the capital budgeting evaluating cash flows

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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
CHAPTER 8
The Capital Budgeting:
Evaluating Cash Flows
 8.1 Overview
 8.2 Payback Period
 8.3 Net Present Value
 8.4 Profitability Index
 8.5 Internal Rate of Return
 Unequal lives
 Economic life
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
8.1 Overview
 Analysis of potential projects.
 Long-term decisions; involve large
expenditures.
 Very important to firm’s future.
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
Steps in Capital Budgeting
 Estimate cash flows (inflows &
outflows).
 Assess risk of cash flows.

 Determine r = WACC for project.
 Evaluate cash flows.
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
8.2 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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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
Payback for Franchise L
(Long: Most CFs in out years)
10 80 60
0 1 2 3
-100
=
CF
t
Cumulative -100 -90 -30 50
Payback
L
2 + 30/80 = 2.375 years
0
100
2.4
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
Franchise S (Short: CFs come
quickly)
70 20 50
0 1 2 3
-100 CF
t
Cumulative -100 -30 20 40

Payback
S
1 + 30/50 = 1.6 years
100
0
1.6
=
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
10 80 60
0 1 2 3
CF
t
Cumulative -100 -90.91 -41.32 18.79
Discounted
payback

2 + 41.32/60.11 = 2.7 yrs
Discounted Payback: Uses discounted
rather than raw CFs.
PVCF
t
-100
-100
10%
9.09 49.59 60.11
=
Recover invest. + cap. costs in 2.7 yrs.
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
8.3 Net Present Value

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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
 
.
1
0
t
t
n
t
r

CF
NPV




NPV: Sum of the PVs of inflows and
outflows.
Cost often is CF
0
and is negative.
 
.
1
0
1
CF
r
CF
NPV
t
t
n
t





12

B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
What’s Franchise L’s NPV?
10 80 60
0 1 2 3
10%
Project L:
-100.00
9.09
49.59
60.11
18.79 = NPV
L
NPV
S
= $19.98.
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
Calculator Solution
Enter in CFLO for L:
-100
10
60
80
10
CF
0

CF
1
NPV
CF
2
CF
3
I
= 18.78 = NPV
L
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
Using NPV method, which
franchise(s) should be accepted?
 If Franchise S and L are

mutually exclusive, accept S
because NPV
s
> NPV
L
.
 If S & L are independent,
accept both; NPV > 0.
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012

8.4 Profitability Index

Profitability index (PI), also known as profit investment
ratio (PIR) and value investment ratio (VIR), is the ratio of
payoff to investment of a proposed project. It is a useful tool
for ranking projects because it allows you to quantify the
amount of value created per unit of investment.
The ratio is calculated as follows:

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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
8.5 Internal Rate of Return
0 1 2 3
CF
0

CF
1
CF
2
CF
3
Cost Inflows
IRR is the discount rate that forces
PV inflows = cost. This is the same
as forcing NPV = 0.
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
 
.
1
0
NPV
r
CF
t
t
n
t




 

t
n
t
t
CF
IRR




0
1
0.
NPV: Enter r, solve for NPV.
IRR: Enter NPV = 0, solve for IRR.
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
What’s Franchise L’s IRR?
10 80 60
0 1 2 3
IRR = ?
-100.00
PV
3
PV
2
PV
1

0 = NPV
Enter CFs in CFLO, then press IRR:
IRR
L
= 18.13%. IRR
S
= 23.56%.
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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%
N I/YR PV PMT FV
INPUTS
OUTPUT
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
Decisions on Projects S and L per IRR
 If S and L are independent, accept
both. IRRs > r = 10%.
 If S and L are mutually exclusive,
accept S because IRR
S
> IRR
L
.
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
Construct NPV Profiles
Enter CFs in CFLO and find NPV
L
and
NPV
S
at different discount rates:

r
0
5
10
15
20

NPV
L
50
33
19
7

NPV
S
40
29
20
12
5
(4)
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
-10
0
10
20

30
40
50
60
0 5 10 15 20 23.6
NPV ($)
Discount Rate (%)
IRR
L
= 18.1%
IRR
S
= 23.6%
Crossover
Point = 8.7%
r
0
5
10
15
20
NPV
L
50
33
19
7
(4)
NPV
S

40
29
20
12
5
S
L
25
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
NPV and IRR always lead to
the same accept/reject
decision for independent
projects:
r > IRR
and NPV < 0.
Reject.
NPV ($)
r (%)
IRR
IRR > r
and NPV > 0
Accept.
26
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
Mutually Exclusive Projects
r 8.7 r

