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1 Capital Budgeting For 9.220

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

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

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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.

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

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

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7 NPV - An Example uAssume 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 $ ,000 1, ,200 2, ,600 1,400 uDraw a time line and compute the NPV of project X.

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8 The Time Line & NPV of Project X Initial outlay ($1,100) Revenues$1,000 Expenses500 Cash flow$500 Revenues$2,000 Expenses1,300 Cash flow $700 – $1, $ $500 x $700 x NPV 3 Revenues$2,200 Expenses2,700 Cash flow(500) 1 - $500 x Revenues$2,600 Expenses1,400 Cash flow$1,200 1 $1,200 x NPV = -C 0 + PV 0 (Future CFs) = -C 0 + C 1 /(1+r) + C 2 /(1+r) 2 + C 3 /(1+r) 3 + C 4 /(1+r) 4 = ______ + ______ + ______ + _______ + _______ = $ > 0

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9 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 CF j I/YR Key in CF 0 Key in CF 4 Key in r Key in CF 3 +/-CF j 500 1,200 CF j Key in CF CF j Key in CF /-CF j 1,100 The display should show: 1 P_Yr Input 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 PRC Compute NPV Display should show: Yellow NPV

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10 NPV: Strengths and Weaknesses §Strengths l Resulting number is easy to interpret: shows how wealth will change if the project is accepted. l Acceptance criteria is consistent with shareholder wealth maximization. l Relatively straightforward to calculate §Weaknesses l 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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11 The Payback Period Rule uHow long does it take the project to “pay back” its initial investment? uPayback Period = # of years to recover costs of project uMinimum Acceptance Criteria: set by management uRanking Criteria: set by management

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12 Discounted Payback - An Example Initial outlay -$1,000 r = 10% PV of Year Cash flow Cash flow 1$ 200$ Accumulated Year discounted cash flow 1$ ,039 41,244 Discounted payback period is just under 3 years

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

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

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

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

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

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

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19 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 CF j 500 1,600 CF j 800 CF j 900 +/-CF j 2,200 The display should show: 1 P_Yr Input 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 CST Compute IRR Display should show: % Yellow IRR/YR Key in CF 0 Key in CF 4 Key in CF 3 Key in CF 1 Key in CF 2

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20 The NPV Profile Discount ratesNPV 0%$1, %1, % % % % l IRR is between 20% and 25% -- about 23.30% l If required rate of return (r) is lower than IRR => accept the project (e.g. r = 15%) l 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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21 Year Cash flow 0– $2, ,600 The Net Present Value Profile Discount rate 2% 6% 10% 14% 18% 1, , Net present value – % IRR=23.30% 0

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

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

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24 The NPV Profile of a Financing Project: Discount ratesNPV 0%-$1, % % % % l IRR is between 10% and 15% -- about 14.37% For a Financing Project, the required rate of return is the cost of financing, thus l If required rate of return (r) is lower than IRR => reject the project (e.g. r = 10%) l 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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25 The NPV Profile for a Financing Project

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26 Assume you are considering a project for which the cash flows are as follows: Year Cash flows 0 -$ , , ,200 Multiple Internal Rates of Return Example 1

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27 Multiple IRRs and the NPV Profile - Example 1 IRR 2 =72.25% IRR 1 =-29.35%

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28 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 CF j 1,200 CF j 1,200 CF j 1,300 +/-CF j 900 The display should show: 1 P_Yr Input 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 CST Compute 1 st IRR Display should show: % Yellow IRR/YR +/- CST Compute 2 nd IRR by guessing it first Display should show: % Yellow IRR/YR 30 +/-RCL Yellow STO Key in CF 0 Key in CF 3 Key in CF 1 Key in CF 2

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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 l 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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30 Assume you are considering a project for which the cash flows are as follows: Year Cash flows 0 -$ Multiple Internal Rates of Return Example 2

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31 Multiple IRRs and the NPV Profile - Example 2 IRR 1 =11.52% IRR 2 =29.84%

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32 Assume you are considering a project for which the cash flows are as follows: Year Cash flows 0 $ Multiple Internal Rates of Return Example 3

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33 Multiple IRRs and the NPV Profile - Example 3 IRR 1 =8.05% IRR 2 =33.96%

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

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

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36 uThe NPV of Project Y is equal to: NPV = (500/1.1) + (1,000/1.12) - 1,100 = ($ ) - 1,100 = $1, ,100 = $ uPI = PV Cashflows/Initial Investment = uThis is a good project according to the PI rule.

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

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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. l 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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39 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% Year Cash flows of Project A Cash flows of Project B 0-$100,000-$50 1+$150,000+$100

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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.

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41 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) 0-$100,000-$50-$99,950 1+$150,000+$100+$149,900

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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”).

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

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

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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).

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46 Capital Rationing – Example (All $ numbers are in thousands) YearProj. AProj. BProj. CProj. DProj. E 0-$50-$20 -$10 1$60$24.2-$10$25$12.6 2$0 $37.862$0 NPV$4.545$2.0$2.2$2.727$ IRR20%21%14.84%25%26% PI

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

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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).

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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.

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