1. Capital Budgeting
For 9.220

2. Outline Introduction Net Present Value (NPV) Payback Period Rule (PP)
Discounted Payback Period Rule
Average Accounting Return (AAR)
Internal Rate of Return Rule (IRR)
Profitability Index Rule (PI)
Special Situations
Mutually Exclusive, Differing Scales
Capital Rationing
Summary and Conclusions

3. Returns from Investment Returns to Security Holders
Recall the Flows of funds and decisions important to the financial manager
Investment Decision
Financing Decision
Reinvestment
Refinancing
Financial Manager
Financial Markets
Real Assets
Returns from Investment
Returns to Security Holders
Capital Budgeting is used to make the Investment Decision

4. Introduction
Capital Budgeting is the process of determining which real investment projects should be accepted and given an allocation of funds from the firm.
To evaluate capital budgeting processes, their consistency with the goal of shareholder wealth maximization is of utmost importance.

5. Capital Budgeting Mutually Exclusive versus Independent Project
Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g. acquiring an accounting system.
RANK all alternatives and select the best one.
Independent Projects: accepting or rejecting one project does not affect the decision of the other projects.
Must exceed a MINIMUM acceptance criteria.

6. The Net Present Value (NPV) Rule
Total PV of future CF’s - Initial Investment
Estimating NPV:
1. Estimate future cash flows: how much? and when?
2. Estimate discount rate
3. Estimate initial costs
Minimum Acceptance Criteria:
Accept if: NPV > 0
Ranking Criteria: Choose the highest NPV

7. NPV - An Example Assume you have the following information on
Project X:
Initial outlay -$1,100 Required return = 10%
Annual cash revenues and expenses are as follows:
Year Revenues Expenses
$1, $500
, ,300
, ,700
, ,400
Draw a time line and compute the NPV of project X.

8. The Time Line & NPV of Project X1 2 3 4
Initial outlay
($1,100)
Revenues $1,000
Expenses 500
Cash flow $500
Revenues $2,000
Expenses 1,300
Cash flow $700
Revenues $2,200
Expenses 2,700
Cash flow (500)
Revenues $2,600
Expenses 1,400
Cash flow $1,200
– $1,100.00
+$377.02 1
$500 x
1.10 1
$700 x
1.10 2 1
- $500 x
1.10 3 1
$1,200 x
1.10 4
NPV
NPV = -C0 + PV0(Future CFs)
= -C0 + C1/(1+r) + C2/(1+r)2 + C3/(1+r)3 + C4/(1+r)4
= ______ + ______ + ______ + _______ + _______
= $ > 0

9. NPV in your HP 10B Calculator
First, clear previous data, and check that your calculator is set to 1 P/YR:
CLEAR ALL
The display should show: 1 P_Yr
Input data (based on above NPV example)
Yellow
INPUT
Display should show: CF 0
Key in CF0
1,100
+/-
CFj
Display should show: CF 1
Key in CF1
500
CFj
Display should show: CF 2
Key in CF2
700
CFj
Display should show: CF 3
Key in CF3
500
+/-
CFj
Display should show: CF 4
Key in CF4
1,200
CFj
Key in r 10
I/YR
NPV
Display should show:
Compute NPV
Yellow
PRC

10. NPV: Strengths and Weaknesses
Resulting number is easy to interpret: shows how wealth will change if the project is accepted.
Acceptance criteria is consistent with shareholder wealth maximization.
Relatively straightforward to calculate
Weaknesses
An improper NPV analysis may lead to the wrong choices of projects when the firm has capital rationing – this will be discussed later.

11. The Payback Period Rule
How long does it take the project to “pay back” its initial investment?
Payback Period = # of years to recover costs of project
Minimum Acceptance Criteria: set by management
Ranking Criteria: set by management

12. Discounted Payback - An Example
Initial outlay -$1,000
r = 10%
PV of
Year Cash flow Cash flow
1 $ $ 182
Accumulated
Year discounted cash flow
1 $ 182
2 513
3 1,039
4 1,244
Discounted payback period is just under 3 years

13. Average Accounting Return (AAR)
Also known as Accounting Rate of Return (ARR)
Method: using accounting data on profits and book value of the investment
AAR = Average Net Income / Average Book Value
If AAR > some target book rate of return, then accept the project

14. Average Accounting Return (AAR)
You want to invest in a machine that produces squash balls.
The machine costs $90,000.
The machine will ‘die’ after 3 years (assume straight line depreciation, the annual depreciation is $30,000).
You estimate for the life of the project:
Year 1 Year 2 Year 3
Sales
Expenses
EBD

15. Calculating Projected NI
Year 1 Year 2 Year 3
Sales
Expenses
E.B.D.
Depreciation
E.B.T.
Taxes (40%)
NI:

16. We calculate:
(i) Average NI =
(ii) Average book value (BV) of the investment (machine):
time-0 time-1 time-2 time-3
BV of investment:
=> Average BV = (divide by 4 - not 3)
(iii) The Average Accounting Return:
AAR = = 44.44%
Conclusion: If target AAR < 44.44% => accept
If target AAR > 44.44% => reject

