Capital Budgeting, Risk
Considerations and Other
Special Issues
Lecture Agenda
•
•
•
•
•
•
•
•
•
•
Learning Objectives
Important Terms
The Nature of Capital Expenditure Decisions
The Appropriate Discount Rate
Evaluation of Investment Alternatives using NPV, IRR, PI
and Payback Approaches
Capital Rationing
Independent and Interdependent Projects
Comparing Mutually Exclusive Projects with Unequal
Lives
International Considerations
Summary and Conclusions
– Concept Review Questions
13 - 2
Learning Objectives
1.
2.
3.
4.
The similarities between corporate investment techniques
and the techniques used to value shares
The basic capital budgeting process
The most important approaches used to determine the value
of a firm’s capital expenditures (capex)
The reasons that firms sometimes use techniques that may
seem inconsistent with value maximization.
13 - 3
Important Chapter Terms
•
•
•
•
•
•
•
•
Bottom-up analysis
Capital budgeting
Capital expenditures
Capital rationing
Chain replication approach
Contingent projects
Crossover rate
Discounted cash flow (DCF)
methodologies
• Discounted payback period
• Equivalent annual NPV
approach
• Five Forces
• Independent projects
• Internal rate of return (IRR)
• Investment opportunity
schedule (IOS)
• Mutually exclusive projects
• Net present value (NPV)
• Payback period
• Profitability index
• Pure play approach
• Risk-adjusted discount
rates (RADRs)
• Top-down analysis
13 - 4
Capital Expenditures (capex)
Capital expenditures are a firm’s investments
in long-lived assets.
Long-lived assets may be:
– Tangible (property, plant and equipment)
– Intangible (research and development, patents,
copyrights, trademarks, brand names, and
franchise agreements)
13 - 5
Capital Expenditures
Importance
Capex decisions determine the future
direction of the company.
• CAPEX decisions are among the most important that
the firm can make because:
– Often involve very significant outlay of money and
managerial time
– Often take many years to demonstrate their returns
– Are often irrevocable
– Because of their size and long-term nature, they can
significantly alter the risk of the entire firm.
13 - 6
Capital Expenditure Decisions
Capital Budgeting
Capital budgeting is the process through
which a firm makes capital expenditure
decisions by:
1. Identifying investment alternatives
2. Evaluating these alternatives
3. Implementing the chosen investment decisions,
and
4. Monitoring and evaluating the implemented
decisions.
13 - 7
Capital Expenditure Decisions
Five Forces
Michael Porter’s Five Forces model identified five critical factors
that determine the attractiveness of an industry:
1.
2.
3.
4.
5.
Entry barriers
Threat of substitutes
Bargaining power of buyers
Bargaining power of suppliers
Rivalry among existing competitors
Companies do exert control over how they strive to create a
competitive advantage within their industry.
They can strive for:
1.
2.
Cost leadership: strive to be a low-cost producer
Differentiation: offer “differentiated” products
Once attained, competitive advantage is difficult to sustain, and
this requires on-going planning and investment.
CAPEX must be made with a strategic focus and be subject to
and pass rigorous financial analysis.
13 - 8
Capital Expenditure Decisions
Bottom-up and Top-Down Analysis
Bottom-up Analysis is an investment strategy
in which capex decisions are considered in
isolation, without regard for whether the
firm should continue in this business or for
general industry and economic trends.
Top-down Analysis is an investment strategy
that focuses on strategic decisions, such as
which industries or products the firm should
be involved in, looking at the overall
economic picture.
13 - 9
Capital Expenditure Decisions
DCF Methodolgies
Capex decisions, like security valuation, must take
into account the timing, magnitude and riskiness of
the net incremental, after-tax cash flow benefits that
an initial investment is forecast to produce.
Unlike security valuation decisions, analysts can
change the underlying cash flows by changing the
structure of the project.
13 - 10
Capital Expenditure Decisions
DCF Methodologies
The ability to restructure capex proposals means
that capex analysis can be iterative and circular as
illustrated below:
Project
Proposal
Project
Analysis
Restructure
Proposal
Forecast Outcome
Positive (+ NPV)
Proceed with
Implementation
Planning
Forecast
Outcome Not
Viable (- NPV)
13 - 11
Capital Expenditure Decisions
DCF Methodologies
All discounted cash flow approaches
require:
– Estimate of the initial cost of the CAPEX
– Estimate of the net incremental after-tax cash
flow benefits the investment is forecast to
produce (we need to know when these cash flows
will occur and how large they will be)
– Estimate of the required rate of return on the
project (relevant discount rate k)
13 - 12
Evaluating Investment Alternatives
The Cash Flow Pattern for a Traditional Capital Expenditure
13-1 FIGURE
0
1
CF1
2
CF2
…
3
CF3
…
n
CFn
CF0
Where CFt = estimated future after-tax incremental cash flow at
time t
CF0 = the initial after-tax incremental cash outlay
13 - 13
Firm’s Cost of Capital (WACC = k)
• The firm’s cost of capital determines the minimum rate of
return that would be acceptable for a capital project.
• WACC is the discount rate (k) we use in NPV analysis and the
hurdle rate when using IRR
• The weighted average cost of capital (WACC) is the relevant
discount rate for NPV analysis. (assuming the risk of the
project being evaluated is similar to the risk of the overall firm)
• If the risk of the project differs from the risk of the overall firm
a risk-adjusted discount rate (RADR) should be used.
13 - 14
Risk-Adjusted Discount Rates (RADRs = k)
•
RADRs can be estimated using a number of alternative
techniques:
1.
Use the CAPM formula after determining the project beta and using
the current risk-free rate (RF) and an estimate of the market risk
premium
•
2.
This approach involves forecast ROA that must be regressed against the
ROA of the market index. Estimation errors can be significant.
Pure play approach where you find the cost of capital of a firm in the
industry associated with the project.
•
The key to this approach is that the firm must not be diversified across
industries but truly represent an investment solely in that industry.
13 - 15
Evaluation of Investment Alternatives
DCF Methodologies
• Net Present Value (NPV)
• Internal Rate of Return (IRR)
• Payback Period and Discounted Payback
Period
• Profitability Index (PI)
13 - 16
Project Evaluation Techniques
Net Present Value (NPV) Formula
CF3
CF1
CF2
NPV 


