# Chapter 13 Capital Budgeting Techniques

```Chapter 13
Capital Budgeting
Techniques
13-1
Fundamentals of Financial Management, 12/e
Created by: Gregory A. Kuhlemeyer, Ph.D.
Carroll College, Waukesha, WI
After studying Chapter 13,
you should be able to:








13-2
Understand the payback period (PBP) method of project evaluation and
selection, including its: (a) calculation; (b) acceptance criterion; (c)
profitability.
Understand the three major discounted cash flow (DCF) methods of
project evaluation and selection – internal rate of return (IRR), net
present value (NPV), and profitability index (PI).
Explain the calculation, acceptance criterion, and advantages (over the
PBP method) for each of the three major DCF methods.
Define, construct, and interpret a graph called an “NPV profile.”
Understand why ranking project proposals on the basis of IRR, NPV, and
PI methods “may” lead to conflicts in ranking.
Describe the situations where ranking projects may be necessary and
justify when to use either IRR, NPV, or PI rankings.
Understand how “sensitivity analysis” allows us to challenge the singlepoint input estimates used in traditional capital budgeting analysis.
Explain the role and process of project monitoring, including “progress
reviews” and “post-completion audits.”
Capital Budgeting
Techniques
13-3

Project Evaluation and Selection

Potential Difficulties

Capital Rationing

Project Monitoring

Post-Completion Audit
Project Evaluation:
Alternative Methods
13-4

Payback Period (PBP)

Internal Rate of Return (IRR)

Net Present Value (NPV)

Profitability Index (PI)
Proposed Project Data
Julie Miller is evaluating a new project
for her firm, Basket Wonders (BW).
She has determined that the after-tax
cash flows for the project will be
\$10,000; \$12,000; \$15,000; \$10,000;
and \$7,000, respectively, for each of
the Years 1 through 5. The initial
cash outlay will be \$40,000.
13-5
Independent Project
For
this project, assume that it is
independent of any other potential
undertake.
Independent -- A project whose
acceptance (or rejection) does not
prevent the acceptance of other
projects under consideration.
13-6
Payback Period (PBP)
0
1
2
3
-40 K
10 K
12 K
15 K
4
10 K
PBP is the period of time
required for the cumulative
expected cash flows from an
investment project to equal
the initial cash outflow.
13-7
5
7K
Payback Solution (#1)
0
-40 K (-b)
Cumulative
Inflows
13-8
1
2
10 K
10 K
12 K
22 K
PBP
3 (a)
15 K
37 K(c)
4
10 K(d)
47 K
=a+(b-c)/d
= 3 + (40 - 37) / 10
= 3 + (3) / 10
= 3.3 Years
5
7K
54 K
Payback Solution (#2)
0
1
2
-40 K
10 K
12 K
15 K
10 K
-40 K
-30 K
-18 K
-3 K
7K
PBP
Cumulative
Cash Flows
13-9
3
4
5
7K
14 K
= 3 + ( 3K ) / 10K
= 3.3 Years
Note: Take absolute value of last
negative cumulative cash flow
value.
PBP Acceptance Criterion
has set a maximum PBP of 3.5
years for projects of this type.
Should this project be accepted?
Yes! The firm will receive back the
initial cash outlay in less than 3.5
years. [3.3 Years < 3.5 Year Max.]
13-10
PBP Strengths
and Weaknesses
Strengths:
Weaknesses:

Easy to use and
understand

Does not account
for TVM

Can be used as a
measure of
liquidity

Does not consider
cash flows beyond
the PBP

Easier to forecast
ST than LT flows

Cutoff period is
subjective
13-11
Internal Rate of Return (IRR)
IRR is the discount rate that equates the
present value of the future net cash
flows from an investment project with
the project’s initial cash outflow.
CF1
CF2
+
ICO =
(1+IRR)1 (1+IRR)2
13-12
+...+
CFn
(1+IRR)n
IRR Solution
\$10,000
\$12,000
\$40,000 =
+
+
(1+IRR)1 (1+IRR)2
\$15,000
\$10,000
\$7,000
+
+
(1+IRR)3
(1+IRR)4 (1+IRR)5
Find the interest rate (IRR) that causes the
discounted cash flows to equal \$40,000.
13-13
IRR Solution (Try 10%)
\$40,000 = \$10,000(PVIF10%,1) + \$12,000(PVIF10%,2) +
\$15,000(PVIF10%,3) + \$10,000(PVIF10%,4) +
\$ 7,000(PVIF10%,5)
\$40,000 = \$10,000(.909) + \$12,000(.826) +
\$15,000(.751) + \$10,000(.683) +
\$ 7,000(.621)
\$40,000 = \$9,090 + \$9,912 + \$11,265 +
\$6,830 + \$4,347
= \$41,444
[Rate is too low!!]
