Chapter 12
Capital Budgeting:
Decision Criteria
1
Topics


Overview
Methods






NPV
IRR, MIRR
Profitability Index
Payback, discounted payback
Unequal lives
Economic life
2
Capital Budgeting:





Analysis of potential projects
Long-term decisions
Large expenditures
Difficult/impossible to reverse
Determines firm’s strategic direction
3
Steps in Capital Budgeting




Estimate cash flows (Ch 13)
Assess risk of cash flows (Ch 13)
Determine r = WACC for project (Ch10)
Evaluate cash flows – Chapter 12
4
Independent versus Mutually
Exclusive Projects

Independent:


The cash flows of one are unaffected by
the acceptance of the other
Mutually Exclusive:

The acceptance of one project precludes
accepting the other
5
Cash Flows for Projects L and S
6
NPV: Sum of the PVs of all
cash flows.
n
NPV = ∑
t=0
CFt .
(1 + r)t
NOTE: t=0
Cost often is CF0 and is negative
n
NPV = ∑
t=1
CFt
(1 + r)t
- CF0
7
Project S’s NPV
NPV for Project S
10%
t =
S's CFs
0
1
2
3
4
-1000
500
400
300
100
-1000
454.55
330.58
225.39
68.30
$78.82
8
Project L’s NPV
NPV for Project L
10%
t =
L's CFs
0
1
2
3
4
-1000
100
300
400
600
-1000
90.91
247.93
300.53
409.81
$49.18
9
TI BAII+: Project L NPV
Display
Cash Flows:
You Enter
'
CF0
=
-1000
CF1
=
100
CF2
=
300
CF3
=
400
CF4
=
600
C00
C01
F01
C02
F02
C03
F03
C04
F04
I
NPV
49.18
1000
100
1
300
1
400
1
600
1
10
%
S !#
!#
!#
!#
!#
!#
!#
!#
!# (
!#
10
Rationale for the NPV Method

NPV = PV inflows – Cost




NPV=0 → Project’s inflows are “exactly sufficient to repay
the invested capital and provide the required rate of return.”
NPV = net gain in shareholder wealth
Choose between mutually exclusive projects on basis
of higher NPV
Rule: Accept project if NPV > 0
11
NPV Method

Meets all desirable criteria






Considers all CFs
Considers TVM
Can rank mutually exclusive projects
Value-additive
Directly related to increase in VF
Dominant method; always prevails
12
Using NPV method, which
franchise(s) should be accepted?


Project S NPV = $78.82
Project L NPV = $49.18
If Franchise S and L are mutually
exclusive, accept S because NPVs >
NPVL
If S & L are independent, accept both;
NPV > 0
13
Internal Rate of Return: IRR
• IRR = the discount rate that forces
PV inflows = cost
•  Forcing NPV = 0
• ≈ YTM on a bond
• Preferred by executives 3:1
14
NPV vs IRR
NPV: Enter r, solve for NPV
n CF
t
=
NPV
∑ (1 + r)t
t=0
IRR: Enter NPV = 0, solve for IRR
n
∑
t=0
CFt
=0
(1 + IRR)t
15
Franchise L’s IRR
IRR for Project L
?%
t =
L's CFs
NPV =
0
1
2
3
4
-1000
100
300
400
600
-1000
PV(1)
PV(2)
PV(3)
PV(4)
$0.00
16
TI BAII+: Project L IRR
Display
Cash Flows:
You Enter
'
CF0
=
-1000
CF1
=
100
CF2
=
300
CF3
=
400
CF4
=
600
C00
C01
F01
C02
F02
C03
F03
C04
F04
I
IRR
11.79
1000
100
1
300
1
400
1
600
1
10
%
S !#
!#
!#
!#
!#
!#
!#
!#
!# (
!#
17
Decisions on Projects S and L
per IRR





Project S IRR = 14.5%
Project L IRR = 11.8%
Cost of capital = 10.0%
If S and L are independent, accept
both: IRRS > r and IRRL > r
If S and L are mutually exclusive,
accept S because IRRS > IRRL
18
Construct NPV Profiles

