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1 Chapter 12 Capital Budgeting: Decision Criteria

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2 Topics Overview Methods NPV IRR, MIRR Profitability Index Payback, discounted payback Unequal lives Economic life

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3 Capital Budgeting: Analysis of potential projects Long-term decisions Large expenditures Difficult/impossible to reverse Determines firm’s strategic direction

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4 Steps in Capital Budgeting Estimate cash flows (Ch 13) Assess risk of cash flows (Ch 13) Determine r = WACC for project (Ch10) Evaluate cash flows – Chapter 12

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5 Independent versus Mutually Exclusive Projects Independent: The cash flows of one are unaffected by the acceptance of the other Mutually Exclusive: The acceptance of one project precludes accepting the other

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6 Cash Flows for Projects L and S

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7 NPV: Sum of the PVs of all cash flows. Cost often is CF 0 and is negative NPV = ∑ n t = 0 CF t (1 + r) t. NPV = ∑ n t = 1 CF t (1 + r) t - CF 0 NOTE: t=0

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8 Project S’s NPV

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9 Project L’s NPV

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10 TI BAII+: Project L NPV DisplayYou Enter ' C001000 S !# C01100 !# F011 !# C02300 !# F021 !# C03400 !# F031 !# C04600 !# F041 !# ( I10 !# NPV % 49.18 Cash Flows: CF0= -1000 CF1=100 CF2=300 CF3=400 CF4=600

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11 Rationale for the NPV Method NPV = PV inflows – Cost NPV=0 → Project’s inflows are “exactly sufficient to repay the invested capital and provide the required rate of return.” NPV = net gain in shareholder wealth Choose between mutually exclusive projects on basis of higher NPV Rule: Accept project if NPV > 0

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12 NPV Method Meets all desirable criteria Considers all CFs Considers TVM Can rank mutually exclusive projects Value-additive Directly related to increase in V F Dominant method; always prevails

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13 Using NPV method, which franchise(s) should be accepted? Project S NPV = $78.82 Project L NPV = $49.18 If Franchise S and L are mutually exclusive, accept S because NPV s > NPV L If S & L are independent, accept both; NPV > 0

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14 Internal Rate of Return: IRR IRR = the discount rate that forces PV inflows = cost Forcing NPV = 0 ≈ YTM on a bond Preferred by executives 3:1

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15 NPV vs IRR IRR: Enter NPV = 0, solve for IRR = NPV ∑ n t = 0 CF t (1 + r) t = 0 ∑ n t = 0 CF t (1 + IRR) t NPV: Enter r, solve for NPV

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16 Franchise L’s IRR

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17 TI BAII+: Project L IRR DisplayYou Enter ' C001000 S !# C01100 !# F011 !# C02300 !# F021 !# C03400 !# F031 !# C04600 !# F041 !# ( I10 !# IRR % 11.79 Cash Flows: CF0= -1000 CF1=100 CF2=300 CF3=400 CF4=600

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18 Decisions on Projects S and L per IRR Project S IRR = 14.5% Project L IRR = 11.8% Cost of capital = 10.0% If S and L are independent, accept both: IRR S > r and IRR L > r If S and L are mutually exclusive, accept S because IRR S > IRR L

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19 Construct NPV Profiles Enter CFs in CFLO and find NPV L and NPV S at different discount rates:

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20 NPV Profile

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21 To Find the Crossover Rate Find cash flow differences between the projects. Enter these differences in CFLO register, then press IRR. Crossover rate = 7.17%, rounded to 7.2%. Can subtract S from L or vice versa If profiles don’t cross, one project dominates the other

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22 Finding the Crossover Rate

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23 r > IRR and NPV < 0. Reject NPV ($) r (%) IRR IRR > r and NPV > 0 Accept NPV and IRR: No conflict for independent projects

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24 Mutually Exclusive Projects 7.2 NPV % IRR S IRR L L S r < 7.2% NPV L > NPV S IRR S > IRR L CONFLICT r > 7.2% NPV S > NPV L IRR S > IRR L NO CONFLICT

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25 Mutually Exclusive Projects r < 7.2% NPV L > NPV S IRR S > IRR L r > 7.2% NPV S > NPV L IRR S > IRR L CONFLICT NO CONFLICT