 ...  CF0
1
2
3
(1  k ) (1  k ) (1  k )
[ 13-1]
n

 CF
i 1
t
(1  k )
t
 CF0
13 - 17
Evaluating Investment Alternatives
Net Present Value (NPV) Analysis
NPV = the sum of the present value of all benefits minus the
present value of costs
n
Cash Flow Benefitsi
NPV  
 Initial Co st
i
( 1  k)
i 1
If benefits > cost, NPV will be positive and the project
is acceptable.
If benefits < cost, NPV will be negative and the
project is unacceptable because it destroys firm
value.
13 - 18
Evaluating Investment Alternatives
Net Present Value Interpreted
Example:
If NPV is forecast to be + $250,000, then the PV of incremental
benefits exceeds the present value of costs today by $250,000.
Remember the PV is determined by discounting the forecast
cash flows by the investor’s required return. A positive NPV
indicates that returns are greater than what investors require.
This means a positive NPV adds value to the firm.
In this case, if there were 1,000,000 shares outstanding,
acceptance of a $250,000 NPV project in an efficient market
means that the market price of each share should rise by:
NPV
Number of Shares Outstandin g
$250,000

 $0.25
1,000,000
Increase in Share Price 
13 - 19
Evaluating Investment Alternatives
Net Present Value Interpreted
NPV is an absolute measure (expressed in
present dollars) of the net incremental benefits
the project is forecast to bring to the
shareholders.
In a perfectly efficient market, the total value of
the firm should rise by the value of the NPV if the
project is undertaken.
Remember – it is the manager’s responsibility to
maximize shareholder wealth
13 - 20
NPV Example
The Formula-based Approach
Problem:
•
•
•
Initial outlay = $12,000
After-tax cash flow benefits:
– Year 1 = $5,000
– Year 2 = $5,000
– Year 3 = $8,000
Discount rate (k) = 15%
CF3
CF1
CF2


 CF0
1
2
3
(1  k ) (1  k ) (1  k )
$5,000 $5,000 $8,000



 $12,000
1
2
3
(1.15) (1.15) (1.15)
 $4,348  $3,781  $6,260  $12,000
NPV 
 $1,389
13 - 21
NPV Example
The Spreadsheet Approach
Problem:
•
•
•
Initial outlay = $12,000
After-tax cash flow benefits:
– Year 1 = $5,000
– Year 2 = $5,000
– Year 3 = $8,000
Discount rate (k) = 15%
Year
0
1
2
3
Initial cost =
Cost of Capital =
Cashflow
Initial cost
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
$12,000
15.0%
After-tax
incremental CF
-$12,000
5,000
5,000
8,000
NPV =
PV Factor
1
0.869565
0.756144
0.657516
Present
Value
-$12,000
$4,348
$3,781
$5,260
$1,389
13 - 22
NPV Example
The Financial Calculator Approach
Problem:
•
•
•
Initial outlay = $12,000
After-tax cash flow benefits:
– Year 1 = $5,000
– Year 2 = $5,000
– Year 3 = $8,000
Discount rate (k) = 15%
13 - 23
NPV Example
Solution Using a Financial Calculator (TI BA II Plus)
CLR WORK
CF
2ND
-12000
ENTER
5000
ENTER
5000
ENTER
8000
NPV
CPT
$5,000 $5,000 $8,000