Enter CFs in CFLO and find NPVL and NPVS
at different discount rates:
r
0
5%
10%
15%
20%
NPV (S)
$300.00
$180.42
$78.82
($8.33)
($83.72)
NPV(L)
$400.00
$206.50
$49.18
($80.14)
($187.50)
19
NPV Profile
20
To Find the Crossover Rate





Find cash flow differences between the
projects.
Enter these differences in CFLO register, then
press IRR.
Crossover rate = 7.17%, rounded to 7.2%.
Can subtract S from L or vice versa
If profiles don’t cross, one project dominates
the other
21
Finding the Crossover Rate
t
0
1
2
3
4
S
-1000
500
400
300
100
L
-1000
100
300
400
600
Diff
0
400
100
-100
-500
7.2%
22
NPV and IRR:
No conflict for independent projects
NPV ($)
IRR > r
and NPV > 0
Accept
r > IRR
and NPV < 0.
Reject
IRR
r (%)
23
Mutually Exclusive Projects
r > 7.2%
NPVS> NPVL
IRRS > IRRL
NO CONFLICT
NPV
L
S
7.2
r < 7.2%
NPVL> NPVS
IRRS > IRRL
CONFLICT
IRRS
%
IRRL
24
Mutually Exclusive Projects
CONFLICT
r
0
5%
10%
15%
20%
IRR
NPV (S)
$300.00
$180.42
$78.82
($8.33)
($83.72)
14.5%
NPV(L)
$400.00
$206.50
$49.18
($80.14)
($187.50)
11.8%
r < 7.2%
NPVL> NPVS
IRRS > IRRL
r > 7.2%
NPVS > NPVL
IRRS > IRRL
NO CONFLICT
25
Two Reasons NPV Profiles Cross

Size (scale) differences



Smaller project frees up funds sooner for
investment
The higher the opportunity cost, the more
valuable these funds, so high r favors small
projects
Timing differences


Project with faster payback provides more CF in
early years for reinvestment
If r is high, early CF especially good, NPVS > NPVL
26
Issues with IRR
Reinvestment rate assumption
 Non-normal cash flows

27
Reinvestment Rate Assumption




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
28
Modified Internal Rate of
Return (MIRR)

MIRR = discount rate which causes the
PV of a project’s terminal value (TV) to
equal the PV of costs


TV = inflows compounded at WACC
MIRR assumes cash inflows
reinvested at WACC
29
MIRR for Project S:
First, find PV and TV (r = 10%)
MIRR for Project S
r = 10%
t =
S's CFs
0
1
2
3
4
-1000
500
400
300
100
330
484
665.5
-1000.00
PV Outflows
1579.5
TV Inflows
30
Second: Find discount rate
that equates PV and TV
MIRR for Project S
r = 10%
t =
S's CFs
0
1
2
3
4
-1000
500
400
300
100
330
484
665.5
-1000.00
PV Outflows
1579.5
TV Inflows
1579.5
M IRR 
( 1  M IRR) 4
MIRR = 12.1%
31
Second: Find discount rate
that equates PV and TV

PV = PV(Outflows) = -1000
FV = TV(Inflows) = 1579.5
N=4
PMT = 0
CPY I/Y = 12.1063 = 12.1%

EXCEL: =MIRR(Value Range, FR, RR)




32
MIRR versus IRR



MIRR correctly assumes reinvestment at
opportunity cost = WACC
MIRR avoids the multiple IRR problem
Managers like rate of return comparisons,
and MIRR is better for this than IRR
33
Normal vs. Nonnormal Cash Flows

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
For example, nuclear power plant or strip mine
34
Pavilion Project: NPV and IRR?
0
-800
r = 10%
1
2
5,000
-5,000
Enter CFs, enter I = 10
NPV = -386.78
IRR = ERROR
35
Nonnormal CFs:
Two sign changes, two IRRs
NPV Profile
NPV
IRR2 = 400%
450
0
-800
100
400
r
IRR1 = 25%
36
Multiple IRRs

Descartes Rule of Signs
n
CFt
0

t
t  0 ( 1  IRR )

Polynomial of degree n→n roots


1 real root per sign change
Rest = imaginary (i2 = -1)
37
Logic of Multiple IRRs

At very low
discount rates:


The PV of CF2 is
large & negative
NPV < 0

At very high discount
rates:



Year
0
1
2
CF
$ (800,000)
$ 5,000,000
$ (5,000,000)
NPV
$
The PV of both CF1
and CF2 are low
CF0 dominates
Again NPV < 0
Discounted Cash Flows
10%
50%
($800,000.0)
($800,000.0)
$4,545,454.5
$3,333,333.3
($4,132,231.4)
($2,222,222.2)
(386,776.76) $
311,111.61 $
500%
($800,000.0)
$833,333.3
($138,888.9)
(105,550.56)
38
Logic of Multiple IRRs

In between:



Year
0
1
2
The discount rate hits CF2 harder
than CF1
NPV > 0
Result: 2 IRRs
CF
$ (800,000)
$ 5,000,000
$ (5,000,000)
NPV
$
Discounted Cash Flows
10%
50%
($800,000.0)
($800,000.0)
$4,545,454.5
$3,333,333.3
($4,132,231.4)
($2,222,222.2)
(386,776.76) $
311,111.61 $
500%
($800,000.0)
$833,333.3
($138,888.9)
(105,550.56)
39
The Pavillion Project:
Non-normal CFs and MIRR:
1
0
-800,000
2
5,000,000
-5,000,000
RR
FR
PV outflows @ 10% = -4,932,231.40
TV inflows @ 10% = 5,500,000.00
MIRR = 5.6%
40
Profitability Index


PI =present value of future cash flows
divided by the initial cost
Measures the “bang for the buck”
41
Project S’s PV of Cash Inflows
t =
S's CFs
0
-1000
PV of Inflows for Project S
10%
1
2
500
400
3
4
300
100
454.55
330.58
225.39
68.30
$1,078.82
42
Profitability Indexs
PIS =
PV future CF
Initial Cost
=
$1078.82
$1000
PIS = 1.0788
PIL = 1.0492
43
Profitability Index




Rule: If PI>1.0  Accept
Useful in capital rationing
Closely related to NPV
Can conflict with NPV if projects are
mutually exclusive
44
Profitability Index

Strengths:




Considers all CFs
Considers TVM
Useful in capital rationing
Weaknesses:


Cannot rank mutually exclusive
Not Value-additive
45
Payback Period




The number of years required to
recover a project’s cost
How long does it take to get the
business’s money back?
A breakeven-type measure
Rule: Accept if PB<Target
46
Payback for Projects S and L
Payback Years before full recovery 
Unrecovered cost at start of year
Cash flow during year
47
Payback for Projects S and L
t =
S's CFs
Cumulative
0
-1000
-1000
Payback for Project S
1
2
500
-500
400
-100
Payback =
t =
L's CFs
Cumulative
0
-1000
-1000
300
-600
Payback =
Payback Years before full recovery 
4
300
200
100
300
3
4
400
-200
600
400
2.33
Payback for Project L
1
2
100
-900
3
3.33
Unrecovered cost at start of year
Cash flow during year
48
Strengths and Weaknesses of
Payback

Strengths:



Provides indication of project risk and liquidity
Easy to calculate and understand
Weaknesses:




Ignores the TVM
Ignores CFs occurring after the payback period
Biased against long-term projects
ASKS THE WRONG QUESTION!
49
Discounted Payback:
Use discounted CFs
r = 10%
S's CFs
Discounted CFs
Cumulative
Discounted Payback for Project S
0
1
2
-1000
-1000
-1000
500
454.55
-545.45
L's CFs
Discounted CFs
Cumulative
4
300
225.39
10.52
100
68.30
78.82
3
4
400
300.53
-360.63
600
409.81
49.18
400
330.58
-214.88
Discounted Payback =
r = 10%
3
2.95
Discounted Payback for Project L
0
1
2
-1000
-1000
-1000
100
90.91
-909.09
Discounted Payback =
300
247.93
-661.16
3.88
50
Summary

Calculate ALL -- each has value
Method





NPV
Payback
IRR
MIRR
PI





What it measures
Metric
$ increase in VF
Liquidity
E(R), risk
Corrects IRR
If rationed
$$
Years
%
%
Ratio
51
Business Practices
52
Special Applications

