Chapter 8
May 04
1
Capital Budgeting
2
The decision-making process for investment in fixed
assets; specifically, it involves measuring the
incremental cash flows associated with investment
proposals and evaluating the attractiveness of these
cash flows relative to the project’s cost.
Process to analyze investment (any investment)
Net Present Value
And Other Investment Criteria
Capital Budgeting Concepts
1. Determine the future expected dollar earnings from
investment
2. Determine an appropriate required rate of return,
(R), for this investment
3. Calculate Value–using one of many criteria
4. Make Decision
3
Cash Flows
™Cost of Project - amount of capital spent to get
project going.
™If spend $10 million to build new plant then the Cost
of the Project = $10 million
CF0 = Cash Flow time 0 = -10 million
™Annual Cash Inflows
™Cash inflows from the project
CFt = Sales – Operating Costs
Chapter 9 will
cover Cash Flow
estimation
Capital Budgeting Methods
Net present value (NPV)
Payback period (PB)
Internal rate of return (IRR)
We will not do Accounting Rate of Return or
Profitability Index
4
Chapter 8
May 04
5
Capital Budgeting Methods
Net Present Value
Net Present Value
™Present Value of all costs and benefits of a project.
™Concept is similar to Intrinsic Value of a security but
subtracts of cost of project.
™Measures the increase in value to the firm if the
project is undertaken.
CF
CF
Net Present Value
Time
0
1
2
3
4
P R O J E C T
A
B
(10,000.) (10,000.)
3,500
500
3,500
500
3,500
4,600
3,500
10,000
0
1
(10,000)
500
2
500
3
4
4,600
455
413
3,456
6,830
CFn
– Cost of
(1+R)n
Project
11
Capital Budgeting Methods
Time
0
1
2
3
4
R=10%
NPV = PV of Inflows – Cost of Project
CF1
3
2
NPV = (1+R)
+ (1+R)
2 + (1+R)3 +···+
10
Capital Budgeting Methods
P R O J E C T
A
B
(10,000.) (10,000.)
3,500
500
3,500
500
3,500
4,600
3,500
10,000
10,000
$10,000
(1.10) 4
13
Financial Calculator
Capital Budgeting Solutions
™Additional Keys used to
enter Cash Flows and
compute the Net Present
Value (NPV)
0.00
N
xP/YR
I/YR
NOM
%
INPUT
PV
PMT
FV
IRR/Y
R
NPV
BEG/END
EFF%
P/YR
CFj
R=10%
Nj
0
1
(10,000)
500
2
500
3
4,600
455
PV Benefits > Cost (-CF0)
413
$11,154 > $ 10,000
3,456
6,830
$11,154
$1,154 = NPV
4
10,000
NPV > $0
$1,154 > $0
+/–
Used to add CF0, CF1,
CF2, . . . CFN into memory
C
C ALL
RC
ST
L
O
7
8
9
÷
4
5
6
x
1
2
3
–
=
+
0
HP10BII Calculator
.
./,
DISP
yx
Chapter 8
May 04
14
Financial Calculator
Capital Budgeting Solutions
™Additional Keys used to
enter Cash Flows and
compute the Net Present
Value (NPV)
0.00
N
xP/YR
I/YR
NOM
%
INPUT
PV
PMT
FV
IRR/Y
R
NPV
BEG/END
EFF%
P/YR
Capital Budgeting Solutions
™Additional Keys used to
enter Cash Flows and
compute the Net Present
Value (NPV)
C
C ALL
RC
ST
L
O
7
8
9
÷
4
5
6
x
1
2
3
–
0
.
=
+
./,
PMT
FV
IRR/Y
R
NPV
BEG/END
P/YR
Computes the NPV
yx
C
C ALL
RC
ST
L
O
7
8
9
÷
4
5
6
x
1
2
3
–
=
+
0
DISP
.
./,
HP10BII Calculator
Time
0
1
2
3
4
PV
PMT
FV
IRR/Y
R
NPV
NPV
BEG/END
P/YR
16
P R O J E C T
A
B
(10,000.) (10,000.)
3,500
500
3,500
500
3,500
4,600
3,500
10,000
22
Capital Budgeting Methods
Time
0
1
2
3
4
1,153.95
N
xP/YR
INPUT
CFj
I/YR
NOM
%
PV
PMT
FV
IRR/Y
R
NPV
BEG/END
EFF%
P/YR
Nj
P R O J E C T
A
B
(10,000.) (10,000.)