 $12,000
(1.15)1 (1.15) 2 (1.15) 3
 $4,348  $3,781  $6,260  $12,000
NPV 
 $1,389
ENTER
15
ENTER
gives $1,388.67
13 - 24
NPV Profile
• Is a set of NPVs for a project that are created by varying
the discount rate used to find the present value of the
cash flows.
• The slope of the NPV line that is created when you graph
these results, depends on the useful life of the project
and on the timing of the receipt of the net incremental
benefits.
– The longer the life of the project, the steeper the slope of the
NPV profile line because more distant cash flows are affected
more by the discounting process.
(The following slide demonstrates what an NPV Profile looks like)
13 - 25
NPV Profile
NPV ($)
Discount Rate (k) (%)
13 - 26
NPV Example
A Spreadsheet Modeling Approach
Here
is a spreadsheet
model
used
calculate
a $100,000
projectthe
that
The NPV
result is positive
and
the to
project
is acceptable
because
has
a 6 looks
year life,
equal annual
after-tax
cash
project
likeoffers
it will increase
the value
of the
firmflow
withbenefits
these over that
life
of $60,000 per annum when the relevant cost of capital is 12%.
assumptions.
Year
0
1
2
3
4
5
6
Initial cost =
AT cash flow benefits =
Useful life(years) =
Cost of Capital =
$100,000
$60,000
6
12%
Cashflow
Initial cost
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
After-tax incremental CF
-$100,000
60,000
60,000
60,000
60,000
60,000
60,000
NPV =
PV Factor Present Value
1
-$100,000
0.892857
$53,571
0.797194
$47,832
0.71178
$42,707
0.635518
$38,131
0.567427
$34,046
0.506631
$30,398
$146,684
13 - 27
NPV Example
Stress Testing the Project
Noticeletthat
Now,
us at
stress
a 0%– discount
test the model.
rate, all We
of the
canpresent
start byvalue
setting
the discount
factors
become
rate1.toAnd
0%.we
(ie.work
No time
with value
absolute
to money)
dollar values.
NPV is forecast to be it’s greatest at a 0% discount rate.
Initial cost =
AT cash flow benefits =
Useful life(years) =
Cost of Capital =
Year
0
1
2
3
4
5
6
Cashflow
Initial cost
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
$100,000
$60,000
6
0%
After-tax incremental CF PV Factor Present Value
-$100,000
1
-$100,000
60,000
1
$60,000
60,000
1
$60,000
60,000
1
$60,000
60,000
1
$60,000
60,000
1
$60,000
60,000
1
$60,000
NPV =
$260,000
13 - 28
NPV Example
Stress Testing the Project
Increasing the discount rate to 5%, we discount the more
distant cash flows more heavily and the NPV of the project
falls from $260,000 to $204,542.
Year
0
1
2
3
4
5
6
Initial cost =
AT cash flow benefits =
Useful life(years) =
Cost of Capital =
$100,000
$60,000
6
5%
Cashflow
Initial cost
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
After-tax incremental CF
-$100,000
60,000
60,000
60,000
60,000
60,000
60,000
NPV =
PV Factor Present Value
1
-$100,000
0.952381
$57,143
0.907029
$54,422
0.863838
$51,830
0.822702
$49,362
0.783526
$47,012
0.746215
$44,773
$204,542
13 - 29
NPV Example
Stress Testing the Project
Increasing the discount rate to 10%, the NPV of the project
falls from $204,542 (at 5%) to $161,316.
Year
0
1
2
3
4
5
6
Initial cost =
AT cash flow benefits =
Useful life(years) =
Cost of Capital =
$100,000
$60,000
6
10%
Cashflow
Initial cost
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
After-tax incremental CF
-$100,000
60,000
60,000
60,000
60,000
60,000
60,000
NPV =
PV Factor Present Value
1
-$100,000
0.909091
$54,545
0.826446
$49,587
0.751315
$45,079
0.683013
$40,981
0.620921
$37,255
0.564474
$33,868
$161,316
13 - 30
NPV Example
Stress Testing the Project
Increasing the discount rate to 20%, the NPV of the project
falls to $99,531.
Year
0
1
2
3
4
5
6
Initial cost =
AT cash flow benefits =
Useful life(years) =
Cost of Capital =
$100,000
$60,000
6
20%
Cashflow
Initial cost
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
After-tax incremental CF
-$100,000
60,000
60,000
60,000
60,000
60,000
60,000
NPV =
PV Factor Present Value
1
-$100,000
0.833333
$50,000
0.694444
$41,667
0.578704
$34,722
0.482253
$28,935
0.401878
$24,113
0.334898
$20,094
$99,531
13 - 31
NPV Example
Stress Testing the Project
ItIncreasing
is hard to imagine
the discount
a project
rate to
having
50%, risk
the that
NPVrequires
of the project
a return
offalls
more
to $9,465.
than 50%. Even at a discount rate of 50%, the
project has a positive NPV!
Year
0
1
2
3
4
5
6
Initial cost =
AT cash flow benefits =
Useful life(years) =
Cost of Capital =
$100,000
$60,000
6
50%
Cashflow
Initial cost
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
After-tax incremental CF
-$100,000
60,000
60,000
60,000
60,000
60,000
60,000
NPV =
PV Factor Present Value
1
-$100,000
0.666667
$40,000
0.444444
$26,667
0.296296
$17,778
0.197531
$11,852
0.131687
$7,901
0.087791
$5,267
$9,465
13 - 32
NPV Example
Stress Testing the Project
Somewhere
60%,the
theNPV
NPVofturned
to $0.
Increasing
thebetween
discount50%
rateand
to 60%,
the project
Remember,
the IRR
of the
projectrate,
is that
rate that
falls
to -$5,960.
At that
discount
thediscount
project would
causes the
to of
bethe
equal
decrease
theNPV
value
firmtoif$0.00
accepted.
Year
0
1
2
3
4
5
6
Initial cost =
AT cash flow benefits =
Useful life(years) =
Cost of Capital =
$100,000
$60,000
6
60%
Cashflow
Initial cost
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
After-tax incremental CF
-$100,000
60,000
60,000
60,000
60,000
60,000
60,000
NPV =
PV Factor Present Value
1
-$100,000
0.625
$37,500
0.390625
$23,438
0.244141
$14,648
0.152588
$9,155
0.095367
$5,722
0.059605
$3,576
-$5,960
13 - 33
NPV Example
Stress Testing the Project
Now
we can
graph
the resultscauses
of the stress
test.
NPV
is on
A discount
rate
of 55.8055%
the NPV
to be
equal
to
the
because IRR.
it is the dependent variable and
$0. vertical
This isaxis
the project’s
discount rate is on the horizontal.
Year
0
1
2
3
4
5
6
Initial cost =
AT cash flow benefits =
Useful life(years) =
Cost of Capital =
$100,000
$60,000
6
55.8055%
Cashflow
Initial cost
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
After-tax incremental CF
-$100,000
60,000
60,000
60,000
60,000
60,000
60,000
NPV =
PV Factor Present Value
1
-$100,000
0.641826
$38,510
0.41194
$24,716
0.264394
$15,864
0.169695
$10,182
0.108915
$6,535
0.069904
$4,194
$0
13 - 34
Project NPV Profile
NPV
$
$260,000
0
0% 5%
10%
20%
40%
50%
60%
IRR = 55.8%
Discount Rate (%)
13 - 35
Project NPV Profile
NPV
$
$260,000
IF the appropriate
discount rate (k) is
12%, then the NPV is
forecast to be positive.
$146,684
0
0% 5%
10%
20%
40%
50%
60%
IRR = 55.8%
Discount Rate (%)
13 - 36
Project NPV Profile
NPV
$
Even if your estimate of the
project’s required return (RADR)
is wrong, the project’s NPV
remains positive over a wide
range of values for k (from 0% to
55%)
$260,000
$146,684
0
0% 5%
10%
20%
40%
50%
60%
IRR = 55.8%
Discount Rate (%)
13 - 37
NPV Profiles
• The slope of the NPV profile depends on the
timing and magnitude of cash flows.
• Projects with cash flows that occur late in the
project’s life will have an NPV that is more
sensitive to discount rate changes.
13 - 38
IRR
• The internal rate of return (IRR) is that discount rate that
causes the NPV of the project to equal zero.
• If IRR > WACC, then the project is acceptable because it
will return a rate of return on invested capital that is
likely to be greater than the cost of funds used to invest
in the project.
13 - 39
Project Evaluation Techniques
Internal Rate of Return (IRR)
CF3
CFn
CF1
CF2



