Post on 15-Jan-2016
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Capital Budgeting
For 9.220
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Outline IntroductionNet Present Value (NPV)Payback Period Rule (PP)
Discounted Payback Period RuleAverage Accounting Return (AAR) Internal Rate of Return Rule (IRR)Profitability Index Rule (PI)Special Situations
Mutually Exclusive, Differing Scales Capital Rationing
Summary and Conclusions
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Recall the Flows of funds and decisions important to the financial manager
Financial Manager
Financial Markets
Real Assets
Financing Decision
Investment Decision
Returns from Investment Returns to Security Holders
Reinvestment Refinancing
Capital Budgeting is used to make the Investment Decision
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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.
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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.
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The Net Present Value (NPV) Rule Net Present Value (NPV) =
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
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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 $1,000 $500
2 2,000 1,300
3 2,200 2,700
4 2,600 1,400
Draw a time line and compute the NPV of project X.
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The Time Line & NPV of Project X0 1 2
Initial outlay($1,100)
Revenues $1,000Expenses 500
Cash flow $500
Revenues $2,000Expenses 1,300
Cash flow $700
– $1,100.00
+454.54
+578.51
-375.66
+819.62
+$377.02
1$500 x 1.10
1$700 x 1.10
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NPV
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Revenues $2,200Expenses 2,700
Cash flow (500)
1- $500 x 1.10
3
4
Revenues $2,600Expenses 1,400
Cash flow $1,200
1$1,200 x 1.10
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NPV = -C0 + PV0(Future CFs)= -C0 + C1/(1+r) + C2/(1+r)2 + C3/(1+r)3 + C4/(1+r)4
= ______ + ______ + ______ + _______ + _______ = $377.02 > 0
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First, clear previous data, and check that your calculator is set to 1 P/YR:NPV in your HP 10B Calculator
INPUT
CLEAR ALL
Yellow
CFj
I/YR
Key in CF0
Key in CF4
Key in r
Key in CF3 +/- CFj500
1,200
CFjKey in CF1500
CFjKey in CF2700
+/- CFj1,100
The display should show: 1 P_YrInput data (based on above NPV example)
Display should show: CF 0
Display should show: CF 1
Display should show: CF 2
Display should show: CF 3
Display should show: CF 4
PRCCompute NPVDisplay should show:
377.01659723
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Yellow
NPV
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NPV: Strengths and Weaknesses
Strengths 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.
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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
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Discounted Payback - An Example
Initial outlay -$1,000r = 10%
PV of Year Cash flow Cash flow 1 $ 200 $ 182 2 400 331 3 700 526 4 300 205
Accumulated Year discounted cash flow 1 $ 182 2 513 3 1,039 4 1,244
Discounted payback period is just under 3 years
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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
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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 140 160 200
Expenses 120 100 90
EBD 20 60 110
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Year 1 Year 2 Year 3
Sales 140 160 200
Expenses 120 100 90
E.B.D.
Depreciation
E.B.T.
Taxes (40%)
NI:
Calculating Projected NI
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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: 90 60 30 0
=> 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
203
603
48186
454
0306090
4520
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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
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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)2 (1+IRR)3 (1+IRR)4
800 900 500 1,600
2,200 = + + + (1+IRR)1 (1+IRR)2 (1+IRR)3 (1+IRR)4
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First, clear previous data, and check that your calculator is set to 1 P/YR:IRR in your HP 10B Calculator
INPUT
CLEAR ALL
Yellow
CFj
CFj500
1,600
CFj800
CFj900
+/- CFj2,200
The display should show: 1 P_YrInput data (based on above NPV example)
Display should show: CF 0
Display should show: CF 1
Display should show: CF 2
Display should show: CF 3
Display should show: CF 4
CSTCompute IRRDisplay should show:
23.29565668%Yellow
IRR/YR
Key in CF0
Key in CF4
Key in CF3
Key in CF1
Key in CF2
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The NPV Profile
Discount rates NPV
0% $1,600.00
5% 1,126.47
10% 739.55
15% 419.74
20% 152.62
25% -72.64
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%)
Internal Rate of Return and the NPV Profile
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Year Cash flow
0 – $2,200 1 800 2 900 3 500 4 1,600
The Net Present Value Profile
Discount rate2% 6% 10
%14% 18%
1,600.00
1,126.47
739.55
419.74
Net present value
159.62
– 72.64 22%
IRR=23.30%
0
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IRR: Strengths and Weaknesses Strengths
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
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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)2 (1+IRR)3
-1,200 -800 -3,500
- 4,000 = + + (1+IRR)1 (1+IRR)2 (1+IRR)3
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The NPV Profile of a Financing Project:
Discount rates NPV
0% -$1,500.00
5% -891.91
10% -381.67
15% 50.2
20% 418.98
