1
Chapter 11
Capital Budgeting and Net Present Value
Should we
build this
plant?
Ch 13: Capital Budgeting Techniques
 Payback period rule
 Discounted Cash Flow Approaches
 Discounted payback period
 Net present value (NPV)
 Internal rate of return (IRR)
• Modified internal rate of return (MIRR)
 Profitability index (PI)
 Why is the NPV the best?
 NPV vs. Payback period
 NPV vs. IRR
• Mutually exclusive projects
• Multiple IRRs
 NPV vs. PI
 The practice of capital budgeting
2
3
What is capital budgeting?
 Capital budgeting: Total process of planning,
evaluating, and selecting on capital expenditures for
long-lived assets. Usually requires a large amount of
capital expenditures. It could be anything that requires
lots of money.
 “In February 2000, Corning, Inc., announced plans to
spend $170 million to expand by 50 percent its
manufacturing capacity of optical fiber, a crucial
component of today’s high-speed communications
networks.”
 To do or not to do? That is the question!
 Is there any financial method that Corning can use to
make this investment decision?
4
Capital Budgeting: Steps
1. Estimate CFs (inflows & outflows).
2. Assess riskiness of CFs.
3. Determine r = WACC for project.
4. Find NPV, IRR and/or others.
5. Accept or reject project based on the
results from sep 4.
5
Example 1
 Coca Cola and Procter & Gamble just announced that
they will consider a joint venture (JV) for new beverage
and snack business. The new idea is to form a limitedliability company, with 50-50 ownership, that will
develop and market juice-based drinks and snacks.
Coca-Cola will invest $2 billions and the investments
will be deprecated on a straight-line basis with zero
salvage value for four-year investment period. You are
a CFO of Coca Cola and just created a pro forma
income statement for this project. Previously, Coca
Cola hired the consulting company to study market
research for new beverage and snack business, and paid
$300,000. The tax rate is 30 percent. The similar
project with a similar risk level yields 10%. Your job is
to evaluate this project. Is this project acceptable?
6
Coca Cola Pro Forma Income Statement
Year
Sales
Cost of Goods
Sold
Gross Profit
Operating
Expenses
2002
$2,000
1,000
2003
$2,000
1,000
2004
$2,000
1,000
2005
$2,000
1,000
1,000
50
1,000
50
1,000
50
1,000
50
Depreciation
EBT
Taxes (30%)
500
450
135
500
450
135
500
450
135
500
450
135
Net Income
315
315
315
315
What is a pro forma income statement?
7
Q1. What is the operating cash flow
(OCF)?
 Operating Cash Flow (OCF)
= EBIT (1 – T) + Depreciation
=
- Why operating cash flow, instead of accounting
income?
Q2. Is the consulting fee of $300,000
relevant in capital budgeting decision?
What is the sunk cost?
8
9
Time Line for the Joint Venture
0
1
r = 10%
-2,000
815
2
3
4
815
815
815
10
Q3. Is this project acceptable?
 We will use several capital budgeting techniques to
evaluate new projects.
 Payback period
 Discounted cash flow (DCF) approaches
• Discounted payback period
• Net Present Value (NPV) - most important
• Internal rate of return (IRR) – most popular
Modified Internal Rate of Return
• Profitability index (PI)
11
Q3. Is this project acceptable?
Payback period
Payback Period: Length of time until initial
investment is recovered, or “How long will it
take to recover initial investments?”
Computation: Subtract the future cash flows
from the initial cost until the initial
investment has been recovered
Decision Rule: Accept if the payback period
is less than some preset limit
Payback period of JV
=
12
Payback Period Computation
2.454
0
1
CFt
-2,000
Cumulative -2,000
Payback
= 2
2
815
-1,185
+
815
-370 0
3
815
370/815 = 2.454 years
4
815
13
Q3. Is this project acceptable?
Discounted payback period
Discounted Payback Period: Use discounted
CFs rather than raw CFs.
Computation: Subtract the future discounted
cash flows from the initial cost until the initial
investment has been recovered
Decision Rule: Accept if the discounted
payback period is less than some preset limit
Discounted payback period of JV
=
14
Discounted Payback Period
0
10%
1
2
3
4
815
815
CFt
-2000
815
815
PVCFt
-2000
741
674
612
Cumulative -2000
-1259
-586
27
Discounted
=
payback
+ 586 / 612 = 2.96 yrs
2
Still this method requires arbitrary cut-off point and
ignores cash flows occurring later than cut-off point
15
Q3. Is this project acceptable?