...
 CF0
1
2
3
n
(1  IRR ) (1  IRR ) (1  IRR )
(1  IRR )
n
 CF
[ 13-2]
or ,
i 1
t
(1  IRR )
t
 CF0
13 - 40
IRR Example
This Example Will Be Used To Demonstrate Alternative Approaches to
Solve for IRR
Problem:
•
•
•
Initial outlay = $12,000
After-tax cash flow benefits:
– Year 1 = $5,000
– Year 2 = $5,000
– Year 3 = $8,000
Cost of Capital = 15%
13 - 41
IRR Example
Formula-based Approach to the Solution
CF3
CF1
CF2


(1  IRR )1 (1  IRR ) 2 (1  IRR ) 3
$5,000
$5,000
$8,000
$12,000 


1
2
(1  IRR ) (1  IRR ) (1  IRR )3
CF0 
The only way you can use the formula is to use the iterative approach t o solving for IRR. That is, substitute different values
for IRR until the mathematic al expression becomes an equality.
13 - 42
IRR Example
Formula-based Approach to the Solution
CF3
CF1
CF2


1
2
(1  IRR ) (1  IRR )
(1  IRR ) 3
$5,000
$5,000
$8,000
$12,000 


(1  IRR )1 (1  IRR ) 2 (1  IRR ) 3
CF0 
The only way you can use the formula is to use the iterative approach t o solving for IRR. That is, substitute different values
for IRR until the mathematic al expression becomes an equality.
Let IRR  20%
$12,000 
$5,000 $5,000 $8,000


 $12,268.52
(1.2)1
(1.2) 2
(1.2) 3
Since $12,000  $12,268.52 then we need to increase the discount rate to lower the
PV of future cash flows until they equal $12,000.
13 - 43
IRR Example
Formula-based Approach to the Solution
Let IRR  25%
$12,000 
$5,000 $5,000 $8,000