3,500
500
3,500
500
3,500
4,600
3,500
10,000
Compute NPV
CFj
Nj
R=10%
R=10%
0
1
(10,000)
500
yx
DISP
Net Present Value
CF 0 = -10,000
INPUT
PV
EFF%
Nj
+/–
Net Present Value
EFF%
NOM
%
CFj
Capital Budgeting Methods
NOM
%
I/YR
INPUT
HP10BII Calculator
I/YR
N
xP/YR
Nj
+/–
N
0.00
CFj
Stores the required rate
xP/YR
15
Financial Calculator
2
500
3
4,600
4
10,000
0
1
(10,000)
500
2
500
3
4,600
4
10,000
Chapter 8
May 04
26
Capital Budgeting Methods
Net Present Value
Time
0
1
2
3
4
P R O J E C T
A
B
(10,000.) (10,000.)
3,500
500
3,500
500
3,500
4,600
3,500
10,000
27
Financial Calculator
Capital Budgeting Solutions
™Additional Keys used to
enter Cash Flows and
compute the Net Present
Value (NPV)
0.00
N
I/YR
xP/YR
NOM
%
INPUT
2
3,500
3
3,500
4
3,500
3,500
3,500
(1+ .1)2 + (1+ .1 )3 +
1
1
3,500( .10
- .10(1+.10)
4 ) – 10,000
3,500
+/–
3,500
3,500
(1+ .1 )4
NPV = (1+ .1 )+
=
Enters multiple equal
Cash Flows
– 10,000
C
C ALL
Net Present Value
Time
0
1
2
3
4
CF 1 = 3,500
I/YR
NOM
%
PV
PMT
FV
IRR/Y
R
NPV
BEG/END
EFF%
P/YR
31
P R O J E C T
A
B
(10,000.) (10,000.)
3,500
500
3,500
500
3,500
4,600
3,500
10,000
BEG/END
8
9
÷
4
5
6
x
1
2
3
–
=
+
.
./,
Nj
33
Net Present Value
Time
0
1
2
3
4
1,094.53
N
xP/YR
I/YR
NOM
%
PV
PMT
FV
IRR/Y
R
NPV
BEG/END
EFF%
P/YR
P R O J E C T
A
B
(10,000.) (10,000.)
3,500
500
3,500
500
3,500
4,600
3,500
10,000
Compute NPV
CFj
Nj
R=10%
R=10%
0
1
2
3
4
0
1
2
3
4
(10,000)
3,500
3,500
3,500
3,500
(10,000)
3,500
3,500
3,500
3,500
3
4
1
Nj = 4
yx
DISP
Capital Budgeting Methods
INPUT
Enter Multiple Cash Flows
CFj
2
NPV
HP10BII Calculator
Capital Budgeting Methods
N
IRR/Y
R
RC
ST
L
O
7
0
= 11,095 – 10,000 = $1,095
xP/YR
FV
P/YR
Nj
1
(10,000)
PMT
CFj
R=10%
0
PV
EFF%
Chapter 8
May 04
34
Capital Budgeting Methods
™Classify Projects
NPV Decision Rules
™ Mutually Exclusive - accept ONE project out of entire
population of projects
™ Independent - accept ALL profitable projects out of
the entire population
I can only
catch one
fish today
Mutually Exclusive
I want to fill
the freezer
today
™If projects are independent then
accept all projects with NPV ≥ 0.
™If projects are mutually exclusive,
accept higher with NPV ≥ 0.
ACCEPT A & B
ACCEPT B only
Independent
NPV - Final Thoughts
Advantages
37
™ NPV is consistent with the goal of shareholder wealth
maximization
™ It considers the magnitude and the timing of cash
flows over a project’s expected life
™ A firm can be thought of as a series of projects and
the firm’s total value is the sum of the NPVs of all the
independent projects that make it up
™ NPV approach indicates whether a proposed project
will yield the rate of return required by the firm’s
investors
Weakness
36
Capital Budgeting Methods
™ People can find NPV, expressed in absolute dollars,
more difficult to explain rather than a concept which
expresses result as a rate of return.
40
Capital Budgeting Methods
Payback Period
™Number of years needed to recover the initial cost of
the project.
P R O J E C T
A
B
(10,000.) (10,000.)