17. The Internal Rate of Return (IRR) Rule
IRR: the discount rate that sets the NPV to zero
Minimum Acceptance Criteria:
Accept if: IRR > required return
Ranking Criteria: Select alternative with the highest IRR
Reinvestment assumption: the IRR calculation assumes that all future cash flows are reinvested at the IRR

18. Internal Rate of Return - An Example
Initial outlay = -$2,200
Year Cash flow
1 800
2 900
3 500
4 1,600
Find the IRR such that NPV = 0
______ _______ ______ _______
0 =
(1+IRR)1 (1+IRR) (1+IRR) (1+IRR)4
,600
2,200 =

19. IRR in your HP 10B Calculator
First, clear previous data, and check that your calculator is set to 1 P/YR:
CLEAR ALL
The display should show: 1 P_Yr
Input data (based on above NPV example)
Yellow
INPUT
Display should show: CF 0
Key in CF0
2,200
+/-
CFj
Display should show: CF 1
Key in CF1
800
CFj
Display should show: CF 2
Key in CF2
900
CFj
Display should show: CF 3
Key in CF3
500
CFj
Key in CF4
1,600
CFj
Display should show: CF 4
IRR/YR
Display should show: %
Compute IRR
Yellow
CST

20. Internal Rate of Return and the NPV Profile
Discount rates NPV
0% $1,600.00
5% 1,126.47
10%
15%
20%
25%
IRR is between 20% and 25% -- about 23.30%
If required rate of return (r) is lower than IRR => accept the project (e.g. r = 15%)
If required rate of return (r) is higher than IRR => reject the project (e.g. r = 25%)

21. The Net Present Value Profile
Year Cash flow
0 – $2,200
1 800
2 900
3 500
4 1,600
1,600.00
1,126.47
739.55
419.74
159.62
Discount rate
– 72.64 2% 6%
10%
14%
18%
22%
IRR=23.30%

22. IRR: Strengths and Weaknesses
IRR number is easy to interpret: shows the return the project generates.
Acceptance criteria is generally consistent with shareholder wealth maximization.
Weaknesses
Does not distinguish between investing and financing scenarios
IRR may not exist or there may be multiple IRR
Problems with mutually exclusive investments

23. IRR for Investment and Financing Projects
Initial outlay = $4,000
Year Cash flow
1 -1,200
2 -800
3 -3,500
Find the IRR such that NPV = 0
_______ _______ _______
0 =
(1+IRR)1 (1+IRR) (1+IRR)3
-1, ,500
- 4,000 =

24. Internal Rate of Return and the NPV Profile for a Financing Project
The NPV Profile of a Financing Project:
Discount rates NPV
0% -$1,500.00 5%
10%
15% 50.2
20%
IRR is between 10% and 15% -- about 14.37%
For a Financing Project, the required rate of return is the cost of financing, thus
If required rate of return (r) is lower than IRR => reject the project (e.g. r = 10%)
If required rate of return (r) is higher than IRR => accept the project (e.g. r = 15%)

25. The NPV Profile for a Financing Project

26. Multiple Internal Rates of Return
Example 1
Assume you are considering a project for which the cash flows are as follows:
Year Cash flows
$900
,200
,300
,200

27. Multiple IRRs and the NPV Profile - Example 1

28. INPUT Multiple IRRs in your HP 10B Calculator
First, clear previous data, and check that your calculator is set to 1 P/YR:
CLEAR ALL
The display should show: 1 P_Yr
Input data (based on above NPV example)
Yellow
INPUT
Display should show: CF 0
Key in CF0
900
+/-
CFj
Display should show: CF 1
Key in CF1
1,200
CFj
Display should show: CF 2
Key in CF2
1,300
CFj
Display should show: CF 3
Key in CF3
1,200
+/-
CFj
IRR/YR
Display should show: %
Compute 1st IRR
Yellow
CST
STO
IRR/YR
Compute 2nd IRR by guessing it first 30
+/-
Yellow
RCL
Yellow
CST
Display should show: %

29. No or Multiple IRR Problem – What to do?
IRR cannot be used in this circumstance, the only solution is to revert to another method of analysis. NPV can handle these problems.
How to recognize when this IRR problem can occur
When changes in the signs of cash flows happen more than once the problem may occur (depending on the relative sizes of the individual cash flows).
Examples: +-+ ; -+- ; -+++-; +---+

30. Multiple Internal Rates of Return
Example 2
Assume you are considering a project for which the cash flows are as follows:
Year Cash flows
$260

31. Multiple IRRs and the NPV Profile - Example 2

32. Multiple Internal Rates of Return
Example 3
Assume you are considering a project for which the cash flows are as follows:
Year Cash flows
$660

33. Multiple IRRs and the NPV Profile - Example 3

34. The Profitability Index (PI) Rule
Total Present Value of future CF’s / Initial Investment
Minimum Acceptance Criteria: Accept if PI > 1
Ranking Criteria: Select alternative with highest PI

35. Profitability Index - An Example
Consider the following information on Project Y:
Initial outlay -$1,100
Required return = 10%
Annual cash benefits:
Year Cash flows
1 $ 500
,000
What’s the NPV?
What’s the Profitability Index (PI)?

