Transcript No Slide Title

8- 1
Fundamentals
of Corporate
Finance
Sixth Edition
Chapter 7
Net Present Value and Other
Investment Criteria
Richard A. Brealey
Stewart C. Myers
Alan J. Marcus
Slides by
Matthew Will
McGraw
McGraw Hill/Irwin
Hill/Irwin
Copyright ©Copyright
2009 by The
McGraw-Hill
Companies, Inc.
All rights
reserved
© 2009
by The McGraw-Hill
Companies,
Inc.
All rights reserved
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Topics Covered
 Net Present Value
 Other Investment Criteria
 Mutually Exclusive Projects
 Capital Rationing
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Net Present Value
Net Present Value - Present value of cash
flows minus initial investments.
Opportunity Cost of Capital - Expected rate
of return given up by investing in a project
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Net Present Value
Example
Q: Suppose we can invest $50 today & receive $60
later today. What is our increase in value?
A: Profit = - $50 + $60
= $10
$10
$50
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Added Value
Initial Investment
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Net Present Value
Example
Suppose we can invest $50 today and receive $60 in
one year. What is our increase in value given a 10%
expected return?
60
Profit = -50 +
 $4.55
1.10
$4.55
This is the definition of NPV
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$50
Added Value
Initial Investment
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Valuing an Office Building
Step 1: Forecast cash flows
Cost of building = C0 = 350,000
Sale price in Year 1 = C1 = 400,000
Step 2: Estimate opportunity cost of capital
If equally risky investments in the capital market
offer a return of 7%, then
Cost of capital = r = 7%
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Valuing an Office Building
Step 3: Discount future cash flows
PV 
C1
(1r )

400 , 000
(1.07 )
 373,832
Step 4: Go ahead if PV of payoff exceeds investment
NPV  350,000 373,832
 23,832
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Risk and Present Value
 Higher risk projects require a higher
rate of return
 Higher required rates of return cause
lower PVs
P V of C1  $400,000at 7%
400,000
PV 
 373,832
1  .07
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Risk and Present Value
P V of C1  $400,000at 12%
400,000
PV 
 357,143
1  .12
P V of C1  $400,000at 7%
400,000
PV 
 373,832
1  .07
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Net Present Value
NPV = PV - required investment
Ct
NPV  C0 
t
(1  r )
C1
C2
Ct
NPV  C0 

...
1
2
t
(1  r ) (1  r )
(1  r )
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Net Present Value
Terminology
C = Cash Flow
t = time period of the investment
r = “opportunity cost of capital”
 The Cash Flow could be positive or negative at any
time period.
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Net Present Value
Net Present Value Rule
Managers increase shareholders’ wealth by
accepting all projects that are worth more
than they cost.
Therefore, they should accept all projects
with a positive net present value.
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Net Present Value
Example
You have the opportunity to purchase
an office building. You have a tenant
lined up that will generate $16,000 per
year in cash flows for three years. At
the end of three years you anticipate
selling the building for $450,000. How
much would you be willing to pay for
the building?
Assume a 7% opportunity cost of capital
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Net Present Value
$466,000
Example - continued
$450,000
Present Value
0
$16,000
$16,000
1
2
$16,000
3
14,953
13,975
380,395
$409,323
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Net Present Value
Example - continued
If the building is being
offered for sale at a price
of $350,000, would you
buy the building and what
is the added value
generated by your
purchase and management
of the building?
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Net Present Value
Example - continued
If the building is being offered for sale at a price of $350,000,
would you buy the building and what is the added value
generated by your purchase and management of the
building?
16,000 16,000 466,000
NPV  350,000 


1
2
3
(1.07 )
(1.07 )
(1.07 )
NPV  $59,323
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Payback Method
Payback Period - Time until cash flows recover the
initial investment of the project.
 The payback rule specifies that a project be accepted
if its payback period is less than the specified cutoff
period. The following example will demonstrate the
absurdity of this statement.
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Payback Method
Example
The three project below are available. The company accepts
all projects with a 2 year or less payback period. Show how
this decision will impact our decision.
Project C0
A
B
C
C1
Cash Flows
C2
C3
-2,000 +1,000 +1,000 +10,000
-2,000 +1,000 +1,000
0
-2,000
0
+2,000
0
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Payback NPV@10%
2
2
2
+ 7,249
- 264
- 347
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Other Investment Criteria
Internal Rate of Return (IRR) - Discount rate at
which NPV = 0.
Rate of Return Rule - Invest in any project offering a
rate of return that is higher than the opportunity cost
of capital.
C1 - investment
Rate of Return =
investment
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Internal Rate of Return
Example
You can purchase a building for $350,000. The
investment will generate $16,000 in cash flows (i.e.
rent) during the first three years. At the end of three
years you will sell the building for $450,000. What
is the IRR on this investment?
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Internal Rate of Return
Example
You can purchase a building for $350,000. The investment will generate
$16,000 in cash flows (i.e. rent) during the first three years. At the end of
three years you will sell the building for $450,000. What is the IRR on
this investment?
16,000
16,000
466,000
0  350,000 


