Title: Chapter 13  Capital Budgeting Techniques
1Chapter 13
Capital Budgeting Techniques
2After Studying Chapter 13, you should be able to
 Understand the payback period (PBP) method of
project evaluation and selection, including its
(a) calculation (b) acceptance criterion (c)
advantages and disadvantages and (d) focus on
liquidity rather than 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 rankings.  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
postcompletion audits.
3Capital Budgeting Techniques
 Project Evaluation and Selection
 Potential Difficulties
 Capital Rationing
 Project Monitoring
 PostCompletion Audit
4Overview Of Capital Budgeting Techniques
 Capital budgeting techniques are used to assess
and rank proposed projects.  Preferred techniques should include
 Time value considerations
 Risk and return considerations
 Valuation considerations
 Are used to ensure projects selected are
consistent with the firms goal of maximising
shareholder wealth.
5Project Evaluation Alternative Methods
 Payback Period (PBP)
 Internal Rate of Return (IRR)
 Net Present Value (NPV)
 Profitability Index (PI)
 Refer to the additional PowerPoint slides and the
Excel spreadsheet VW13E13b.xlsx for
computerbased solutions.
6Proposed Project Data
Julie Miller is evaluating a new project for her
firm, Basket Wonders (BW). She has determined
that the aftertax 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.
7Independent Project
 For this project, assume that it is independent
of any other potential projects that Basket
Wonders may undertake.
 Independent A project whose acceptance (or
rejection) does not prevent the acceptance of
other projects under consideration.
8Payback Period (PBP)
0 1 2 3
4 5
40 K 10 K 12 K 15
K 10 K 7 K
PBP is the period of time required for the
cumulative expected cash flows from an investment
project to equal the initial cash outflow.
9Payback Solution (1)
(a)
0 1 2 3
4 5
(b)
40 K 10 K 12 K 15
K 10 K 7 K
(d)
(c)
10 K 22 K 37 K 47 K
54 K
Cumulative Inflows
PBP a ( b c ) / d 3 (40 37) /
10 3 (3) / 10 3.3
Years
10Payback Solution (2)
0 1 2 3
4 5
40 K 10 K 12 K 15
K 10 K 7 K
40 K 30 K 18 K 3 K
7 K 14 K
PBP 3 ( 3K ) / 10K 3.3 Years Note
Take absolute value of last negative cumulative
cash flow value.
Cumulative Cash Flows
11PBP Acceptance Criterion
The management of Basket Wonders 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 lt 3.5
Year Max.
12Payback Period
 Peng Xi is currently contemplating two projects
project A, requiring an initial investment of
42,000 and project B, requiring an initial
investment of 45,000. The projected incremental
(relevant) operating net cash inflows for the two
projects are shown below
13Payback Period
 Project A 42,000
 14,000
 3 years
 Project B 28,000 (Year 1)
 12,000 (Year 2)
 40,000
 5,000/10,000 (Year 3)
 3.5 years
14PBP Strengths and Weaknesses
 Strengths
 Easy to use and understand
 Can be used as a measure of liquidity
 Easier to forecast ST than LT flows
 Weaknesses
 Does not account for TVM
 Does not consider cash flows beyond the PBP
 Cutoff period is subjective
15Internal 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 projects initial
cash outflow.  We equate the NPV of the investment opportunity
with 0.
CF1 CF2 CFn
ICO
. . .
(1 IRR)1 (1 IRR)2 (1 IRR)n
16Internal Rate of Return (IRR)
 Calculated by

Equation
13.1  Where
 CF0 Projects initial investment
 CFt Net cash inflows for year t
 t Year t
17Internal Rate of Return (IRR)
 Requires a trial and error approach, substituting
different discount rates until the equation
balances.  Get 2 NPVs one positive, the other negative,
then interpolate.  Decision criteria
 Accept if IRR gt Hurdle rate (Cost Of Capital)
 Reject if IRR lt Hurdle rate (Cost Of Capital)
18 IRR Solution
10,000 12,000
40,000
(1IRR)1 (1IRR)2
15,000 10,000 7,000
(1IRR)3 (1IRR)4 (1IRR)5
Find the interest rate (IRR) that causes the
discounted cash flows to equal 40,000.
19IRR 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(0.909) 12,000(0.826)
15,000(0.751) 10,000(0.683)
7,000(0.621) 40,000 9,090 9,912
11,265 6,830 4,347
41,444 Rate is too low!!