13-14
IRR Solution (Try 15%)
\$40,000 = \$10,000(PVIF15%,1) + \$12,000(PVIF15%,2) +
\$15,000(PVIF15%,3) + \$10,000(PVIF15%,4) +
\$ 7,000(PVIF15%,5)
\$40,000 = \$10,000(.870) + \$12,000(.756) +
\$15,000(.658) + \$10,000(.572) +
\$ 7,000(.497)
\$40,000 = \$8,700 + \$9,072 + \$9,870 +
\$5,720 + \$3,479
= \$36,841
[Rate is too high!!]
13-15
IRR Solution (Interpolate)
.05
X
.10
IRR \$40,000
.15
X
.05
13-16
=
\$41,444
\$36,841
\$1,444
\$4,603
\$1,444
\$4,603
IRR Solution (Interpolate)
.05
X
.10
IRR \$40,000
.15
X
.05
13-17
=
\$41,444
\$36,841
\$1,444
\$4,603
\$1,444
\$4,603
IRR Solution (Interpolate)
.05
X
.10
\$41,444
\$1,444
IRR \$40,000
.15
\$4,603
\$36,841
X = (\$1,444)(0.05)
\$4,603
X = .0157
IRR = .10 + .0157 = .1157 or 11.57%
13-18
IRR Acceptance Criterion
has determined that the hurdle rate
is 13% for projects of this type.
Should this project be accepted?
No! The firm will receive 11.57% for
each dollar invested in this project at
a cost of 13%. [ IRR < Hurdle Rate ]
13-19
IRRs on the Calculator
We will use the
cash flow registry
to solve the IRR
for this problem
quickly and
accurately!
13-20
Actual IRR Solution Using
Steps in the Process
Step 1:
Press
Step 2:
Press
Step 3: For CF0 Press
CF
2nd
CLR Work
-40000 Enter
key
keys
 keys
Step 4:
Step 5:
Step 6:
Step 7:
For C01 Press
For F01 Press
For C02 Press
For F02 Press
10000
1
12000
1
Enter
Enter
Enter
Enter

Step 8: For C03 Press
13-21 Step 9: For F03 Press
15000
1
Enter
Enter





keys
keys
keys
keys
keys
keys
Actual IRR Solution Using
Steps in the Process (Part II)
Step 10:For C04 Press
Step 11:For F04 Press
Step 12:For C05 Press
Step 13:For F05 Press
13-22
10000
1
7000
1

Enter
Enter
Enter
Enter





keys
keys
keys
keys
Step 14:
Step 15:
Press
Press
IRR
keys
key
Step 16:
Press
CPT
key
Result:
Internal Rate of Return = 11.47%
IRR Strengths
and Weaknesses
Strengths:

Accounts for
TVM

Considers all
cash flows

13-23
Less
subjectivity
Weaknesses:

Assumes all cash
flows reinvested at
the IRR

Difficulties with
project rankings and
Multiple IRRs
Net Present Value (NPV)
NPV is the present value of an
investment project’s net cash
flows minus the project’s initial
cash outflow.
CF1
NPV =
(1+k)1
13-24
+
CF2
(1+k)2
CFn
- ICO
+...+
n
(1+k)
NPV Solution
Basket Wonders has determined that the
appropriate discount rate (k) for this
project is 13%.
NPV = \$10,000 +\$12,000 +\$15,000 +
(1.13)1
(1.13)2
(1.13)3
\$10,000 \$7,000
+
\$40,000
4
5
(1.13)
(1.13)
13-25
NPV Solution
NPV = \$10,000(PVIF13%,1) + \$12,000(PVIF13%,2) +
\$15,000(PVIF13%,3) + \$10,000(PVIF13%,4) +
\$ 7,000(PVIF13%,5) - \$40,000
NPV = \$10,000(.885) + \$12,000(.783) +
\$15,000(.693) + \$10,000(.613) +
\$ 7,000(.543) - \$40,000
NPV = \$8,850 + \$9,396 + \$10,395 +
\$6,130 + \$3,801 - \$40,000
= - \$1,428
13-26
NPV Acceptance Criterion
has determined that the required
rate is 13% for projects of this type.
Should this project be accepted?
No! The NPV is negative. This means
that the project is reducing shareholder
wealth. [Reject as NPV < 0 ]
13-27
NPV on the Calculator
We will use the cash
flow registry to solve
the NPV for this
problem quickly and
accurately!