 $11,296
(1.25)1 (1.25) 2 (1.25)3
Since $12,000  $11,296 then we know the IRRis between 20% and 25%.
You can continue to substitute different values into the equation t o iterativel y
find the IRR, or you can use linear interpolat ion to ESTIMATE the approximat e value of the IRR.
13 - 44
IRR Example
Formula-based Approach to the Solution – Linear Interpolation
Summarizing our results:
IRR is
between
20% and
25%
Discount Rate
20%
IRR
25%
Present Value of Benefits
$12,268.52
$12,000
$11,296
We can now estimate the IRR assuming a linear relationship between PV of benefits (which
isn’t exactly true because compound interest is a curvilinear relationship)
IRR  20 12,000  12,268.50

25  20 11,296  12,268.50
 268.52
IRR  20  5 
 1.3805
 972.52
IRR  21.38%
13 - 45
IRR Example
Solution Using a Financial Calculator (TI BA II Plus)
CF
2ND
-12,000
ENTER
5,000
ENTER
5,000
ENTER
8,000
ENTER
CLR WORK
$5,000 $5,000 $8,000


(1  r )1 (1  r ) 2 (1  r ) 3
r  IRR  the discount rate that equates the PV of
$12,000 
IRR
CPT
gives 21.31%
cash flow benefits after - tax with the initial cost o
project.
Since IRR (21.3%)  WACC (15%) the project is
13 - 46
IRR Example
Spreadsheet Model-based Approach to the Solution
A
1
2
3
4
5
6
7
B
Time
0
1
2
3
C
Type of Cash Flow
Initial Project cost =
Incremental ATCF Benefit=
Incremental ATCF Benefit=
Incremental ATCF Benefit=
IRR =
D
E
ATCF
-$12,000
$5,000
$5,000
$8,000
21.31282726%
Simply place the cash flows into their own individual cells on the
spreadsheet, remembering that the cost of the project is a negative cash
flow representing funds leaving the firm.
Next, insert the built-in IRR function (fx) into a cell and provide the function
values in the format of: =IRR(value 0, value 1, value 2,…, guess)
=IRR(D2:D5,0.10)
13 - 47
IRR versus NPV
• Both methods use the same basic decision
inputs.
• The only difference is the assumed discount
rate.
• The IRR assumes intermediate cashflows are
reinvested at IRR…NPV assumes they are
reinvested at WACC
– This difference, however, can produce conflicting
decision results under specific conditions
13 - 48
Evaluating Investment Alternatives
Comparing NPV and IRR
Table 13 - 1 NPV versus IRR
Issue
NPV
IRR
1.
Future cash flows
change sign
It still works the same for both
accept/reject and ranking
decisions.
Multiple IRRs may result - in this
case, the IRR cannot be used for
either accept/reject or ranking
decisions.
2.
Ranking projects
Higher NPV implies greater
contribution to firm wealth - it is
an absolute measure of wealth.
3.
Reinvestment rate
assumed for future cash
flows received
Assumes all future cash flows are
reinvested at the discount rate.
This is appropriate because it
treats the reinvestment of all
future cash flows consistently,
and k is the investor's opportunity
cost.
The higher IRR project may have a
lower NPV, and vice versa,
depending on the appropriate
discount rate, and the size of the
Assumes cash flows from each
project are reinvested at that
project's IRR. This is
inappropriate, particularly when
the IRR is high.
13 - 49
IRR versus NPV
Conditions Where NPV and IRR Will Give Conflicting Decision Results
1. Evaluating two or more mutually exclusive
investment proposals
2. NPV profiles of the projects have different
slopes and cross at a positive NPV
3. The cost of capital (relevant discount rate k) is
lower than the crossover discount rate.
13 - 50
Evaluating Investment Alternatives
Two NPV Profiles
13 - 2 FIGURE
NPV ($)
700
500
Crossover Rate = 9%
Discount Rate (k) (%)
0
12
15
A
B
13 - 51
Evaluating Investment Alternatives
Two NPV Profiles
13 - 2 FIGURE
If k IRR
is less
than 9%,
B>IRRA
thenIRR
project
A will
The
approach
have
a higher
NPV
would
lead us
to
than B and A should
believe the Project
be chosen to
B is best!
maximize
the value
of the firm.
NPV ($)
700
500
Crossover Rate = 9%
However, NPVA is
greater when
k<9%
Discount Rate (k) (%)
0
12
15
A
B
13 - 52
Evaluating Investment Alternatives
Comparing NPV and IRR
• Both techniques use the same inputs
• NPV measures in absolute terms, the estimated
increase in the value of the firm today the project is
expected to produce.
– NPV assumes cash flows are reinvested at WACC
• IRR estimates the rate of return on the project
– IRR assumes cash flows produced by the project are
reinvested by the firm at the project’s IRR.
The reason for the different accept/reject decisions is
the different reinvestment rate assumptions used by
the two techniques.
13 - 53
Evaluating Investment Alternatives
NPV and IRR Compared
Which method should be relied upon?
– It depends on which reinvestment assumption is
most realistic.
– Most often, the NPV assumption of reinvestment at
WACC is the most realistic because no rational
manager would reinvest cash flows at rates lower
than the firm’s cost of capital.
– Projects with high IRRs are not common – to
assume that future cash flows will be reinvested at
the inflated IRR rate is probably wrong.
13 - 54
Evaluation Techniques
