Internal Rate of Return

Principles of
Corporate
Finance
Seventh Edition
Richard A. Brealey
Chapter 5
Why Net Present Value Leads
to Better Investment
Decisions than Other Criteria
Stewart C. Myers
Slides by
Matthew Will
McGraw Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved
5- 2
Topics Covered
Š NPV and its Competitors
Š The Payback Period
Š The Book Rate of Return
Š Internal Rate of Return
Š Capital Rationing
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NPV and Cash Transfers
Š Every possible method for evaluating projects
impacts the flow of cash about the company
as follows.
Cash
Investment
opportunity (real
asset)
Firm
Invest
McGraw Hill/Irwin
Shareholder
Alternative:
pay dividend
to shareholders
Investment
opportunities
(financial assets)
Shareholders invest
for themselves
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Payback
Š The payback period of a project is the number
of years it takes before the cumulative
forecasted cash flow equals the initial outlay.
Š The payback rule says only accept projects
that “payback” in the desired time frame.
Š This method is very flawed, primarily
because it ignores later year cash flows and
the present value of future cash flows.
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Payback
Example
Examine the three projects and note the mistake we
would make if we insisted on only taking projects
with a payback period of 2 years or less.
Project
C0
C1
A
B
- 2000
- 2000
500
500
C
- 2000 1800
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C2
C3
Payback
Period
NPV@ 10%
500 5000
1800
0
500
0
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Payback
Example
Examine the three projects and note the mistake we
would make if we insisted on only taking projects
with a payback period of 2 years or less.
Project
C0
C1
A
B
- 2000
- 2000
500
500
C
- 2000 1800
McGraw Hill/Irwin
C2
C3
Payback
Period
500 5000
3
1800
0
2
500
0
2
NPV@ 10%
+ 2,624
- 58
+ 50
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Book Rate of Return
Book Rate of Return - Average income divided by
average book value over project life. Also called
accounting rate of return.
book income
Book rate of return =
book assets
Managers rarely use this measurement to make
decisions. The components reflect tax and
accounting figures, not market values or cash flows.
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Internal Rate of Return
Example
You can purchase a turbo powered machine tool
gadget for $4,000. The investment will generate
$2,000 and $4,000 in cash flows for two years,
respectively. What is the IRR on this investment?
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Internal Rate of Return
Example
You can purchase a turbo powered machine tool gadget for $4,000. The
investment will generate $2,000 and $4,000 in cash flows for two years,
respectively. What is the IRR on this investment?
2,000
4,000
NPV = −4,000 +
+
=0
1
2
(1 + IRR ) (1 + IRR )
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Internal Rate of Return
Example
You can purchase a turbo powered machine tool gadget for $4,000. The
investment will generate $2,000 and $4,000 in cash flows for two years,
respectively. What is the IRR on this investment?
2,000
4,000
NPV = −4,000 +
+
=0
1
2
(1 + IRR ) (1 + IRR )
IRR = 28.08%
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Internal Rate of Return
2500
2000
IRR=28%
1000
500
10
0
90
80
70
60
50
40
30
-500
20
0
10
NPV (,000s)
1500
-1000
-1500
-2000
Discount rate (%)
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Internal Rate of Return
Pitfall 1 - Lending or Borrowing?
Š With some cash flows (as noted below) the NPV of
the project increases as the discount rate increases.
Š This is contrary to the normal relationship between
NPV and discount rates.
C0
C1
C2
C3
IRR
NPV @ 10%
+ 1,000 − 3,600 4,320 − 1,728 + 20%
− .75
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Internal Rate of Return
Pitfall 1 - Lending or Borrowing?
Š With some cash flows (as noted below) the NPV of the project
increases s the discount rate increases.
Š This is contrary to the normal relationship between NPV and discount
rates.
NPV
Discount
Rate
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Internal Rate of Return
Pitfall 2 - Multiple Rates of Return
Š Certain cash flows can generate NPV=0 at two
different discount rates.
Š The following cash flow generates NPV=0 at both
(-50%) and 15.2%.
C0
C1
C2
C3
C4
C5
C6
− 1,000 + 800 + 150 + 150 + 150 + 150 − 150
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Internal Rate of Return
Pitfall 2 - Multiple Rates of Return
Š Certain cash flows can generate NPV=0 at two different discount rates.
Š The following cash flow generates NPV=0 at both (-50%) and 15.2%.
