1. Capital Budgeting Techniques
Chapter 13
Capital Budgeting Techniques

2. After Studying Chapter 13, you should be able to:
Understand the payback period (PBP) method of project evaluation and selection, including its: (a) calculation; (b) acceptance criterion; (c) advantages and disadvantages; and (d) focus on liquidity rather than profitability.
Understand the three major discounted cash flow (DCF) methods of project evaluation and selection – internal rate of return (IRR), net present value (NPV), and profitability index (PI).
Explain the calculation, acceptance criterion, and advantages (over the PBP method) for each of the three major DCF methods.
Define, construct, and interpret a graph called an “NPV profile.”
Understand why ranking project proposals on the basis of IRR, NPV, and PI methods “may” lead to conflicts in rankings.
Describe the situations where ranking projects may be necessary and justify when to use either IRR, NPV, or PI rankings.
Understand how “sensitivity analysis” allows us to challenge the single-point input estimates used in traditional capital budgeting analysis.
Explain the role and process of project monitoring, including “progress reviews” and “post-completion audits.”

3. Capital Budgeting Techniques
Project Evaluation and Selection
Potential Difficulties
Capital Rationing
Project Monitoring
Post-Completion Audit

4. Project Evaluation: Alternative Methods
Payback Period (PBP)
Internal Rate of Return (IRR)
Net Present Value (NPV)
Profitability Index (PI)
Refer to the additional PowerPoint slides and the Excel spreadsheet “VW13E-13b.xlsx” for computer-based solutions.

5. Proposed Project Data
Julie Miller 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. The initial cash outlay will be $40,000.

6. Independent Project
For this project, assume that it is independent of any other potential projects that Basket Wonders may undertake.
Independent – A project whose acceptance (or rejection) does not prevent the acceptance of other projects under consideration.

7. Payback Period (PBP)
–40 K K K K K K
PBP is the period of time required for the cumulative expected cash flows from an investment project to equal the initial cash outflow.

8. Payback Solution (#1)
(a)
–40 K K K K K K
(-b)
(d)
10 K K K K K
(c)
Cumulative
Inflows
PBP = a + ( b – c ) / d = 3 + (40 – 37) / 10 = 3 + (3) / = 3.3 Years

9. Note: Take absolute value of last negative cumulative cash flow value.
Payback Solution (#2)
–40 K K K K K K
–40 K –30 K –18 K –3 K K K
PBP = 3 + ( 3K ) / 10K = 3.3 Years
Note: Take absolute value of last negative cumulative cash flow value.
Cumulative
Cash Flows

10. PBP Acceptance Criterion
The management of Basket Wonders has set a maximum PBP of 3.5 years for projects of this type.
Should this project be accepted?
Yes! The firm will receive back the initial cash outlay in less than 3.5 years. [3.3 Years < 3.5 Year Max.]

11. PBP Strengths and Weaknesses
Easy to use and understand
Can be used as a measure of liquidity
Easier to forecast ST than LT flows
Weaknesses:
Does not account for TVM
Does not consider cash flows beyond the PBP
Cutoff period is subjective

12. Internal Rate of Return (IRR)
IRR is the discount rate that equates the present value of the future net cash flows from an investment project with the project’s initial cash outflow.
CF CF CFn
ICO = +
(1 + IRR)1 (1 + IRR) (1 + IRR)n

13. IRR Solution $10,000 $12,000 $40,000 = + + (1+IRR)1 (1+IRR)2
$10, $12,000
$40,000 = + +
(1+IRR) (1+IRR)2
$15, $10, $7,000 + +
(1+IRR) (1+IRR) (1+IRR)5
Find the interest rate (IRR) that causes the discounted cash flows to equal $40,000.

14. IRR Solution (Try 10%)
$40,000 = $10,000(PVIF10%,1) + $12,000(PVIF10%,2) + $15,000(PVIF10%,3) + $10,000(PVIF10%,4) + $ 7,000(PVIF10%,5)
$40,000 = $10,000(0.909) + $12,000(0.826) + $15,000(0.751) + $10,000(0.683) + $ 7,000(0.621)
$40,000 = $9,090 + $9,912 + $11, $6,830 + $4, = $41,444 [Rate is too low!!]

