Transcript No Slide Title

10 - 1
Chapter 10:
The Basics of Capital Budgeting:
Evaluating Cash Flows
Overview and “vocabulary”
Methods
Payback, discounted payback
NPV
IRR, MIRR
Profitability Index
Unequal lives
Economic life
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MINICASE 10
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What is capital budgeting?
Analysis of potential projects.
Long-term decisions; involve large
expenditures.
Very important to firm’s future.
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Steps in Capital Budgeting
Estimate cash flows (inflows &
outflows).
Assess risk of cash flows.
Determine r = WACC for project.
Evaluate cash flows.
Digression:
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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 Project
Nonnormal Project
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Normal Project
Cost (negative CF) followed by a
series of positive cash inflows.
Nonnormal Project
One or more outflows occur after
inflows have begun. 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
-
+
+
-
+
-
NN
NN
N
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c(1). What is the payback period?
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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
our money back?
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Payback for Project L
(Long: Most CFs in out years)
CFt
Cumul
0
1
2
-100
-100
10
-90
60
-30
2.4
3
0
80
50
PaybackL = 2 + 30/80 = 2.375 years.
n.b. Assumes CF’s occur evenly over the year.
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Project S (Short: CFs come quickly)
0
1
CFt
-100
70
Cumul
-100
-30
1.6
0
2
3
50
20
20
40
PaybackS = 1 + 30/50 = 1.6 years.
Payback is a type of breakeven analysis.
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Strengths of Payback
Weaknesses of Payback
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c(2). Strengths of Payback
 Provides an indication of a project’s
risk and liquidity.
 Easy to calculate and understand.
Weaknesses of Payback
 Ignores the TVM.
 Ignores CFs occurring
after the payback period.
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c(3):Discounted Payback: Uses discounted
rather than raw CFs. Apply to Project L.
0
1
2
2.7 3
10
60
80
49.59
60.11
10%
CFt
-100
PVCFt
-100
9.09
-100
-90.91
-41.32
Cumul
Disc.
payback = 2 + 41.32/60.11 = 2.7 years.
18.79
Recover invest. + cap. costs in 2.7 years.
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d(1) Net Present Value (NPV)
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Net Present Value (NPV)
Sum of the PVs of inflows and outflows.
n
CFt
NPV = 
t
(1
+
k)
t=0
If one expenditure at t = 0, then
n
CFt
NPV =  (1 + k)t +CF0.
t=1
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NET PRESENT VALUE
NPV = CF0 + CF1/(1+k) + CF2/(1+k)2 +
... + CFn/(1+k)n
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What is Project L’s NPV?
Project L:
(Beware use of comp. fns)
0
1
2
3
10
60
80
10%
-100.00
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What is Project L’s NPV?
Project L:
0
1
2
3
10
60
80
10%
-100.00
9.09
49.58
60.11
18.78 = 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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d(2) Rationale for the NPV Method
If NPV = 0, project breaks even;
recovers cost of investment
investors earn required rate of
return (i.e. opportunity cost of
capital)
If NPV > 0;
investors get above, plus
additional $.
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CONSIDER PROJECT L:
SUM OF undiscounted CF’s = 150
Investors get $100 back
Cover their 10% cost of capital;
and have $18.79 left over.
Who does this $18.79 belong to?
Stockholders.
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Rationale for the NPV Method
NPV = PV inflows - PV of 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, ?
If S & L are independent, ?
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Using NPV method, which project(s)
should be accepted?
If Projects S and L are mutually
exclusive,…..
If S & L are independent,
accept…..
What happens to the NPV as the
cost of capital changes?
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e(1) What is the Internal Rate of Return
(IRR)
0
1
2
3
CF0
CF1
CF2
CF3
Cost
Inflows
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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

t  NPV.
t  0 1  k 
IRR:
Enter NPV = 0, solve for IRR.
n
CFt
 0.

t
t  0 1  IRR
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What is Project L’s IRR?
0
1
2
3
10
60
80
IRR = ?
-100.00
PV1
PV2
PV3
0 = NPV
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What is Project L’s IRR?
0
1
2
3
10
60
80
IRR = ?
-100.00
PV1
PV2
PV3
0 = NPV
Enter CFs in CFLO, then
press IRR:
IRRL = 18.13%. IRRS = 23.56%.
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e(2) How is a project’s IRR related to a
bond’s YTM?
0
1
2
10
90
90
1090
IRR = ?
-1134.2
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How is a project’s IRR related to a
bond’s YTM?
They both measure percentage (rate of)
return. A bond’s YTM is its IRR.
