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Capital Budgeting Technigue Chapter 9

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2 Key Concepts and Skills Understand the payback rule and its shortcomings Understand accounting rates of return and their problems Understand the internal rate of return and its strengths and weaknesses Understand the net present value rule and why it is the best decision criteria

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3 Capital budgeting Personal capital budgeting; Company’s capital budgeting; National fiscal budgeting.

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5 8 Good Decision Criteria We need to ask ourselves the following questions when evaluating decision criteria Does the decision rule adjust for the time value of money? Does the decision rule adjust for risk? Does the decision rule provide information on whether we are creating value for the firm?

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10 8.1.2 Net Present Value (NPV, 净现值 ) NPV is the difference between the market value of a project and its cost How much value is created from undertaking an investment? The first step is to estimate the expected future cash flows. The second step is to estimate the required return for projects of this risk level. The third step is to find the present value of the cash flows and subtract the initial investment.

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11 8.1.3 NPV Decision Rule If the NPV is positive, accept the project A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners. Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal.

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12 8.1.1 Project Example Information You are looking at a new project and you have estimated the following cash flows: Year 0:CF = -165,000 Year 1:CF = 63,120; Year 2: CF = 70,800; Year 3: CF = 91,080; Your required return for assets of this risk is 12%.

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13 8.1.4 Computing NPV for the Project Using the formulas: NPV = 63,120/(1.12) + 70,800/(1.12) 2 + 91,080/(1.12) 3 – 165,000 = 12,627.42 Using the calculator: CF 0 = -165,000; C01 = 63,120; F01 = 1; C02 = 70,800; F02 = 1; C03 = 91,080; F03 = 1; NPV; I = 12; CPT NPV = 12,627.42 Do we accept or reject the project?

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14 8.1.5 Decision Criteria Test - NPV Does the NPV rule account for the time value of money?-Y Does the NPV rule account for the risk of the cash flows?-N Does the NPV rule provide an indication about the increase in value?-Y Should we consider the NPV rule for our primary decision criteria?-Y

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15 8.1.6 Calculating NPVs with a Spreadsheet Spreadsheets are an excellent way to compute NPVs, especially when you have to compute the cash flows as well. Using the NPV function The first component is the required return entered as a decimal The second component is the range of cash flows beginning with year 1 Subtract the initial investment after computing the NPV

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16 8.2 Payback Period ( 回收期 ) How long does it take to get the initial cost back in a nominal sense? Computation Estimate the cash flows Subtract the future cash flows from the initial cost until the initial investment has been recovered Decision Rule – Accept if the payback period is less than some preset limit

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17 8.2.1 Computing Payback For The Project Assume we will accept the project if it pays back within two years. Year 1: 165,000 – 63,120 = 101,880 still to recover Year 2: 101,880 – 70,800 = 31,080 still to recover Year 3: 31,080 – 91,080 = -60,000 project pays back in year 3 Do we accept or reject the project?

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20 8.2.3 Decision Criteria Test - Payback Does the payback rule account for the time value of money?-N Does the payback rule account for the risk of the cash flows?-N Does the payback rule provide an indication about the increase in value?-Y Should we consider the payback rule for our primary decision criteria?-Y

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21 8.2.4 Advantages and Disadvantages of Payback Advantages Easy to understand Adjusts for uncertainty of later cash flows （调整 了更晚的现金流 不确定性） Biased towards liquidity( 偏好流动 性 ) Disadvantages Ignores the time value of money Requires an arbitrary ( 任意 的 ) cutoff point Ignores cash flows beyond the cutoff date Biased against long-term projects （ 不偏好长期项 目）, such as research and development, and new projects

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22 8.3 Average Accounting Return ( 平均会计收益 ) There are many different definitions for average accounting return The one used in the book is: Average net income / average book value Note that the average book value depends on how the asset is depreciated. Need to have a target cutoff rate Decision Rule: Accept the project if the AAR is greater than a preset rate.

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23 8.3.1 Computing AAR For The Project You are looking at a new project and you have estimated the following cash flows: Year 0:CF = -165,000 Year 1:CF = 63,120; NI = 13,620 Year 2: CF = 70,800; NI = 3,300 Year 3: CF = 91,080; NI = 29,100 Average Book Value = 59,660 Assume we require an average accounting return of 25% Average Net Income: (13,620 + 3,300 + 29,100) / 3 = 15,340 AAR = 15,340 / 59,660 =.257 = 25.7% Do we accept or reject the project?