Hint: If you have not
cleared the cash flows
13-28
Actual NPV Solution Using
Steps in the Process
Step 1:
Press
Step 2:
Press
Step 3: For CF0 Press
CF
2nd
CLR Work
-40000 Enter
key
keys
 keys
Step 4:
Step 5:
Step 6:
Step 7:
For C01 Press
For F01 Press
For C02 Press
For F02 Press
10000
1
12000
1
Enter
Enter
Enter
Enter

Step 8: For C03 Press
13-29 Step 9: For F03 Press
15000
1
Enter
Enter





keys
keys
keys
keys
keys
keys
Actual NPV Solution Using
Steps in the Process (Part II)
13-30
Step 10:For C04 Press
Step 11:For F04 Press
Step 12:For C05 Press
Step 13:For F05 Press
10000
1
7000
1
Step 14:
Step 15:

Press
Press

Enter
Enter
Enter
Enter




keys
key
NPV
Enter
keys
keys
keys
keys

Step 16: For I=, Enter
13
keys
Step 17:
Press
CPT
Result:
Net Present Value = -\$1,424.42
key
NPV Strengths
and Weaknesses
Weaknesses:
Strengths:


Cash flows
assumed to be
reinvested at the
hurdle rate.

Accounts for TVM.

Considers all
cash flows.
13-31
May not include
managerial
options embedded
in the project. See
Chapter 14.
Net Present Value Profile
Net Present Value
\$000s
15
Sum of CF’s
Plot NPV for each
discount rate.
10
5
IRR
[email protected]%
0
-4
0
13-32
3
6
9
12
Discount Rate (%)
15
Creating NPV Profiles
Using the Calculator
Hint: As long as you
do not “clear” the
cash flows from the
registry, simply start
at Step 15 and enter
a different discount
rate. Each resulting
NPV will provide a
Profile!
13-33
Profitability Index (PI)
PI is the ratio of the present value of
a project’s future net cash flows to
the project’s initial cash outflow.
Method #1:
CF1
PI =
(1+k)1
+
CF2
CFn
+...+
2
(1+k)
(1+k)n
<< OR >>
Method #2:
13-34
PI = 1 + [ NPV / ICO ]
ICO
PI Acceptance Criterion
PI
= \$38,572 / \$40,000
= .9643 (Method #1, 13-34)
Should this project be accepted?
No! The PI is less than 1.00. This
means that the project is not profitable.
[Reject as PI < 1.00 ]
13-35
PI Strengths
and Weaknesses
Strengths:
Weaknesses:

Same as NPV

Same as NPV

Allows
comparison of
different scale
projects

Provides only
relative profitability

Potential Ranking
Problems
13-36
Evaluation Summary
Method Project Comparison Decision
13-37
PBP
3.3
3.5
Accept
IRR
11.47%
13%
Reject
NPV
-\$1,424
\$0
Reject
PI
.96
1.00
Reject
Other Project
Relationships
 Dependent
-- A project whose
acceptance depends on the
acceptance of one or more other
projects.
 Mutually Exclusive -- A project
whose acceptance precludes the
acceptance of one or more
alternative projects.
13-38
Potential Problems
Under Mutual Exclusivity
Ranking of project proposals may
A. Scale of Investment
B. Cash-flow Pattern
C. Project Life
13-39
A. Scale Differences
Compare a small (S) and a
large (L) project.
END OF YEAR
13-40
NET CASH FLOWS
Project S
Project L
0
-\$100
-\$100,000
1
0
0
2
\$400
\$156,250
Scale Differences
Calculate the PBP, IRR, [email protected]%,
and [email protected]%.
Which project is preferred? Why?
Project
IRR
S
100%
L
25%
13-41
NPV
\$
PI
231
3.31
\$29,132
1.29
B. Cash Flow Pattern
Let us compare a decreasing cash-flow (D)
project and an increasing cash-flow (I) project.
END OF YEAR
13-42
NET CASH FLOWS
Project D
Project I
0
1
-\$1,200
1,000
-\$1,200
100
2
500
600
3
100
1,080
Cash Flow Pattern
Calculate the IRR, [email protected]%,
and [email protected]%.
Which project is preferred?
Project
13-43
IRR
NPV
PI
D
23%
\$198
1.17
I
17%
\$198
1.17
13-44
600
Plot NPV for each
project at various
discount rates.
400
Project I
200
[email protected]%
IRR
Project D
0
-200
Net Present Value (\$)
Examine NPV Profiles
0
5
10
15
20
Discount Rate (%)
25
Net Present Value (\$)
600
-200 0 200 400
Fisher’s Rate of Intersection
0
13-45
At k<10%, I is best!
Fisher’s Rate of
Intersection
At k>10%, D is best!
5
10
15
20
Discount Rate (\$)
25
C. Project Life Differences
Let us compare a long life (X) project
and a short life (Y) project.
END OF YEAR
13-46
NET CASH FLOWS
Project X
Project Y
0
1
-\$1,000
0
-\$1,000
2,000
2
0
0
3
3,375
0
Project Life Differences
Calculate the PBP, IRR, [email protected]%,
and [email protected]%.