15. IRR Solution (Try 15%)
$40,000 = $10,000(PVIF15%,1) + $12,000(PVIF15%,2) + $15,000(PVIF15%,3) + $10,000(PVIF15%,4) + $ 7,000(PVIF15%,5)
$40,000 = $10,000(0.870) + $12,000(0.756) + $15,000(0.658) + $10,000(0.572) + $ 7,000(0.497)
$40,000 = $8,700 + $9,072 + $9, $5,720 + $3, = $36,841 [Rate is too high!!]

16. IRR Solution (Interpolate)
0.10 $41,444
0.05 IRR $40, $4,603
0.15 $36,841
X $1, $4,603
$1,444 X =

17. IRR Solution (Interpolate)
0.10 $41,444
0.05 IRR $40, $4,603
0.15 $36,841
X $1, $4,603
$1,444 X =

18. IRR Solution (Interpolate)
0.10 $41,444
0.05 IRR $40, $4,603
0.15 $36,841
($1,444)(0.05) $4,603
$1,444 X
X =
X =
IRR = = or 11.57%

19. IRR Acceptance Criterion
The management of Basket Wonders has determined that the hurdle rate is 13% for projects of this type.
Should this project be accepted?
No! The firm will receive 11.57% for each dollar invested in this project at a cost of 13%. [ IRR < Hurdle Rate ]

20. IRRs on the Calculator
We will use the cash flow registry to solve the IRR for this problem quickly and accurately!

21. Actual IRR Solution Using Your Financial Calculator
Steps in the Process
Step 1: Press CF key
Step 2: Press 2nd CLR Work keys
Step 3: For CF0 Press Enter  keys
Step 4: For C01 Press Enter  keys
Step 5: For F01 Press Enter  keys
Step 6: For C02 Press Enter  keys
Step 7: For F02 Press Enter  keys
Step 8: For C03 Press Enter  keys
Step 9: For F03 Press Enter  keys

22. Actual IRR Solution Using Your Financial Calculator
Steps in the Process (Part II)
Step 10:For C04 Press Enter  keys
Step 11:For F04 Press Enter  keys
Step 12:For C05 Press Enter  keys
Step 13:For F05 Press Enter  keys
Step 14: Press   keys
Step 15: Press IRR key
Step 16: Press CPT key
Result: Internal Rate of Return = 11.47%

23. IRR Strengths and Weaknesses
Accounts for TVM
Considers all cash flows
Less subjectivity
Weaknesses:
Assumes all cash flows reinvested at the IRR
Difficulties with project rankings and Multiple IRRs

24. Net Present Value (NPV)
NPV is the present value of an investment project’s net cash flows minus the project’s initial cash outflow.
CF CF CFn
- ICO
NPV = +
(1+k)1 (1+k) (1+k)n

25. NPV Solution
Basket Wonders has determined that the appropriate discount rate (k) for this project is 13%.
$10, $12,000 $15,000
NPV = + + +
(1.13) (1.13) (1.13)3
$10, $7,000 +
- $40,000
(1.13) (1.13)5

26. NPV Solution
NPV = $10,000(PVIF13%,1) + $12,000(PVIF13%,2) + $15,000(PVIF13%,3) + $10,000(PVIF13%,4) + $ 7,000(PVIF13%,5) – $40,000
NPV = $10,000(0.885) + $12,000(0.783) + $15,000(0.693) + $10,000(0.613) + $ 7,000(0.543) – $40,000
NPV = $8,850 + $9,396 + $10, $6,130 + $3,801 – $40,000
= - $1,428

27. NPV Acceptance Criterion
The management of Basket Wonders has determined that the required rate is 13% for projects of this type.
Should this project be accepted?
No! The NPV is negative. This means that the project is reducing shareholder wealth. [Reject as NPV < 0 ]

28. NPV on the Calculator
We will use the cash flow registry to solve the NPV for this problem quickly and accurately!
Hint: If you have not cleared the cash flows from your calculator, then you may skip to Step 15.