Net present value (NPV)
 Net Present Value (NPV)
= PVs of inflows – PVs of outflows, or
= PVs of inflows – Initial Investment (usually occurs in year 0)
=
 Decision criteria: If the NPV is positive, accept the project
 A positive NPV means that the project is expected to add
value to the firm and will therefore increase the wealth of the
owners.
 Since our goal is to increase owner’s wealth, NPV is a direct
measure of how well this project will meet our goal.
 Should we accept or reject new joint venture proposal?
16
NPV (continued)
n
CFt
NPV  
.
t
t  0 1  r 
Cost often is CF0 and is negative.
n
CFt
NPV  
t 1 1  r 
t
 CF0 .
17
What’s JV’s NPV?
Project JV:
0
1
2
3
4
815
815
815
815
r =10%
-2,000
741
674
612
557
$584 = NPV
Since NPV > 0, Accept!
18
NPV (continued)
Calculator Solution
Enter in CFj for JV:
-2,000
CF0
815
CF1
815
CF2
815
CF3
815
CF4
10
I/YR
NPV
= 583.44
19
Q3. Is this project acceptable?
Internal rate of return (IRR)
Definition: IRR is the return that makes the
NPV = 0
Decision Rule: Accept the project if the IRR is
greater than the required return
Internal Rate of Return (IRR) of JV =
Should we accept or reject new joint venture
proposal?
20
Internal Rate of Return (IRR)
0
1
2
3
CF0
Cost
CF1
CF2
Inflows
CF3
IRR is the discount rate that forces
PV inflows = cost. This is the same
as forcing NPV = 0.
21
NPV: Enter r, solve for NPV.
n
CFt
 1  r 
t 0
t
 NPV .
IRR: Enter NPV = 0, solve for IRR.
n
CFt

t  0.
t  0 1  IRR
22
Coca Cola Example: IRR
Sensitivity Analysis: NPV
$1,400.00
$1,200.00
NPV >0
ACCEPT!
$1,000.00
$800.00
IRR = 22.87%
NPV
$600.00
$400.00
NPV < 0
REJECT!
$200.00
$0.00
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
($200.00)
($400.00)
($600.00)
Discount Rate (%)
23
Computing IRR For The Project
If you do not have a financial calculator,
then this becomes a trial and error process
Calculator
 Enter the cash flows as you did with NPV
 Press IRR
 If IRR > 10%, required return, then
accept the project.
Should we accept or reject the new JV?
24
Rationale for the IRR Method
If IRR > WACC, then the project’s rate of
return is greater than its cost-- some
return is left over to boost stockholders’
returns.
Example: WACC = 10%, IRR = 22.87%.
Profitable.
25
Q3. Is this project acceptable?
Profitability Index (PI)
Definition:
 PV of future cash flows @ R (discount rate)
divided by Initial Investment
 “Bang for the buck”
 Benefit-cost ratio
 Decision rule: If PI > 1 then accept project
 PI of JV =
 Should we accept or reject the JV?
26
Profitability Index
Measures the benefit per unit cost, based on
the time value of money
A profitability index of 1.1 implies that for
every $1 of investment, we create an
additional $0.10 in value
This measure can be very useful in
situations where we have limited capital
27
Q4: What are the relationships
among NPV, IRR, and PI?
 The discount rate is 10%. Are the discount rate,
opportunity cost, and cost of capital the same things?
 In this case, the IRR is 22.87%. When you use
22.87% as new discount rate, what is the new NPV?
 What if the discount rate is 20%? What is the new
NPV? What if the discount rate is 24%? Does the
higher discount rate means the lower NPV? If so,
why ?
 When NPV > 0, IRR > r? When NPV > 0, PI >1?
 In general, if NPV > 0, then IRR > R and PI > 1.
So far,
We learned payback period, discounted
payback period, NPV, IRR and PI to
evaluate new projects.
 Now, we will be making a case that the
NPV is the best, and
 We will see why it is the best.
 Also, we will see some cases that NPV
and other criteria lead us to conflicting
results.

