The Basics of Capital Budgeting: Evaluating Cash Flows: Should We Build This Plant?

13 - 1
CHAPTER 13
The Basics of Capital Budgeting:
Evaluating Cash Flows
Should we
build this
plant?
Copyright © 2002 Harcourt, Inc. All rights reserved.

13 - 2
What is capital budgeting?
 Analysis of potential additions to

fixed assets.
 Long-term decisions; involve large
expenditures.
 Very important to firm’s future.

13 - 3
Steps
1. Estimate CFs (inflows & outflows).

2. Assess riskiness of CFs.
3. Determine k = WACC for project.
4. Find NPV and/or IRR.
5. Accept if NPV > 0 and/or IRR >
WACC.
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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.
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An Example of Mutually Exclusive

Projects
BRIDGE vs. BOAT to get

products across a river.
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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.
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Inflow (+) or Outflow (-) in Year
0 1 2 3 4 5 N NN
- + + + + + N
- + + + + - NN
- - - + + + N
+ + + - - - N
- + + - + - NN

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What is the payback period?
The number of years required to

recover a project’s cost,
or how long does it take to get the

business’s money back?

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Payback for Project L

(Long: Most CFs in out years)
0 1 2 2.4 3
CFt -100 10 60 100 80

Cumulative -100 -90 -30 0 50
PaybackL = 2 + 30/80 = 2.375 years

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Project S (Short: CFs come quickly)
0 1 1.6 2 3
CFt -100 70 100 50 20
Cumulative -100 -30 0 20 40
PaybackS = 1 + 30/50 = 1.6 years

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Strengths of Payback:
1. Provides an indication of a
project’s risk and liquidity.
2. Easy to calculate and understand.
Weaknesses of Payback:
1. Ignores the TVM.
2. Ignores CFs occurring after the
payback period.
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Discounted Payback: Uses discounted

rather than raw CFs.
0 1 2 3
10%
CFt -100 10 60 80
PVCFt -100 9.09 49.59 60.11
Cumulative -100 -90.91 -41.32 18.79
Discounted
payback = 2 + 41.32/60.11 = 2.7 yrs
Recover invest. + cap. costs in 2.7 yrs.

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NPV: Sum of the PVs of inflows and

outflows.
CFt
n
NPV = ∑ .
t = 0 (1 + k )
t
Cost often is CF0 and is negative.

n
CFt
NPV = ∑ − CF0 .
t =1 (1+ k) t

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What’s Project L’s NPV?
Project L:
0 1 2 3
10%
-100.00 10 60 80
9.09
49.59
60.11
18.79 = NPVL NPVS = $19.98.
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Calculator Solution
Enter in CFLO for L:

-100 CF0
10 CF1
60 CF2
80 CF3
10 I NPV = 18.78 = NPVL

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Rationale for the NPV Method
NPV = PV inflows - Cost

= Net gain in wealth.
Accept project if NPV > 0.
Choose between mutually

exclusive projects on basis of
higher NPV. Adds most value.
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Using NPV method, which project(s)

should be accepted?
 If Projects S and L are mutually

exclusive, accept S because
NPVs > NPVL .
 If S & L are independent,
accept both; NPV > 0.

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Internal Rate of Return: IRR
0 1 2 3
CF0 CF1 CF2 CF3

Cost Inflows
IRR is the discount rate that forces

PV inflows = cost. This is the same
as forcing NPV = 0.
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NPV: Enter k, solve for NPV.

n CFt
∑ = NPV.
t = 0 (1 + k )
t
IRR: Enter NPV = 0, solve for IRR.

n CFt
∑ t = 0.
t = 0 (1 + IRR)

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What’s Project L’s IRR?
0 1 2 3
IRR = ?
-100.00 10 60 80
PV1
PV2
PV3
0 = NPV
Enter CFs in CFLO, then press IRR:
IRRL = 18.13%. IRRS = 23.56%.
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Find IRR if CFs are constant:
0 1 2 3
IRR = ?
-100 40 40 40
INPUTS 3 -100 40 0
N I/YR PV PMT FV
OUTPUT 9.70%
Or, with CFLO, enter CFs and press

IRR = 9.70%.
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Q. How is a project’s IRR
related to a bond’s YTM?
A. They are the same thing.
A bond’s YTM is the IRR
if you invest in the bond.
0 1 2 10
IRR = ? ...
-1,134.2 90 90 1,090
IRR = 7.08% (use TVM or CFLO).

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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 = 15%.

Profitable.

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IRR Acceptance Criteria
 If IRR > k, accept project.
 If IRR < k, reject project.

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Decisions on Projects S and L per IRR
 If S and L are independent, accept

both. IRRs > k = 10%.
 If S and L are mutually exclusive,
accept S because IRRS > IRRL .