29. Actual NPV Solution Using Your Financial Calculator
Steps in the Process
Step 1: Press CF key
Step 2: Press 2nd CLR Work keys
Step 3: For CF0 Press Enter  keys
Step 4: For C01 Press Enter  keys
Step 5: For F01 Press Enter  keys
Step 6: For C02 Press Enter  keys
Step 7: For F02 Press Enter  keys
Step 8: For C03 Press Enter  keys
Step 9: For F03 Press Enter  keys

30. Actual NPV Solution Using Your Financial Calculator
Steps in the Process (Part II)
Step 10:For C04 Press Enter  keys
Step 11:For F04 Press Enter  keys
Step 12:For C05 Press Enter  keys
Step 13:For F05 Press Enter  keys
Step 14: Press   keys
Step 15: Press NPV key
Step 16: For I=, Enter 13 Enter  keys
Step 17: Press CPT key
Result: Net Present Value = -$1,424.42

31. NPV Strengths and Weaknesses
Cash flows assumed to be reinvested at the hurdle rate.
Accounts for TVM.
Considers all cash flows.
Weaknesses:
May not include managerial options embedded in the project. See Chapter 14.

32. Net Present Value Profile
Sum of CF’s
Plot NPV for each
discount rate. 15 10
Three of these points are easy now!
Net Present Value 5
IRR -4
Discount Rate (%)

33. Creating NPV Profiles Using the Calculator
Hint: As long as you do not “clear” the cash flows from the registry, simply start at Step 15 and enter a different discount rate. Each resulting NPV will provide a “point” for your NPV Profile!

34. 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.
Method #1:
CF CF CFn
PI =
ICO +
(1+k)1 (1+k) (1+k)n
<< OR >>
Method #2:
PI = 1 + [ NPV / ICO ]

35. PI Acceptance Criterion
= (Method #1, previous slide)
Should this project be accepted?
No! The PI is less than This means that the project is not profitable. [Reject as PI < 1.00 ]

36. PI Strengths and Weaknesses
Same as NPV
Allows comparison of different scale projects
Weaknesses:
Same as NPV
Provides only relative profitability
Potential Ranking Problems

37. Evaluation Summary
Basket Wonders Independent Project

38. Project Evaluation: Remember Chapter 12 ‘New Asset’ project?
We will start with the cash flows of the project and also calculate the cumulative cash flow values.
We can use Excel functions / approaches to calculate each of the following methods from the above cash flows.

39. Other Project Relationships
Dependent – A project whose acceptance depends on the acceptance of one or more other projects.
Mutually Exclusive – A project whose acceptance precludes the acceptance of one or more alternative projects.

40. Potential Problems Under Mutual Exclusivity
Ranking of project proposals may create contradictory results.
A. Scale of Investment
B. Cash-flow Pattern
C. Project Life

41. Compare a small (S) and a large (L) project.
A. Scale Differences
Compare a small (S) and a large (L) project.
NET CASH FLOWS
END OF YEAR
Project S Project L
$ $100,000
$ $156,250

42. A. Scale Differences Calculate the PBP, IRR, NPV@10%, and PI@10%.
Which project is preferred? Why?
Project IRR NPV PI
S % $
L % $29,

43. Remember to refer to Excel spreadsheet ‘VW13E-13b
Remember to refer to Excel spreadsheet ‘VW13E-13b.xlsx’ and the ‘Scale’ tab.
A. Scale Differences
Refer to VW13E-13b.xlsx on the ‘Scale’ tab.

44. B. Cash Flow Pattern
Let us compare a decreasing cash-flow (D) project and an increasing cash-flow (I) project.
NET CASH FLOWS
END OF YEAR
Project D Project I
$1, $1,200 ,
,080

45. Calculate the IRR, NPV@10%, and PI@10%. Which project is preferred?
Cash Flow Pattern
Calculate the IRR, and
Which project is preferred?
Project IRR NPV PI
D % $
I % $ ?

46. Examine NPV Profiles Plot NPV for each project at various
discount rates.
Project I
Net Present Value ($)
IRR
Project D
Discount Rate (%)

47. Fisher’s Rate of Intersection
At k<10%, I is best!
Fisher’s Rate of
Intersection
Net Present Value ($)
At k>10%, D is best!
Discount Rate ($)

48. Remember to refer to Excel spreadsheet ‘VW13E-13b
Remember to refer to Excel spreadsheet ‘VW13E-13b.xlsx’ and the ‘Pattern’ tab.
B. Cash Flow Pattern
Refer to VW13E-13b.xlsx on the ‘Pattern’ tab.