0
1
2
10
90
90
1090
IRR = ?
-1134.2
IRR = 7.08% (use TVM or CFLO).
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e(3) Rationale for the IRR Method?
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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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Using IRR method, which project(s)
should be accepted?
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Using IRR method, which project(s)
should be accepted?
If S and L are independent, ……….
If S and L are mutually exclusive,
accept………….
What effect does a change in the cost
of capital have on the IRR?
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f(1) Define Profitability Index (PI)
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Define Profitability Index (PI)
PV of inflows
PI =
.
PV of outflows
PI measures a project’s “bang for
the buck”.
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Calculate each project’s PI.
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Calculate each project’s PI.
Project L:
$9.09 + $49.59 + $60.11
PIL =
= 1.19.
$100
Project S:
$63.64 + $41.32 + $15.03
PIS =
= 1.20.
$100
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PI Acceptance Criteria
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PI Acceptance Criteria
If PI > 1, accept.
If PI < 1, reject.
The higher the PI, the better the
project.
For mutually exclusive projects,
take the one with the highest PI.
Therefore, accept L and S if
independent; only accept S if
mutually exclusive.
Any problems with using PI?
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g(1) Construct NPV Profiles
Enter CFs in CFLO and find NPVL and
NPVS at different discount rates:
k
0
5
10
15
20
NPVL
50
33
19
7
(4)
NPVS
40
29
20
12
5
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NPV ($)
50
40
Crossover
Point = 8.7%
30
20
NPVL
50
33
19
7
(4)
k
0
5
10
15
20
NPVS
40
29
20
12
5
S
IRRS = 23.6%
10
L
0
5
-10
10
15
IRRL = 18.1%
20
23.6
Discount Rate (%)
Vertical intercept
horizontal intercept
crossover point
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NPV and IRR always lead to the same
accept/reject decision for independent
projects.
NPV ($)
IRR > k
and NPV > 0
Accept.
k > IRR
and NPV < 0.
Reject.
k (%)
IRR
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g(2) Mutually Exclusive Projects
NPV
k < 8.7: NPVL > NPVS , IRRS > IRRL
CONFLICT
L
k > 8.7: NPVS > NPVL , IRRS > IRRL
NO CONFLICT
S
k
8.7
IRRs
%
k
IRRL
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To Find the Crossover Rate
1. Find cash flow differences between
the projects.
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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How do you calculate the crossover
point?
MI N I C S
9
I n t . Ra t e :
Ye a r
1 0 . 0 0 %
Pr o j
De l t a
L
Pr o j
T V( L )
- 1 0 0
T V( S )
MI R R ( L )
0
- 1 0 0
1
1 0
$ 9 . 0 9
7 0
$ 6 3 . 6 4
1 2 . 1
8 4 . 7
2
6 0
$ 4 9 . 5 9
5 0
$ 4 1 . 3 2
6 6
5 5
3
8 0
$ 6 0 . 1 1
2 0
$ 1 5 . 0 3
8 0
2 0
Su m
( $ 1 0 0 . 0 0 )
S
( $ 1 0 0 . 0 0 )
$ 1 8 . 7 8
$ 1 9 . 9 8
1 8 . 7 8 2 8 7
1 9 . 9 8 4 9 7
MI R R ( S )
- 1 0 0
- 1 0 0
0
0
0
- 6 0
0
0
1 0
1 5 8 . 1
1 5 9 . 7
6 0
Cr o s s o v e r
Ra t e
I RR
1 8 . 1 3 %
2 3 . 5 6 %
S u m( T V )
1 5 8 . 1
Da t a T a b l e 1
1 5 9 . 7
MI R R
Pr o j e c t
L Pr o j e c t
S
1 6 . 5 0 %
1 6 . 8 9 %
8 . 6 8 %
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Which project do you choose?
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h(1) Why do NPV profiles cross?
 Size (scale) differences. Smaller
project frees up funds at t = 0 for
investment. The higher the opp. cost,
the more valuable these funds, so high
k favors small projects.
 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 reinvestment at k
(opportunity cost of capital).
IRR assumes reinvestment at IRR.
Reinvestment 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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i(1) Managers prefer IRR to NPV. Can
we give them a better IRR?
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Managers prefer IRR to NPV. Can we
give them a better IRR?
Yes, modified IRR (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 forces cash inflows to be
reinvested at WACC.
