2Outline Introduction Net 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 SituationsMutually Exclusive, Differing ScalesCapital RationingSummary and Conclusions
3Returns from Investment Returns to Security Holders Recall the Flows of funds and decisions important to the financial managerInvestment DecisionFinancing DecisionReinvestmentRefinancingFinancial ManagerFinancial MarketsReal AssetsReturns from InvestmentReturns to Security HoldersCapital Budgeting is used to make the Investment Decision
4IntroductionCapital 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.
5Capital 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.
6The Net Present Value (NPV) Rule Total PV of future CF’s - Initial InvestmentEstimating NPV:1. Estimate future cash flows: how much? and when?2. Estimate discount rate3. Estimate initial costsMinimum Acceptance Criteria:Accept if: NPV > 0Ranking Criteria: Choose the highest NPV
7NPV - 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, ,400Draw a time line and compute the NPV of project X.
9NPV in your HP 10B Calculator First, clear previous data, and check that your calculator is set to 1 P/YR:CLEAR ALLThe display should show: 1 P_YrInput data (based on above NPV example)YellowINPUTDisplay should show: CF 0Key in CF01,100+/-CFjDisplay should show: CF 1Key in CF1500CFjDisplay should show: CF 2Key in CF2700CFjDisplay should show: CF 3Key in CF3500+/-CFjDisplay should show: CF 4Key in CF41,200CFjKey in r10I/YRNPVDisplay should show:Compute NPVYellowPRC
10NPV: 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 calculateWeaknessesAn improper NPV analysis may lead to the wrong choices of projects when the firm has capital rationing – this will be discussed later.
11The Payback Period Rule How long does it take the project to “pay back” its initial investment?Payback Period = # of years to recover costs of projectMinimum Acceptance Criteria: set by managementRanking Criteria: set by management
12Discounted Payback - An Example Initial outlay -$1,000r = 10%PV ofYear Cash flow Cash flow1 $ $ 182AccumulatedYear discounted cash flow1 $ 1822 5133 1,0394 1,244Discounted payback period is just under 3 years
13Average Accounting Return (AAR) Also known as Accounting Rate of Return (ARR)Method: using accounting data on profits and book value of the investmentAAR = Average Net Income / Average Book ValueIf AAR > some target book rate of return, then accept the project
14Average 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 3SalesExpensesEBD
15Calculating Projected NI Year 1 Year 2 Year 3SalesExpensesE.B.D.DepreciationE.B.T.Taxes (40%)NI:
16We calculate:(i) Average NI =(ii) Average book value (BV) of the investment (machine):time-0 time-1 time-2 time-3BV of investment:=> Average BV = (divide by 4 - not 3)(iii) The Average Accounting Return:AAR = = 44.44%Conclusion: If target AAR < 44.44% => acceptIf target AAR > 44.44% => reject
17The Internal Rate of Return (IRR) Rule IRR: the discount rate that sets the NPV to zeroMinimum Acceptance Criteria:Accept if: IRR > required returnRanking Criteria: Select alternative with the highest IRRReinvestment assumption: the IRR calculation assumes that all future cash flows are reinvested at the IRR
18Internal Rate of Return - An Example Initial outlay = -$2,200Year Cash flow1 8002 9003 5004 1,600Find the IRR such that NPV = 0______ _______ ______ _______0 =(1+IRR)1 (1+IRR) (1+IRR) (1+IRR)4,6002,200 =
19IRR in your HP 10B Calculator First, clear previous data, and check that your calculator is set to 1 P/YR:CLEAR ALLThe display should show: 1 P_YrInput data (based on above NPV example)YellowINPUTDisplay should show: CF 0Key in CF02,200+/-CFjDisplay should show: CF 1Key in CF1800CFjDisplay should show: CF 2Key in CF2900CFjDisplay should show: CF 3Key in CF3500CFjKey in CF41,600CFjDisplay should show: CF 4IRR/YRDisplay should show: %Compute IRRYellowCST
20Internal Rate of Return and the NPV Profile Discount rates NPV0% $1,600.005% 1,126.4710%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%)
21The Net Present Value Profile Year Cash flow0 – $2,2001 8002 9003 5004 1,6001,600.001,126.47739.55419.74159.62Discount rate– 72.642%6%10%14%18%22%IRR=23.30%
