Chapter 7: Net Present Value

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Chapter 7 Net Present Value

• And other investment criteria

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NPV rule NPV gt 0 gt Do it!

• NPV PV(cash in) PV(cash out)

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Assumption No capital rationing

• Hard capital rationing NO
• Soft capital rationing self-imposed
• Divisional discipline?
• Internal funds preference
• Info signaling problem?
• Capital markets avoidance?
• Agency problem? Or
• Capital markets problem?

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NPV ?? SH wealth max

• NPV gt 0
• Positive Investment Opportunity
• Stock market values as asset

• Other investment criteria
• Payback
• Internal Rate of Return (IRR)
• (Profitability index)

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Payback method

• Specify cutoff time
• Estimate years to pay back initial investment
• Rule Payback period lt (gt) cutoff gt
  Accept (Reject)
• E.g.,
• (Discounted payback version)

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Payback risk

• Projected future CFs are uncertain
• Ignoring CF past cutoff is more arbitrary
• BMM on risk r

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Internal Rate of Return method(IRR)

• Rate of return as profit/investment
• Over entire project life
• Rule IRR gt (lt) r gt Accept (Reject)
• E.g.,
• IRR discount rate at which NPV 0

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IRR and NPV

• When IRR works, equivalent
• If IRR r at which NPV 0,
• IRR gt r gt NPV gt 0
• E.g.,
• CAUTION not always valid

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IRR pitfalls

• NPV not smoothly decreasing function of r
• Term structure of interest rates matters
• Mutually exclusive projects(project
  interactions)
• Different scales (e.g.,)
• Different time patterns (e.g.,)

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Moral

• If MEPs (project interactions) gt cant take all
  for which IRR gt r, use NPV!
• Some standard capital budgeting examples
• Optimal timing
• Long- vs short-lived assets
• Replacement

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Optimal timing

• Can do project at one time or another
• Find net FVs if taken at different times
• Discount back to NPVs
• Highest one wins
• E.g., timber-cutting problem

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Long- vs short-lived assets

• Find PV of CFs over lifetime of each
• Find equivalent annual annuity of each PV
• PV EAA x AF (r, T) gt EAA PV/AF
• Best EAA wins (cost lowest EAA)
• E.g.,Cheaper, vs costlier but longer lasting

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EAA assumptions implications

• Replacing indefinitely with identical projects
• Thus CFs are real
• and so must be r used

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Replace now or wait?

• For old
• Find net CF of another year
• For new
• Find (N)PV over lifetime
• Calculate EAA
• Take best option
• E.g.