Chapte
12
Slides Developed by:
Terry Fegarty
Seneca College
Capital Budgeting
Chapter 12 – Outline (1)
• Capital Budgeting
• Characteristics of Business Projects
• Capital Budgeting Techniques
 Capital Budgeting Techniques—Payback
 Capital Budgeting Techniques—Net Present Value
(NPV)
 Capital Budgeting Techniques—Internal Rate of
Return (IRR)
 NPV Profile
 Conflicting Results Between IRR and NPV
 NPV and IRR Solutions Using Spreadsheets
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Chapter 12 – Outline (2)




Projects with a Single Outflow and Regular Inflows
Profitability Index (PI)
Comparing Projects with Unequal Lives
Capital Rationing
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Capital Budgeting
• Capital budgeting involves planning and
justifying large expenditures on longterm projects
 Projects can be classified as:
• Replacements
• Expansions
• New business ventures
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Characteristics of Business
Projects
• Project Types and Risk
 Capital projects have increasing risk according to
whether they are replacements, expansions or new
ventures
• Stand-Alone and Mutually Exclusive Projects
 A stand-alone project has no competing
alternatives
• The project is judged on its own viability
 Mutually exclusive projects—when selecting one
project excludes selecting the other
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Characteristics of Business
Projects
• Project Cash Flows
 First and usually most difficult step in capital
budgeting is reducing projects to series of
cash flows
 Business projects involve early cash outflows
and later inflows
•Initial outlay is required to get started
•Annual net inflows, after tax, generated
by project
•Terminal value from sale or salvage of
project
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Characteristics of Business
Projects
• Cost of Capital
 Firm’s cost of capital is average rate it pays
its investors for use of their money
•In general, firm can raise money from two
sources: debt and equity
•If potential project is expected to generate
return greater than cost of money to
finance it, it is a good investment
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Capital Budgeting Techniques
• Four techniques for determining a
project’s financial viability:
 Payback—how many years to recover
project’s initial cost
 Net Present Value—how much the present
value of project’s inflows exceeds present
value of its outflows
 Internal Rate of Return—return on
investment in the project
 Profitability Index—ratio of project’s
inflows vs. outflows—in present value terms)
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Capital Budgeting Techniques—
Payback
• Payback period—time to recover early cash
outflows
 Shorter paybacks are better
• Payback Decision Rules
 Stand-alone projects
• If payback period < (>) policy maximum accept (reject)
 Mutually Exclusive Projects
• If PaybackA < PaybackB  choose Project A
• Weaknesses of the Payback Method
 Ignores time value of money
 Ignores cash flows after the payback period
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Capital Budgeting Techniques—
Payback—Example
• Consider the following cash flows
Year
Example
Cash flow (Cn)
0
1
2
3
4
($200,000)
$60,000
$60,000
$60,000
$60,000
• Payback period is easy to see by the cumulative cash flows
Year
0
1
2
3
4
Cash flow (Cn)
($200,000)
$60,000
$60,000
$60,000
$60,000
Cumulative
cash flows
($200,000)
($140,000)
($80,000) ($20,000)
$40,000
Payback period occurs at 3.33 years
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Capital Budgeting
Techniques—Payback
Example 12.1:
Q: Use the payback period technique to choose between mutually
exclusive projects A and B.
Example
Example
Project A
Project B
C0
($1,200)
($1,200)
C1
400
400
C2
400
400
C3
400
350
C4
200
800
C5
200
800
A: Project A’s payback is 3 years as its initial outlay is fully
recovered in that time. Project B doesn’t fully recover until
sometime in the 4th year. Thus, according to the payback
method, Project A is better than B.
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Capital Budgeting Techniques—
Payback
• Why Use the Payback Method?
 Quick and easy to apply
 Serves as rough screening device
• The Present Value Payback Method
 Involves finding present value of project’s
cash flows, then calculating project’s payback
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Capital Budgeting Techniques—Net
Present Value (NPV)
• NPV—sum of present values of project’s
cash flows, discounted at cost of capital
Cn
C1
C2
NPV  C0 

 ... 
1
2
(1  k ) (1  k )
(1  k ) n
PVoutflows
PVinflows
If PVinflows > PVoutflows, NPV > 0
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Capital Budgeting Techniques—Net
Present Value (NPV)
• NPV and Shareholder Wealth
 Project’s NPV is net effect that undertaking
project is expected to have on firm’s value
• A project with NPV > (<) 0 should increase
(decrease) firm value
 Since firm desires to maximize shareholder
wealth, it should select capital spending
program with highest total NPV
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Capital Budgeting Techniques—Net
Present Value (NPV)
• NPV Decision Rules
 Stand-alone Projects
• NPV > 0  accept
• NPV < 0  reject
 Mutually Exclusive Projects
• NPVA > NPVB  choose Project A over B
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Capital Budgeting
Techniques—Net Present Value
Example 12.2:
Example
Q: Project Alpha has the following cash flows. If the firm considering
Alpha has a cost of capital of 12%, should the project be undertaken?
C0
($5,000)
C1
$1,000
C2
$2,000
C3
$3,000
A: The NPV is found by summing the present value of the cash flows when
discounted at the firm’s cost of capital.
NPV Alpha
 -5,000 
1,000
1.12 
1