36. The NPV of Project Y is equal to:
= $1, ,100 = $
PI = PV Cashflows/Initial Investment =
This is a good project according to the PI rule.

37. The Profitability Index (PI) Rule
Disadvantages:
Problems with mutually exclusive investments (to be discussed later)
Advantages:
May be useful when available investment funds are limited (to be discussed later).
Easy to understand and communicate
Correct decision when evaluating independent projects

38. Special situations
When projects are independent and the firm has few constraints on capital, then we check to ensure that projects at least meet a minimum criteria – if they do, they are accepted.
NPV≥0; IRR≥hurdle rate; PI≥1
Sometimes a firm will have plenty of funds to invest, but it must choose between projects that are mutually exclusive. This means that the acceptance of one project precludes the acceptance of any others. In this case, we seek to choose the one highest ranked of the acceptable projects.
If the firm has capital rationing, then its funds are limited and not all independent projects may be accepted. In this case, we seek to choose those projects that best use the firm’s available funds. PI is especially useful here.

39. Using IRR and PI correctly when projects are mutually exclusive and are of differing scales
Year
Cash flows of Project A
Cash flows of Project B
-$100,000
-$50 1
+$150,000
+$100
Consider the following two mutually exclusive projects. Assume the opportunity cost of capital is 12%

40. Incremental Cash Flows: Solving the Problem with IRR and PI
As you can see, individual IRRs and PIs are not good for comparing between two mutually exclusive projects.
However, we know IRR and PI are good for evaluating whether one project is acceptable.
Therefore, consider “one project” that involves switching from the smaller project to the larger project. If IRR or PI indicate that this is worthwhile, then we will know which of the two projects is better.
Incremental cash flow analysis looks at how the cash flows change by taking a particular project instead of another project.

41. Incremental Cash flows of A instead of B (i.e., A-B)
Using IRR and PI correctly when projects are mutually exclusive and are of differing scales
Year
Cash flows of Project A
Cash flows of Project B
Incremental Cash flows of A instead of B (i.e., A-B)
-$100,000
-$50
-$99,950 1
+$150,000
+$100
+$149,900

42. Using IRR and PI correctly when projects are mutually exclusive and are of differing scales
IRR and PI analysis of incremental cash flows tells us which of two projects are better.
Beware, before accepting the better project, you should always check to see that the better project is good on its own (i.e., is it better than “do nothing”).

43. IRR, NPV, and Mutually Exclusive Projects
Year
Project A: – $
Project B: – $

44. IRR, NPV, and the Incremental Project
Year
Project A: – $
Project B: – $
(A-B):
The Crossover Rate
= IRRA-B = 8.07%

45. Capital Rationing
Recall: If the firm has capital rationing, then its funds are limited and not all independent projects may be accepted. In this case, we seek to choose those projects that best use the firm’s available funds. PI is especially useful here.
Note: capital rationing is a different problem than mutually exclusive investments because if the capital constraint is removed, then all projects can be accepted together.
Analyze the projects on the next page with NPV, IRR, and PI assuming the opportunity cost of capital is 10% and the firm is constrained to only invest $50,000 now (and no constraint is expected in future years).

46. Capital Rationing – Example (All $ numbers are in thousands)
Year
Proj. A
Proj. B
Proj. C
Proj. D
Proj. E
-$50
-$20
-$10 1
$60
$24.2
$25
$12.6 2 $0
$37.862
NPV
$4.545
$2.0
$2.2
$2.727
$1.4545
IRR
20%
21%
14.84%
25%
26% PI
1.0909
1.1
1.11
1.136
1.145

47. Capital Rationing Example: Comparison of Rankings
NPV rankings (best to worst)
A, D, C, B, E
A uses up the available capital
Overall NPV = $4,545.45
IRR rankings (best to worst)
E, D, B, A, C
E, D, B use up the available capital
Overall NPV = NPVE+D+B=$6,181.82
PI rankings (best to worst)
E, D, C, B, A
E, D, C use up the available capital
Overall NPV = NPVE+D+C=$6,381.82
The PI rankings produce the best set of investments to accept given the capital rationing constraint.

48. Capital Rationing Conclusions
PI is best for initial ranking of independent projects under capital rationing.
Comparing NPV’s of feasible combinations of projects would also work.
IRR may be useful if the capital rationing constraint extends over multiple periods (see project C).

49. Summary and Conclusions
Discounted Cash Flow (DCF) techniques are the best of the methods we have presented.
In some cases, the DCF techniques need to be modified in order to obtain a correct decision. It is important to completely understand these cases and have an appreciation of which technique is best given the situation.