Projects with Unequal Lives

Economic vs. Physical life

The Optimal Capital Budget

Capital Rationing
53
SS and LL are mutually exclusive.
r = 10%.
0
1
2
Project SS:
60
(100)
60
Project LL:
33.5
(100)
33.5
3
4
33.5
33.5
54
NPVLL > NPVSS
But is LL better?
SS
CF0
CF1
F
I
NPV
LL
-100,000 -100,000
60,000
33,500
2
4
10
10
4,132
6,190
55
Solving for EAA
PMT = EAA
Project SS
2
,
10
4132 S.
0
0
%/ = 2.38
=PMT(0.10,2,-4132,0)
Project LL
4
,
10
6190 S.
0
0
%/ = 1.95
=PMT(0.10,4,-6190,0)
56
Unequal Lives



Project SS could be repeated after 2
years to generate additional profits
Use Replacement Chain to put
projects on a common life basis
Note: equivalent annual annuity
analysis is alternative method.
57
Replacement Chain Approach (000s)
Project SS with Replication:
0
1
2
3
4
60
(100)
(40)
60
60
60
60
Project SS:
(100)
(100)
60
60
NPVSS = $7,547
.
Compare: NPVLL = $6,190
58
Or, use NPVss:
0
4,132
3,415
7,547
1
10%
2
3
4
4,132
Compare to Project LL NPV = $6,190
59
Suppose cost to repeat SS in two
years rises to $105,000
0
1
Project SS:
(100)
60
2
3
4
60
(105)
(45)
60
60
NPVSS = $3,415 < NPVLL = $6,190
60
Economic Life vs. Physical Life



Consider a 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?
61
Economic Life vs. Physical Life
62
Economic vs. Physical Life
ECONOMIC vs. PHYSICAL LIFE
YR
0
1
2
3
CF
-$4,800
$2,000
$2,000
$1,750
SV
$4,800
$3,000
$1,650
$0
NPV
r = 10%
CFs if Terminated in Year
3
2
1
-$4,800
-$4,800
-$4,800
$2,000
$2,000
$5,000
$2,000
$3,650
$1,750
($14.12)
$34.71
($254.55)
63
Conclusions


NPV(3) = -$14.12
NPV(2) = $34.71
NPV(1) = -$254.55
The project is acceptable only if
operated for 2 years.
A project’s engineering life does not
always equal its economic life.
64
The Optimal Capital Budget

Finance theory says:


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
65
Increasing Marginal Cost of Capital

Externally raised capital  large flotation
costs


Investors often perceive large capital budgets
as being risky


Increases the cost of capital
Drives up the 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
66
Increasing Marginal Cost of Capital
% 16
15
14
WACC2 = 12.5%
13
12
WACC1 = 11.0%
External
debt & equity
10
9
No external funds
8
500
700 Capital Required
61
Capital Rationing


Firm chooses not to fund all positive
NPV projects
Company typically sets an upper limit
on the total amount of capital
expenditures that it will make in the
upcoming year
68
Capital Rationing – Reason 1

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
Then accept all projects that still have a
positive NPV with the higher cost of capital
69
Capital Rationing – Reason 2

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
70
Capital Rationing – Reason 3

Reason:



Companies believe that the project’s managers
forecast unreasonably high cash flow estimates
“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
71
Excel Spreadsheet Functions







FV(Rate,Nper,Pmt,PV,0/1)
PV(Rate,Nper,Pmt,FV,0/1)
RATE(Nper,Pmt,PV,FV,0/1)
NPER(Rate,Pmt,PV,FV,0/1)
PMT(Rate,Nper,PV,FV,0/1)
Inside parens: (RATE,NPER,PMT,PV,FV,0/1)
“0/1” Ordinary annuity = 0 (default; no entry needed)
Annuity Due = 1 (must be entered)
72
Excel Spreadsheet Functions



NPV(Rate, Value Range**)
IRR(Value Range)
MIRR(Value Range, FR, RR)
** NPV value range includes CF1 through CFn
CF0 must be handled independently, outside the function
=NPV(Rate, CF1-CFn) + CF0
73