2,000
3,000
1.12 
1.12 

2
3
 -5,000  892.90  1,594.40  2,135.40
 -5,000  4,622.70
Since Alpha’s
NPV<0, it
should not be
undertaken
 ($377.30)
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Capital Budgeting
Techniques—Net Present Value
Example 12.2:
0
-$5,000
1
$1,000
2
3
$2,000
$3,000
Example
$892.90
$1,594.40
$2,135.40
-$377.30
Solution is calculated by discount each of the
cash flows back to time period zero using a
discount rate of 12%.
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Capital Budgeting Techniques—
Internal Rate of Return (IRR)
• Project’s IRR is return it generates on
investment of its cash outflows
 For example, if a project has the following cash flows
0
1
2
3
-5,000
1,000
2,000
3,000
The “price” of receiving
the inflows
• The IRR is the interest rate at which the present
value of the three inflows just equals the $5,000
outflow
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Capital Budgeting Techniques—
Internal Rate of Return (IRR)
• Defining IRR Through the NPV Equation
 The IRR is the interest rate that makes a
project’s NPV zero
—
IRR :
C0
PV outflows

C1
1IRR 
1

C2
1IRR 
2


Cn
1IRR 
n
PV inflows
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Techniques—Internal Rate of
Return
• IRR Decision Rules
 Stand-alone Projects
• If IRR > cost of capital (or k)  accept
• If IRR < cost of capital (or k)  reject
 Mutually Exclusive Projects
• IRRA > IRRB  choose Project A over Project B
• If NPV > 0, IRR > k
 If NPV < 0, IRR < k
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Techniques—Internal Rate of
Return
• Calculating IRRs
 Finding IRRs usually requires an iterative,
trial-and-error technique
• Guess at project’s IRR
• Calculate project’s NPV using this interest rate
• If NPV is zero, the guessed interest rate is the project’s
IRR
• If NPV > (<) 0, try a new, higher (lower) interest rate
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Example 12.3: Capital Budgeting
Techniques—Internal Rate of Return
Q: Find the IRR for the following series of cash flows:
C0
C1
($5,000)
C2
$1,000
C3
$2,000
$3,000
Example
If the firm’s cost of capital is 8%, is the project a good idea? What if the cost of capital
is 10%?
A: We’ll start by guessing an IRR of 12%. We’ll calculate the project’s NPV at this
interest rate.
NPV
 -5,000 
1,000
1.12 
1

