Finance Lecture 6

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Finance Lecture 6
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Outline Lecture 6

• NPVs Tempting Cousin, IRR
• Assorted Insights on Capital Budgeting

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The Internal Rate Of Return IsThe Interest Rate
At Which PV 0

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Or, More Formally, SolveFor IRR In This Equation
Can be hard to solve by hand, but easy for a
computer to solve numerically
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Typically, NPV And IRR AnalysesWill Give The
Same Answer

• If NPV of a prospective project is positive, do
  it
• If prospective projects IRR is greater than
  firms cost of capital (e.g., interest rate), do
  it
• For many scenarios, NPV and IRR analyses agree
  with one another
• Plus IRR additionally provides information on
  how high interest rates can be with a project
  remaining desirable
• Unfortunately, there are certain pathological
  cases where IRR gives the wrong answer

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IRR And NPV Can ConflictOn Mutually Exclusive
Projects
Project A Spend 1 now, get 2 next
year Project B Spend 1000 now, get 1500 next
year
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IRR Likes Small, High Rate Projects
IRR(A)100 IRR(B)50 But if i15, NPV(A)
0.74 NPV(B)304.35
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Primarily Use NPV In Decisionmaking

• NPV is contribution to shareholder wealth
• IRR falsely assumes unused capital
• (in small/large case) is reinvested at IRR
• IRR-based decisionmaking is OK if
• projects are independent (e.g., both A and
• B are good projects if you can do both)
• IRR does give intuition on safety margin

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Outline Lecture 6

• NPVs Tempting Cousin, IRR
• Assorted Insights on Capital Budgeting

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Mutually Exclusive Projects With UnequalLengths
Pose An Analytical Challenge

• NPV alone may be insufficient
• What will happen when shorter project
• ends?
• Two techniques Replacement Chain,
• Equivalent Annuity

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Replacement Chain Assumes YouReplace Each
Project With Copy

• To compare 3 year versus 5 year project,
• compare five 3 years to three 5 years -
• Artificially lengthy chain
• Build as many cases as needed to get
• equal length (e.g., 3 year versus 4 year
• requires 12 year chain)

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Replacement Chain ExampleNPV Is Not Enough
Project A -100/70/70
i10 Project B -100/50/50/50 NPV(A)21.49,
NPV(B)24.34 Project A six year
chain -100/70/-30/70/-30/70/70 NPV(ARC)53.92 Pr
oject B six year chain -100/50/50/-50/50/50/50 NP
V(BRC)42.63
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Equivalent Annuity TranslatesUneven Flows Into
One Annual Value
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Replacement Chains And EquivalentAnnuity Will
Give Same Results

• Methods are symmetric
• Both make assumptions you may not
• like!
• Most notably, both assume static technology
• Shorter projects may be better (worse)
• than calculated if alternatives are better
• (worse) in the future

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With Capital Rationing,Capital Budget Is Capped

• Cap may be below computed optimum
• budget
• Risk-averse management? Worries
• about excess optimism?
• Shareholder value is not maximized
• if NPVgt0 projects are ignored

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Capital Rationing Creates AConstrained
Maximization Problem

• Choose projects with greatest NPVs
• SUBJECT TO capital constraint
• Tends to favor small, short, high IRR
• projects
• Firm likely to eschew long-term
• investments
• Government entities often act this way

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