CFO Preferences
Despite the inherent superiority of the NPV
approach, CFOs continue to use other
approaches and do not favour NPV over IRR.
Perhaps, the reason for this is that it is difficult
for people to understand what a positive
NPV really means.
(See Figure 13 – 3 on the following slide.)
13 - 55
CFO Preferences
Evaluation Technique
13 - 3 FIGURE
Evaluation
Technique
IRR
NPV
Hurdle Rate
Payback
Sensitivity Analysis
P/E multiples
Discounted payback
Real options
Book rate of return
Simulation analysis
Profitability Index
APV
0%
10%
20%
30%
40%
50%
60%
70%
80%
Source: Data from Graham, John R. and Harvey, Campbell R. “The Theory and Practice of Corporate Finance: Evidence from
the Field,” Journal of Financial Economics 60 (2001), p. 187-243.
13 - 56
Payback and Discounted Payback
Capital Budgeting, Risk
Considerations and Other Special
Issues
Payback Method
• This is a simple approach to capital budgeting that is designed
to tell you how many years it will take to recover the initial
investment.
• It is often used by financial managers as one of a set of
investment screens, because it gives the manager an intuitive
sense of the project’s risk.
13 - 58
Simple Payback Example
Initial cost =
AT cash flow benefits =
Useful life(years) =
Cost of Capital =
N/A
Year
0
1
2
3
4
5
6
Cashflow
Initial cost
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
$100,000
$60,000
5
After-tax incremental
PV Factor
Cash Flows
-$100,000
$60,000
$60,000
$60,000
$60,000
$60,000
$60,000
Payback period =
Cumulative
Cash Flows
-$100,000
-$40,000
$20,000
1.7 years
13 - 59
Discounted Payback Example
Initial cost =
AT cash flow benefits =
Useful life(years) =
Cost of Capital =
Year
0
1
2
3
4
5
6
Cashflow
Initial cost
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
ATCF operating benefit
$100,000
$60,000
5
10.0%
After-tax incremental
PV Factor
Cash Flows
-$100,000
1
$60,000 0.90909091
$60,000 0.82644628
$60,000
0.7513148
$60,000 0.68301346
$60,000 0.62092132
$60,000 0.56447393
Payback period =
Present
Cumulative
Value of
ATCFs
Cash Flows
-$100,000
-$100,000
$54,545
-$45,455
$49,587
$4,132
$45,079
$49,211
$40,981
$90,192
$37,255
$127,447
$33,868
$161,316
1.9 years
13 - 60
Discounted Payback Graphed
NPV
$
Discounted Payback
Point
Years
13 - 61
Discounted Payback
• Overcomes the lack of consideration of the time
value of money…
• Graphing the cumulative PV of cash flows can
help us see the pattern of cash flows beyond
the payback point.
• If carried to the end of the project’s useful
life…will tell us the project’s NPV (if you are
using the firm’s WACC)
13 - 62
Profitability Index
• Uses exactly the same decision inputs as NPV
• simply expresses the relative profitability of the projects
incremental after-tax cashflow benefits as a ratio to the
project’s initial cost.
PI =
PV of incremental ATCF benefits
PV of initial cost of project
If PI>1, then we accept; because the PV of benefits exceeds the PV of costs.
13 - 63
Project Evaluation Techniques
Profitability Index (PI)
[ 13-3]
PV(cash inflows)
PI 
PV (cash outflows)
• PI is a ratio of the present value of benefits to costs.
• As a pure coefficient, as long as it exceeds 1.00 the
project will increase the value of the firm if accepted.
• A PI of more than 1.0 indicates that the project is
expected to earn a return greater than the required
return.
13 - 64
Independent and Interdependent Projects
Independent Projects
– Are projects that have no relationship with one another
– Accepting one project has no impact on the decision to
accept another project
Contingent Projects
– Are projects for which the acceptance of one requires the
acceptance of another, either before-hand or
simultaneously.
Mutually Exclusive Projects
– Are projects that are substitutes of one another
– Acceptance of one automatically means the other is
rejected.
13 - 65
Evaluating Mutually Exclusive Projects
with Unequal Lives
There are two approaches to adjust for unequal
lives among mutually exclusive projects:
1. Chain replication approach
•
A way to compare projects with unequal lives by finding a
time horizon into which all the project lives under
consideration divide equally, and then assuming each
project repeats until it reaches this horizon.
2. Equivalent Annual NPV (EANPV) approach
•
A way to compare projects by finding the NPV of the
individual projects, and then determining the amount of an
annual annuity that is economically equivalent to the NPV
generated by each project over its respective time horizon.
13 - 66
Evaluating Mutually Exclusive Projects with
Unequal Lives
The Chain Replication Approach
Consider two mutually exclusive projects A and B.
–
–
Useful life of A is 2 years.
Useful Life of B is 3 years.
A
B
O
1
2
O
O
1
2
1
2
O
1
2
1
2
3
3
O
You can now calculate NPV for both alternatives assuming
replication over a six year time horizon.
13 - 67
Project Evaluation Techniques
Equivalent Annual NPV (EANPV) Approach
[ 13-4]
PANPV 
Project NPV
1 

