Should we

1

CHAPTER 11The Basics of Capital Budgeting
Should we build this plant?
2
What is capital budgeting?

• Analysis of potential additions to fixed assets.
• Long-term decisions involve large expenditures.
• Very important to firms future.

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 gt 0 and/or IRR gt WACC.
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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
projects cost, or how long does it take to get
the businesss money back?
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Payback for Project L(Long Most CFs in out
years)
2.4
0
1
2
3
10
80
60
-100
CFt
100
Cumulative
-100
-90
-30
50
0

PaybackL
2 30/80 2.375 years
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Project S (Short CFs come quickly)
1.6
0
1
2
3
70
20
50
-100
CFt
100
Cumulative
-100
-30
20
40
0
PaybackS
1 30/50 1.6 years

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Strengths of Payback
1. Provides an indication of a projects 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
10
80
60
CFt
-100
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.
Cost often is CF0 and is negative.
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Whats Project Ls NPV?
Project L
0
1
2
3
10
10
80
60
-100.00
9.09
49.59
60.11
18.79 NPVL
NPVS 19.98.
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Calculator Solution
Enter in CFLO for L
-100 10 60 80 10
CF0
CF1
CF2
CF3
NPV
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 gt 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 gt NPVL .
• If S L are independent, accept both NPV gt 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.
IRR Enter NPV 0, solve for IRR.
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Whats Project Ls IRR?
0
1
2
3
IRR ?
10
80
60
-100.00
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 ?
40
40
40
-100
INPUTS
3 -100 40 0 9.70
OUTPUT
Or, with CFLO, enter CFs and press IRR 9.70.
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Q. How is a projects IRR related to a bonds
YTM?
A. They are the same thing. A bonds YTM is the
IRR if you invest in the bond.
0
1
2
10
IRR ?
...
90
1,090
90
-1,134.2
IRR 7.08 (use TVM or CFLO).
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Rationale for the IRR Method
If IRR gt WACC, then the projects 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 gt k, accept project.
• If IRR lt k, reject project.

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Decisions on Projects S and L per IRR

• If S and L are independent, accept both. IRRs gt
  k 10.
• If S and L are mutually exclusive, accept S
  because IRRS gt IRRL .

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Construct NPV Profiles
Enter CFs in CFLO and find NPVL and NPVS at
different discount rates
NPVL 50 33 19 7
NPVS 40 29 20 12 5
k 0 5 10 15 20
(4)
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NPV ()
k 0 5 10 15 20
NPVL 50 33 19 7 (4)
NPVS 40 29 20 12 5
Crossover Point 8.7
S
IRRS 23.6
L
Discount Rate ()
IRRL 18.1
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NPV and IRR always lead to the same accept/reject
decision for independent projects
NPV ()
k gt IRR and NPV lt 0. Reject.
IRR gt k and NPV gt 0 Accept.
k ()
IRR
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Mutually Exclusive Projects
NPV
k lt 8.7 NPVLgt NPVS , IRRS gt IRRL CONFLICT
L
k gt 8.7 NPVSgt NPVL , IRRS gt IRRL NO CONFLICT
IRRS
S

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 dont 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 gt 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 projects 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 for Project L (k 10)
0
1
2
3
10
10.0
80.0
60.0
-100.0
10
66.0 12.1
10
MIRR 16.5
158.1
-100.0
TV inflows
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
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.
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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?
0
1
2
k 10
5,000
-5,000
-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. Heres a
picture
NPV Profile
NPV
IRR2 400
450
0
k
400
100
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 lt 0. 2. At very high
discount rates, the PV of both CF1 and CF2 are
low, so CF0 dominates and again NPV lt 0. 3. In
between, the discount rate hits CF2 harder than
CF1, so NPV gt 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 _at_ 10 -4,932,231.40.
TV inflows _at_ 10 5,500,000.00.
MIRR 5.6
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Accept Project P?
NO. Reject because MIRR 5.6 lt k 10. Also,
if MIRR lt k, NPV will be negative NPV
-386,777.