3,500
500
3,500
500
3,500
4,600
3,500
10,000
Time
0
1
2
3
4
0
1
(10,000)
3,500
Cumulative CF -6,500
2
3,500
-3,000
3
3,500
+500
4
3,500
Payback = 2 3000 years = 2.86 years
3500
Chapter 8
May 04
41
Capital Budgeting Methods
Payback Period
Advantages
™Number of years needed to recover your initial
outlay.
P R O J E C T
A
B
(10,000.) (10,000.)
3,500
500
3,500
500
3,500
4,600
3,500
10,000
Time
0
1
2
3
4
0
1
2
(10,000)
500
Cumulative CF -9,500
500
-9,000
Evaluation:
Company sets maximum
acceptable payback. If
Max PB = 3 years,
accept project A and
reject project B
3
42
PB - Final Thoughts
™Easy and inexpensive to use
™Provides a crude measure of project risk
™Provides a measure of project liquidity
Disadvantages
™No objective decision criterion
™Fails to consider timing of cash flows
™Fails to consider cash flows beyond the PB period
4
4,600
-4,400
10,000
+5,600
Payback = 3 4,400 years = 3.44 years
10,000
43
Net Present Value Profile
™Graphs the Net Present Value of the project at
different discount rates
P R O J E
Time
0
1
2
3
4
6,000
N
P
V
3,000
0
A
(10,000.)
3,500
3,500
3,500
3,500
C T
B
(10,000.)
500
500
4,600
10,000
Required Rate
5%
3,500
10%
15%
3,500
20%
3,500
3,500
NPV(0%) = (1+ 0 ) + (1+ 0)2 + (1+ 0 )3 + (1+ 0)4 – 10,000
= $4,000
44
Net Present Value Profile
™Graphs the Net Present Value of the project at
different discount rates
P R O J E
Time
0
1
2
3
4
6,000
N
P
V
3,000
0
A
(10,000.)
3,500
3,500
3,500
3,500
C T
B
(10,000.)
500
500
4,600
10,000
Required Rate
5%
10%
15%
20%
3,500
NPV(5%) = 3,500 + 3,500 2+ 3,500 +
– 10,000
3
4
(1+ .05 ) (1+ .05)
= $2,411
(1+ .05 )
(1+ .05)
Chapter 8
May 04
45
Net Present Value Profile
™Graphs the Net Present Value of the project at
different discount rates
P R O J E
Time
0
1
2
3
4
6,000
N
P
V
3,000
0
A
(10,000.)
3,500
3,500
3,500
3,500
C T
B
(10,000.)
500
500
4,600
10,000
™Graphs the Net Present Value of the project at
different discount rates
P R O J E
10%
15%
6,000
3,000
0
20%
3,500
NPV(10%) = 3,500 + 3,500 2+ 3,500 +
– 10,000
3
4
(1+ .10 ) (1+ .10)
(1+ .10 )
Time
0
1
2
3
4
6,000
N
P
V
3,000
A
(10,000.)
3,500
3,500
3,500
3,500
C T
B
(10,000.)
500
500
4,600
10,000
Required Rate
15%
20%
3,500
NPV(20%) = 3,500 + 3,500 2+ 3,500 +
– 10,000
3
4
(1+ .20 ) (1+ .20)
= – $939
Required Rate
5%
10%
15%
(1+ .15 ) (1+ .15)
47
™Graphs the Net Present Value of the project at
different discount rates
P R O J E
10%
C T
B
(10,000.)
500
500
4,600
10,000
20%
(1+ .15 )
(1+ .15)
= – $7.58
Net Present Value Profile
5%
A
(10,000.)
3,500
3,500
3,500
3,500
3,500
NPV(15%) = 3,500 + 3,500 2+ 3,500 +
– 10,000
3
4
(1+ .10)
= $1,095
0
Time
0
1
2
3
4
N
P
V
Required Rate
5%
46
Net Present Value Profile
(1+ .20 )
(1+ .20)
48
Net Present Value Profile
™Graphs the Net Present Value of the project at
different discount rates
P R O J E
Time
0
1
2
3
4
6,000
N
P
V
3,000
0
Required Rate
5%
10%
15%
20%
Connect the Points
A
(10,000.)
3,500
3,500
3,500
3,500
C T
B
(10,000.)
500
500
4,600
10,000
Chapter 8
May 04
54
Net Present Value Profile
™Graphs the Net Present Value of the project at
different discount rates
P R O J E
Time
0
1
2
3
4
6,000
N
P
V
Project B
3,000
A
(10,000.)
3,500
3,500
3,500
3,500
C T
B
(10,000.)