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24 8.3.2 Decision Criteria Test - AAR Does the AAR rule account for the time value of money?-N Does the AAR rule account for the risk of the cash flows?-N Does the AAR rule provide an indication about the increase in value?-Y Should we consider the AAR rule for our primary decision criteria?

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25 8.3.3Advantages and Disadvantages of AAR Advantages Easy to calculate Needed information will usually be available Disadvantages Not a true rate of return; time value of money is ignored Uses an arbitrary benchmark cutoff rate Based on accounting net income and book values, not cash flows and market values

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26 8.4 Internal Rate of Return( 内部回 报率 ) This is the most important alternative to NPV It is often used in practice and is intuitively appealing It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere

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27 8.4.1 IRR – Definition and Decision Rule Definition: IRR is the return that makes the NPV = 0 Decision Rule: Accept the project if the IRR is greater than the required return

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28 8.4.2 Computing IRR For The Project Example: You are looking at a new project and you have estimated the following cash flows: Year 0:CF = -165,000 Year 1:CF = 63,120; Year 2: CF = 70,800; Year 3: CF = 91,080; Required return 12% Calculator Enter the cash flows as you did with NPV Press IRR and then CPT IRR = 16.13% > 12% required return Do we accept or reject the project?

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29 8.4.3 NPV Profile For The Project IRR = 16.13%

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30 8.4.4 Decision Criteria Test - IRR Does the IRR rule account for the time value of money?-Y Does the IRR rule account for the risk of the cash flows? -N Does the IRR rule provide an indication about the increase in value? -Y Should we consider the IRR rule for our primary decision criteria?

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31 PROJECT A PROJECT B $500 $500 $500 $300 $300 $300 $300 $300 $300 1 2 3 year 1 2 3 4 5 6 year $1,000 $1,000 NPV = $234.50 NPV = $306.50 PI = 1.2435 PI = 1.306 IRR = 23% IRR = 20% Examining the discounted cash flow criteria, we find that the net present value and profitability index criteria indicate that project B is the better project, whereas the internal rate of return criterion favors project A. this ranking inconsistency is caused by the different life spans of the projects being compared. In this case the decision is a difficult one because the projects are not comparable.

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32 8.4.5 Advantages of IRR Knowing a return is intuitively appealing It is a simple way to communicate the value of a project to someone who doesn’t know all the estimation details If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task

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33 8.5 Summary of Decisions For The Project Summary Net Present ValueAccept Payback PeriodReject Average Accounting ReturnReject Internal Rate of ReturnAccept

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34 8.5.1 Calculating IRRs With A Spreadsheet You start with the cash flows the same as you did for the NPV You use the IRR function You first enter your range of cash flows, beginning with the initial cash flow You can enter a guess, but it is not necessary The default format is a whole percent – you will normally want to increase the decimal places to at least two

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35 8.5.2 NPV Vs. IRR NPV and IRR will generally give us the same decision Exceptions Non-conventional cash flows – cash flow signs change more than once Mutually exclusive projects Initial investments are substantially different Timing of cash flows is substantially different

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36 8.5.2.1 IRR and Nonconventional Cash Flows When the cash flows change sign more than once, there is more than one IRR When you solve for IRR you are solving for the root of an equation and when you cross the x-axis more than once, there will be more than one return that solves the equation (Figure 8.6 on p238) If you have more than one IRR, which one do you use to make your decision?

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37 8.5.2.2 Another Example – Nonconventional Cash Flows Suppose an investment will cost $90,000 initially and will generate the following cash flows: Year 1: 132,000 Year 2: 100,000 Year 3: -150,000 The required return is 15%. By calucualting, we got IRR=10.11% Should we accept or reject the project?