20IRR 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(0.870) 12,000(0.756)
15,000(0.658) 10,000(0.572)
7,000(0.497) 40,000 8,700 9,072 9,870
5,720 3,479
36,841 Rate is too high!!
21IRR Solution (Interpolate)
0.10 41,444 0.05 IRR 40,000
4,603 0.15 36,841 X 1,444
0.05 4,603
1,444
X
22IRR Solution (Interpolate)
0.10 41,444 0.05 IRR 40,000
4,603 0.15 36,841 X 1,444
0.05 4,603
1,444
X
23IRR Solution (Interpolate)
0.10 41,444 0.05 IRR 40,000
4,603 0.15 36,841 (1,444)(0.05)
4,603
1,444
X
X
X 0.0157
IRR 0.10 0.0157 0.1157 or 11.57
24IRR Interpolation Formula
 Interpolate for IRR using this formula
 (N1k2) (N2k1) / (N1 N2)
 Where
 N1 Positive NPV
 N2 Negative NPV
 k1 discount rate for positive NPV
 k2 discount rate for negative NPV
25IRR Interpolation Formula
 Interpolate for IRR
 (N1k2) (N2k1) / (N1 N2)
 (1,444 x 0.15) ( 3,159 x .1)/(41,444
36,841)  (216.6 315.9)/4,603
 532.5/4,603
 11.57
26IRR Acceptance Criterion
The management of Basket Wonders 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 lt Hurdle Rate
27IRR Strengths and Weaknesses
 Strengths
 Accounts for TVM
 Considers all cash flows
 Less subjectivity
 Weaknesses
 Assumes all cash flows reinvested at the IRR
 Difficulties with project rankings and
Multiple IRRs
28Net Present Value (NPV)
NPV is the present value of an investment
projects net cash flows minus the projects
initial cash outflow.
CF1 CF2 CFn
 ICO
NPV
. . .
(1k)1 (1k)2 (1k)n
29Net Present Value (NPV)
 Decision criteria
 Accept if NPV gt 0
 Reject if NPV lt 0
 If the NPV is greater than 0, the firm will earn
a return greater than its hurdle rate (cost of
capital).
30 NPV Solution
Basket Wonders has determined that the
appropriate discount rate (k) for this project is
13.
10,000 12,000 15,000
NPV
(1.13)1 (1.13)2 (1.13)3
10,000 7,000
 40,000
(1.13)4 (1.13)5
31NPV 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(0.885)
12,000(0.783) 15,000(0.693)
10,000(0.613) 7,000(0.543) 40,000 NPV
8,850 9,396 10,395 6,130 3,801
40,000  1,428
32NPV Solution (alternative layout)
 Period CF PVIF13,5 PV
 0 40,000 1.000 40,000
 1 10,000 0.885 8,850
 2 12,000 0.783 9,396
 3 15,000 0.693 10,395
 4 10,000 0.613 6,130
 5 7,000 0.543 3,801
 Net present value  1,428
33NPV Acceptance Criterion
The management of Basket Wonders 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 lt 0
34NPV Strengths and Weaknesses
 Strengths
 Cash flows assumed to be reinvested at the
hurdle rate.  Accounts for TVM.
 Considers all cash flows.
 Weaknesses
 May not include managerial options embedded
in the project. See Chapter 14. (We do not
cover this topic in this course)
35Ranking Conflicting Rankings
 Ranking is necessary when
 Projects are mutually exclusive
 Capital rationing is necessary
 Conflicting rankings arise due to differences in
cash flow  Timing
 Magnitude
 Which are a result of differences in the
underlying assumptions concerning the
reinvestment of intermediate net cash flows.
36Ranking Conflicting Rankings
 NPV assumes minimum opportunity cost the
opportunity cost of the current project would be
the return on a hypothetical alternative project
that just covers the cost of capital.  IRR assumes maximum opportunity cost the
maximum cost of capital a project could sustain
and still be acceptable or the opportunity cost
on a hypothetical alternative project offering a
return equal to the IRR.
37Which Is Better NPV Or IRR?
 On a theoretical basis NPV is preferred as
 it assumes intermediate flows are reinvested at
the firms cost of capital.  avoids possibility of time consuming multiple
IRRs.  it directly reflects the actual project return.
 On a practical basis, many financial managers
prefer IRR because  it works with rates of return not dollars.
 NPV does not measure benefits relative to the
amount invested  Most organisations use both.
