1. Capital Budgeting: Decision Criteria
Chapter 12
Capital Budgeting:
Decision Criteria

2. Topics Overview Methods Unequal lives Economic life 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 firm’s 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
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.∑ n
t = 0
CFt
(1 + r)t .
NOTE: t=0
Cost often is CF0 and is negative
NPV = ∑ n
t = 1
CFt
(1 + r)t
- CF0

8. Project S’s NPV

9. Project L’s NPV

10. TI BAII+: Project L NPV Cash Flows: CF0 = -1000 CF1 = 100 CF2 = 300
Display You Enter '
C S !#
C !#
F !#
C !#
F !#
C !#
F !#
C !#
F !# (
I !#
NPV %
49.18
Cash Flows:
CF0 =
CF1 = 100
CF2 = 300
CF3 = 400
CF4 = 600

11. 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

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 > NPVL
If S & L are independent, accept both; NPV > 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 3:1

15. ∑ ∑ NPV vs IRR NPV: Enter r, solve for NPV CFt = NPV (1 + r)t
IRR: Enter NPV = 0, solve for IRR
= 0 ∑ n
t = 0
CFt
(1 + IRR)t

16. Franchise L’s IRR

17. TI BAII+: Project L IRR Cash Flows: CF0 = -1000 CF1 = 100 CF2 = 300
Display You Enter '
C S !#
C !#
F !#
C !#
F !#
C !#
F !#
C !#
F !# (
I !#
IRR %
11.79
Cash Flows:
CF0 =
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 > r and IRRL > r
If S and L are mutually exclusive, accept S because IRRS > 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 don’t cross, one project dominates the other

22. Finding the Crossover Rate

23. NPV and IRR: No conflict for independent projects
r > IRR
and NPV < 0.
Reject
NPV ($)
r (%)
IRR
IRR > r
and NPV > 0
Accept

24. Mutually Exclusive Projects
NPVS> NPVL
IRRS > IRRL
NO CONFLICT
r < 7.2%
NPVL> NPVS
IRRS > IRRL
CONFLICT
NPV L S
IRRS %
7.2
IRRL

25. Mutually Exclusive Projects
CONFLICT
r < 7.2%
NPVL> NPVS
IRRS > IRRL
r > 7.2%
NPVS > NPVL
IRRS > 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 > 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 project’s 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) =
N = 4
PMT = 0
CPY I/Y = = 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?
5,000
-5,000 1 2
r = 10%
-800
Enter CFs, enter I = 10
NPV =
IRR = ERROR

36. Nonnormal CFs: Two sign changes, two IRRs
NPV Profile
450
-800
400
100
IRR2 = 400%
IRR1 = 25% r
NPV

37. Multiple IRRs Descartes Rule of Signs 1 real root per sign change
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 < 0
At very high discount rates:
The PV of both CF1 and CF2 are low
CF0 dominates
Again NPV < 0

39. Logic of Multiple IRRs In between: Result: 2 IRRs
The discount rate hits CF2 harder than CF1
NPV > 0
Result: 2 IRRs

40. The Pavillion Project: Non-normal CFs and MIRR:1 2
-800,000
5,000,000
-5,000,000 RR FR
PV 10% = -4,932,231.40
TV 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 S’s PV of Cash Inflows

43. Profitability Indexs PV future CF $1078.82 PIS = = Initial Cost $1000
PIL =

44. 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

45. Profitability Index Strengths: Weaknesses: 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 project’s cost
How long does it take to get the business’s money back?
A breakeven-type measure
Rule: Accept if PB<Target

47. Payback for Projects S and L

48. Payback for Projects S and L

49. Strengths and Weaknesses of Payback
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%.1 2 3 4
Project SS:
(100)
Project LL: 60
33.5

55. NPVLL > NPVSS But is LL better?
CF0
-100,000
CF1
60,000
33,500 F 2 4 I 10
NPV
4,132
6,190

56. Solving for EAA PMT = 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) 56

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:
NPVSS = $7, Compare: NPVLL = $6,190 . 1 2 3 4
Project SS:
(100) 60
(40)

59. Or, use NPVss: Compare to Project LL NPV = $6,190 1 2 3 4 4,132 3,4151 2 3 4
4,132
3,415
7,547
10%

60. Suppose cost to repeat SS in two years rises to $105,000
NPVSS = $3,415 < NPVLL = $6,190 1 2 3 4
Project SS:
(100) 60
(105)
(45)

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 project’s 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 12
WACC1 = 11.0%
External debt & equity 10
No external funds 9 8
500
700
Capital Required 61 48

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
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
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

71. Capital Rationing – Reason 3
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

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