Lecture 7– Capital Budgeting: Decision Criteria
Lecture 7 - Capital
Budgeting: Decision
Criteria
What is Capital Budgeting?
Analysis of potential projects.
Long-term decisions; involve large expenditures.
Very important to a firm’s future.
The Ideal Evaluation Method should:
a) include all cash flows that occur during the
life of the project,
b) consider the time value of money,
c) incorporate the required rate of return on the
project. Determine r = WACC for project.
2
Payback Period - The number of years
required to recover a project’s cost
What is the difference between independent and
mutually exclusive projects?
Payback for Franchise Long
(Long: Most CFs in out years)
Projects are:
0
independent, if the cash flows of
one are unaffected by the
acceptance of the other.
1
CFt
-100
Cumulative -100
mutually exclusive, if the cash flows
of one can be adversely impacted
by the acceptance of the other.
PaybackL
3
= 2
2
10
-90
+
30/80
2.4
60 100
-30
0
3
80
50
= 2.375 years
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1
Lecture 7– Capital Budgeting: Decision Criteria
Franchise Short
(Short: CFs come quickly)
0
CFt
Cumulative -100
PaybackS
1.6 2
3
70 100 50
20
1
-100
Another Example
-30
0 20
Ms. Hoa is is evaluating a new project for her firm,
Basket Wonders (BW). She has determined that the
after-tax cash flows for the project will be
$10,000; $12,000; $15,000; $10,000; and $7,000,
respectively, for each of the Years 1 through 5.
40
The initial cash outlay will be $40,000.
= 1 + 30/50 = 1.6 years
5
6
Payback period
0
1
2
3
-40 K
10 K
12 K
15 K
A Payback solution
4
10 K
5
0
-40 K (-b)
7K
PBP is the period of time required
for the cumulative expected cash
flows from an investment project
to equal the initial cash outflow.
Cumulative
Inflows
Note : K = 1000s
7
1
2
10 K
10 K
12 K
22 K
PBP
3 (a)
15 K
37 K(c)
4
10 K (d)
47 K
5
7K
54 K
=a+(b-c)/d
= 3 + (40 - 37) / 10
= 3 + (3) / 10
= 3.3 Years
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2
Lecture 7– Capital Budgeting: Decision Criteria
Strengths of Payback:
Discounted Payback: Uses discounted
rather than raw CFs.
1. Provides an indication of a
project’s risk and liquidity.
2. Easy to calculate and understand.
0
Weaknesses of Payback:
1. Ignores the Time Value of Money.
2. Ignores CFs occurring after the
payback period.
1
2
3
10
60
80
10%
CFt
-100
PVCFt
-100
9.09
49.59
60.11
Cumulative -100
-90.91
-41.32
18.79
Discounted
= 2
payback
+ 41.32/60.11 = 2.7 yrs
Recover invest. + cap. costs in 2.7 yrs.
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10
What is Franchise Long’s NPV?
Net Present Value (NPV) Method
NPV:
Sum of the PVs of inflows and outflows.
NPV =
n
t=0
Project L:
CF t
.
(1 + r )t
0
-100.00
Cost often is CF0 and is negative.
NPV =
n
t =1
10%
1
2
3
10
60
80
9.09
49.59
60.11
18.79 = NPVL
CF t
− CF 0 .
(1 + r )t
Notice difference in t
11
NPVS = $19.98.
12
3
Lecture 7– Capital Budgeting: Decision Criteria
Rationale for the NPV Method
Basket Wonders Example
NPV = PV inflows – Cost = Net gain in wealth.
Basket Wonders has determined that the appropriate
discount rate (r) for this project is 13%.
$10,000
NPV =
Choose between mutually exclusive projects on basis of
higher NPV. Adds most value.
$12,000 $15,000
+
+
(1.13)2
(1.13)3
(1.13)1
+
Accept project if NPV > 0.
$10,000
$7,000
+
(1.13)5
(1.13)4
Using NPV method, which franchise(s) should
be accepted?
- $40,000
If Franchise S and L are mutually exclusive, accept S
because NPVs > NPVL .
NPV = $8,850 + $9,396 + $10,395 + $6,130 + $3,801 - $40,000
=
- $1,428
If S & L are independent, accept both; NPV > 0.
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13
Internal Rate of Return: IRR
NPV: Enter r, solve for NPV.