NPV
%
IRR
S
IRR
L
L
S
r < 8.7: NPV
L
> NPV
S
, IRR
S
> IRR
L

CONFLICT
r > 8.7: NPV
S
> NPV
L
, IRR
S
> IRR
L

NO CONFLICT
27
B02022 – Chapter 8 -The Criteria of Capital

Budgeting
23/8/2012
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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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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 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, NPV
S
> NPV

L
.
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
Reinvestment Rate
Assumptions
 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.
30
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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.
31

B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
MIRR =
16.5%
10.0 80.0 60.0
0 1 2 3
10%
66.0
12.1
158.1
MIRR for Franchise L (r = 10%)
-100.0
10%
10%
TV inflows
-100.0
PV outflows
MIRR
L
= 16.5%
$100 =
$158.1
(1+MIRR
L
)
3
32
B02022 – Chapter 8 -The Criteria of Capital
Budgeting

23/8/2012
To find TV with 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.
CF
0
= 0, CF
1
= 10, CF
2
= 60, CF
3
= 80
33
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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.
34
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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.
35
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
Inflow (+) or Outflow (-) in Year
0 1 2 3 4 5 N NN
- + + + + + N
- + + + + - NN
- - - + + + N
+ + + - - - N
- + + - + - NN
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012

Pavilion Project: NPV and IRR?
5,000 -5,000
0 1 2
r = 10%
-800
Enter CFs in CFLO, enter I = 10.
NPV = -386.78
IRR = ERROR. Why?
37
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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
IRR
2
= 400%
IRR
1
= 25%
r
NPV
38

B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
Logic of Multiple IRRs
1. At very low discount rates, the PV of
CF
2
is large & negative, so NPV < 0.
2. At very high discount rates, the PV of
both CF
1
and CF
2
are low, so CF
0

dominates and again NPV < 0.
3. In between, the discount rate hits CF
2

harder than CF
1
, so NPV > 0.
4. Result: 2 IRRs.
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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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
40
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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%
41
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
Accept Project P?
NO. Reject because MIRR =
5.6% < r = 10%.

Also, if MIRR < r, NPV will be
negative: NPV = -$386,777.
42

B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
S and L are mutually exclusive
and will be repeated. r = 10%.
Which is better? (000s)
0 1 2 3 4
Project S:
(100)
Project L:
(100)

60

33.5

60

33.5



33.5



33.5
43
B02022 – Chapter 8 -The Criteria of Capital
Budgeting

23/8/2012
S L
CF
0
-100,000 -100,000
CF
1
60,000 33,500
N
j
2 4
I 10 10

NPV 4,132 6,190
NPV
L
> NPV
S
. But is L better?
Can’t say yet. Need to perform
common life analysis.
44
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
 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.
45
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
Franchise S with Replication:
NPV = $7,547.
Replacement Chain
Approach (000s)
0 1 2 3 4
Franchise S:
(100)

(100)

60

60

60
(100)
(40)


60
60


60
60

46
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
Compare to Franchise L NPV =
$6,190.
Or, use NPVs:
0 1 2 3 4
4,132
3,415
7,547
4,132
10%
47
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
If the cost to repeat S in two
years rises to $105,000,
which is best? (000s)
NPV
S
= $3,415 < NPV
L
= $6,190.
Now choose L.
0 1 2 3 4
Franchise S:
(100)

60


60
(105)
(45)


60


60
48
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
Year
0
1
2
3
CF
($5,000)
2,100
2,000
1,750
Salvage Value
$5,000
3,100

2,000
0
Consider another project with
a 3-year life. If terminated prior
to Year 3, the machinery will
have positive salvage value.
49
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
1.75

1. No termination
2. Terminate 2 years
3. Terminate 1 year
(5)
(5)
(5)
2.1
2.1
5.2
2
4

0 1 2 3
CFs Under Each
Alternative (000s)
50
B02022 – Chapter 8 -The Criteria of Capital
Budgeting

23/8/2012
NPV
(no)
= -$123.
NPV
(2)
=

$215.
NPV
(1)
= -$273.
Assuming a 10% cost of
capital, what is the project’s
optimal, or economic life?
51
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
 The project is acceptable only if
operated for 2 years.
 A project’s engineering life does not
always equal its economic life.
Conclusions
52
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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
53
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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 )
54
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
 If external funds will be raised, then
the NPV of all projects should be
estimated using this higher marginal
cost of capital.
55

B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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 )
56
B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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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B02022 – Chapter 8 -The Criteria of Capital
Budgeting

23/8/2012
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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B02022 – Chapter 8 -The Criteria of Capital
Budgeting
23/8/2012
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.