Capital Budgeting
Chapter 9
© 2003 South-Western/Thomson Learning
Introduction

Capital budgeting involves planning and
justifying large expenditures on long-term
projects

Projects can be classified as:
• Replacement
• New business ventures
2
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 are involved when
selecting one project excludes selecting the other
3
Characteristics of Business
Projects

Project Cash Flow


The first and usually most difficult step in capital budgeting is
reducing projects to a series of cash flows
Business projects involve early cash outflows and later inflows
• The initial outlay is required to get started

The Cost of Capital

A firm’s cost of capital is the average rate it pays its investors
for the use of their money
• In general a firm can raise money from two sources: debt and
equity
• If a potential project is expected to generate a return greater than
the cost of the money to finance it, it is a good investment
4
Capital Budgeting Techniques

There are four basic techniques for determining
a project’s financial viability:




Payback (determines how many years it takes to
recover a project’s initial cost)
Net Present Value (determines by how much the
present value of the project’s inflows exceeds the
present value of its outflows)
Internal Rate of Return (determines the rate of return
the project earns [internally])
Profitability Index (provides a ratio of a project’s
inflows vs. outflows--in present value terms)
5
Capital Budgeting
Techniques—Payback

The payback period is the time it takes to
recover early cash outflows


Shorter paybacks are better
Payback Decision Rules

Stand-alone projects
• If the payback period < (>) policy maximum accept (reject)

Mutually Exclusive Projects
• If PaybackA < PaybackB  choose Project A

Weaknesses of the Payback Method


Ignores the time value of money
Ignores the cash flows after the payback period
6
Capital Budgeting
Techniques—Payback

Consider the following cash flows
Year
Cash flow (Ci)

0
1
2
3
4
($200,000)
$60,000
$60,000
$60,000
$60,000
Payback period is easily visualized by the cumulative cash flows
Year
0
1
2
3
4
Cash flow (Ci)
($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.
7
Capital Budgeting Techniques—
Payback—Example
Q: Use the payback period technique to choose between mutually exclusive
projects A and B.
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.
8
Capital Budgeting
Techniques—Payback

Why Use the Payback Method?
It’s quick and easy to apply
 Serves as a rough screening device


The Present Value Payback Method

Involves finding the present value of the
project’s cash flows then calculating the
project’s payback
9
Capital Budgeting Techniques—Net
Present Value (NPV)

NPV is the sum of the present values of a
project’s cash flows at the cost of capital
NPV

C0
PV outflows

C1
1+k 
1

C2
1+k 
2


Cn
1+k 
n
PV inflows
 If PVinflows > PVoutflows, NPV > 0
10
Capital Budgeting Techniques—Net
Present Value (NPV)

NPV and Shareholder Wealth

A project’s NPV is the net effect that
undertaking a project is expected to have on
the firm’s value
• A project with an NPV > (<) 0 should increase
(decrease) firm value

Since the firm desires to maximize
shareholder wealth, it should select the
capital spending program with the highest
NPV
11
Capital Budgeting Techniques—Net
Present Value (NPV)

Decision Rules

Stand-alone Projects
• NPV > 0  accept
• NPV < 0  reject

Mutually Exclusive Projects
• NPVA > NPVB  choose Project A over B
12
Capital Budgeting Techniques—Net
Present Value (NPV) Example
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
 ($377.30)
Since Alpha’s
NPV<0, it
should not be
undertaken.
13
Techniques—Internal Rate of
Return (IRR)

A project’s IRR is the return it generates on the
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
14
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
15
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
16
Techniques—Internal Rate of
Return (IRR)

Calculating IRRs

Finding IRRs usually requires an iterative,
trial-and-error technique
• Guess at the project’s IRR
• Calculate the 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
17
Techniques—Internal Rate of
Return (IRR)—Example
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
3,000
1.12
1.12 

2
3
 -5,000  892.90  1,594.40  2,135.40
 -5,000  4,622.70
 ($377.30)
Since NPV<0,
the project’s
IRR must be <
12%.
18
Techniques—Internal Rate of
Return (IRR)—Example
Example
We’ll try a different, lower interest rate, say 10%. At 10%, the project’s
NPV is ($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
10%, the project is not a
good idea.
The exact IRR can be calculated using a financial calculator. The financial
calculator uses the iterative process just demonstrated; however it is capable of
guessing and recalculating much more quickly.
19
Techniques—Internal Rate of
Return (IRR)

