Topic Overview. Learning Objectives. Capital Budgeting Steps: WHAT IS CAPITAL BUDGETING?

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1 Chaper 10: THE BASICS OF CAPITAL BUDGETING Should we build his plan? Topic Overview Projec Types Capial Budgeing Decision Crieria Payback Period Discouned Payback Period Ne Presen Value () Inernal Rae of Reurn (IRR) Modified Inernal Rae of Reurn (MIRR) Learning Objecives Think abou his as we cover Chaper 10 Capial Budgeing Decision Mehods. Undersand how o calculae and use he 5 capial budgeing decision echniques: Payback, Discouned Payback,, IRR, & MIRR. Undersand he advanages and disadvanages of each echnique. Undersand which projec o selec when here is a ranking conflic beween and IRR. Which of he following invesmen opporuniies would you prefer? #1) Give me $1 now and I ll give you $2 a he end of class. #2) Give me $100 now and I ll give you $150 a he end of class. WHAT IS CAPITAL BUDGETING? Capial Budgeing Seps: Analysis of poenial addiions o fixed asses. Long-erm decisions; involve large expendiures. Very imporan o firm s fuure. 1. Esimae CFs (inflows & ouflows). 2. Assess riskiness of CFs. 3. Deermine k = WACC (adj.). 4. Find and/or IRR. 5. Accep if > 0 and/or IRR > WACC. 1

2 Types of Projecs An Example of Muually Exclusive Projecs: Brand new line of business Expansion of exising line of business Replacemen of exising asse Independen vs. Muually Exclusive Normal vs. Non-normal BRIDGE VS. BOAT TO GET PRODUCTS ACROSS A RIVER. Normal vs. Nonnormal Projecs Normal Projec: Cos (negaive CF) followed by a series of posiive cash inflows. One change of signs. Non-normal Projec: Two or more changes of signs. Mos common: Cos (negaive CF), hen sring of posiive CFs, hen cos o close projec. Nuclear power plan, srip mine. Inflow (+) or Ouflow (-) in Year N NN N NN N N NN Our Case Sudy Payback Period (PB) We wan o help Marge Simpson analyze he following business opporuniies by using he following cash flow informaion. Assume Marge's cos of capial is 12%. Time Falafel-Full How 'Bou A Prezel? 0 (20,000) (20,000) 1 15,000 2, ,000 2, ,000 3, ,000 50,000 Measures how long i akes o recovers a projec s cos (CF0 = iniial oulay). Easy o calculae and a good measure of a projec s risk and liquidiy. Decision Rule: Accep if PB < some maximum period of ime. If cash inflows are equal each year (in he form of an annuiy), PB = CF0/Annual CF Oherwise: see our coninuing example. 2

3 Marge s Payback (Assume Marge s max is 2 years) Time Falafel-Full Cumulaive CF How 'Bou A Prezel? Cumulaive CF 0 (20,000) (20,000) (20,000) (20,000) 1 15,000 (5,000) 2,000 (18,000) 2 15,000 10,000 2,500 (15,500) 3 13,000 23,000 3,000 (12,500) 4 3,000 26,000 50,000 37,500 PB = Years Before Full Recovery of Iniial Cos + (Unrecovered CF0)/(Cash inflow during year) Falafel PB = 1 + 5,000/15,000 = 1.33 Prezel PB = ,500/50,000 = 3.25 Marge should choose Falafel using Payback Period. Problems wih Payback Ignores ime value of money! Ignores cash flows beyond payback period. The Discouned Payback Period addresses he firs problem. Disc. PB ells how long i akes o recover capial and financing coss for a projec. Discoun rae = cos of capial. : Sum of he PVs of inflows and ouflows. Marge s Discouned Payback Time Falafel-Full PV(CF) Cumulaive PV(CF) How 'Bou A Prezel? PV(CF) Cumulaive PV(CF) 0 (20,000) (20,000) (20,000) (20,000) (20,000) (20,000) 1 15,000 13,393 (6,607) 2,000 1,786 (18,214) 2 15,000 11,958 5,351 2,500 1,993 (16,221) 3 13,000 9,253 14,604 3,000 2,135 (14,086) 4 3,000 1,907 16,510 50,000 31,776 17,690 PB = Years Before Full Discouned Recovery of Iniial Cos + (Unrecovered Iniial Cos)/(Disc. CF during year) Falafel DPB = 1 + 6,607/11,958 = 1.55 Prezel DPB = ,086/31,776 = 3.44 Discouned Payback sills ignores cash flows beyond he discouned payback period. n CF =. = 0 ( 1 + k) Cos ofen is CF 0 and is negaive. n = = 1 CF ( 1 + k ) CF. 0 Ne Presen Value () = PV of inflows minus Cos = Ne gain in wealh. Accepance of a projec wih a > 0 will add value o he firm. Decision Rule: Accep if >0, Rejec if < 0 Excel and : Why Microsof deserves is legal roubles. Excel s funcion is goofed up. =(k, range of cash flows) Assumes firs cash flow in range occurs a = 1. See spreadshee. Soluion o his spreadshee problem: exclude CF0 ( = 0 cash flow) from cell range and add CF0 (if CF0 is already negaive) or subrac CF0 (if CF0 is posiive) from funcion. 3