NPV
1000
IRR=15.2%
500
Discount
Rate
0
-500
IRR=-50%
-1000
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Internal Rate of Return
Pitfall 3 - Mutually Exclusive Projects
Š IRR sometimes ignores the magnitude of the project.
Š The following two projects illustrate that problem.
Project
E
C0
Ct
IRR
− 10,000 + 20,000 100
F
− 20,000 + 35,000
F − E − 10,000 + 15,000
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75
50
NPV @ 10%
+ 8,182
+ 11,818
+ 3,636
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Internal Rate of Return
Pitfall 3 - Mutually Exclusive Projects
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Internal Rate of Return
Pitfall 4 - Term Structure Assumption
Š We assume that discount rates are stable during the
term of the project.
Š This assumption implies that all funds are reinvested
at the IRR.
Š This is a false assumption.
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Profitability Index
Š When resources are limited, the profitability
index (PI) provides a tool for selecting among
various project combinations and alternatives
Š A set of limited resources and projects can
yield various combinations.
Š The highest weighted average PI can indicate
which projects to select.
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Profitability Index
NPV
Profitability Index =
Investment
Example
We only have $300,000 to invest. Which do we select?
Proj
A
B
C
D
McGraw Hill/Irwin
NPV
230,000
141,250
194,250
162,000
Investment
200,000
125,000
175,000
150,000
PI
1.15
1.13
1.11
1.08
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Profitability Index
Example - continued
Proj NPV
A
230,000
B
141,250
C
194,250
D
162,000
Investment
200,000
125,000
175,000
150,000
PI
1.15
1.13
1.11
1.08
Select projects with highest Weighted Avg PI
WAPI (BD) = 1.13(125) + 1.08(150) + 0.0 (25)
(300)
(300)
(300)
= 1.01
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Profitability Index
Example - continued
Proj NPV
A
230,000
B
141,250
C
194,250
D
162,000
Investment
200,000
125,000
175,000
150,000
PI
1.15
1.13
1.11
1.08
Select projects with highest Weighted Avg PI
WAPI (BD) = 1.01
WAPI (A) = 0.77
WAPI (BC) = 1.12
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Linear Programming
Š Maximize Cash flows or NPV
Š Minimize costs
Example
Kapitalbegrenzung auf 10 pro Jahr
C1
C2 NPV (10%)
Proj C0
A
-10 30
5
21
B
-5
5
20
16
C
-5
5
15
12
D
0
-40 60
13
McGraw Hill/Irwin
PI
2.1
3.2
2.4
0.4
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Linear Programming
Max NPV = 21Xa + 16 Xb + 12 Xc + 13 Xd
subject to
10Xa + 5Xb + 5Xc + 0Xd <= 10
-30Xa - 5Xb - 5Xc + 40Xd <= 10
0<=Xa<=1, 0<=Xb<=1, ...
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Aufgaben in der Vorlesung
Q2: Project
a)
b)
c)
d)
e)
C0
C1
C2
C3
C4
A
B
- 5000 1000 1000 3000
0
- 1000
0
1000 2000 3000
C
- 5000 1000 1000 3000 5000
Payback-Perioden?
Projektwahl bei PBP 2 Jahre?
Projektwahl bei PBP 3 Jahre?
PBP bei r=10% (dynamisch)?
Projektwahl mit NBW-Methode?
f) „Bei einer einheitlichen PBP-Vorgabe für alle
Projekte wählt U zu viele kfr. Projekte.“
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Aufgaben in der Vorlesung
g)Akzeptiert man bei der dyn. PB-Methode Projekte
mit negativem NBW? Lehnt man Projekte mit
positivem NBW ab?
Q6: C0=+5000; C1=+4000; C2=-11000; IZF=13%;
Alternativrendite=10%. Annehmen?
Q8: Zwei einander ausschließende Projekte:
Alpha: -400 +241 +293 IFZ=21%
Beta: -200 +131 +172 IZF=31%
Alternativrendite: 8%. Entscheidung mit IZF?
Hinweis: Differenzinvestition in Alpha beachten.
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Aufgaben in der Vorlesung
Q9: Projektwahl bei Mittel von $90.000?
Projekt
NBW
I0
1
5000
10000
2
5000
5000
3
10000
90000
4
15000
60000
5
15000
75000
6
3000
15000
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Aufgaben zu Hause
Q1
Payback-Methode: PQ2, 5
IZF-Methode: PQ8, 13
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