NPV Analysis

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NPV Analysis

• An Exemplification

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NPV The concept

• NPV Project market value - Project book value
• or
• NPV Project PV - Initial cost

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Project CF

• Project CF OCF - Net capital Spending -
  Additions to NWC

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NPV CalculationExemplification

• Robin Donuts new pastry

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Robin Donuts new pastry

• Robin Donuts is about to develop a new
  revolutionary pastry.  Several concept products
  have been considered, such as the reduced-fat
  multiple-hole donut, the muffin fajita, and the
  triple chocolate holeless donut. The company
  spent in excess of 34 million in research and
  development on these products. The holeless donut
  will have 50 more chocolate than a regular
  donut, and will target individuals with a strong
  craving for chocolate.  The initial investment in
  new equipment is estimated at 100 million. The
  equipment will be depreciated at 20. Robin
  Donuts has a tax rate of 35, and uses a 6
  discount rate.

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Robin Donuts new pastry three-year cash flow
projection
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Robin Donuts new pastry

• Project PV PV OCF - PV Net capital spending -
  PV Additions to NWC

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Robin Donuts new pastry OCF calculation

• Levered OCF - accounts for interest expense ?
• Unlevered OCF - ignores interest expense ?

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Robin Donuts new pastry Un-Levered OCF
calculation

• definition (i) Unlevered NI Depr.
• definition (ii) Sales - Cost - Tax
• definition (iii) ATNOR Depr. tax shield

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Un-Levered OCF calculation (i)

• definition (i) Unlevered NI Depr.

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Clarifications

• Un-Levered NI
• Depreciation Schedule

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Levered vs. Un-Levered Net Income
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Net Income Trivia

• Levered NI lt Un-Levered NI

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Un-levered Net Income
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Robin Donuts new pastry Depreciation Schedule
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Unlevered OCF calculation (i)definition (i)
Un-Levered NI Depreciation
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Robin Donuts new pastry Un-levered OCF
calculation (ii)

• definition (i) Unlevered NI Depr.
• definition (ii) Sales - Cost - Tax
• definition (iii) ATNOR Depr. tax shield

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Un-levered OCF calculation (ii)Definition (ii)
Sales - Cost - Tax
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Robin Donuts new pastry Un-levered OCF
calculation (iii)

• definition (i) Unlevered NI Depr.
• definition (ii) Sales - Cost - Tax
• definition (iii) ATNOR Depr. tax shield

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Side note

• definition (iii) ATNOR Depr. tax shield
• Is the easiest way to calculate OCF
• Quantifies the tax-savings effect of depreciation

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Un-levered OCF calculation (iii)Definition
(iiI) ATNOR Depr. Tax shield
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Robin Donuts new pastry

• Project PV PV OCF - PV Net capital Spending -
  PV Additions to NWC

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NWC requirements
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Robin Donuts new pastry

• Project PV PV OCF - PV Net capital Spending -
  PV Additions to NWC

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Net capital Spending aka Changes in Fixed Assets
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Putting it all together NPV analysis
NPV -110 145.44/(1.06)3 NPV -110 122
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Putting it all together Another approach CCATS
Formula

• NPV PV(ATNOR) PV(Depr. tax shield)
  PV(NCS) - PV(addNWC) - Initial cost

PV (Depr. tax shield) CdT(1 r/2)/(r d)(1
r) - SdT/(r d)(1r)n PV(CCATS)
100(0.2)(0.35)(1.03)/(0.26)(1.06) -
25(0.2)(0.35/(0.26)(1.06)3 PV(CCATS) 26.16 -
5.65 20.51
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More on the PV of tax shields

• Assume salvage value of equipment Salvage gt 
  UCC
• The difference will make future CCA deductions
  smaller than expected

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More on the PV of tax shields (part 2)

• Assume salvage   lt  (UCC)
• The  difference will make future CCA deductions
  larger than expected

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Putting it all together Summary
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Summary Project NPV

• Project PV - Initial cost
• PV(OCF) - PV(Net capital Spending) - PV(AddNWC) -
  Initial cost
• PV(ATNOR) PV(Depr. tax shield) PV(NCS) -
  PV(AddNWC) - Initial cost

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Summary Project NPV

• ATNOR (S - C)(1 - T)
• After-Tax Net Operating Revenues

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Summary Project NPV

• PV (tax shield) CdT(1 r/2)/(r d)(1 r) -
  SdT/(r d)(1r)n
• This formula
• Takes care of all needed tax adjustments in one
  easy step
• Quantifies the tax-saving impact of depreciation

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Conclusion

• NPV accrues mainly to shareholders in the form of
  capital appreciation
• Shares in firms undertaking NPV projects should
  sell at above book value