0
1
2
3
CF0
Cost
CF1
CF2
Inflows
CF3
n
t=0
CF t
= NPV .
(1 + r )t
IRR: Enter NPV = 0, solve for IRR.
n
IRR is the discount rate that forces
PV inflows = cost. This is the same
as forcing NPV = 0.
t =0
15
CFt
(1 + IRR )
t
= 0.
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4
Lecture 7– Capital Budgeting: Decision Criteria
Rationale for the IRR Method
What’s Franchise Long’s IRR?
0
IRR = ?
-100.00
PV1
PV2
PV3
0 = NPV
1
10 (70s)
2
60 (50s)
3
If IRR > WACC, then the project’s
rate of return is greater than its
cost-- some return is left over to
boost stockholders’ returns.
80 (20s)
Example: WACC = 10%, IRR = 15%.
Profitable.
IRRL = 18.13%. IRRS = 23.56%.
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18
Decisions on Projects S and L per IRR
We can construct NPV profiles
We find NPVL and NPVS at different discount rates:
If S and L are independent, accept
both. IRRs > r = 10%.
r
0
5
10
15
20
If S and L are mutually exclusive,
accept S because IRRS > IRRL .
19
NPVL
50
33
19
7
(4)
NPVS
40
29
20
12
5
20
5
Lecture 7– Capital Budgeting: Decision Criteria
NPV ($)
r
0
5
10
15
20
60
50
Crossover
Point = 8.7%
40
30
20
S
10
NPV and IRR always lead to the same
accept/reject decision for independent
projects:
NPVS
40
29
20
12
5
NPV ($)
IRR > r
and NPV > 0
Accept.
r > IRR
and NPV < 0.
Reject.
IRRS = 23.6%
L
Discount Rate (%)
0
-10
NPVL
50
33
19
7
(4)
0
5
10
15
20
23.6
IRRL = 18.1%
IRR
r (%)
21
22
Two Reasons NPV Profiles Cross
Mutually Exclusive Projects
r < 8.7: NPVL> NPVS , IRRS > IRRL
CONFLICT
r > 8.7: NPVS> NPVL , IRRS > IRRL
NO CONFLICT
NPV
L
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 r favors small
projects.
2.
Timing differences. Project with faster payback provides
more CF in early years for reinvestment. If r is high, early
CF especially good, NPVS > NPVL.
Reinvestment Rate Assumptions
S
r
8.7
r
IRRL
IRRS
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.
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24
Lecture 7– Capital Budgeting: Decision Criteria
Managers like rates--prefer IRR to NPV
comparisons. Can we give them a
better IRR?
MIRR for Franchise L (r = 10%)
0
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.
10%
-100.0
1
2
3
10.0
60.0
80.0
10%
66.0
12.1
10%
MIRR =
16.5%
-100.0
Thus, MIRR assumes cash inflows are
reinvested at WACC.
PV outflows
$158.1
$100 =
(1+MIRRL)3
158.1
TV inflows
MIRRL = 16.5%
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26
Normal Cash Flow Project:
Why use MIRR versus IRR?
Cost (negative CF) followed by a series of
positive cash inflows. One change of signs.
MIRR correctly assumes reinvestment at
opportunity cost = WACC. MIRR also
avoids the problem of multiple IRRs.
Nonnormal Cash Flow Project:
Managers like rate of return
comparisons, and MIRR is better for this
than IRR.
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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Lecture 7– Capital Budgeting: Decision Criteria
Pavilion Project: NPV and IRR?
Inflow (+) or Outflow (-) in Year
0
1
2
3
4
5
N
-
+
+
+
+
+
N
-
+
+
+
+
-
-
-
-
+
+
+
N
+
+
+
-
-
-
N
-
+
+
-
+
-
NN
0
NN
-800
r = 10%
1
2
5,000
-5,000
NPV = -386.78
NN
IRR = ERROR. Why?
29
30
We got IRR = ERROR because there
are 2 IRRs. Nonnormal CFs--two sign
changes. Here’s a picture:
2. At very high discount rates, the PV of both
CF1 and CF2 are low, so CF0 dominates and
again NPV < 0.
IRR2 = 400%
450
-800
1. At very low discount rates, the PV of CF2 is
large & negative, so NPV < 0.