13 - 26
Construct NPV Profiles
Enter CFs in CFLO and find NPVL and

NPVS at different discount rates:
k NPVL NPVS
0 50 40
5 33 29
10 19 20
15 7 12
20 (4) 5
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NPV ($)
k NPVL NPVS
60
0 50 40
50 5 33 29
40
Crossover 10 19 20
Point = 8.7% 7 12
15
30
20 (4) 5
20
S
IRRS = 23.6%
10 L
0 Discount Rate (%)
0 5 10 15 20 23.6
-10
IRRL = 18.1%

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NPV and IRR always lead to the same
accept/reject decision for independent
projects:
NPV ($)
IRR > k k > IRR
and NPV > 0 and NPV < 0.
Accept. Reject.
k (%)
IRR
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Mutually Exclusive Projects
NPV k < 8.7: NPVL> NPVS , IRRS > IRRL

CONFLICT
L k > 8.7: NPVS> NPVL , IRRS > IRRL
NO CONFLICT
S IRRS
k 8.7 k %
IRRL
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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 CFLO 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.
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Two Reasons NPV Profiles Cross
1. Size (scale) differences. Smaller

project frees up funds at t = 0 for
investment. The higher the opportunity
cost, the more valuable these funds, so
high k favors small projects.
2. Timing differences. Project with faster
payback provides more CF in early
years for reinvestment. If k is high,
early CF especially good, NPVS > NPVL.
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Reinvestment Rate Assumptions
 NPV assumes reinvest at k

(opportunity cost of capital).
 IRR assumes reinvest at IRR.
 Reinvest at opportunity cost, k, is
more realistic, so NPV method is
best. NPV should be used to choose
between mutually exclusive projects.
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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.
13 - 34
MIRR for Project L (k = 10%)

0 1 2 3
10%
-100.0 10.0 60.0 80.0

10%
66.0
10%
12.1
MIRR = 16.5%
158.1
-100.0 $158.1 TV inflows
$100 =
(1+MIRRL)3
PV outflows
MIRRL = 16.5%
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To find TV with 10B, enter in CFLO:
CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80

I=
10 = 118.78 = PV of inflows.
NPV
Enter PV = -118.78, N = 3, I = 10, PMT =
0.
Press FV == 158.10,
Enter FV 158.10 =PV
FV= of inflows.
-100, PMT = 0,
N = 3.
Press I = 16.50% = MIRR.
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Why use MIRR versus 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.

13 - 37
Pavilion Project: NPV and IRR?
0 1 2
k = 10%
-800 5,000 -5,000
Enter CFs in CFLO, enter I = 10.

NPV = -386.78
IRR = ERROR. Why?
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We got IRR = ERROR because there
are 2 IRRs. Nonnormal CFs--two sign
changes. Here’s a picture:
NPV NPV Profile
IRR2 = 400%
450
0 k
100 400
IRR1 = 25%
-800
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Logic of Multiple IRRs
1. At very low discount rates, the PV of

CF2 is large & negative, so NPV < 0.
2. At very high discount rates, the PV of
both CF1 and CF2 are low, so CF0
dominates and again NPV < 0.
3. In between, the discount rate hits CF2
harder than CF1, so NPV > 0.
4. Result: 2 IRRs.
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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 = 25% = lower IRR
Now guess large IRR, say, 200:
200 STO
IRR = 400% = upper IRR
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When there are nonnormal CFs and

more than one IRR, use MIRR:
0 1 2
-800,000 5,000,000 -5,000,000
PV outflows @ 10% = -4,932,231.40.

TV inflows @ 10% = 5,500,000.00.
MIRR = 5.6%
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Accept Project P?
NO. Reject because MIRR =

5.6% < k = 10%.
Also, if MIRR < k, NPV will be

negative: NPV = -$386,777.

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S and L are mutually exclusive and

will be repeated. k = 10%. Which is
better? (000s)
0 1 2 3 4
Project S:
(100) 60 60
Project L:
(100) 33.5 33.5 33.5 33.5

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S L
CF0 -100,000 -100,000
CF1 60,000 33,500
Nj 2 4
I 10 10
NPV 4,132 6,190

NPVL > NPVS. But is L better?
Can’t say yet. Need to perform
common life analysis.
13 - 45
 Note that Project S could be

repeated after 2 years to generate
additional profits.
 Can use either replacement chain
or equivalent annual annuity
analysis to make decision.

13 - 46
Replacement Chain Approach (000s)
Project S with Replication:

0 1 2 3 4
Project S:
(100) 60 60
(100) 60 60
(100) 60 (40) 60 60
NPV = $7,547.
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Or, use NPVs:
0 1 2 3 4
4,132 4,132
3,415 10%
7,547
Compare to Project L NPV = $6,190.