2,000
1.12 
2

3,000
1.12 
3
 -5,000  892.90  1,594.40  2,135.40
 -5,000  4,622.70
 ($377.30)
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Since NPV<0,
the project’s IRR
must be
< 12%.
22
Example 12.3: Capital Budgeting
Techniques—Internal Rate of Return
A: We’ll try a different, lower interest rate, say 10%. At 10%, the project’s NPV is
Example
($184). Since the NPV is still less than zero, we need to try a still lower
interest rate, say 9%. The following table lists the project’s NPV at different
interest rates.
Interest
Rate Guess
Calculated
NPV
12%
($377)
10
($184)
9
($83)
8
$22
7
$130
Since NPV becomes positive
somewhere between 8% and
9%, the project’s IRR must be
between 8% and 9%. If the
firm’s cost of capital is 8%, the
project is marginal. If the
firm’s cost of capital is 9%, the
project is not a good idea.
The exact IRR can be calculated using a financial calculator
or spreadsheet
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NPV Profile
• Project’s NPV Profile—graph of its NPV
vs. the cost of capital
• It crosses the horizontal axis at the IRR
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Figure 12.1:
NPV Profile
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Techniques—Internal Rate of
Return (IRR)
• Technical Problems with IRR
 Multiple Solutions
• If some future cash flows are negative, project
can have more than one IRR solution
• Normal pattern involves negative initial outlay and
positive future cash flows
• Rarely presents practical difficulties
 The Reinvestment Assumption
• IRR method assumes cash inflows will be
reinvested at project’s IRR
• For projects with extremely high IRRs, this is unlikely
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Conflicting Results Between IRR
and NPV
• NPV and IRR do not always provide the same decision
for a project’s acceptance
 Occasionally give conflicting results in mutually exclusive
decisions
• If two projects’ NPV profiles cross:
 one project is accepted below a certain cost of capital
 the other project is accepted above that cost of capital
 The NPV profiles have to cross in the first quadrant of the
graph, where interest rates are practical
• NPV method is the preferred over IRR method because
the reinvestment interest rate assumption is more
practical
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Projects for Which IRR and
NPV Can Give Different Solutions
Figure 12.2:
At a cost of capital
of k1, Project A is
better than Project
B, while at k2 the
opposite is true.
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NPV and IRR Solutions Using
Spreadsheets
• NPV function in Microsoft® Excel®
=Cash Flow0 + NPV(interest rate, Cash
Flow1:Cash Flown)
 Every cash flow within the parentheses is
discounted at the interest rate
• IRR function in Excel®
=IRR (interest rate, Cash Flow0:Cash Flown)
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Spreadsheet Solution
Example
Example 12.3:
Formula in B6:
=B2 + NPV(C4,C2:E2)
Formula in B8:
=IRR(B2:E2,C4)
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Projects with a Single Outflow and
Regular Inflows
• Many projects have one outflow at time 0 and
inflows representing an annuity stream
• For example, consider the following cash flows
C0
($5,000)
C1
$2,000
C2
$2,000
C3
$2,000
 In this case, the NPV formula can be
rewritten as
• NPV = -C0 + C[PVFAk, n]
 The IRR formula can be rewritten as
• 0 = C0 + C[PVFAIRR, n]
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Projects with a Single
Outflow and Regular Inflows
Example 12.5:
Q: Find the NPV and IRR for the following series of cash flows:
C0
Example
($5,000)
C1
$2,000
C2
$2,000
C3
$2,000
A: Substituting the cash flows into the NPV equation with annuity inflows we
have:
NPV = -$5,000 + $2,000[PVFA12, 3]
NPV = -$5,000 + $2,000[2.4018] = -$196.40
Substituting the cash flows into the IRR equation with annuity inflows we
have:
0 = -$5,000 + $2,000[PVFAIRR, 3]
Solving for the factor gives us:
$5,000  $2,000 = [PVFAIRR, 3]
The interest factor is 2.5 which equates to an interest rate between 9% and
10%.
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Spreadsheet Solution
Example
Example 12.5:
Formula in B6:
=B2 + NPV(C4,C2:E2)
Formula in B8:
=IRR(B2:E2,C4)
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Profitability Index (PI)
• Profitability Index—ratio of the present
value of a project’s inflows to the present
value of a project’s outflows
 a variation on the NPV method
• Projects are acceptable if PI>1
 Larger PIs are preferred
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Profitability Index (PI)
• Also known as the benefit/cost ratio
 Positive future cash flows are the benefit
 Negative initial outlay is the cost
C1
PI 
1+k 
1

C2
1+k 
2


Cn
1+k 
n
C0
or
present value of inflows
PI 
present value of outflows
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Profitability Index (PI)
• PI Decision Rules
 Stand-alone Projects
• If PI > 1.0  accept
• If PI < 1.0  reject
 Mutually Exclusive Projects
• PIA > PIB choose Project A over Project B
• Comparison with NPV
 With mutually exclusive projects, two
methods may not lead to same choice
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Comparing Projects with Unequal
Lives
• If significant difference exists between
lives of mutually exclusive projects,
direct comparison of the projects is
meaningless
• Problem arises due to the NPV method
 Longer lived projects almost always have
higher NPVs
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Comparing Projects
with Unequal Lives
Example
Figure 12.3:
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Comparing Projects with Unequal
Lives—Example
Q: Which of the two following mutually exclusive projects should a
firm purchase?
C0
C1
C2
C3
C4
C5
C6
Example
Short-Lived Project (NPV = $432.82 at an 8% discount rate; IRR = 23.4%)
($1,500)
$750
$750
$750
-
-
-
Long-Lived Project (NPV = $867.16 at an 8% discount rate; IRR = 18.3%)
($2,600)
$750
$750
$750
$750
$750
$750
A: The IRR method favours the Short-Lived Project while the
NPV method favours the Long-Lived Project. We’ll correct for
the unequal life problem by using the EAA Method.
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Comparing Projects with Unequal
Lives
• Equivalent Annual Annuity (EAA) Method
 Replaces each project with an equivalent perpetuity
that equates to the project’s original NPV
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Comparing Projects with Unequal
Lives—Example
Example
A: The EAA Method equates each project’s original NPV to an
equivalent annual annuity.
For the Short-Lived Project the EAA is $167.95 (the equivalent
of receiving $432.82 spread out over 3 years at 8%).
The Long-Lived Project has an EAA of $187.58 (the equivalent
of receiving $867.16 spread out over 6 years at 8%).
Since the Long-Lived Project has the higher EAA, it should be
chosen.
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Comparing Projects
with Unequal Lives
Example
Figure 12.4:
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Capital Rationing
• Capital rationing— exists when there is limit
(maximum) to amount of funds available for new
projects
• Thus, there may be some projects with +NPVs, IRRs >
discount rate or PIs >1 that will be rejected, because
not enough money available
• How do you choose the set of projects in which to
invest?
 Use complex mathematical process called constrained
maximization
 Use intuition and judgment
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Figure 12.5:
Capital Rationing
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