22IRR: Strengths and Weaknesses IRR number is easy to interpret: shows the return the project generates.Acceptance criteria is generally consistent with shareholder wealth maximization.WeaknessesDoes not distinguish between investing and financing scenariosIRR may not exist or there may be multiple IRRProblems with mutually exclusive investments
23IRR for Investment and Financing Projects Initial outlay = $4,000Year Cash flow1 -1,2002 -8003 -3,500Find the IRR such that NPV = 0_______ _______ _______0 =(1+IRR)1 (1+IRR) (1+IRR)3-1, ,500- 4,000 =
24Internal Rate of Return and the NPV Profile for a Financing Project The NPV Profile of a Financing Project:Discount rates NPV0% -$1,500.005%10%15% 50.220%IRR is between 10% and 15% -- about 14.37%For a Financing Project, the required rate of return is the cost of financing, thusIf 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%)
28INPUT Multiple IRRs in your HP 10B Calculator First, clear previous data, and check that your calculator is set to 1 P/YR:CLEAR ALLThe display should show: 1 P_YrInput data (based on above NPV example)YellowINPUTDisplay should show: CF 0Key in CF0900+/-CFjDisplay should show: CF 1Key in CF11,200CFjDisplay should show: CF 2Key in CF21,300CFjDisplay should show: CF 3Key in CF31,200+/-CFjIRR/YRDisplay should show: %Compute 1st IRRYellowCSTSTOIRR/YRCompute 2nd IRR by guessing it first30+/-YellowRCLYellowCSTDisplay should show: %
29No 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 occurWhen 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: +-+ ; -+- ; -+++-; +---+
30Multiple Internal Rates of Return Example 2Assume you are considering a project for which the cash flows are as follows:Year Cash flows$260
34The Profitability Index (PI) Rule Total Present Value of future CF’s / Initial InvestmentMinimum Acceptance Criteria: Accept if PI > 1Ranking Criteria: Select alternative with highest PI
35Profitability Index - An Example Consider the following information on Project Y:Initial outlay -$1,100Required return = 10%Annual cash benefits:Year Cash flows1 $ 500,000What’s the NPV?What’s the Profitability Index (PI)?
36The NPV of Project Y is equal to: = $1, ,100 = $PI = PV Cashflows/Initial Investment =This is a good project according to the PI rule.
37The 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 communicateCorrect decision when evaluating independent projects
38Special situationsWhen 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≥1Sometimes 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.
39Using IRR and PI correctly when projects are mutually exclusive and are of differing scales YearCash flows of Project ACash flows of Project B-$100,000-$501+$150,000+$100Consider the following two mutually exclusive projects. Assume the opportunity cost of capital is 12%
40Incremental 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.
41Incremental 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 scalesYearCash flows of Project ACash flows of Project BIncremental Cash flows of A instead of B (i.e., A-B)-$100,000-$50-$99,9501+$150,000+$100+$149,900
42Using 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”).
44IRR, NPV, and the Incremental Project YearProject A: – $Project B: – $(A-B):The Crossover Rate= IRRA-B = 8.07%
45Capital RationingRecall: 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).
46Capital Rationing – Example (All $ numbers are in thousands) YearProj. AProj. BProj. CProj. DProj. E-$50-$20-$101$60$24.2$25$12.62$0$37.862NPV$4.545$2.0$2.2$2.727$1.4545IRR20%21%14.84%25%26%PI1.09091.11.111.1361.145
47Capital Rationing Example: Comparison of Rankings NPV rankings (best to worst)A, D, C, B, EA uses up the available capitalOverall NPV = $4,545.45IRR rankings (best to worst)E, D, B, A, CE, D, B use up the available capitalOverall NPV = NPVE+D+B=$6,181.82PI rankings (best to worst)E, D, C, B, AE, D, C use up the available capitalOverall NPV = NPVE+D+C=$6,381.82The PI rankings produce the best set of investments to accept given the capital rationing constraint.
48Capital 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).
49Summary 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.