4 Marge s s: k = 12% Time Falafel-Full PV(CF) How 'Bou A Prezel? PV(CF) 0 (20,000) (20,000) (20,000) (20,000) 1 15,000 13,393 2,000 1, ,000 11,958 2,500 1, ,000 9,253 3,000 2, ,000 1,907 50,000 31,776 16,510 17,690 Calculaor Seps. Falafel-Full: CF0 = -20,000, C01 = 15,000, F01 = 2, C02 = 13,000, F02 = 1, C03 = 3,000. : I = 12, CPT = 16,510 Prezel: CF0 = -20,000, C01 = 2,000, C02 = 2,500, C03 = 3,000, C04 = 50,000. : I = 12, CPT = 17,690 Marge s Decision If projecs are independen, Marge should selec boh. Boh have posiive. If he projecs are muually exclusive, selec How Bou A Prezel? Prezel > Falafel. Inernal Rae of Reurn: IRR CF 0 CF 1 CF 2 CF 3 Cos Inflows IRR is he discoun rae ha forces PV inflows = cos. This is he same as forcing = 0. : Ener k, solve for. n CF =. = 0 ( 1 + k) IRR: Ener = 0, solve for IRR. n CF = 0. = 0 ( 1 + IRR) Inernal Rae of Reurn (IRR) Inernal Rae of Reurn is a projec s expeced rae of reurn on is invesmen. IRR is he ineres rae where he PV of he inflows equals he PV of he ouflows. In oher words, he IRR is he rae where a projec s = 0. Decision Rule: Accep if IRR > k (cos of capial). Non-normal projecs have muliple IRRs. Don use IRR o decide on non-normal projecs. Marge s IRRs Bes o use calculaor. Calculaor Seps. Falafel-Full: CF0 = -20,000, C01 = 15,000, F01 = 2, C02 = 13,000, F02 = 1, C03 = 3,000. Press IRR, hen CPT: IRR = 54.7% Prezel: CF0 = -20,000, C01 = 2,000, C02 = 2,500, C03 = 3,000, C04 = 50,000. Press IRR, hen CPT: IRR = 33.3% k = 12%. If independen projecs: selec boh, IRRs > 12%. Muually exclusive: selec Falafel; higher IRR. 4

5 Comparison of & IRR For normal independen projecs, boh mehods give same accep/rejec decision. > 0 yields IRR > k in order o lower o 0. However, he mehods can rank muually exclusive projecs differenly. Wha o do, hen? Profiles A graph which shows a projec s a differen ineres raes (cos of capial). Can illusrae ranking conflics beween and IRR. Below is a able of s for Marge s projecs. k Falafel-Full How 'Bou A Prezel? 0% 26,000 37,500 5% 21,589 27,899 10% 17,849 20,289 12% 16,510 17,690 15% 14,649 14,190 25% 9,485 5,216 35% 5,529 (874) 55% (68) (8,201) Marge s Projecs Deermining /IRR Conflic Range Marge's Profiles 40,000 30,000 20,000 IRR(P) IRR(F) 10, ,000 0% 10% 20% 30% 40% 50% 60% -20,000 Cos of Capial (k) Falafel-Full How 'Bou A Prezel? For each year, subrac one projec s cash flows from he oher. If here is a change of signs of hese cash flow differences, a ranking conflic exiss. Find IRR of hese cash flow differences o find rae where he wo projecs have he same = crossover rae. A a cos of capial less han his crossover rae, a ranking conflic beween and IRR exiss. Marge s crossover rae Two reasons profiles cross: Time Falafel-Fullw 'Bou A Prezel? Fal - Pre 0 (20,000) (20,000) 0 CF0 1 15,000 2,000 13,000 C ,000 2,500 12,500 C ,000 3,000 10,000 C03 4 3,000 50,000 (47,000) C04 IRR = Crossover Rae = 14.1% Marge's Profiles A a cos of capial less han 14.1%, Prezel has higher bu lower IRR = Ranking Conflic. A cos of capial greaer han 14.1%, Falafel has he higher and IRR. 40,000 30,000 20,000 10, ,000-20,000 IRR(P) 0% 10% 20% 30% 40% 50% 60% Cos of Capial (k) IRR(F) Falafel-Full How 'Bou A Prezel? 1) Size (scale) differences. Smaller projec frees up funds a = 0 for invesmen. The higher he opp. cos, he more valuable hese funds, so high k favors small projecs. 2) Timing differences. Projec wih faser payback provides more CF in early years for reinvesmen. If k is high, early CF especially good, S > L. 5