1
2
(1  IRR )
(1  IRR )
(1  IRR ) 3
IRR = 12.96%
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Internal Rate of Return
Calculating IRR by using a spreadsheet
Year
0
1
2
3
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Cash Flow
(350,000.00)
16,000.00
16,000.00
466,000.00
Formula
IRR = 12.96% =IRR(B4:B7)
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Internal Rate of Return
200
150
NPV (,000s)
100
IRR=12.96%
50
0
-50
0
5
10
15
20
25
30
35
-100
-150
-200
Discount rate (%)
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Internal Rate of Return
Calculating the IRR can be a laborious task. Fortunately,
financial calculators can perform this function easily. Note
the previous example.
HP-10B
EL-733A
BAII Plus
-350,000
CFj
-350,000
CFi
CF
16,000
CFj
16,000
CFfi
2nd
16,000
CFj
16,000
CFi
-350,000 ENTER
466,000
CFj
466,000
CFi
16,000
ENTER
16,000
ENTER
{IRR/YR}
IRR
{CLR Work}
466,000 ENTER
All produce IRR=12.96
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IRR
CPT
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Internal Rate of Return
Example
You have two proposals to choice between. The initial proposal (H) has
a cash flow that is different than the revised proposal (I). Using IRR,
which do you prefer?
16
16
466
NPV  350 


0
1
2
3
(1  IRR ) (1  IRR )
(1  IRR )
 12.96%
400
NPV  350 
0
1
(1  IRR )
 14.29%
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Internal Rate of Return
NPV $, 1,000s
50
40
Revised proposal
30
IRR= 12.96%
20
10
IRR= 14.29%
Initial proposal
0
-10
IRR= 12.26%
-20
8
10
12
14
16
Discount rate, %
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Internal Rate of Return
Pitfall 1 - Lending or Borrowing?
 With some cash the NPV of the project increases as the discount
rate increases
 This is contrary to the normal relationship between PV and
discount rates.
Pitfall 2 - Multiple Rates of Return
 Certain cash flows can generate NPV=0 at two different discount
rates.
Pitfall 3 - Mutually Exclusive Projects
 IRR sometimes ignores the magnitude of the project.
 The following two projects illustrate that problem.
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Internal Rate of Return
Example
You have two proposals to choice between. The initial proposal has a
cash flow that is different than the revised proposal. Using IRR, which do
you prefer?
Project
Initial Proposal
Revised Proposal
McGraw Hill/Irwin
C0
-350
-350
C1
400
16
C2
C3
16
466
IRR
14.29%
12.96%
NPV@7%
$
24,000
$
59,000
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Project Interactions
When you need to choose between mutually
exclusive projects, the decision rule is simple.
Calculate the NPV of each project, and, from
those options that have a positive NPV,
choose the one whose NPV is highest.
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Mutually Exclusive Projects
Example
Select one of the two following projects,
based on highest NPV.
System
Faster
Slower
C0
 800
 700
C1
350
300
C2
350
300
C3
NPV
350  118.5
300  87.3
assume 7% discount rate
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Investment Timing
Sometimes you have the ability to defer an
investment and select a time that is more ideal
at which to make the investment decision. A
common example involves a tree farm. You
may defer the harvesting of trees. By doing
so, you defer the receipt of the cash flow, yet
increase the cash flow.
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Investment Timing
Example
You may purchase a computer anytime within the
next five years. While the computer will save your
company money, the cost of computers continues to
decline. If your cost of capital is 10% and given the
data listed below, when should you purchase the
computer?
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Investment Timing
Example
You may purchase a computer anytime within the next five years. While
the computer will save your company money, the cost of computers
continues to decline. If your cost of capital is 10% and given the data
listed below, when should you purchase the computer?
Year
Cost
PV Savings
NPV at Purchase
0
1
2
3
4
5
50
45
40
36
33
31
70
70
70
70
70
70
20
25
30
34
37
39
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NPV Today
20.0
22.7
24.8
Date to purchase 25.5
25.3
24.2
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Equivalent Annual Annuity
Equivalent Annual Cost - The cash flow per
period with the same present value as the cost
of buying and operating a machine.
present value of cash flows
Equivalentannualannuity=
annuityfactor
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Equivalent Annual Annuity
Example
Given the following costs of operating two machines
and a 6% cost of capital, select the lower cost
machine using equivalent annual annuity method.
Mach.1
F
-15
G
-10
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Year
2
3
-4
-4
-6
-6
4
-4
PV@6%
-25.69
-21.00
E.A.A.
- 9.61
-11.45
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Equivalent Annual Annuity
Example (with a twist)
Select one of the two following projects, based on
highest “equivalent annual annuity” (r=9%).
Project C0 C1 C 2
C3 C 4 NPV EAA
A
 15 4.9 5.2 5.9 6.2 2.82 .87
2.78 1.10
B
 20 8.1 8.7 10.4
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Capital Rationing
Capital Rationing - Limit set on the amount of
funds available for investment.
Soft Rationing - Limits on available funds
imposed by management.
Hard Rationing - Limits on available funds
imposed by the unavailability of funds in the
capital market.
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Profitability Index
NPV
Profitabil ity Index 
Initial Investment
Profitability Index
Ratio of net present value to initial investment.
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Profitability Index
Project
J
K
L
M
N
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PV
4
6
10
8
5
Investment
3
5
7
6
4
NPV
1
1
3
2
1
Profitability
Index
1/3 = .33
1/5 = .20
3/7 = .43
2/6 = .33
1/4 = .25
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Capital Budgeting Techniques
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Web Resources
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