1
 (1  k) n 


k




13 - 68
Capital Rationing
• The corporate practice of limiting the amount of
funds dedicated to capital investments in any
one year.
• Is academically illogical.
– Why would a manager not invest in a project that will
offer a greater return than the cost of capital used to
finance it?
• In the long-run could threaten a firm’s
continuing existence through erosion of its
competitive position.
13 - 69
Capital Rationing
Practical Reasons for This Practice
• The firm may have owners who do not want to
raise additional external equity because it will
mean ownership dilution to them
• The firm may have so many great investment
projects that they exceed the firm’s short-term
managerial capacity to take advantage of them.
13 - 70
Capital Rationing
Ranking Projects
• Under capital rationing, the cost of capital is no
longer the appropriate opportunity cost
• IRR may have more validity because the firm may be
able to reinvest its cash flows at rates that are
higher than the cost of capital.
• The PI may be a useful starting point because it
ranks projects on PV per unit of investment.
• In the absence of capital rationing, NPV, IRR and PI
will select value-maximizing projects.
See Figure 13 – 4 on the following slide for Rothman’s unconstrained
Investment opportunity schedule.
13 - 71
Optimal Investment
Rothman’s Inc.’s Investment and Internal Fund Availability, 2006
13 - 4 FIGURE
OPTIMAL INVESTMENT
Rate of
Return
IOS
WACC
Internal Funds Available
$11,976
Million
$177,607
Million
13 - 72
Investment Opportunity Schedule (IOS)
• An Investment opportunity schedule is the prioritized list
of capital projects, ranked from highest to lowest.
• At the same time, the cumulative investment required is
listed.
Example:
Consider a firm that has six different capital investment proposals this
year. Each project has it’s own IRR, NPV, PI and capital cost.
(See the next slide)
13 - 73
Investment Opportunity Schedule (IOS)
Example:
Consider a firm that has six different capital investment proposals this year.
Each project has it’s own IRR, NPV, PI and capital cost. Each project has the
same risk as the firm as a whole.
Firm's Cost of Capital =
Capital
Project Initial Cost
A
$1,500,000
B
$3,000,000
C
$4,000,000
D
$70,000
E
$1,000,000
F
$960,000
Annual
Useful
ATCF
Benefits
Life
$290,000
7
$700,000
6
$1,040,000
6
$20,000
7
$290,000
5
$200,000
8
10.00%
NPV
-$88,159
$48,682
$529,471
$27,368
$99,328
$106,985
IRR
8.19%
10.55%
14.40%
21.08%
13.82%
12.99%
PI
0.94
1.02
1.13
1.39
1.10
1.11
13 - 74
Investment Opportunity Schedule (IOS)
Projects Ranked by NPV
Example:
In the absence of capital rationing the projects as ranked by NPV would be:
Firm's Cost of Capital =
Capital
Project Initial Cost
C
$4,000,000
F
$960,000
E
$1,000,000
B
$3,000,000
D
$70,000
$9,030,000
A
$1,500,000
Annual
Useful
ATCF
Benefits
Life
$1,040,000
6
$200,000
8
$290,000
5
$700,000
6
$20,000
7
$290,000
7
10.00%
NPV
$529,471
$106,985
$99,328
$48,682
$27,368
$811,835
-$88,159
IRR
14.40%
12.99%
13.82%
10.55%
21.08%
PI
1.13
1.11
1.10
1.02
1.39
8.19%
0.94
Project A would be unacceptable because of a forecast negative NPV
13 - 75
Investment Opportunity Schedule (IOS)
Projects Ranked by IRR
Example:
In the absence of capital rationing the projects as ranked by IRR would be:
Firm's Cost of Capital =
Capital
Project Initial Cost
D
$70,000
C
$4,000,000
E
$1,000,000
F
$960,000
B
$3,000,000
$9,030,000
A
$1,500,000
Annual
Useful
ATCF
Benefits
Life
$20,000
7
$1,040,000
6
$290,000
5
$200,000
8
$700,000
6
$290,000
7
10.00%
NPV
$27,368
$529,471
$99,328
$106,985
$48,682
$811,835
IRR
21.08%
14.40%
13.82%
12.99%
10.55%
-$88,159 8.19%
PI
1.39
1.13
1.10
1.11
1.02
0.94
Project A would be unacceptable because forecast IRR < WACC.
13 - 76
Investment Opportunity Schedule (IOS)
Projects Ranked by PI
Example:
In the absence of capital rationing the projects as ranked by PI would be:
Firm's Cost of Capital =
Capital
Project Initial Cost
D
$70,000
C
$4,000,000
F
$960,000
E
$1,000,000
B
$3,000,000
$9,030,000
A
$1,500,000