38Net Present Value Profile
000s
Sum of CFs
Plot NPV for each discount rate.
15
10
Three of these points are easy now!
Net Present Value
IRR
5
NPV_at_13
0
4
0 3 6 9 12
15
Discount Rate ()
39Profitability Index (PI)
PI is the ratio of the present value of a
projects future net cash flows to the projects
initial cash outflow.
Method 1
CF1 CF2 CFn
ICO
PI
. . .
(1k)1 (1k)2 (1k)n
ltlt OR gtgt
PI 1 NPV / ICO
Method 2
40 PI Acceptance Criterion
PI 38,572 / 40,000 .9643 (Method
1, previous slide) Should this project be
accepted?
No! The PI is less than 1.00. This means
that the project is not profitable. Reject as
PI lt 1.00
41PI Strengths and Weaknesses
 Strengths
 Same as NPV
 Allows comparison of different scale
projects
 Weaknesses
 Same as NPV
 Provides only relative profitability
 Potential Ranking Problems
42Evaluation Summary
Basket Wonders Independent Project
43Project Evaluation Remember Chapter 12 New
Asset project?
We will start with the cash flows of the project
and also calculate the cumulative cash flow
values.
We can use Excel functions / approaches to
calculate each of the following methods from the
above cash flows.
44Other 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.
45Potential Problems Under Mutual Exclusivity
Ranking of project proposals may create
contradictory results.
A. Scale of Investment B. Cashflow Pattern C.
Project Life
46A. Scale Differences
Compare a small (S) and a large (L) project.
NET CASH FLOWS
Project S Project L
END OF YEAR
0 100
100,000
1 0
0
2 400
156,250
47A. Scale Differences
Calculate the PBP, IRR, NPV_at_10, and
PI_at_10. Which project is preferred? Why? Project
IRR NPV PI
S 100 231 3.31
L 25 29,132 1.29
48Remember to refer to Excel spreadsheet
VW13E13b.xlsx and the Scale tab.
A. Scale Differences
Refer to VW13E13b.xlsx on the Scale tab.
49B. Cash Flow Pattern
Let us compare a decreasing cashflow (D) project
and an increasing cashflow (I) project.
NET CASH FLOWS
Project D Project I
END OF YEAR
0 1,200
1,200
1 1,000
100
2
500 600
3
100 1,080
50Cash Flow Pattern
Calculate the IRR, NPV_at_10, and
PI_at_10. Which project is preferred? Project
IRR NPV PI
D 23 198 1.17
I 17 198 1.17
?
51Examine NPV Profiles
Plot NPV for each project at various discount
rates.
Project I
NPV_at_10
Net Present Value ()
200 0 200 400 600
IRR
Project D
0 5 10 15 20
25
Discount Rate ()
52Fishers Rate of Intersection
At klt10, I is best!
Fishers Rate of Intersection
Net Present Value ()
200 0 200 400 600
At kgt10, D is best!
0 5 10 15 20
25
Discount Rate ()
53Remember to refer to Excel spreadsheet
VW13E13b.xlsx and the Pattern tab.
B. Cash Flow Pattern
Refer to VW13E13b.xlsx on the Pattern tab.
54C. Project Life Differences
Let us compare a long life (X) project and
a short life (Y) project.
NET CASH FLOWS
Project X Project Y
END OF YEAR
0 1,000
1,000
1
0 2,000
2
0 0
3 3,375
0
55Project Life Differences
Calculate the PBP, IRR, NPV_at_10, and
PI_at_10. Which project is preferred? Why?
Project IRR NPV PI
?
X 50
1,536 2.54 Y
100 818 1.82
56Remember to refer to Excel spreadsheet
VW13E13b.xlsx and the Life tab.
C. Project Life Differences
57Comparing Projects With Unequal Lives
 Often a financial manager will need to select a
project from a group of unequal life project
options.  When unequal life projects are mutually
exclusive, the impact of differing lives must be
considered as the projects will not provide
benefits over comparable time periods. This is
especially important when continuing service is
needed from the project under consideration.
58Annualised Net Present Value (ANPV) Approach
 Converts the net present value of unequal life
projects into an equivalent annual amount (in NPV
terms).  Calculated by

 Decision criteria
 Select the project with the highest ANPV
59Annualised Net Present Value Approach
 Xi Chen Limited is evaluating two projects, X and
Y. The relevant cash flows for each project are
given in the table below. The applicable cost of
capital for use in evaluating these equally risky
projects is 10.