Technical Problems with IRR

Multiple Solutions
• Unusual projects can have more than one IRR
• Rarely presents practical difficulties
• The number of positive IRRs to a project depends on the
number of sign reversals to the project’s cash flows
• Normal pattern involves only one sign change

The Reinvestment Assumption
• IRR method implicitly assumes cash inflows will be
reinvested at the project’s IRR
• For projects with extremely high IRRs, this is unlikely
20
NPV Profile
A project’s NPV profile is a graph of its
NPV vs. the cost of capital
 It crosses the horizontal axis at the IRR

21
Figure 9.1: NPV Profile
22
Comparing IRR and NPV

NPV and IRR do not always provide the same decision
for a project’s acceptance


If two projects’ NPV profiles cross it means below a
certain cost of capital one project is acceptable over the
other and above that cost of capital the other project is
acceptable over the first


Occasionally give conflicting results in mutually exclusive
decisions
The NPV profiles have to cross in the first quadrant of the
graph, where interest rates are of practical interest
The NPV method is the preferred decision-making
criterion because the reinvestment interest rate
assumption is more practical
23
Figure 9.2: Projects for Which IRR
and NPV Can Give Different Solutions
At a cost of capital of
k1, Project A is better
than Project B, while at
k2 the opposite is true.
24
NPV and IRR Solutions Using
Financial Calculators

Modern financial calculators and
spreadsheets remove the drudgery from
calculating NPV and IRR


Especially IRR
The process involves inputting a project’s
cash flows and then having the
calculators calculate NPV and IRR

Note that a project’s interest rate is needed
to calculate NPV
25
Spreadsheets

NPV function in Microsoft Excel

=NPV(interest rate, Cash Flow1:Cash Flown)
+ Cash Flow0
• Every cash flow within the parentheses is
discounted at the interest rate

IRR function in Microsoft Excel

=IRR(Cash Flow0:Cash Flown)
26
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]
27
Projects with a Single Outflow
and Regular Inflows—Example
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%.
28
Profitability Index (PI)
The profitability index is a variation on the
NPV method
 It is a ratio of the present value of a
project’s inflows to the present value of a
project’s outflows
 Projects are acceptable if PI>1


Larger PIs are preferred
29
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
30
Profitability Index (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 the two
methods may not lead to the same choices
31
Comparing Projects with
Unequal Lives
If a significant difference exists between
mutually exclusive projects’ lives, a direct
comparison of the projects is
meaningless
 The problem arises due to the NPV
method


Longer lived projects almost always have
higher NPVs
32
Comparing Projects with
Unequal Lives

Two solutions exist

Replacement Chain Method
• Extends projects until a common time horizon is reached
• For example, if mutually exclusive Projects A (with a life of 3
years) and B (with a life of 5 years) are being compared, both
projects will be replicated so that they each last 15 years

Equivalent Annual Annuity (EAA) Method
• Replaces each project with an equivalent perpetuity that
equates to the project’s original NPV
33
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 argues for undertaking the Short-Lived Project
while the NPV method argues for the Long-Lived Project. We’ll
correct for the unequal life problem by using both the Replacement
Chain Method and the EAA Method. Both methods will lead to the
same decision.
34
Comparing Projects with
Unequal Lives—Example
Example
The Replacement Chain Method involves replicating all projects (if needed) until
each project being evaluated has a common time horizon. If the Short-Lived
Project is replicated for a total of two times, it will have the same life (6 years) as
the Long-Lived Project. This involves buying the Short-Lived Project again in
year 3 and receiving the same stream of cash flows as originally expected for
the following three years. This stream of cash flows is represented in the table
below.
C0
C1
C2
C3
C4
C5
C6
Short-Lived Project replicated for a total of two times
($1,500)
$750
$750
$750
-
-
-
($1,500)
$750
$750
$750
($750)
Thus, buying the Long-Lived Project is a
better decision than buying the Short-Lived
Project twice.
The NPV of this
stream of cash
flows is $776.41.
35
Example
Comparing Projects with
Unequal Lives—Example
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%); while
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 LongLived Project has the higher EAA, it should be chosen. This is the
same decision reached by the Replacement Chain Method.
36
Capital Rationing



Capital rationing exists when there is a limit (cap) to the
amount of funds available for investment in new
projects
Thus, there may be some projects with +NPVs, IRRs >
discount rate or PIs >1 that will be rejected, simply
because there isn’t enough money available
How do you choose the set of projects in which to
invest?

Use complex mathematical process called constrained
maximization
37
Figure 9.6: Capital Rationing
38