Annual
Useful
ATCF
Benefits
Life
$20,000
7
$1,040,000
6
$200,000
8
$290,000
5
$700,000
6
$290,000
7
10.00%
NPV
$27,368
$529,471
$106,985
$99,328
$48,682
$811,835
IRR
21.08%
14.40%
12.99%
13.82%
10.55%
-$88,159 8.19%
PI
1.39
1.13
1.11
1.10
1.02
0.94
Project proposal A would be unacceptable because the forecast PI is less than 1.0.
13 - 77
Ranking of Projects
In the Absence of Capital Rationing
Project
1
2
3
4
5
NPV
C
F
E
B
D
IRR
D
C
E
F
B
PI
D
C
F
E
B
Capital Budget
Total NPV
$9,369,000
$679,803
$9,369,000
$679,803
$9,369,000
$679,803
Clearly, in the absence of capital rationing, all three methods choose value
maximizing projects and reject value-destroying projects.
13 - 78
Investment Opportunity Schedule (IOS)
Projects Selected by NPV under Capital Rationing Limit of $6 million
Example:
Under capital rationing the projects selected by NPV would be:
Firm's Cost of Capital =
Capital
Project Initial Cost
C
$4,000,000
F
$960,000
E
$1,000,000
$5,960,000
B
$3,000,000
D
$70,000
A
$1,500,000
Annual
Useful
ATCF
Benefits
Life
$1,040,000
6
$200,000
8
$290,000
5
10.00%
$700,000
$20,000
6
7
NPV
$529,471
$106,985
$99,328
$735,785
$48,682
$27,368
IRR
14.40%
12.99%
13.82%
PI
1.13
1.11
1.10
10.55%
21.08%
1.02
1.39
$290,000
7
-$88,159 8.19%
0.94
13 - 79
Investment Opportunity Schedule (IOS)
Projects Selected by IRR under Capital Rationing Limit of $6 million
Example:
Under capital rationing the projects selected by IRR would be:
Firm's Cost of Capital =
Capital
Project Initial Cost
D
$70,000
C
$4,000,000
E
$1,000,000
$5,070,000
F
$960,000
B
$3,000,000
A
$1,500,000
Annual
Useful
ATCF
Benefits
Life
$20,000
7
$1,040,000
6
$290,000
5
10.00%
$200,000
$700,000
8
6
NPV
$27,368
$529,471
$99,328
$656,168
$106,985
$48,682
$290,000
7
-$88,159 8.19%
IRR
21.08%
14.40%
13.82%
PI
1.39
1.13
1.10
12.99%
10.55%
1.11
1.02
0.94
13 - 80
Investment Opportunity Schedule (IOS)
Projects Selected by PI under Capital Rationing Limit of $6 million
Example:
Under capital rationing the projects selected by PI would be:
Firm's Cost of Capital =
Capital
Project Initial Cost
D
$70,000
C
$4,000,000
$4,070,000
F
$960,000
E
$1,000,000
B
$3,000,000
A
$1,500,000
Annual
Useful
ATCF
Benefits
Life
$20,000
7
$1,040,000
6
$200,000
$290,000
$700,000
8
5
6
$290,000
7
10.00%
NPV
$27,368
$529,471
$556,840
$106,985
$99,328
$48,682
IRR
21.08%
14.40%
PI
1.39
1.13
12.99%
13.82%
10.55%
1.11
1.10
1.02
-$88,159 8.19%
0.94
13 - 81
Ranking of Projects
Assuming a Limit on Capital Expenditures to $6,000,000
Project
1
2
3
NPV
C
F
E
IRR
D
C
E
PI
D
C
Capital Budget
Total NPV
$5,960,000
$735,785
$5,070,000
$656,168
$4,070,000
$556,840
Capital rationing is an artificial limit on capex.
Only NPV ranking will ensure maximization of shareholder wealth
under these constrained conditions.
13 - 82
International Considerations
• Capex decisions involving direct foreign
investment must take into account additional
factors:
–
–
–
–
–
Political risk
Potential legal and regulatory issues
Adjust for foreign exchange risk
Adjust for foreign taxation
How can the project be financed if local capital
markets are poorly developed?
13 - 83
International Investment
• Export Development Canada (EDC) is a federal
crown corporation that helps Canadian firms export
and make foreign direct investment decisions (FDI)
• EDC provides insurance products to help mitigate
some of the risks of FDI
• FDI outside Canada is a growing phenomenon in
Canada as Canadian companies increasingly are
seeking international investment opportunities.
• EDC is encouraging Canadian companies to look
beyond the U.S. as FDI targets.
13 - 84
Summary and Conclusions
In this chapter you have learned:
– How capital decisions are made in companies
– About capital expenditure evaluation tools including
NPV, IRR, profitability index, payback period and
discounted payback period
– Why NPV is the preferred evaluation approach
– How to adjust analysis for conditions of capital
rationing, risk differences across corporate divisions,
and effects of foreign direct investment.
13 - 85