6 Which projec is bes for Marge? Think back o my indecen proposal. Which of he following invesmen opporuniies would you prefer? #1) Give me $1 now and I ll give you $2 a he end of class. #2) Give me $100 now and I ll give you $150 a he end of class. Reconciling Ranking Conflics absen capial raioning. Reinvesmen Rae Assumpion: assumes cash flows are reinvesed a company s cos of capial (i.e.: he invesors required rae of reurn). IRR assumes cash flows are reinvesed a IRR. The reinvesmen rae assumpion is more realisic. Shareholder Wealh Maximizaion: Wan o add more value o he firm han less. Resul: Choose projec wih highes when /IRR ranking conflic exiss for muually exclusive projecs. Acme, Inc. Rocke-Powered Roller Blade Projec Acme is considering he following projec which would marke hese roller blades o coyoes rying o cach road runners. Acme expecs a cash inflow in he year 1, bu an ouflow in he 2 nd (las) year of he projec due o liabiliy claims from injured caroon coyoes. Acme s opporuniy cos of capial is 13%. Year Cash Flow (5) 30 (30) = IRR = 26.8% -6 Rocke-Powered Roller Blade Profile 4-1 0% 50% 100% 150% 200% 250% 300% 350% 400% 450% 500% 550% A Acme s 13% opporuniy cos of capial, he projec has a negaive even hough he IRRs (~27% & 374%) are greaer han 13%. Because of his conflic, don use IRR o make decisions for nonnormal projecs! Why even mess wih IRR? Since we like, why mess wih somehing like IRR? A rae of reurn or ineres rae is more inuiive for ousiders and easier o undersand. Bu IRR assumes an unrealisic reinvesmen rae an leads o muliple IRRs for non-normal projecs. Soluion: Modified Inernal Rae of Reurn (MIRR). Modified Inernal Rae of Reurn, MIRR The ineres rae where he FV of a projec s inflows (TV) are discouned o equal he PV of a projec s ouflows. Assumes cash inflows are reinvesed a he projec s cos of capial (k). PV(ouflows) = TV/(1+MIRR) n, where TV = ΣCIF (1+k) n-, and PV(ouflows) = ΣCOF /(1+k) Where CIF = annual cash inflow, and COF = annual cash ouflow. 6

7 Seps o finding MIRR. Find TV of inflows by finding FV of each annual inflow o he end of he projec s life a he cos of capial. Find PV of ouflows a he cos of capial oday. Then find ineres rae over he n years of he projec ha equaes he TV (=FV) o he PV of he ouflows(=pv). Decision rule same as IRR: Compare MIRR o cos of capial. The MIRR for Marge s projecs. Tim e Falafel- Full FV a y r 4 a 1 2 % How 'Bou A Prezel? FV a y r 4 a 1 2 % 0 (20,000) (20,000) 1 15,000 21,074 2,000 2, ,000 18,816 2,500 3, ,000 14,560 3,000 3, ,000 3,000 50,000 50,000 TV = 57,450 TV = 59,306 Falafel-Full: -20,000 = PV, 57,450 = FV, 4 = N, 0 = PMT, CPT I/Y = 30.2% = MIRR How Bou A Prezel: -20,000 = PV, 59,306 = FV, 4 = N, 0 = PMT, CPT I/Y = 31.2% = MIRR Accep boh projecs if independen since MIRRs are greaer han he 12% cos of capial. Prefer prezel if muually exclusive. CF Workshee soluion o MIRR MIRR if more han one ouflow Find of inflows only firs, hen find FV of his single PV. YR FALAFEL ACIF CF WORK 0 0 CF0 = ,000 C01 = 15, ,000 F01 = ,000 C02 = 13,000 F02 =1 4 3,000 C03 = 3,000 F03 = 1 : I = 12, CPT = 36,510-36,510 =PV, 12 = I/Y, 4 = N, 0 = PMT, CPT FV = 57,450. Now 20,000 = PV, MIRR: CPT I/Y = 30.2% ACME Rocke Roller Blades YR CF Cos of capial = 13% FV of inflows a yr 2 = 30(1.13) = 33.9 PV of ouflows oday (yr 0) = -5 30/(1.13) 2 = = PV, 33.9 = FV, 0 = PMT, 2 = N, CPT I/Y = 9.1% MIRR less han 13% consisen wih negaive Summary of Capial Budgeing Mehods Wan a mehod he uses he ime value of money wih all projec cash flows:, IRR & MIRR. IRR can give erroneous decision for nonnormal projecs. Overall, is he bes and preferred mehod. 7

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