60Annualised Net Present Value Approach
 Table use The NPV of each project at a 10 cost
of capital is calculated by finding the present
value of each net cash inflow, summing these
values and subtracting the initial investment
from the sum of the present values.  NPVX 28,000 (0.909) 33,000 (0.826)
38,000 (0.751) 70,000  (25,452 27,258 28,538) 70,000
11,248  NPVY 35,000 (0.909) 30,000 (0.826)
25,000 (0.751) 20,000 (0.683)
15,000 (0.621) 10,000 (0.564) 85
000  (31,815 24,780 18,775 13,660 9,315
5,640) 85,000 18 985  The NPV for project X is 11,248 that for
project Y is 18,985.
61Annualised Net Present Value Approach
 Ignoring the differences in project lives, we can
see that both projects are acceptable (NPVs
greater than zero) and that project Y is
preferred to project X.  If the projects are independent and only one
could be accepted, project Y, with the larger
NPV, would be preferred.  However, if the projects are mutually exclusive,
their differing lives must be considered, as
project Y provides three more years of service
than project X.
62Annualised Net Present Value Approach
 Calculate the ANPV for each project.
 ANPVx 11,248/PVIFA10, 3 yrs
 11,248/2.487
 4,523
 ANPVY 18,985/PVIFA10, 6 yrs
 18,985/4.355
 4,359
63Annualised Net Present Value Approach
 Reviewing the ANPVs calculated above, we can see
that project X would be preferred to project Y.  Given that projects X and Y are mutually
exclusive, project X would be the recommended
project because it provides the higher ANPV.
64Another 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 _at_10 for 2 years. Year
0 1 2
3 CF 1,000 0 0
2,420 Results IRR 34.26 NPV
818 Lower IRR from adjusted cashflow stream.
X is still Best.
65Replacing Projects with Identical Projects
2. Use Replacement Chain Approach (Appendix B)
when project Y will be replaced.
0 1
2 3
1,000 2,000
1,000 2,000
1,000 2,000
1,000 1,000 1,000
2,000
Results IRR 100 NPV 2,238.17 Higher
NPV, but the same IRR. Y is Best.
66Remember to refer to Excel spreadsheet
VW13E13b.xlsx and the Life2 tab.
C. Project Life Differences
67Capital 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.
68Available Projects for BW
Project ICO IRR NPV
PI A 500 18 50
1.10 B 5,000 25 6,500 2.30 C
5,000 37 5,500 2.10 D 7,500 20
5,000 1.67 E 12,500 26 500 1.04
F 15,000 28 21,000 2.40
G 17,500 19 7,500 1.43 H 25,000 15
6,000 1.24
69Choosing by IRRs for BW
Project ICO IRR NPV
PI C 5,000 37 5,500 2.10
F 15,000 28 21,000 2.40
E 12,500 26 500 1.04 B 5,000 25
6,500 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.
70Choosing by NPVs for BW
Project ICO IRR NPV PI
F 15,000 28 21,000 2.40
G 17,500 19 7,500 1.43 B 5,000 25
6,500 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.
71Choosing by PIs for BW
Project ICO IRR NPV
PI F 15,000 28 21,000 2.40 B
5,000 25 6,500 2.30 C
5,000 37 5,500 2.10 D
7,500 20 5,000 1.67 G 17,500
19 7,500 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.
72Summary of Comparison
Method Projects Accepted Value Added
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.
73SinglePoint Estimate and Sensitivity Analysis
Sensitivity Analysis A type of whatif
uncertainty analysis in which variables or
assumptions are changed from a base case in order
to determine their impact on a projects measured
results (such as NPV or IRR).
 Allows us to change from singlepoint (i.e.,
revenue, installation cost, salvage, etc.)
estimates to a what if analysis  Utilise a basecase to compare the impact of
individual variable changes  E.g., Change forecasted sales units to see impact
on the projects NPV
74PostCompletion Audit
Postcompletion 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!
75Multiple 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.
Refer to Appendix A
76NPV Profile Multiple IRRs
75
Multiple IRRs at k 12.95 and 191.15
50
Net Present Value (000s)
25
0
100
0 40 80 120 160 200
Discount Rate ()
77NPV Profile Multiple IRRs
Hint Your calculator will only find ONE IRR
even if there are multiple IRRs. It will give
you the lowest IRR. In this case, 12.95.