500
500
4,600
10,000
™Compare NPV of the two projects at different
discount rates
Crossover point
6,000
N
P
V
Project B
For any discount rate >
crossover point choose A
3,000
0
57
Net Present Value Profile
Required Rate
5%
10%
For any discount rate <
crossover point choose B
20%
15%
Project A
Required Rate
0
5%
58
Capital Budgeting Methods
Internal Rate of Return
™Measures the rate of return on a project
Definition:
The IRR is the Required Return in which NPV = 0
6,000
N
P
V
Project B
3,000
IRRA ≈ 15%
IRRB ≈ 14%
5%
10%
15%
15%
20%
20%
62
Capital Budgeting Methods
Internal Rate of Return
For Project B
Cannot solve for IRR
directly, must use a
calculator, computer or
trial & error
6,000
Project B
N
P
V
3,000
IRRB ≈ 14%
0
NPV = $0
0
10%
5%
10%
15%
20%
10,000 = 500 + 500 2 + 4,600 3 + 10,000 4
(1+ IRR ) (1+ IRR )
(1+ IRR )
(1+ IRR )
Try 14% for IRR
10,000 = 500 + 500 2 + 4,6003 + 10,000 4
(1+ .14 ) (1+ .14 )
(1+ .14 )
(1+ .14)
?
10,000 = 9,849 Therefore 14% is not the IRR
Chapter 8
May 04
63
Capital Budgeting Methods
Internal Rate of Return
For Project B
Time
0
1
2
3
4
13.50
N
xP/YR
INPUT
I/YR
NOM
%
PV
PMT
FV
IRR/Y
R
NPV
BEG/END
EFF%
P/YR
P R O J E C T
A
B
(10,000.) (10,000.)
3,500
500
3,500
500
3,500
4,600
3,500
10,000
CFj
Time
0
1
2
3
4
14.96
N
xP/YR
I/YR
NOM
%
PV
PMT
FV
IRR/Y
R
NPV
BEG/END
EFF%
P/YR
P R O J E C T
A
B
(10,000.) (10,000.)
3,500
500
3,500
500
3,500
4,600
3,500
10,000
Enter the Cash Flows into memory
CFj
Nj
Compute IRR
Internal Rate of Return
For Project A
INPUT
Enter the Cash Flows into memory
64
Capital Budgeting Methods
Nj
R=10%
0
(10,000)
1
500
2
3
500
4,600
Compute IRR
4
10,000
Capital Budgeting Methods
Decision Rule for Internal Rate of Return
Independent Projects
Accept Projects with
IRR ≥ required rate
Mutually Exclusive Projects
Accept project at highest
IRR ≥ required rate
However we will see Internal Rate of Return
is NOT the best method of evaluation with
mutually exclusive projects.
65
0
1
(10,000)
3,500
2
3,500
3
4
3,500
3,500
IRR - Final Thoughts
66
Advantages
™ Widely used in industry, nearly 54% use it as their
primary capital budgeting technique.
™ Considers both the magnitude and timing of cash
flows over the project’s life
Disadvantages
™ When there occur both positive and negative CFs
during the the project's life, there may exist more than
one IRR. In fact, there can be as many IRRs as there
are sign changes in the cash flows.
™ The best solution to this problem is to use NPV.
™ IRR and NPV can give conflicting signals for mutually
exclusive decisions. The two models are based on
different assumptions regarding the reinvestment
rate.
Chapter 8
May 04
67
Comparison of Methods
Project A
Payback 2.86 yrs
NPV
$1,095
IRR
14.96%
Project B
3.44 yrs
$1,154
13.50%
Choose
A
B
A
™ NPV indicated accept Project B while IRR indicated that
Project A should be accepted. Why?
™ Reinvestment Rate
™ NPV assume cash flows are reinvested at the required rate, R.
™ IRR assumes cash flows are reinvested at IRR.
™ Reinvestment Rate of R more realistic as most projects earn
approximately R (due to competition)
™ Conclusion: NPV is the Better Method for project evaluation
68
Comparison of Methods
™Time Value of Money
™Payback - Does not adjust for timing differences
™NPV & IRR take into account the time value of
money
™Relevant Cash Flows?
™NPV & IRR use all Cash Flows
™Payback method ignores Cash Flows that occur
after the Payback Period.
Project 1
0
1
(10,000)
5,000
2
Both Projects have
Identical Payback
5,000
Project 2
0
(10,000)
1
5,000
2
5,000
3
10,000