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MIRR for Project L (k = 10%):
0
1
2
10.0
60.0
3
10%
-100.0
80.0
10%
66.0
10%
-100.0
PV
outflows
MIRR =
16.5%
$100 = $158.1
(1+MIRRL)3
MIRRL = 16.5%
12.1
158.1
TV inflows
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MIRR for Project L (k = 10%):
0
1
2
3
10.0
60.0
10%
-100.0
80.0
10%
66.0
10%
12.1
-100.0
0
0
158.1
TV inflows
PV
outflows
MIRRL = 16.5%
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EXCEL HAS MIRR FUNCTION!
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Why use MIRR rather than IRR?
MIRR correctly assumes reinvestment
at opportunity cost = k.
MIRR also avoids problems with
multiple IRR’s with nonnormal
projects.
Managers like rate of return
comparisons, and MIRR is better for
this than IRR.
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J: Pavillion Project: NPV and IRR?
0
1
2
5,000
-5,000
k = 10%
-800
What is NPV?, IRR?
What is MIRR?
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Pavillion Project: NPV and IRR?
0
1
2
5,000
-5,000
k = 10%
-800
Enter CFs in CFj, enter I/YR = 10.
NPV = -$386.78
IRR = ERROR. Why?
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How do we find the IRR on a 12c?
 Make a guess for i and key it in i.
 RCL g R/S.
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We got IRR = ERROR because there
are 2 IRRs. Nonnormal CFs with two
sign changes. Here’s a picture:
NPV
NPV Profile
IRR2 = 400%
450
0
-800
100
IRR1 = 25%
400
k
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Logic of Multiple IRRs
 At very low disc. rates, the PV of CF2
is large & negative, so NPV < 0.
 At very high disc. rates, the PV of CF1
and CF2 are both low, so CF0
dominates and again NPV < 0.
 In between, the disc. rate hits CF2
harder than CF1 , so NPV > 0.
 Result: 2 IRRs.
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When there are nonnormal CFs, use
MIRR:
0
-800,000
1
5,000,000
2
-5,000,000
PV outflows @ 10% = -4,932,231.40.
TV inflows @ 10% = 5,500,000.00.
MIRR = 5.6%
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j(2) Accept Project P?
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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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NEW QUESTION: Which of the
following mutually exclusive project’s
is better? (000s)
0
1
2
Project S:
(100)
60
60
Project L:
(100)
33.5
33.5
3
4
33.5
33.5
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CF0
CF1
Nj
I
NPV
S
-100,000
60,000
2
10
L
-100,000
33,500
4
10
4,132
6,190
NPVL > NPVS. But is L better?
Can’t say yet. Need to perform
common life analysis.
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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.
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Replacement Chain Approach (000s)
Franchise S with Replication:
0
1
Franchise S:
(100)
60
(100)
60
NPV = $7,547.
2
3
4
60
(100)
(40)
60
60
60
60
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Or, use NPVs:
0
4,132
3,415
7,547
1
10%
2
3
4,132
Compare to Franchise L NPV =
$6,190.
4
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Equivalent Annual Annuity
(EAA) Approach
Finds the constant annuity payment
whose PV is equal to the project’s
raw NPV over its original life.
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EAA Calculator Solution
Project S
PV = Raw NPV = $4,132.
n = Original project life = 2.
k = 10%.
Solve for PMT = EAAS = $2,381.
Project L
PV = $6,190; n = 4; k = 10%.
Solve for PMT = EAAL = $1,953.
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The project, in effect, provides an
annuity of EAA.
EAAS > EAAL so pick S.
Replacement chains and EAA
always lead to the same decision if
cash flows are expected to stay the
same.
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If the cost to repeat S in two years rises
to $105,000, which is best? (000s)
0
1
Franchise S:
(100)
60
2
3
4
60
(105)
(45)
60
60
NPVS = $3,415 < NPVL = $6,190.
Now choose L.
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Types of Abandonment
Sale to another party who can obtain
greater cash flows, e.g., IBM sold
typewriter division.
Abandon because losing money, e.g.,
smokeless cigarette.
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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
0
1
2
3
CF
($5,000)
2,100
2,000
1,750
Salvage Value
$5,000
3,100
2,000
0
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CFs Under Each Alternative (000s)
0
(5)
1
2.1
2
2
2. Terminate 2 years (5)
2.1
4
3. Terminate 1 year
5.2
1. No termination
(5)
3
1.75
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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.
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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.
The ability to abandon a project may
make an otherwise unattractive
project acceptable.
Abandonment possibilities will be
very important when we get to risk.
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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
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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
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.
(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...)
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Reason: Companies don’t have
enough managerial, marketing, or
engineering staff to implement all
positive NPV projects.
Solution: Use linear programming to
maximize NPV subject to not
exceeding the constraints on staffing.
(More...)
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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.