1. Capital Budgeting

2. After studying this section, 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 ranking.
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. Uses of 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)

5. Proposed Project Data
Miller Manufacturers is evaluating a new project for the firm. The organization is 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 Miller Manufacturers 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 + ( ) / 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 K K 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 Miller Manufacturers 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
Weaknesses:
Does not account for TVM
Does not consider cash flows beyond the PBP
Cutoff period is subjective

12. Net Present Value (NPV)
The Net Present Value technique involves discounting net cash flows for a project, then subtracting net investment from the discounted net cash flows.
The result is called the Net Present Value(NPV).

13. 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

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

15. NPV Solution
NPV = $10,000(PVIF13%,1) + $12,000(PVIF13%,2) + $15,000(PVIF13%,3) + $10,000(PVIF13%,4) + $ (PVIF13%,5) - $40,000
NPV = $10,000(.885) + $12,000(.783) +$15,000(.693) + $10,000(.613) + $7000 (.543) - $40,000
NPV = $8,850 + $9,396 + $10, $6,130 + $3,801 - $40,000
= - $1,428

16. NPV Acceptance Criterion
The management of Miller Manufacturers 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 ]

17. Whether the company chooses to do that will depend on their selection strategies.
If they pick all projects that add to the value of the company, they would choose all projects with positive net present values even if that value is just $1.
On the other hand, if they have limited resources, they will rank the projects and pick those with the highest NPV's.
The discount rate used most frequently is the company's cost of capital.

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

19. 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 (%)

20. 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

21. 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.

22. 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(.909) + $12,000(.826) $15,000(.751) + $10,000(.683) $ 7,000(.621)
$40,000 = $9,090 + $9,912 + $11, $6,830 + $4, = $41,444 [Rate is too low!!]

23. 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(.870) + $12,000(.756) $15,000(.658) + $10,000(.572) $ 7,000(.497)
$40,000 = $8,700 + $9,072 + $9, $5,720 + $3, = $36,841 [Rate is too high!!]

24. IRR Solution (Interpolate)
.10 $41,444
.05 IRR $40, $4,603
.15 $36,841
X $1, $4,603
$1,444 X =

25. IRR Solution (Interpolate)
.10 $41,444
.05 IRR $40, $4,603
.15 $36,841
X $1, $4,603
$1,444 X =

26. IRR Solution (Interpolate)
.10 $41,444
.05 IRR $40, $4,603
.15 $36,841
($1,444)(0.05) $4,603
$1,444 X
X = .0157
X =
IRR = = or 11.57%

27. IRR Solution (Interpolate)
IRR can also be calculated by using the following method:
IRR = A + [(a/(a+b)][B-A]
A= the lower discount rate which produces a positive NPV
a = the NPV resulting from a discount rate of A%
B = the higher discount rate which produces a negative NPV
b = the NPV resulting from a discount rate of B%

28. IRR = A + [(a/(a+b))][B-A]=
= 11.57%

29. IRR Acceptance Criterion
The management of Miller Manufacturers 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 ]

30. 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

31. 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 ]

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

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

34. Evaluation Summary
Miller Manufacturers Independent Project

35. 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.

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

37. 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

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

39. 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

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

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

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

43. 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 ,

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

45. 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.

46. 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.

47. Conflict Between NPV and IRR
There may be a conflict between the decision resulting from an NPV analysis and that resulting from an IRR analysis.
This conflict arises when the projects are mutually exclusive rather than independent.

48. For independent projects, the NPV and the IRR always lead to the same accept / reject decision, that is if NPV says accept, IRR also says accept.
The criterion for acceptance is that the project’s cost of capital [RRR] is less than [to the left of] the IRR.
Whenever the project’s cost of capital is less than the IRR, its NPV is positive, therefore the project is acceptable using both methods.
Both methods reject the project if the cost of capital is greater than the IRR.

49. If IRR  COST OF CAPITAL, then NPV  0
If two projects, A and B are mutually exclusive, we can choose either A or B, or we can reject both, but we cannot accept both projects.

50. Why Conflicts arise Conflicts arise for two reasons:
When project size [scale] differences exist, that is when the initial capital outlay on one project is greater than that on the other.
When timing differences exist, that is the timing of the cash flows from the two projects differs such that most cash flows from one project come in the early years and most of the cash flows from the other project come in the later years.

51. Modified IRR
In spite of the strong academic preference for the NPV over the IRR, surveys have shown that the IRR is by far the preferred method of investment appraisal.
The IRR is easier to understand as it looks at percentages rather than absolute figures.
In order to take into account the objections regarding the re-investment assumption, we can modify the IRR by assuming that the cash flows are re invested at the required rate of return before calculating the IRR. (Workings)

52. MIRR = PV Costs = TV / ( 1 + MIRR )
Where : TV = the future value of the inflows reinvested at the cost of capital [known as the terminal value ]
 The discount rate that forces the present value of the terminal value to equal the present value of the costs is the MIRR.
The following example illustrates this.

