```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
2009 by The
McGraw-Hill
Companies, Inc.
All rights
reserved
by The McGraw-Hill
Companies,
Inc.
8- 2
Topics Covered
 Net Present Value
 Other Investment Criteria
 Mutually Exclusive Projects
 Capital Rationing
McGraw Hill/Irwin
8- 3
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
McGraw Hill/Irwin
8- 4
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
McGraw Hill/Irwin
Initial Investment
8- 5
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?
P ro fit = -5 0 +
60
 \$ 4 .5 5
1 .1 0
\$4.55
This is the definition of NPV
McGraw Hill/Irwin
\$50
Initial Investment
8- 6
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%
McGraw Hill/Irwin
8- 7
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
McGraw Hill/Irwin
8- 8
Risk and Present Value
 Higher risk projects require a higher
rate of return
 Higher required rates of return cause
lower PVs
PV of C 1  \$400,000 at 7%
PV 
McGraw Hill/Irwin
400,000
1  .07
 373 ,832
8- 9
Risk and Present Value
PV of C 1  \$400,000 at 12%
PV 
400,000
1  .12
 357 ,143
PV of C 1  \$400,000 at 7%
PV 
McGraw Hill/Irwin
400,000
1  .07
 373 ,832
8- 10
Net Present Value
NPV = PV - required investment
N PV  C0 
NPV  C0 
McGraw Hill/Irwin
C1
(1  r )
1

Ct
(1  r )
C2
(1  r )
2
t
 . . .
Ct
(1  r )
t
8- 11
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.
McGraw Hill/Irwin
8- 12
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.
McGraw Hill/Irwin
8- 13
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
McGraw Hill/Irwin
8- 14
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
McGraw Hill/Irwin
8- 15
Net Present Value
Example - continued
If the building is being
offered for sale at a price
of \$350,000, would you
generated by your
purchase and management
of the building?
McGraw Hill/Irwin
8- 16
Net Present Value
Example - continued
If the building is being offered for sale at a price of \$350,000,
generated by your purchase and management of the
building?
N P V   3 5 0 ,0 0 0 
1 6 ,0 0 0
( 1.0 7 )
1

1 6 ,0 0 0
( 1.0 7 )
2

4 6 6 ,0 0 0
( 1.0 7 )
N P V  \$ 5 9 ,3 2 3
McGraw Hill/Irwin
3
8- 17
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.
McGraw Hill/Irwin
8- 18
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
McGraw Hill/Irwin
Payback NPV@10%
2
2
2
+ 7,249
- 264
- 347
8- 19
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.
R ate o f R e tu rn =
C 1 - in v estm en t
in v estm en t
McGraw Hill/Irwin
8- 20
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?
McGraw Hill/Irwin
8- 21
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?
0   3 5 0 ,0 0 0 
1 6 ,0 0 0
( 1  IR R )
1

1 6 ,0 0 0
( 1  IR R )
2

4 6 6 ,0 0 0
( 1  IR R )
IRR = 12.96%
McGraw Hill/Irwin
3
8- 22
Internal Rate of Return
Calculating IRR by using a spreadsheet
Year
0
1
2
3
McGraw Hill/Irwin
Cash Flow
(350,000.00)
16,000.00
16,000.00
466,000.00
Formula
IRR = 12.96% =IRR(B4:B7)
8- 23
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 (%)
McGraw Hill/Irwin
8- 24
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
McGraw Hill/Irwin
IRR
CPT
8- 25
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?
NPV  350 
16
(1  IRR )
1

16
(1  IRR )
2

466
(1  IRR )
3
0
 12.96%
NPV  350 
400
(1  IRR )
1
0
 14.29%
McGraw Hill/Irwin
8- 26
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, %
McGraw Hill/Irwin
8- 27
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.
McGraw Hill/Irwin
8- 28
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
8- 29
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.
McGraw Hill/Irwin
8- 30
Mutually Exclusive Projects
Example
Select one of the two following projects,
based on highest NPV.
System
C0
C1
C2
C3
NPV
Faster
 800
350
350
350
 118 . 5
Slower
 700
300
300
300
 87 . 3
assume 7% discount rate
McGraw Hill/Irwin
8- 31
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.
McGraw Hill/Irwin
8- 32
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?
McGraw Hill/Irwin
8- 33
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
McGraw Hill/Irwin
NPV Today
20.0
22.7
24.8
Date to purchase 25.5
25.3
24.2
8- 34
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.
Equivalent
annual annuity
=
present va lue of cash flows
annuity
McGraw Hill/Irwin
factor
8- 35
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
McGraw Hill/Irwin
Year
2
3
-4
-4
-6
-6
4
-4
PV@6%
-25.69
-21.00
E.A.A.
- 9.61
-11.45
8- 36
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
C2
C3
C4
NPV
EAA
A
 15
4 .9
5 .2
5 .9
6 .2
B
 20
8 .1
8 .7
10 . 4
2.82
2.78
.87
1.10
McGraw Hill/Irwin
8- 37
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.
McGraw Hill/Irwin
8- 38
Profitability Index
Profitabil
ity Index 
NPV
Initial Investment
Profitability Index
Ratio of net present value to initial investment.
McGraw Hill/Irwin
8- 39
Profitability Index
Project
J
K
L
M
N
McGraw Hill/Irwin
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
8- 40
Capital Budgeting Techniques
McGraw Hill/Irwin
8- 41
Web Resources
McGraw Hill/Irwin
```