Which project is preferred? Why?
13-47
Project
IRR
NPV
PI
X
50%
\$1,536
2.54
Y
100%
\$ 818
1.82
Another Way to
Look at Things
1.
Adjust cash flows to a common terminal
year if project “Y” will NOT be replaced.
Compound Project Y, Year 1 @10% for 2 years.
Year
CF
0
1
2
3
-\$1,000
\$0
\$0
\$2,420
Results:
IRR* = 34.26%
NPV = \$818
*Lower IRR from adjusted cash-flow stream. X is still Best.
13-48
Replacing Projects
with Identical Projects
2.
Use Replacement Chain Approach (Appendix B)
when project “Y” will be replaced.
0
1
-\$1,000
-\$1,000
Results:
\$2,000
-1,000
\$1,000
IRR = 100%
2
3
\$2,000
-1,000
\$2,000
\$1,000
\$2,000
NPV* = \$2,238.17
*Higher NPV, but the same IRR. Y is Best.
13-49
Capital Rationing
Capital Rationing occurs when a
constraint (or budget ceiling) is placed
on the total size of capital expenditures
during a particular period.
Example: Julie Miller must determine what
investment opportunities to undertake for
Basket Wonders (BW). She is limited to a
maximum expenditure of \$32,500 only for
this capital budgeting period.
13-50
Available Projects for BW
Project
A
B
C
D
E
F
G
H
13-51
ICO
\$
500
5,000
5,000
7,500
12,500
15,000
17,500
25,000
IRR
18%
25
37
20
26
28
19
15
\$
NPV
PI
50
6,500
5,500
5,000
500
21,000
7,500
6,000
1.10
2.30
2.10
1.67
1.04
2.40
1.43
1.24
Choosing by IRRs for BW
Project
C
F
E
B
ICO
IRR
NPV
PI
\$ 5,000
15,000
12,500
5,000
37%
28
26
25
\$ 5,500
21,000
500
6,500
2.10
2.40
1.04
2.30
Projects C, F, and E have the
three largest IRRs.
The resulting increase in shareholder wealth
is \$27,000 with a \$32,500 outlay.
13-52
Choosing by NPVs for BW
Project
F
G
B
ICO
\$15,000
17,500
5,000
IRR
NPV
PI
28%
19
25
\$21,000
7,500
6,500
2.40
1.43
2.30
Projects F and G have the
two largest NPVs.
The resulting increase in shareholder wealth
is \$28,500 with a \$32,500 outlay.
13-53
Choosing by PIs for BW
Project
F
B
C
D
G
ICO
IRR
NPV
PI
\$15,000
5,000
5,000
7,500
17,500
28%
25
37
20
19
\$21,000
6,500
5,500
5,000
7,500
2.40
2.30
2.10
1.67
1.43
Projects F, B, C, and D have the four largest PIs.
The resulting increase in shareholder wealth is
\$38,000 with a \$32,500 outlay.
13-54
Summary of Comparison
Method Projects Accepted
PI
F, B, C, and D
\$38,000
NPV
F and G
\$28,500
IRR
C, F, and E
\$27,000
PI generates the greatest increase in
shareholder wealth when a limited capital
budget exists for a single period.
13-55
Single-Point Estimate
and Sensitivity Analysis
Sensitivity Analysis: A type of “what-if”
uncertainty analysis in which variables or
assumptions are changed from a base case in
order to determine their impact on a project’s
measured results (such as NPV or IRR).


13-56
Allows us to change from “single-point” (i.e.,
revenue, installation cost, salvage, etc.) estimates
to a “what if” analysis
Utilize a “base-case” to compare the impact of
individual variable changes
 E.g., Change forecasted sales units to see
impact on the project’s NPV
Post-Completion Audit
Post-completion Audit
A formal comparison of the actual costs and
benefits of a project with original estimates.


Identify any project weaknesses
Develop a possible set of corrective actions

Provide appropriate feedback
Result: Making better future decisions!
13-57
Multiple IRR Problem*
Let us assume the following cash flow
pattern for a project for Years 0 to 4:
-\$100 +\$100 +\$900 -\$1,000
How many potential IRRs could this
project have?
Two!! There are as many potential
IRRs as there are sign changes.
13-58
* Refer to Appendix A
NPV Profile -- Multiple IRRs
Net Present Value
(\$000s)
75
50
25
0
-100
13-59
Multiple IRRs at
k = 12.95% and 191.15%
0
40
80
120
160
Discount Rate (%)
200
NPV Profile -- Multiple IRRs
will only find ONE
IRR – even if there
are multiple IRRs. It
will give you the
lowest IRR. In this
case, 12.95%.
13-60
```