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26 Two Reasons NPV Profiles Cross Size (scale) differences Smaller project frees up funds sooner for investment The higher the opportunity cost, the more valuable these funds, so high r favors small projects Timing differences Project with faster payback provides more CF in early years for reinvestment If r is high, early CF especially good, NPV S > NPV L

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27 Issues with IRR Reinvestment rate assumption Non-normal cash flows

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28 Reinvestment Rate Assumption NPV assumes reinvest at r (opportunity cost of capital) IRR assumes reinvest at IRR Reinvest at opportunity cost, r, is more realistic, so NPV method is best NPV should be used to choose between mutually exclusive projects

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29 Modified Internal Rate of Return (MIRR) MIRR = discount rate which causes the PV of a project’s terminal value (TV) to equal the PV of costs TV = inflows compounded at WACC MIRR assumes cash inflows reinvested at WACC

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30 MIRR for Project S: First, find PV and TV (r = 10%)

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31 Second: Find discount rate that equates PV and TV MIRR = 12.1%

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32 Second: Find discount rate that equates PV and TV PV = PV(Outflows) = -1000 FV = TV(Inflows) = 1579.5 N = 4 PMT = 0 CPY I/Y = 12.1063 = 12.1% EXCEL: =MIRR(Value Range, FR, RR)

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33 MIRR versus IRR MIRR correctly assumes reinvestment at opportunity cost = WACC MIRR avoids the multiple IRR problem Managers like rate of return comparisons, and MIRR is better for this than IRR

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34 Normal vs. Nonnormal Cash Flows Normal Cash Flow Project: Cost (negative CF) followed by a series of positive cash inflows One change of signs Nonnormal Cash Flow Project: Two or more changes of signs Most common: Cost (negative CF), then string of positive CFs, then cost to close project For example, nuclear power plant or strip mine

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35 Pavilion Project: NPV and IRR? 5,000-5,000 012 r = 10% -800 Enter CFs, enter I = 10 NPV = -386.78 IRR = ERROR

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36 NPV Profile 450 -800 0 400100 IRR 2 = 400% IRR 1 = 25% r NPV Nonnormal CFs: Two sign changes, two IRRs

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37 Multiple IRRs Descartes Rule of Signs Polynomial of degree n → n roots 1 real root per sign change Rest = imaginary (i 2 = -1)

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38 Logic of Multiple IRRs At very low discount rates: The PV of CF 2 is large & negative NPV < 0 At very high discount rates: The PV of both CF 1 and CF 2 are low CF 0 dominates Again NPV < 0

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39 Logic of Multiple IRRs In between: The discount rate hits CF2 harder than CF1 NPV > 0 Result: 2 IRRs

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40 0 12 -800,0005,000,000-5,000,000 PV outflows @ 10% = -4,932,231.40 TV inflows @ 10% = 5,500,000.00 MIRR = 5.6% The Pavillion Project: Non-normal CFs and MIRR: RR FR

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41 Profitability Index PI =present value of future cash flows divided by the initial cost Measures the “bang for the buck”

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42 Project S’s PV of Cash Inflows

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43 Profitability Indexs PI S = PV future CF Initial Cost $1078.82 = PI S = 1.0788 PI L = 1.0492 $1000

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44 Profitability Index Rule: If PI>1.0 Accept Useful in capital rationing Closely related to NPV Can conflict with NPV if projects are mutually exclusive

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45 Profitability Index Strengths: Considers all CFs Considers TVM Useful in capital rationing Weaknesses: Cannot rank mutually exclusive Not Value-additive

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46 Payback Period The number of years required to recover a project’s cost How long does it take to get the business’s money back? A breakeven-type measure Rule: Accept if PB

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47 Payback for Projects S and L

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48 Payback for Projects S and L

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49 Strengths and Weaknesses of Payback Strengths: Provides indication of project risk and liquidity Easy to calculate and understand Weaknesses: Ignores the TVM Ignores CFs occurring after the payback period Biased against long-term projects ASKS THE WRONG QUESTION!