28
29
Example 2:
NPV vs. Payback period
Discount rate, r = 10%
0
1
2
3
4
Payback NPV
A
-100 20
30
50
60
3 yr
21.52
B
-100 50
30
20
60
3 yr
26.26
C
-100 50
30
20
6,000 3 yr
?
Advantages and Disadvantages of
Payback
Advantages
 Easy to understand
 Provides an
indication of a
project’s liquidity.
 Disadvantages
 Ignores the time value of
money
 Requires an arbitrary cutoff
point
 Ignores cash flows beyond
the cutoff date
 Biased against long-term
projects, such as research
and development, and new
projects
30
31
Special cases: What is the
difference between independent
and mutually exclusive projects?
Projects are:
independent, if the cash flows of one are
unaffected by the acceptance of the other.
mutually exclusive, if the cash flows of
one can be adversely impacted by the
acceptance of the other.
32
An Example of Mutually Exclusive
Projects
BRIDGE vs. BOAT to get
products across a river.
33
Example 3: NPV vs. IRR
(Mutually Exclusive Projects)
 Option #1: You give me $1 now and I’ll give you
$1.50 back at the end of the class period.
 Option #2: You give me $10 now and I’ll give you
$11 back at the end of the class period.
You can choose only one of two options. Assume a
zero rate of interest because our class lasts only 2
hours. Which option would you choose?
34
Example 4: NPV vs. IRR
(Mutually Exclusive Projects)
Suppose r = 5%.
Project 0
1
2
3
IRR
NPV
@5%
$33
Higher
$29
Long
-100 10
60
80
18.1%
Short
-100 70
50
20
23.6%
Higher
Which one should we take?
35
Construct NPV Profiles
Enter CFs in CFj and find NPVL and
NPVS at different discount rates:
r
0
5
10
15
20
NPVL
50
33
19
7
(4)
NPVS
40
29
20
12
5
36
NPV ($)
Double click on the icon
60
50
Crossover
Point = 8.7%
40
30
20
IRRS = 23.6%
10
Discount Rate (%)
0
0
-10
5
10
15
20
23.6
IRRL = 18.1%
37
To Find the Crossover Rate
1. Find cash flow differences between the
projects. See data at beginning of the
case.
2. Enter these differences in CFj register,
then press IRR. Crossover rate = 8.68%,
rounded to 8.7%.
3. Can subtract S from L or vice versa, but
better to have first CF negative.
4. If profiles don’t cross, one project
dominates the other.
38
Which project(s) should be
accepted at r=5%?
 If S and L are independent, accept both. NPV
> 0. IRRS and IRRL > r = 5%.
 If Projects S and L are mutually exclusive,
accept L because NPVS < NPVL at r = 5%,
although IRRS > IRRL . Conflict!!!
 Choose between mutually exclusive projects
on basis of higher NPV. Adds most value in
dollar.
39
NPV and IRR always lead to the same
accept/reject decision for independent
projects:
NPV ($)
IRR > r
and NPV > 0
Accept.
r > IRR
and NPV < 0.
Reject.
r (%)
IRR
40
Mutually Exclusive Projects
r < 8.7: NPVL> NPVS , IRRS > IRRL
CONFLICT
r> 8.7: NPVS> NPVL , IRRS > IRRL
NO CONFLICT
NPV
L
S
r
8.7
r
IRRS
%
IRRL
41
Reinvestment Rate Assumptions
NPV assumes reinvest at r (opportunity cost
of capital).
IRR assumes reinvest at IRR.
Reinvest at opportunity cost, r, is more
realistic, so NPV method is best. NPV
should be used to choose between mutually
exclusive projects.
Another Problem with IRR

IRR has another problem so-called
“Multiple IRRs.”
42
43
Two kinds of Cash Flows
Normal Cash Flow Project:
Cost (negative CF) followed by a
series of positive cash inflows.
One change of signs.
Nonnormal Cash Flow Project:
Two or more changes of signs.
Most common: Cost (negative
CF), then string of positive CFs,
then cost to close project.
Nuclear power plant, strip mine.
