Cff311.ppt

11 - 1
Copyright © 2002 by Harcourt, Inc. All rights reserved.
Should we
build this
plant?
CHAPTER 11
The Basics of Capital Budgeting

11 - 2
What is capital budgeting?
Analysis of potential additions to
fixed assets.
Long-term decisions; involve large
expenditures.
Very important to firm’s future.

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Steps
1. Estimate CFs (inflows & outflows).
2. Assess riskiness of CFs.
3. Determine k = WACC (adj.).
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.

11 - 6
Normal Cash Flow Project:
Cost (negative CF) followed by a
series of positive cash inflows.
One change of signs.
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.
Normal Cash Flow Project
Nonnormal Cash Flow Project

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Inflow (+) or Outflow (-) in Year
0 1 2 3 4 5 N NN
- + + + + + N
- + + + + - NN
- - - + + + N
+ + + - - - N
- + + - + - NN

11 - 8
What is the payback period?
The number of years required to
recover a project’s cost,
or how long does it take to get our
money back?

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Payback for Project L
(Long: Large CFs in later years)
10 60
0 1 2 3
-100
=
CFt
Cumulative -100 -90 -30 50
PaybackL 2 + 30/80 = 2.375 years
0
100
2.4
80

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

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

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

11 - 13
 
.
k
1
CF
NPV t
t
n
0
t 
 

NPV: Sum of the PVs of inflows and
outflows.

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

11 - 15
Calculator Solution
Enter in CFLO for L:
-100
10
60
80
10
CF0
CF1
NPV
CF2
CF3
I = 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.

11 - 17
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
k
1
CF
t
t
n
0
t




 
.
0
IRR
1
CF
t
t
n
0
t




NPV: Enter k, solve for NPV.
IRR: Enter NPV = 0, solve for IRR.

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What’s Project L’s IRR?
10 80
60
0 1 2 3
IRR = ?
-100.00
PV3
PV2
PV1
0 = NPV
Enter CFs in CFLO, then press IRR:
IRRL = 18.13%. IRRS = 23.56%.

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40 40
40
0 1 2 3
IRR = ?
Find IRR if CFs are constant:
-100
Or, with CFLO, enter CFs and press
IRR = 9.70%.
3 -100 40 0
9.70%
INPUTS
OUTPUT
N I/YR PV PMT FV

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90 1090
90
0 1 2 10
IRR = ?
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.
-1134.2
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 .

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Construct NPV Profiles
Enter CFs in CFLO and find NPVL and
NPVS at different discount rates:
k
0
5
10
15
20
NPVL
50
33
19
7
(4
NPVS
40
29
20
12
5
(4)

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

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NPV and IRR always lead to the same
accept/reject decision for independent
projects:
k > IRR
and NPV < 0.
Reject.
NPV ($)
k (%)
IRR
IRR > k
and NPV > 0
Accept.

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Mutually Exclusive Projects
k 8.7 k
NPV
%
IRRS
IRRL
L
S
k < 8.7: NPVL> NPVS , IRRS > IRRL
CONFLICT
k > 8.7: NPVS> NPVL , IRRS > IRRL
NO CONFLICT

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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 that
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.

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MIRR = 16.5%
10.0 80.0
60.0
0 1 2 3
10%
66.0
12.1
158.1
MIRR for Project L (k = 10%)
-100.0
10%
10%
TV inflows
-100.0
PV outflows
MIRRL = 16.5%
$100 =
$158.1
(1 + MIRRL)3

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To find TV with HP 10B, enter in CFLO:
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.
CF0 = 0, CF1 = 10, CF2 = 60, CF3 =
80

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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.

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Pavilion Project: NPV and IRR?
5,000 -5,000
0 1 2
k = 10%
-800
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 Profile
450
-800
0
400
100
IRR2 = 400%
IRR1 = 25%
k
NPV

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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.

Cff311.ppt

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