13 - 48
If the cost to repeat S in two years

rises to $105,000, which is best? (000s)
0 1 2 3 4
Project S:
(100) 60 60
(105) 60 60
(45)
NPVS = $3,415 < NPVL = $6,190.
Now choose L.
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Consider another project with a 3-year

life. If terminated prior to Year 3, the
machinery will have positive salvage
value.
Year CF Salvage Value

0 ($5,000) $5,000
1 2,100 3,100
2 2,000 2,000
3 1,750 0

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CFs Under Each Alternative (000s)
0 1 2 3
1. No termination (5) 2.1 2 1.75
2. Terminate 2 years (5) 2.1 4
3. Terminate 1 year (5) 5.2

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Assuming a 10% cost of capital, what is

the project’s optimal, or economic life?
NPV(no) = -$123.
NPV(2) = $215.
NPV(1) = -$273.

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Conclusions
 The project is acceptable only if

operated for 2 years.
 A project’s engineering life does not
always equal its economic life.

13 - 53
Choosing the Optimal Capital Budget
 Finance theory says to accept all

positive NPV projects.
 Two problems can occur when there
is not enough internally generated
cash to fund all positive NPV projects:
An increasing marginal cost of
capital.
Capital rationing
13 - 54
Increasing Marginal Cost of Capital
 Externally raised capital can have

large flotation costs, which increase
the cost of capital.
 Investors often perceive large capital
budgets as being risky, which drives
up the cost of capital.
(More...)
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 If external funds will be raised, then

the NPV of all projects should be
estimated using this higher marginal
cost of capital.

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Capital Rationing
 Capital rationing occurs when a

company chooses not to fund all
 The company typically sets an
upper limit on the total amount
of capital expenditures that it will
make in the upcoming year.
(More...)

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Reason: Companies want to avoid the

direct costs (i.e., flotation costs) and
the indirect costs of issuing new
capital.
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.
(More...)
13 - 58
Reason: Companies don’t have

enough managerial, marketing, or
engineering staff to implement all
Solution: Use linear programming to

maximize NPV subject to not
exceeding the constraints on staffing.
(More...)
13 - 59
Reason: Companies believe that the

project’s managers forecast
unreasonably high cash flow estimates,
so companies “filter” out the worst
projects by limiting the total amount of
projects that can be accepted.
Solution: Implement a post-audit
process and tie the managers’
compensation to the subsequent
performance of the project.

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13 - 1

Copyright © 2002 Harcourt, Inc. All rights reserved.

What is capital budgeting?

 Analysis of potential additions to

Copyright © 2002 Harcourt, Inc. All rights reserved.

1. Estimate CFs (inflows & outflows).

An Example of Mutually Exclusive

BRIDGE vs. BOAT to get

Nonnormal Cash Flow Project:

Inflow (+) or Outflow (-) in Year

Copyright © 2002 Harcourt, Inc. All rights reserved.

What is the payback period?

The number of years required to

or how long does it take to get the

Copyright © 2002 Harcourt, Inc. All rights reserved.

Payback for Project L

CFt -100 10 60 100 80

PaybackL = 2 + 30/80 = 2.375 years

Copyright © 2002 Harcourt, Inc. All rights reserved.

Project S (Short: CFs come quickly)

CFt -100 70 100 50 20

Cumulative -100 -30 0 20 40

PaybackS = 1 + 30/50 = 1.6 years

Copyright © 2002 Harcourt, Inc. All rights reserved.

Discounted Payback: Uses discounted

Recover invest. + cap. costs in 2.7 yrs.

NPV: Sum of the PVs of inflows and

Cost often is CF0 and is negative.

Copyright © 2002 Harcourt, Inc. All rights reserved.

What’s Project L’s NPV?

Enter in CFLO for L:

10 I NPV = 18.78 = NPVL

Rationale for the NPV Method

NPV = PV inflows - Cost

Accept project if NPV > 0.

Choose between mutually

Using NPV method, which project(s)

 If Projects S and L are mutually

Copyright © 2002 Harcourt, Inc. All rights reserved.

Internal Rate of Return: IRR

CF0 CF1 CF2 CF3

IRR is the discount rate that forces

NPV: Enter k, solve for NPV.

IRR: Enter NPV = 0, solve for IRR.

Copyright © 2002 Harcourt, Inc. All rights reserved.

What’s Project L’s IRR?

Or, with CFLO, enter CFs and press

IRR = 7.08% (use TVM or CFLO).

Rationale for the IRR Method

If IRR > WACC, then the project’s

Example: WACC = 10%, IRR = 15%.

Copyright © 2002 Harcourt, Inc. All rights reserved.

IRR Acceptance Criteria

 If IRR > k, accept project.

 If IRR < k, reject project.

Copyright © 2002 Harcourt, Inc. All rights reserved.

Decisions on Projects S and L per IRR

 If S and L are independent, accept

Copyright © 2002 Harcourt, Inc. All rights reserved.