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Chapter 12 Capital Budgeting: Decision Criteria 1 Topics Overview Methods NPV IRR, MIRR Profitability Index Payback, discounted payback Unequal lives Economic life 2 Capital Budgeting: Analysis of potential projects Long-term decisions Large expenditures Difficult/impossible to reverse Determines firm’s strategic direction 3 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 4 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 5 Cash Flows for Projects L and S 6 NPV: Sum of the PVs of all cash flows. n NPV = ∑ t=0 CFt . (1 + r)t NOTE: t=0 Cost often is CF0 and is negative n NPV = ∑ t=1 CFt (1 + r)t - CF0 7 Project S’s NPV NPV for Project S 10% t = S's CFs 0 1 2 3 4 -1000 500 400 300 100 -1000 454.55 330.58 225.39 68.30 $78.82 8 Project L’s NPV NPV for Project L 10% t = L's CFs 0 1 2 3 4 -1000 100 300 400 600 -1000 90.91 247.93 300.53 409.81 $49.18 9 TI BAII+: Project L NPV Display Cash Flows: You Enter ' CF0 = -1000 CF1 = 100 CF2 = 300 CF3 = 400 CF4 = 600 C00 C01 F01 C02 F02 C03 F03 C04 F04 I NPV 49.18 1000 100 1 300 1 400 1 600 1 10 % S !# !# !# !# !# !# !# !# !# ( !# 10 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 11 NPV Method Meets all desirable criteria Considers all CFs Considers TVM Can rank mutually exclusive projects Value-additive Directly related to increase in VF Dominant method; always prevails 12 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 NPVs > NPVL If S & L are independent, accept both; NPV > 0 13 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 14 NPV vs IRR NPV: Enter r, solve for NPV n CF t = NPV ∑ (1 + r)t t=0 IRR: Enter NPV = 0, solve for IRR n ∑ t=0 CFt =0 (1 + IRR)t 15 Franchise L’s IRR IRR for Project L ?% t = L's CFs NPV = 0 1 2 3 4 -1000 100 300 400 600 -1000 PV(1) PV(2) PV(3) PV(4) $0.00 16 TI BAII+: Project L IRR Display Cash Flows: You Enter ' CF0 = -1000 CF1 = 100 CF2 = 300 CF3 = 400 CF4 = 600 C00 C01 F01 C02 F02 C03 F03 C04 F04 I IRR 11.79 1000 100 1 300 1 400 1 600 1 10 % S !# !# !# !# !# !# !# !# !# ( !# 17 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: IRRS > r and IRRL > r If S and L are mutually exclusive, accept S because IRRS > IRRL 18 Construct NPV Profiles Enter CFs in CFLO and find NPVL and NPVS at different discount rates: r 0 5% 10% 15% 20% NPV (S) $300.00 $180.42 $78.82 ($8.33) ($83.72) NPV(L) $400.00 $206.50 $49.18 ($80.14) ($187.50) 19 NPV Profile 20 To Find the Crossover Rate Find cash flow differences between the projects. Enter these differences in CFLO register, then press IRR. Crossover rate = 7.17%, rounded to 7.2%. Can subtract S from L or vice versa If profiles don’t cross, one project dominates the other 21 Finding the Crossover Rate t 0 1 2 3 4 S -1000 500 400 300 100 L -1000 100 300 400 600 Diff 0 400 100 -100 -500 7.2% 22 NPV and IRR: No conflict for independent projects NPV ($) IRR > r and NPV > 0 Accept r > IRR and NPV < 0. Reject IRR r (%) 23 Mutually Exclusive Projects r > 7.2% NPVS> NPVL IRRS > IRRL NO CONFLICT NPV L S 7.2 r < 7.2% NPVL> NPVS IRRS > IRRL CONFLICT IRRS % IRRL 24 Mutually Exclusive Projects CONFLICT r 0 5% 10% 15% 20% IRR NPV (S) $300.00 $180.42 $78.82 ($8.33) ($83.72) 14.5% NPV(L) $400.00 $206.50 $49.18 ($80.14) ($187.50) 11.8% r < 7.2% NPVL> NPVS IRRS > IRRL r > 7.2% NPVS > NPVL IRRS > IRRL NO CONFLICT 25 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, NPVS > NPVL 26 Issues with IRR Reinvestment rate assumption Non-normal cash flows 27 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 28 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 29 MIRR for Project S: First, find PV and TV (r = 10%) MIRR for Project S r = 10% t = S's CFs 0 1 2 3 4 -1000 500 400 300 100 330 484 665.5 -1000.00 PV Outflows 1579.5 TV Inflows 30 Second: Find discount rate that equates PV and TV MIRR for Project S r = 10% t = S's CFs 0 1 2 3 4 -1000 500 400 300 100 330 484 665.5 -1000.00 PV Outflows 1579.5 TV Inflows 1579.5 M IRR ( 1 M IRR) 4 MIRR = 12.1% 31 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) 32 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 33 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 34 Pavilion Project: NPV and IRR? 0 -800 r = 10% 1 2 5,000 -5,000 Enter CFs, enter I = 10 NPV = -386.78 IRR = ERROR 35 Nonnormal CFs: Two sign changes, two IRRs NPV Profile NPV IRR2 = 400% 450 0 -800 100 400 r IRR1 = 25% 36 Multiple IRRs Descartes Rule of Signs n CFt 0 t t 0 ( 1 IRR ) Polynomial of degree n→n roots 1 real root per sign change Rest = imaginary (i2 = -1) 37 Logic of Multiple IRRs At very low discount rates: The PV of CF2 is large & negative NPV < 0 At very high discount rates: Year 0 1 2 CF $ (800,000) $ 5,000,000 $ (5,000,000) NPV $ The PV of both CF1 and CF2 are low CF0 dominates Again NPV < 0 Discounted Cash Flows 10% 50% ($800,000.0) ($800,000.0) $4,545,454.5 $3,333,333.3 ($4,132,231.4) ($2,222,222.2) (386,776.76) $ 311,111.61 $ 500% ($800,000.0) $833,333.3 ($138,888.9) (105,550.56) 38 Logic of Multiple IRRs In between: Year 0 1 2 The discount rate hits CF2 harder than CF1 NPV > 0 Result: 2 IRRs CF $ (800,000) $ 5,000,000 $ (5,000,000) NPV $ Discounted Cash Flows 10% 50% ($800,000.0) ($800,000.0) $4,545,454.5 $3,333,333.3 ($4,132,231.4) ($2,222,222.2) (386,776.76) $ 311,111.61 $ 500% ($800,000.0) $833,333.3 ($138,888.9) (105,550.56) 39 The Pavillion Project: Non-normal CFs and MIRR: 1 0 -800,000 2 5,000,000 -5,000,000 RR FR PV outflows @ 10% = -4,932,231.40 TV inflows @ 10% = 5,500,000.00 MIRR = 5.6% 40 Profitability Index PI =present value of future cash flows divided by the initial cost Measures the “bang for the buck” 41 Project S’s PV of Cash Inflows t = S's CFs 0 -1000 PV of Inflows for Project S 10% 1 2 500 400 3 4 300 100 454.55 330.58 225.39 68.30 $1,078.82 42 Profitability Indexs PIS = PV future CF Initial Cost = $1078.82 $1000 PIS = 1.0788 PIL = 1.0492 43 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 44 Profitability Index Strengths: Considers all CFs Considers TVM Useful in capital rationing Weaknesses: Cannot rank mutually exclusive Not Value-additive 45 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<Target 46 Payback for Projects S and L Payback Years before full recovery Unrecovered cost at start of year Cash flow during year 47 Payback for Projects S and L t = S's CFs Cumulative 0 -1000 -1000 Payback for Project S 1 2 500 -500 400 -100 Payback = t = L's CFs Cumulative 0 -1000 -1000 300 -600 Payback = Payback Years before full recovery 4 300 200 100 300 3 4 400 -200 600 400 2.33 Payback for Project L 1 2 100 -900 3 3.33 Unrecovered cost at start of year Cash flow during year 48 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! 49 Discounted Payback: Use discounted CFs r = 10% S's CFs Discounted CFs Cumulative Discounted Payback for Project S 0 1 2 -1000 -1000 -1000 500 454.55 -545.45 L's CFs Discounted CFs Cumulative 4 300 225.39 10.52 100 68.30 78.82 3 4 400 300.53 -360.63 600 409.81 49.18 400 330.58 -214.88 Discounted Payback = r = 10% 3 2.95 Discounted Payback for Project L 0 1 2 -1000 -1000 -1000 100 90.91 -909.09 Discounted Payback = 300 247.93 -661.16 3.88 50 Summary Calculate ALL -- each has value Method NPV Payback IRR MIRR PI What it measures Metric $ increase in VF Liquidity E(R), risk Corrects IRR If rationed $$ Years % % Ratio 51 Business Practices 52 Special Applications Projects with Unequal Lives Economic vs. Physical life The Optimal Capital Budget Capital Rationing 53 SS and LL are mutually exclusive. r = 10%. 0 1 2 Project SS: 60 (100) 60 Project LL: 33.5 (100) 33.5 3 4 33.5 33.5 54 NPVLL > NPVSS But is LL better? SS CF0 CF1 F I NPV LL -100,000 -100,000 60,000 33,500 2 4 10 10 4,132 6,190 55 Solving for EAA PMT = EAA Project SS 2 , 10 4132 S. 0 0 %/ = 2.38 =PMT(0.10,2,-4132,0) Project LL 4 , 10 6190 S. 0 0 %/ = 1.95 =PMT(0.10,4,-6190,0) 56 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. 57 Replacement Chain Approach (000s) Project SS with Replication: 0 1 2 3 4 60 (100) (40) 60 60 60 60 Project SS: (100) (100) 60 60 NPVSS = $7,547 . Compare: NPVLL = $6,190 58 Or, use NPVss: 0 4,132 3,415 7,547 1 10% 2 3 4 4,132 Compare to Project LL NPV = $6,190 59 Suppose cost to repeat SS in two years rises to $105,000 0 1 Project SS: (100) 60 2 3 4 60 (105) (45) 60 60 NPVSS = $3,415 < NPVLL = $6,190 60 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? 61 Economic Life vs. Physical Life 62 Economic vs. Physical Life ECONOMIC vs. PHYSICAL LIFE YR 0 1 2 3 CF -$4,800 $2,000 $2,000 $1,750 SV $4,800 $3,000 $1,650 $0 NPV r = 10% CFs if Terminated in Year 3 2 1 -$4,800 -$4,800 -$4,800 $2,000 $2,000 $5,000 $2,000 $3,650 $1,750 ($14.12) $34.71 ($254.55) 63 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. 64 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 65 Increasing Marginal Cost of Capital Externally raised capital large flotation costs Investors often perceive large capital budgets as being risky Increases the cost of capital 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 66 Increasing Marginal Cost of Capital % 16 15 14 WACC2 = 12.5% 13 12 WACC1 = 11.0% External debt & equity 10 9 No external funds 8 500 700 Capital Required 61 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 68 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 69 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 70 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 71 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) 72 Excel Spreadsheet Functions NPV(Rate, Value Range**) IRR(Value Range) MIRR(Value Range, FR, RR) ** NPV value range includes CF1 through CFn CF0 must be handled independently, outside the function =NPV(Rate, CF1-CFn) + CF0 73