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38 8.5.2.2.1 Summary of Decision Rules The NPV is positive at a required return of 15%, so you should Accept If you use the financial calculator, you would get an IRR of 10.11% which would tell you to Reject You need to recognize that there are non- conventional cash flows and look at the NPV profile. (example 8.4 on p239)

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39 8.5.2.3 IRR and Mutually Exclusive Projects Mutually exclusive projects If you choose one, you can’t choose the other Example: You can choose to attend graduate school next year at either Harvard or Stanford, but not both Intuitively you would use the following decision rules: NPV – choose the project with the higher NPV IRR – choose the project with the higher IRR

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40 8.5.2.3.1 Example With Mutually Exclusive Projects PeriodProject AProject B 0-500-400 1325 2 200 IRR19.43%22.17% NPV64.0560.74

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41 8.5.2.3.2 Example With Mutually Exclusive Projects The required return for both projects is 10%. Which project should you accept and why? B has greater total cash flow, but it pays back more slowly than A. As a result, it has a higher NPV at lower discount rate We are ultimately interested in creating value for the stockholders, so we choose whichever provides bigger NPV.

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42 8.5.2.3.2 NPV Profiles IRR for A = 19.43% IRR for B = 22.17% Crossover Point = 11.8%

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43 8.5.3 Conflicts Between NPV and IRR NPV directly measures the increase in value to the firm Whenever there is a conflict between NPV and another decision rule, you should always use NPV IRR is unreliable in the following situations Non-conventional cash flows Mutually exclusive projects//

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44 8.6 Profitability Index ( 盈利能力指 数 ) Measures the benefit per unit cost, based on the time value of money （ p242 ） A profitability index of 1.1 implies that for every $1 of investment, we create an additional $0.10 in value This measure can be very useful in situations where we have limited capital

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49 8.6.1 Advantages and Disadvantages of Profitability Index Advantages Closely related to NPV, generally leading to identical decisions Easy to understand and communicate May be useful when available investment funds are limited Disadvantages May lead to incorrect decisions in comparisons of mutually exclusive investments

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50 500 000700 000 600 000 0.70 0.30 第1年第1年 现金流量 / 美元 概率 /% 500 000 300 000 0.40 0.60 第2年第2年 如果第 1 年的现 金流量是 / 美元 第 2 年的现金流量是 以下其中的一个 / 美 元 概率 /% 300 000 200 000 100 000 0.40 0.50 0.10

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52 Objective 4 PROBLEMS IN PROJECT RANKING-CAPITAL RATIONING, MUTUALLY EXCLUSIVE PROJECTS, AND PROBLEMS WITH THE IRR. 1Size disparity 2Time disparity 3Unequal live

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53 Capital-Rationing Example of Five Indivisible Projects Project Initial Outlay Profitability Index Net Present Value A $200,000 2.4 $280,000 B 200,000 2.3 260,000 C 800,000 1.7 560,000 D 300,000 1.3 90,000 E 300,000 1.2 60,000

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54 Investment Evaluation A Primary A Secondary Total Using Methods Used: Method Method This Method Payback period 24% 59% 83% Internal rate of return 88% 11% 99% Net present value 63% 22% 85% Profitability index 15% 18% 33%

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55 Project Size and Decision-Making Authority Project Size Typical Boundaries Primary Decision Site Very small Up to $100,000 Plant Small $100,000 to $1 million Division Medium $1 million to $10 million Corporate investment committee Large Over $10 million CEO & board

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56 8.7 Capital Budgeting In Practice p243 We should consider several investment criteria when making decisions NPV and IRR are the most commonly used primary investment criteria Payback is a commonly used secondary investment criteria

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57 Quick Quiz Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9% and required payback is 4 years. What is the payback period? What is the NPV? What is the IRR? Should we accept the project? What decision rule should be the primary decision method? When is the IRR rule unreliable?

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58 未进行风险调整 （贴现率为 12% ） 风险调整 （ k*=20% ） 年份期望现金 流量 / 美元 现值利 率系数 贴现后的现 金流量 / 美元 现值利 率系数 贴现后的现金 流量 / 美元 1234512345 30 000 20 000 40 000 30 000 0.8929 0.7972 0.7118 0.6355 0.5674 26 787 15 944 28 472 25 420 17 022 0.8333 0.6944 0.5787 0.4823 0.4019 24 999 13 888 23 148 19 292 12 057 现金流量的现值 = 113 645 美元 减：初始投资 = 100 000 美元 净现值 =13 645 美元 现金流量的现值 = 93 384 美 元 减：初始投资 = 100 000 美元 风险调整后的净 现 = － 6 616 美元

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