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%)
Internal Rate of Return and the NPV Profile for a Financing Project
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The NPV Profile for a Financing Project
-$2,000.00
-$1,500.00
-$1,000.00
-$500.00
$0.00
$500.00
$1,000.00
$1,500.00
$2,000.00
0% 5% 10% 15% 20% 25% 30% 35% 40% 45%
Rate of Return (%)
NP
V (
$)
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Assume you are considering a project for which the cash flows are as follows:
Year Cash flows
0 -$900
1 1,200
2 1,300
3 -1,200
Multiple Internal Rates of Return
Example 1
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-$1,000.00
-$800.00
-$600.00
-$400.00
-$200.00
$0.00
$200.00
$400.00
$600.00
-60% -40% -20% 0% 20% 40% 60% 80% 100% 120% 140%
Rate of Return (%)
NP
V (
$)Multiple IRRs and the NPV Profile - Example 1
IRR2=72.25%IRR1=-29.35%
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First, clear previous data, and check that your calculator is set to 1 P/YR:Multiple IRRs in your HP 10B Calculator
INPUT
CLEAR ALL
Yellow
CFj1,200
CFj1,200
CFj1,300
+/- CFj900
The display should show: 1 P_YrInput data (based on above NPV example)
Display should show: CF 0
Display should show: CF 1
Display should show: CF 2
Display should show: CF 3
CSTCompute 1st IRRDisplay should show:
72.252175%Yellow
IRR/YR
+/-
CSTCompute 2nd IRR by guessing it first
Display should show: -29.352494%
Yellow
IRR/YR
30 +/- RCLYellow
STO
Key in CF0
Key in CF3
Key in CF1
Key in CF2
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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: +-+ ; -+- ; -+++-; +---+
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Assume you are considering a project for which the cash flows are as follows:
Year Cash flows
0 -$260
1 250
2 300
3 20
4 -340
Multiple Internal Rates of Return
Example 2
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-$80.00
-$70.00
-$60.00
-$50.00
-$40.00
-$30.00
-$20.00
-$10.00
$0.00
$10.00
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Rate of Return (%)
NP
V (
$)Multiple IRRs and the NPV Profile - Example 2
IRR1=11.52%IRR2=29.84%
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Assume you are considering a project for which the cash flows are as follows:
Year Cash flows
0 $660
1 -650
2 -750
3 -50
4 850
Multiple Internal Rates of Return
Example 3
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-$50.00
$0.00
$50.00
$100.00
$150.00
$200.00
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Rate of Return (%)
NP
V($
)Multiple IRRs and the NPV Profile - Example 3
IRR1=8.05%IRR2=33.96%
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The Profitability Index (PI) Rule PI =
Total Present Value of future CF’s / Initial Investment
Minimum Acceptance Criteria: Accept if PI > 1
Ranking Criteria: Select alternative with highest PI
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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
2 1,000
What’s the NPV? What’s the Profitability Index (PI)?
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The NPV of Project Y is equal to:
NPV = (500/1.1) + (1,000/1.12) - 1,100 = ($454.54 + 826.45) - 1,100
= $1,280.99 - 1,100 = $180.99.
PI = PV Cashflows/Initial Investment =
This is a good project according to the PI rule.
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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
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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.
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Using IRR and PI correctly when projects are mutually exclusive and are of differing scales
Consider the following two mutually exclusive projects. Assume the opportunity cost of capital is 12%
YearCash flows of Project A
Cash flows of Project B
0 -$100,000 -$50
1 +$150,000 +$100
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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.
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Using IRR and PI correctly when projects are mutually exclusive and are of differing scales
YearCash flows of
Project ACash flows of
Project B
Incremental Cash flows of A
instead of B (i.e., A-B)
0 -$100,000 -$50 -$99,950
1 +$150,000 +$100 +$149,900
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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”).
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-200
-150
-100
-50
0
50
100
150
200
0% 5% 10% 15% 20% 25% 30% 35% 40% 45%
Rate of Return (%)
NP
V (
$)
Project A Project B
IRR, NPV, and Mutually Exclusive Projects
Year
0 1 2 3
4
Project A: – $350 50 100 150 200
Project B: – $250 125 100 75 50%80.17BIRR
%91.12AIRR
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-200
-150
-100
-50
0
50
100
150
200
0% 5% 10% 15% 20% 25% 30% 35% 40% 45%
Rate o Return (%)
NP
V (
$)
Project A Project B Incremental (A-B)
IRR, NPV, and the Incremental Project Year
0 1 2 3
4
Project A: – $350 50 100 150 200
Project B: – $250 125 100 75 50
(A-B):
The Crossover Rate = IRRA-B = 8.07%
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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).
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Capital Rationing – Example(All $ numbers are in thousands)
Year Proj. A Proj. B Proj. C Proj. D Proj. E
0 -$50 -$20 -$20 -$20 -$10
1 $60 $24.2 -$10 $25 $12.6
2 $0 $0 $37.862 $0 $0
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
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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.
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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).
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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.