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50 Discounted Payback: Use discounted CFs

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51 Summary Calculate ALL -- each has value Method What it measures Metric NPV $ increase in VF$$ Payback LiquidityYears IRR E(R), risk% MIRR Corrects IRR% PI If rationedRatio

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52 Business Practices

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53 Special Applications Projects with Unequal Lives Economic vs. Physical life The Optimal Capital Budget Capital Rationing

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54 01234 Project SS: (100) Project LL: (100) 60 33.5 60 33.5 SS and LL are mutually exclusive. r = 10%.

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55 NPV LL > NPV SS But is LL better? SSLL CF 0 -100,000 CF 1 60,00033,500 F24 I10 NPV4,1326,190

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56 Solving for EAA PMT = EAA 2, 10 - 4132 S. 0 %/ = 2.38 =PMT(0.10,2,-4132,0) Project SS Project LL 4, 10 - 6190 S. 0 %/ = 1.95 =PMT(0.10,4,-6190,0)

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57 Unequal Lives Project SS could be repeated after 2 years to generate additional profits Use Replacement Chain to put projects on a common life basis Note: equivalent annual annuity analysis is alternative method.

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58 Replacement Chain Approach (000s) Project SS with Replication: NPV SS = $7,547 Compare: NPV LL = $6,190. 01234 Project SS : (100) (100) 60 60 (100) (40) 60

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59 Compare to Project LL NPV = $6,190 01234 4,132 3,415 7,547 4,132 10% Or, use NPV ss :

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60 NPV SS = $3,415 < NPV LL = $6,190 01234 Project SS: (100) 60 (105) (45) 60 Suppose cost to repeat SS in two years rises to $105,000

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61 Economic Life vs. Physical Life Consider a project with a 3-year life If terminated prior to Year 3, the machinery will have positive salvage value Should you always operate for the full physical life?

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62 Economic Life vs. Physical Life

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63 Economic vs. Physical Life

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64 Conclusions NPV(3)= -$14.12 NPV(2)= $34.71 NPV(1)= -$254.55 The project is acceptable only if operated for 2 years. A project’s engineering life does not always equal its economic life.

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65 The Optimal Capital Budget Finance theory says: Accept all positive NPV projects Two problems can occur when there is not enough internally generated cash to fund all positive NPV projects: An increasing marginal cost of capital Capital rationing

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66 Increasing Marginal Cost of Capital Externally raised capital large flotation costs Increases the cost of capital Investors often perceive large capital budgets as being risky Drives up the cost of capital If external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital

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500 700 % Capital Required WACC 1 = 11.0% WACC 2 = 12.5% 8 9 10 12 13 14 15 16 Increasing Marginal Cost of Capital 61 No external funds External debt & equity

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68 Capital Rationing Firm chooses not to fund all positive NPV projects Company typically sets an upper limit on the total amount of capital expenditures that it will make in the upcoming year

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69 Capital Rationing – Reason 1 Reason: Companies want to avoid the direct costs (i.e., flotation costs) and the indirect costs of issuing new capital Solution: Increase the cost of capital by enough to reflect all of these costs Then accept all projects that still have a positive NPV with the higher cost of capital

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70 Capital Rationing – Reason 2 Reason: Companies don’t have enough managerial, marketing, or engineering staff to implement all positive NPV projects Solution: Use linear programming to maximize NPV subject to not exceeding the constraints on staffing

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71 Capital Rationing – Reason 3 Reason: Companies believe that the project’s managers forecast unreasonably high cash flow estimates “Filter” out the worst projects by limiting the total amount of projects that can be accepted Solution: Implement a post-audit process and tie the managers’ compensation to the subsequent performance of the project

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72 Excel Spreadsheet Functions FV(Rate,Nper,Pmt,PV,0/1) PV(Rate,Nper,Pmt,FV,0/1) RATE(Nper,Pmt,PV,FV,0/1) NPER(Rate,Pmt,PV,FV,0/1) PMT(Rate,Nper,PV,FV,0/1) Inside parens: (RATE,NPER,PMT,PV,FV,0/1) “0/1” Ordinary annuity = 0 (default; no entry needed) Annuity Due = 1 (must be entered)

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73 Excel Spreadsheet Functions NPV(Rate, Value Range**) IRR(Value Range) MIRR(Value Range, FR, RR) ** NPV value range includes CF 1 through CF n CF0 must be handled independently, outside the function =NPV(Rate, CF 1 -CF n ) + CF 0

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