44
Inflow (+) or Outflow (-) in Year
0
1
2
3
4
5
N
-
+
+
+
+
+
N
-
+
+
+
+
-
-
-
-
+
+
+
N
+
+
+
-
-
-
N
-
+
+
-
+
-
NN
NN
NN
45
Example 5: NPV vs. IRR (Multiple IRRs)
Greenspan Mining Co. is considering a project to strip
mine coal. The project requires an investment of $22
million and is expected to produce a cash inflow of
$15 million in each Year 1 through 4. However, the
Company is obligated to pay $40 million in Year 5 to
restore the terrain. The Company’s opportunity cost
of capital is 10%. What are the IRR(s) and NPV?
0
1
2
3
4
5
NPV
NPV
NPV
@5.62% @27.78% @10%
-22 15 15 15 15 -40 ?
?
$0.7M
46
Multiple IRRs
$1.50
$1.00
NPV
$0.50
$0.00
1.00%
4.00%
7.00%
10.00%
13.00%
16.00%
19.00%
($0.50)
($1.00)
($1.50)
($2.00)
Discount Rate
22.00%
25.00%
28.00%
31.00%
47
Could find IRR with calculator:
1. Enter CFs as before.
2. Enter a “guess” as to IRR by
storing the guess. Try 10%:
10
STO
IRR = 6% = lower IRR
Now guess large IRR, say, 30%:
30
STO
IRR = 28% = upper IRR
48
Multiple IRRs (continued)
The previous slides shows that there are two
IRRs  Multiple IRRs
You need to recognize that there are nonconventional cash flows and look at the
NPV profile
Rely on NPV instead of IRR in this case
49
Managers like rates--prefer IRR
to NPV comparisons. Can we give
them a better IRR?
Yes, MIRR is the discount rate which
causes the PV of a project’s terminal
value (TV) to equal the PV of costs.
TV is found by compounding inflows
at WACC.
Thus, MIRR assumes cash inflows are
reinvested at WACC.
Example 6: Starbucks estimates the
cash flows for the new project,
“Mocha.” Find MIRR. r = 10%.
0
1
2
3
10.0
60.0
80.0
10%
-100.0
10%
10%
MIRR =
16.5%
-100.0
PV outflows
$158.1
$100 =
(1+MIRRL)3
MIRRL = 16.5%
66.0
12.1
158.1
TV inflows
50
51
To find TV with a calculator, enter in CFj:
CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80
I = 10
NPV = 118.78 = PV of inflows.
Enter PV = -118.78, N = 3, I = 10, PMT = 0.
Press FV = 158.10 = FV of inflows.
Enter FV = 158.10, PV = -100, PMT = 0,
N = 3.
Press I = 16.50% = MIRR.
52
Accept Project ?
YES. Reject because MIRR =
16.50% > r= 10%.
Also, if MIRR > r, NPV will be
positive: NPV = +$18.78.
53
Why use MIRR rather than IRR?
MIRR correctly assumes reinvestment
at opportunity cost = WACC. MIRR
also avoids the problem of multiple
IRRs.
Managers like rate of return
comparisons, and MIRR is better for
this than IRR.
54
Advantages and Disadvantages of
IRR
 Advantages
 closely related to NPV, often leading to
identical decisions
 Knowing a return is intuitively appealing
 It is a simple way to communicate the value of a
project to someone who doesn’t know all the
estimation details
 Disadvantages
 may lead to incorrect decisions in comparisons
of mutually exclusive investments – to be
explained later
 May result in multiple answers (so-called,
Multiple IRRs)
55
Summary: NPV vs. IRR
 NPV and IRR will generally give us the same
decision
 Exceptions: IRR is unreliable in the following
situations
 Non-conventional cash flows – cash flow signs
change more than once
 Mutually exclusive projects
• Initial investments are substantially different
• Timing of cash flows is substantially
different
 Whenever there is a conflict between NPV and
another decision rule, you should always use NPV
56
NPV (continued)
Does the NPV rule account for the time
value of money?
Does the NPV rule provide an indication
about the increase in value?
Should we consider the NPV rule for our
primary decision criteria?
Does the NPV have serious flaws?
57
Example 7: NPV vs. PI
Mutually Exclusive Projects
Suppose Project A and B are mutually exclusive.