49. C. Project Life Differences
Let us compare a long life (X) project and a short life (Y) project.
NET CASH FLOWS
END OF YEAR
Project X Project Y
$1, $1,000
,000 ,

50. Project Life Differences
Calculate the PBP, IRR, and
Which project is preferred? Why?
Project IRR NPV PI ?
X % $1,
Y % $

51. C. Project Life Differences
Remember to refer to Excel spreadsheet ‘VW13E-13b.xlsx’ and the ‘Life’ tab.
C. Project Life Differences

52. Another Way to Look at Things
1. Adjust cash flows to a common terminal year if project “Y” will NOT be replaced.
Compound Project Y, Year for 2 years.
Year
CF –$1, $ $ $2,420
Results: IRR* = 34.26% NPV = $818
*Lower IRR from adjusted cash-flow stream. X is still Best.

53. Replacing Projects with Identical Projects
2. Use Replacement Chain Approach (Appendix B) when project “Y” will be replaced.
–$1, $2,000
–1, $2,000
–1, $2,000
–$1, $1, $1, $2,000
Results: IRR = 100% NPV* = $2,238.17
*Higher NPV, but the same IRR. Y is Best.

54. C. Project Life Differences
Remember to refer to Excel spreadsheet ‘VW13E-13b.xlsx’ and the ‘Life2’ tab.
C. Project Life Differences

55. Capital Rationing
Capital Rationing occurs when a constraint (or budget ceiling) is placed on the total size of capital expenditures during a particular period.
Example: Julie Miller must determine what investment opportunities to undertake for Basket Wonders (BW). She is limited to a maximum expenditure of $32,500 only for this capital budgeting period.

56. Available Projects for BW
Project ICO IRR NPV PI
A $ % $ B 5, , C 5, , D 7, , E 12, F 15, , G 17, , H 25, ,

57. Projects C, F, and E have the three largest IRRs.
Choosing by IRRs for BW
Project ICO IRR NPV PI
C $ 5,000 37% $ 5, F 15, , E 12, B 5, ,
Projects C, F, and E have the three largest IRRs.
The resulting increase in shareholder wealth is $27,000 with a $32,500 outlay.

58. Projects F and G have the two largest NPVs.
Choosing by NPVs for BW
Project ICO IRR NPV PI
F $15, % $21, G 17, , B 5, ,
Projects F and G have the two largest NPVs.
The resulting increase in shareholder wealth is $28,500 with a $32,500 outlay.

59. Projects F, B, C, and D have the four largest PIs.
Choosing by PIs for BW
Project ICO IRR NPV PI
F $15, % $21, B , , C , , D , , G 17, ,
Projects F, B, C, and D have the four largest PIs.
The resulting increase in shareholder wealth is $38,000 with a $32,500 outlay.

60. Summary of Comparison Method Projects Accepted Value Added
PI F, B, C, and D $38,000
NPV F and G $28,500
IRR C, F, and E $27,000
PI generates the greatest increase in shareholder wealth when a limited capital budget exists for a single period.

61. Single-Point Estimate and Sensitivity Analysis
Sensitivity Analysis: A type of “what-if” uncertainty analysis in which variables or assumptions are changed from a base case in order to determine their impact on a project’s measured results (such as NPV or IRR).
Allows us to change from “single-point” (i.e., revenue, installation cost, salvage, etc.) estimates to a “what if” analysis
Utilize a “base-case” to compare the impact of individual variable changes
E.g., Change forecasted sales units to see impact on the project’s NPV

62. Post-Completion Audit
A formal comparison of the actual costs and benefits of a project with original estimates.
Identify any project weaknesses
Develop a possible set of corrective actions
Provide appropriate feedback
Result: Making better future decisions!

63. Multiple IRR Problem*
Let us assume the following cash flow pattern for a project for Years 0 to 4:
–$100 +$100 +$900 –$1,000
How many potential IRRs could this project have?
Two!! There are as many potential IRRs as there are sign changes.
* Refer to Appendix A

64. NPV Profile – Multiple IRRs75
Multiple IRRs at
k = 12.95% and % 50
Net Present Value
($000s) 25
–100
Discount Rate (%)

65. NPV Profile – Multiple IRRs
Hint: Your calculator will only find ONE IRR – even if there are multiple IRRs. It will give you the lowest IRR. In this case, 12.95%.