Capital Budgeting:

1
Chapter 12

• Capital Budgeting
• Decision Criteria

2
Topics

• Overview
• Methods
• NPV
• IRR, MIRR
• Profitability Index
• Payback, discounted payback
• Unequal lives
• Economic life

3
Capital Budgeting

• Analysis of potential projects
• Long-term decisions
• Large expenditures
• Difficult/impossible to reverse
• Determines firms strategic direction

4
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

5
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

6
Cash Flows for Projects L and S
7
NPV Sum of the PVs of all cash flows.
NOTE t0
Cost often is CF0 and is negative
8
Project Ss NPV
9
Project Ls NPV
10
TI BAII Project L NPV

• Display You Enter
• '
• C00 1000 S !
• C01 100 !
• F01 1 !
• C02 300 !
• F02 1 !
• C03 400 !
• F03 1 !
• C04 600 !
• F04 1 ! (
• I 10 !
• NPV
• 49.18

Cash Flows CF0 -1000 CF1 100 CF2 300 CF3
400 CF4 600
11
Rationale for the NPV Method

• NPV PV inflows Cost
• NPV0 ? Projects 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 gt 0

12
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

13
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 gt NPVL
• If S L are independent, accept both NPV gt 0

14
Internal Rate of Return IRR

• IRR the discount rate that forces
• PV inflows cost
• ? Forcing NPV 0
• YTM on a bond
• Preferred by executives 31

15
NPV vs IRR
NPV Enter r, solve for NPV
IRR Enter NPV 0, solve for IRR
16
Franchise Ls IRR
17
TI BAII Project L IRR

• Display You Enter
• '
• C00 1000 S !
• C01 100 !
• F01 1 !
• C02 300 !
• F02 1 !
• C03 400 !
• F03 1 !
• C04 600 !
• F04 1 ! (
• I 10 !
• IRR
• 11.79

Cash Flows CF0 -1000 CF1 100 CF2 300 CF3
400 CF4 600
18
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 gt
  r and IRRL gt r
• If S and L are mutually exclusive, accept S
  because IRRS gt IRRL

19
Construct NPV Profiles

• Enter CFs in CFLO and find NPVL and NPVS at
  different discount rates

20
NPV Profile
21
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 dont cross, one project dominates
  the other

22
Finding the Crossover Rate
23
NPV and IRR No conflict for independent projects
24
Mutually Exclusive Projects
r lt 7.2 NPVLgt NPVS IRRS gt IRRL
CONFLICT
r gt 7.2 NPVSgt NPVL IRRS gt IRRL NO
CONFLICT
NPV
L
IRRS
S

7.2
IRRL
25
Mutually Exclusive Projects
CONFLICT
r lt 7.2 NPVLgt NPVS IRRS gt IRRL
r gt 7.2 NPVS gt NPVL IRRS gt IRRL
NO CONFLICT
26
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 gt
  NPVL

27
Issues with IRR

• Reinvestment rate assumption
• Non-normal cash flows

28
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

29
Modified Internal Rate of Return (MIRR)

• MIRR discount rate which causes the PV of a
  projects terminal value (TV) to equal the PV of
  costs
• TV inflows compounded at WACC
• ?MIRR assumes cash inflows reinvested at WACC

30
MIRR for Project S First, find PV and TV (r
10)
31
Second Find discount rate that equates PV and TV
MIRR 12.1
32
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)

33
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

34
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

35
Pavilion Project NPV and IRR?
36
Nonnormal CFsTwo sign changes, two IRRs
37
Multiple IRRs

• Descartes Rule of Signs
• Polynomial of degree n?n roots
• 1 real root per sign change
• Rest imaginary (i2 -1)

38
Logic of Multiple IRRs

• At very low discount rates
• The PV of CF2 is large negative
• NPV lt 0

• At very high discount rates
• The PV of both CF1 and CF2 are low
• CF0 dominates
• Again NPV lt 0

39
Logic of Multiple IRRs

• In between
• The discount rate hits CF2 harder than CF1
• NPV gt 0
• Result 2 IRRs

40
The Pavillion ProjectNon-normal CFs and MIRR
1
2
0
-800,000
5,000,000
-5,000,000
RR
FR
PV outflows _at_ 10 -4,932,231.40
TV inflows _at_ 10 5,500,000.00
MIRR 5.6
41
Profitability Index

• PI present value of future cash flows divided by
  the initial cost
• Measures the bang for the buck

42
Project Ss PV of Cash Inflows
43
Profitability Indexs
PV future CF
1078.82
PIS

Initial Cost
1000
PIS 1.0788 PIL 1.0492
44
Profitability Index

• Rule If PIgt1.0 ? Accept
• Useful in capital rationing
• Closely related to NPV
• Can conflict with NPV if projects are mutually
  exclusive

45
Profitability Index

• Strengths
• Considers all CFs
• Considers TVM
• Useful in capital rationing
• Weaknesses
• Cannot rank mutually exclusive
• Not Value-additive

46
Payback Period

• The number of years required to recover a
  projects cost
• How long does it take to get the businesss money
  back?
• A breakeven-type measure
• Rule Accept if PBltTarget

47
Payback for Projects S and L
48
Payback for Projects S and L
49
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!

50
Discounted Payback Use discounted CFs
51
Summary

• Calculate ALL -- each has value
• Method What it measures Metric
• NPV ? increase in VF
• Payback ? Liquidity Years
• IRR ? E(R), risk
• MIRR ? Corrects IRR
• PI ? If rationed Ratio

52
Business Practices
53
Special Applications

• Projects with Unequal Lives
• Economic vs. Physical life
• The Optimal Capital Budget
• Capital Rationing

54
SS and LL are mutually exclusive. r 10.
55
NPVLL gt NPVSS But is LL better?
SS LL
CF0 -100,000 -100,000
CF1 60,000 33,500
F 2 4
I 10 10
NPV 4,132 6,190
56
Solving for EAAPMT EAA
Project SS
Project LL
2 , 10 - 4132 S. 0 0 / 2.38
4 , 10 - 6190 S. 0 0 / 1.95
PMT(0.10,2,-4132,0)
PMT(0.10,4,-6190,0)
57
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.

58
Replacement Chain Approach (000s)Project SS with
Replication
59
Or, use NPVss
60
Suppose cost to repeat SS in two years rises to
105,000
61
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?

62
Economic Life vs. Physical Life
63
Economic vs. Physical Life
64
Conclusions

• NPV(3) -14.12
• NPV(2) 34.71
• NPV(1) -254.55
• The project is acceptable only if operated for 2
  years.
• A projects engineering life does not always
  equal its economic life.

65
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

66
Increasing Marginal Cost of Capital

• Externally raised capital ? large flotation costs
• Increases the cost of capital
• Investors often perceive large capital budgets as
  being risky
• 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

67
Increasing Marginal Cost of Capital
16

15
14
WACC2 12.5
13
WACC1 11.0
12
External debt equity
10
No external funds
9
8
700
500
Capital Required
61
68
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

69
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

70
Capital Rationing Reason 2

• Reason
• Companies dont 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

71
Capital Rationing Reason 3

• Reason
• Companies believe that the projects 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

72
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)

73
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