0
1
2
A
$-20M 70M
10M
PV@12% PI@
12%
$70.5M
$3.52
B
$-10M 15M
40M
$45.3M
$4.53
Higher
NPV@
12%
$50.5
Higher
$35.3
58
Advantages and Disadvantages of
Profitability Index
 Advantages
 Disadvantages
 Closely related to NPV,
 May lead to incorrect
generally leading to
decisions in
identical decisions
comparisons of
mutually exclusive
 Easy to understand and
investments (To be
communicate
explained later)
 May be useful when
available investment
funds are limited (socalled, capital rationing,
to be explained later)
59
Capital Rationing: “imposing
maximum capital expenditures”
Capital rationing occurs when a company
chooses not to fund all positive NPV
projects.
The company typically sets an upper limit
on the total amount of capital expenditures
that it will make in the upcoming year.
60
Reason: Companies want to avoid the direct
costs (i.e., flotation costs) and the indirect
costs of issuing new capital. Or companies
avoid a high debt ratio or earnings dilution.
Solution: Increase the cost of capital by
enough to reflect all of these costs, and then
accept all projects that still have a positive
NPV with the higher cost of capital. Or, Use
profitability index, instead of NPVs.
61
Capital Rationing Example
Projects
A
B
C
D
E
Total Required
0
-100
-200
-300
-400
-500
-1500
1
50
100
100
100
100
2
60
80
200
200
200
3
r
50 10%
100 10%
120 10%
250 10%
410 10%
Total NPV
NPV
$ 33
$ 32
$ 46
$ 44
$ 64
$ 97
$
$
$
$
$
$
PI
1.33
1.16
1.15
1.11
1.13
111
Rank Rank
NPV
PI
4
1
5
2
2
3
3
5
1
4
What if the company has only $700 million?
Which project(s) should you choose?
62
Capital Budgeting In Practice
 We should consider several investment criteria
when making decisions.
 NPV and IRR are the most commonly used
primary investment criteria.
 Payback is a commonly used secondary
investment criteria.
 Use more than one
 Also exercise qualitative judgments in conjunction
with quantitative analysis.
Summary – Discounted Cash Flow Criteria
63
 Net present value
 Difference between PV of future cash flows and cost
 Take the project if the NPV is positive
 Has no serious problems
 Preferred decision criterion
 Internal rate of return
 Discount rate that makes NPV = 0
 Take the project if the IRR is greater than required return
 Same decision as NPV with conventional cash flows
 IRR is unreliable with non-conventional cash flows or mutually
exclusive projects
 Profitability Index
 Benefit-cost ratio
 Take investment if PI > 1
 Cannot be used to rank mutually exclusive projects
 May be useful to rank projects in the presence of capital
rationing
A challenging problem incorporating
beta, WACC, and capital budgeting.
Returns on the market and Company Y's stock during the
last 3 years are shown below:
Year Market Company Y
2001
–24%
– 22%
2002
10
13
2003
22
36
The risk-free rate is 5 percent, and the required return on
the market is 11 percent. You are considering a low-risk
project whose project beta is 0.5 less than the company's
overall corporate beta. You finance only with equity, all of
which comes from retained earnings. The project has a
cost of $500 million, and it is expected to provide cash
flows of $100 million per year at the end of Years 1 through
5 and then $50 million per year at the end of Years 6
through 10. What is the project's NPV (in millions of
dollars)?
64
65
Market
Mean
SD
VAR
Y
M-mean
Y-mean
Product
Weight
Product*weight
-24%
-22%
-26.67%
-31.00%
8.27%
33.33%
2.76%
10%
13%
7.33%
4.00%
0.29%
33.33%
0.10%
22%
36%
19.33%
27.00%
5.22%
33.33%
1.74%
2.67%
9.00%
19.48%
4.59%
4.59% COV
3.80%
COV
1.21 BETA
Regression Statistics
Multiple R
0.9886929
R Square
0.9775136
Adjusted R Square
0.9550272
Standard Error
0.0619369
Observations
3
ANOVA
df
SS
MS
Regression
1
0.166764
0.166764
Residual
1
0.003836
0.003836
Total
2
0.1706
CoefficientsStandard Error t Stat
Intercept
X Variable 1
F
Significance F
43.47129 0.0958256
P-value
Lower 95% Upper 95%Lower 95.0%
Upper 95.0
0.0577283
0.036093
1.599445
0.355715 -0.400871
0.516328
-0.40087 0.516328
1.2102
0.183549
6.593276
0.095826
3.542385
-1.12201 3.542385
-1.12201