been asked to value a possible change in the depreciation scheme which will accelerate this process by depreciating the machine over a 6 year period (let’s assume this is legal to do). If you accelerate depreciation, you will still be depreciating to a final book value of $100k. If the project’s discount rate is 12% and the firm’s tax rate is 35%, by how much will the project’s NPV change if you switch to the accelerated depreciation schedule?

Answer 1

• If we want to have the salvage value of 100K then we will deduct this from the cost of 800k to find the annual depreciation
• Depreciation schedules are as follows when the machinery is depreciated to 100K in 10 year and in 6 years respectively:
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  • 
• Investment = cost - salvage value
• Closing balance = Opening balance + investment -depreciation
• Opening balance = previous year's closing balance
• Depreciation = investment/depreciable life

Now as depreciation provides the tax shield we need to find out the PV of this tax shield in both the cases

1. Tax shield = tax rate x annual depreciation
   • 0.35 x 70000 = 24500
   • PV of this tax shield can be found by solving the following equation:
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     • 
     • 
2. Tax shield = tax rate x annual depreciation
   • 0.35 x 116666.67= 40833.33
   • PV of this tax shield can be found by solving the following equation:
     • 
     • 
     • 

Therefore the NPV will be higher when the depreciable life is 6 years by 167882.47-138430.46 = $29452