53. Example: Calculating the MIRR
Suppose we have the following time line for a particular project with a cost of capital of 10% : S
330.00
484.00
665.50
MIRR = 12.1%
1000

54. Step 1. Find the terminal value [TV]
Step 1. Find the terminal value [TV] . This is the total of the future values of all the cash flows reinvested, that is compounded, at the cost of capital, 10%. The TV =
Step 2. Find the discount rate that will give a present value of $1 000 on a future value of $ , the IRR. This is found by trial and error in the normal way . This discount rate is 12.1%, which is the MIRR for the project.
Since the MIRR is greater than the cost of capital, 10%, the project is acceptable. The conventional IRR for this project would have been 14.5%.

55. The Accounting Rate of Return (ARR
The accounting rate of return (ARR) is based on the return on investment ratio (ROI).
The ROI is the ratio between the operating income for the year (from the income statement) and the total assets employed (from the balance sheet).
It is a measure of the effectiveness with which the company is utilizing its assets to generate profits.

56. Since management is often evaluated on the basis of this ratio, it is also an appropriate measure of the likely performance of a project.
When applied to projects, the ratio is known as the ARR.
Using this ratio, a project can be evaluated on the basis of an appropriate ARR.
A project with a good ARR will in turn contribute positively to the firm’s overall ROI.

57. The ARR is given by: Average incremental net income ARR =
Average investment
Where :
1. Average incremental net income is the expected annual average increase in net income if the project is accepted. This is equal to:
Total net Income from the project
Project economic life

58. However, as we have discussed before, when we are analyzing project cash flows, we must first deduct depreciation and other non-cash flow items from the net income.
Cost of the investment
Average investment = 2

59. Example
A firm is considering a project with an expected economic life of five years. The following data also relate to the project: 
Capital outlay: $
Residual value : nil (assuming straight line depreciation)
Expected Annual Net Income : Year 1: 60000; Year 2:80000, Year 3:76000; Year 4:58000; Year 5:0
Calculate the project’s ARR.

60. Solution Total net income = 274 000.
Average net income = / 5 years = per year.
Depreciation per year = / 5 year = per year
Average investment = / 2 =
Average net cash flow = – $ =
ARR = average net incremental income/ average investment
ARR = 14800/ = =14.8%

61. The ARR can alternatively be calculated on the basis of the total investment rather than the average investment as follows :
ARR = /
= 0.074, or 7.4%.

62. Criticism of ARR
A major criticism of the ARR is that it ignores the time value of money and is therefore inferior to other methods which are based on discounting techniques.
If the ARR is calculated purely on the basis of accounting income, without adjusting for depreciation and other non-cash flow items, it becomes even less suitable to apply to project appraisal.

63. Decision Rule Based on ARR
If the firm/government has a target ARR we compare the target with the calculated ARR.
If for example the organisation has an ARR of 50% and obtain 58.18% as calculated ARR, we accept the project.
NB// Based on the Accounting Rate and Return Rate, a project is acceptable if its Accounting Rate of Return exceeds a target Accounting Rate of Return

64. Needed information will usually be available
Strength
Weaknesses
Needed information will usually be available
Easy to calculate
Not a true rate of return – time value of money is ignored
Based on accounting book value, not cash flows and market values

65. Capital Rationing
Capital Rationing occurs when a constraint (or budget ceiling) is placed on the total size of capital expenditures during a particular period.
Capital rationing is a situation in which the firm does not have adequate funds for all its viable projects.

66. Single period capital rationing is where capital is limited for the current period only but will be freely available in the future.
Multi-period capital rationing is where capital will be limited for several periods.
Divisible projects are those that can be undertaken completely or infractions. This also means that the NPV is divisible.
Indivisible projects are those which must be undertaken completely or not at all because it is not possible to invest in a fraction of the project.

67. Example:
Miller Manufacturers must determine what investment opportunities to undertake for production project. Assume the organization is limited to a maximum expenditure of $32,500 only for this capital budgeting period.

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

69. Projects C, F, and E have the three largest
Choosing by IRRs for MM
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.

70. Projects F and G have the two largest NPVs.
Choosing by NPVs for MM
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.

71. Projects F, B, C, and D have the four largest PIs.
Choosing by PIs for MM
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.

72. 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.

73. 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

74. In sensitivity analysis we would want to find out what would happen to the estimate of the NPV under different assumptions regarding each input variable.
We then determine the input variables to which the NPV is most sensitive and put more resources and effort in estimating those input variables.
We then put more attention to controlling those variables once the project has been implemented.

75. Drawbacks of Sensitivity Analysis
It assumes that we can alter each input variable in isolation from others. However, most input variables are interrelated. For example, changing the selling price per unit may also affect the number of units sold.
It ignores the probability distribution of each input variable. Since each variable is being estimated, it would have its own probability distribution.

76. Example
A project requires an initial investment of $ and provides annual net cash flows of $ each for a period of 5 years. The cost of capital is 24%
1. Calculate the NPV of the project.
NPV = ( x ) = $

77. 2. Suppose the variable cost per unit increases by 10%, resulting in the decrease of 20% in the estimated net annual cash flows. Will the project still be acceptable?
New cash flow estimate = ( ) = $
NPV=( x ) =-$

78. 3. By how much should the annual cash flows decline before the NPV falls to zero?
 Let the annual cash flow be equal to a, therefore:
0 = a
= a
a =
This means that annual cash flows should fall to $ for the NPV to fall to zero, that is by 63.58% from the current estimate.