NPV Profile
NPV
0
Logic of Multiple IRRs
100
400
3. In between, the discount rate hits CF2
harder than CF1, so NPV > 0.
r
4. Result: 2 IRRs.
IRR1 = 25%
31
32
8
Lecture 7– Capital Budgeting: Decision Criteria
When there are nonnormal CFs and
more than one IRR, use MIRR:
0
1
-800,000
Accept Project P?
NO. Reject because MIRR = 5.6% < r =
10%.
2
5,000,000
-5,000,000
Also, if MIRR < r, NPV will be negative:
NPV = -$386,777.
PV outflows @ 10% = -4,932,231.40.
TV inflows @ 10% = 5,500,000.00.
MIRR = 5.6%
Should We Accept Project P?
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34
S and L are mutually exclusive
and will be repeated. r = 10%.
Profitability Index (PI)
PI is the ratio of the present value of a project’s future net cash
flows to the project’s initial cash outflow.
It measures the “bang for the buck.”
PI =
CF1
(1+r)1
+
CF2
(1+r)2
+...+
CFt
(1+r)t
0
ICO
Profitability Index Acceptance Criterion
Reject if PI < 1.00 ]
35
1
2
Project S:
60
(100)
60
Project L:
33.5
(100)
33.5
3
4
33.5
33.5
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Lecture 7– Capital Budgeting: Decision Criteria
Replacement Chain Approach
Franchise S with Replication:
NPVL > NPVS. But is L better?
All values in thousands
0
1
Franchise S:
60
(100)
(100)
Note that Project S could be repeated after 2 years
to generate additional profits.
60
2
3
4
60
(100)
(40)
60
60
60
60
NPV = $7,547.
37
38
Suppose cost to repeat S in two
years rises to $105,000.
Or, use NPVs:
0
4,132
3,415
7,547
1
10%
2
3
0
4
1
Franchise S:
(100)
60
4,132
Compare to Franchise L, where NPV = $6,190.
2
3
4
60
(105)
(45)
60
60
NPVS = $3,415 < NPVL = $6,190.
Now choose L.
39
10
40
Lecture 7– Capital Budgeting: Decision Criteria
Economic Life versus Physical Life
(Continued)
Economic Life versus Physical Life
Consider another project with a 3-year
life.
If terminated prior to Year 3, the
machinery will have positive salvage
value.
Should you always operate for the full
physical life?
See next slide for cash flows.
41
42
CFs Under Each Alternative (000s)
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&#
%
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!' $%
&# ( )
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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:
NPVs under Alternative Lives (Cost of capital = 10%)
NPV(3)
= -$123.
NPV(2)
= $215.
NPV(1)
= -$273.
An increasing marginal cost of capital.
The project is acceptable
only if operated for 2 years.
Capital rationing
A project’s engineering life
does not always equal its
economic life.
43
44
11
Lecture 7– Capital Budgeting: Decision Criteria
Capital Rationing
Increasing Marginal Cost of Capital
Capital rationing occurs when a company chooses not to fund all positive
NPV projects.
Externally raised capital can have large
flotation costs, which increase the cost of
capital.
The company typically sets an upper limit on the total amount of capital
expenditures that it will make in the upcoming year.
Investors often perceive large capital budgets
as being risky, which drives up the cost of
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.
If external funds will be raised, then the NPV of
all projects should be estimated using this
higher marginal cost of capital.
Solution: Use linear programming to maximize NPV subject to not
exceeding the constraints on staffing.
Reason: Companies want to avoid the direct costs (i.e., flotation costs)
and the indirect costs of issuing new capital.
Reason: Companies don’t have enough managerial, marketing, or
engineering staff to implement all positive NPV projects.
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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46
International Capital Budgeting
Increasing Marginal Cost of Capital
Find the PV of the foreign CF’s denominated in the foreign
currency and discounted by the foreign country’s cost of capital
Externally raised capital can have large flotation
costs, which increase the cost of capital.
Convert the PV of the CF’s to the home country’s currency
multiplying by the spot exchange rate
Investors often perceive large capital budgets as
being risky, which drives up the cost of capital.
Subtract the parent company’s initial cost from the Present values
of net cash flows to get the NPV
If external funds will be raised, then the NPV of all
projects should be estimated using this higher
marginal cost of capital.
Amount and Timing of Foreign CF’s will depend on
Differential tax rates
Legal and political constraints on CF
Government subsidized loans
47
48
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