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. Half
  of it is financed with debt at 5, and half with
  equity. The equipment will be depreciated at 20.
  Robin Donuts has a tax rate of 40, and uses a
  10 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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Levered vs. Un-Levered Net Income
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Levered vs. Un-Levered Net Income
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Levered vs. Un-Levered Net Income
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Levered vs. Un-Levered Net Income
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Levered vs. Un-Levered Net Income
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Levered vs. Un-Levered Net Income
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Levered vs. Un-Levered Net Income
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Robin Donuts new pastry Levered vs. Un-Levered
Net Income
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Robin Donuts new pastry Levered vs. Un-Levered
Net Income
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Robin Donuts new pastry Levered vs. Un-Levered
Net Income
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Robin Donuts new pastry Levered vs. Un-Levered
Net Income
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Robin Donuts new pastry Levered vs. Un-Levered
Net Income
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Robin Donuts new pastry Levered vs. Un-Levered
Net Income
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Robin Donuts new pastry Levered vs. Un-Levered
Net Income
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Net Income Trivia

• Levered NI lt Un-Levered NI

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Net Income Trivia

• Note that
• Un-Levered NI - Levered NI Interest(1 - T)
• 33,000 - 31,500 2,500(0.6) 1,500

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Robin Donuts new pastry Depreciation Schedule
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Robin Donuts new pastry Depreciation Schedule
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Robin Donuts new pastry Depreciation Schedule
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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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Unlevered OCF calculation (i)definition (i)
Un-Levered NI Depreciation
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Unlevered OCF calculation (i)definition (i)
Un-Levered NI Depreciation
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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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Un-levered OCF calculation (ii)Definition (ii)
Sales - Cost - Tax
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Un-levered OCF calculation (ii)Definition (ii)
Sales - Cost - Tax
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Un-levered OCF calculation (ii)Definition (ii)
Sales - Cost - Tax
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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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Clarifications

• ATNOR After-Tax Net Operating Revenue
• Depreciation Tax Shield

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ATNOR

• ATNOR (S - C)(1 - T)
• ATNOR(1) (120,000 - 55,000)(0.6)
• ATNOR(1) 39,000

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Depreciation Tax Shield
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Depreciation Tax Shield
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Depreciation Tax Shield
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Depreciation Tax Shield
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Depreciation Tax Shield
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Depreciation Tax Shield
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Depreciation Tax Shield
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Un-levered OCF calculation (iii)ATNOR
Depreciation tax shield
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Un-levered OCF calculation (iii)ATNOR
Depreciation tax shield
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Un-levered OCF calculation (iii)ATNOR
Depreciation tax shield
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Un-levered OCF calculation (iii)ATNOR
Depreciation tax shield
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Un-levered OCF calculation (iii)ATNOR
Depreciation tax shield
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Un-levered OCF calculation (iii)ATNOR
Depreciation 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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NWC requirements
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NWC requirements
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NWC requirements
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NWC requirements
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NWC requirements
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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

• Assume equipment is disposed of at UCC 57,600
• PV Net capital spending 57,600/(1.1)3

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Putting it all together NPV analysis
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Putting it all together NPV analysis
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Putting it all together NPV analysis
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Putting it all together NPV analysis
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Putting it all together NPV analysis
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Putting it all together NPV analysis
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Putting it all together NPV analysis
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Putting it all together NPV analysis
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Putting it all together NPV analysis
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Putting it all together NPV analysis
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Putting it all together Another approach - a
simpler approach

• NPV PV(ATNOR) PV(Depr. tax shield)
  PV(NCS) - PV(addNWC) - Initial cost
• NPV 71,021.78       13,914.34        
  43,275.73   -   2,088.64   -   100,000 
• NPV   26,123

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More on the PV of tax shields

• Assume salvage value of equipment 60,000 gt 
  57,600(UCC)
• The difference (2,400) will make future CCA
  deductions smaller than expected

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More on the PV of tax shields

• Adjustment
• 2,400(0.2)(0.4)/(0.2 0.1)(1.1)3 2,400(0.2)
  480
• PV (tax shield) 13,914.34  - 480
  13,434.34

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More on the PV of tax shieldsA simpler approach

• PV (tax shield) CdT(1 r/2)/(r d)(1 r) -
  SdT/(r d)(1 r)n
• C Initial cost of fixed asset
• S Salvage value of fixed asset
• d CCA rate
• T Corporate tax rate
• r discount rate
• PV(tax shield) 100,000 (0.25454545) -
  60,000(0.2) 13,454.5

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More on the PV of tax shields

• When asset pool is closed
• PV (tax shield) 13,914.34 - 2,400(0.4)
  12,954.34

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More on the PV of tax shields (part 2)

• Assume salvage 50,000  lt  57,600 (UCC)
• The  difference (7,600) will make future CCA
  deductions larger than expected

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More on the PV of tax shields (part 2)

• Adjustment
• 7,600(0.2)(0.4)/(0.2 0.1)(1.1)3 7,600(0.2)
  1,520
• PV (tax shield) 13,914.34 1,520
  15,434.34

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More on the PV of tax shields (part 2)A simpler
approach

• PV (tax shield) CdT(1 r/2)/(r d)(1 r) -
  SdT/(r d)(1 r)n
• C Initial cost of fixed asset
• S Salvage value of fixed asset
• d CCA rate
• T Corporate tax rate
• r discount rate
• PV(tax shield) 100,000(0.25454) - 50,000(0.2)
  15,454.54

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More on the PV of tax shields (part 2)

• When the asset pool is closed
• PV (tax shield) 13,914.34 7,600(0.4)
  16,954.34

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Putting it all together (again) Salvage value
of equipment 50,000 instead of 57,600
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Putting it all together (again) Salvage value
of equipment 50,000 instead of 57,600
NPV 20,413 Depreciation tax shield
adjustment   NPV 20,413 1,520 21,933
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Putting it all together (again)

• NPV PV(ATNOR) PV(Depr. tax shield) PV(NCS) -
  PV(addNWC) - Initial cost
• NPV 71,021.78     15,434.34        
      37,565.74   -   2,088.64    -   100,000 
• NPV 21,933

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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