What s next? Capital Budgeting: involves making decisions about real asset investments. Chapter 7: Net Present Value and Other Investment Criteria Chapter 8: Estimating cash flows for a potential investment. Chapter 12: Estimating a required rate of return for a potential investment = opportunity cost of capital. Chapter 7 Net Present Value & Other Investment Criteria Topic Overview Project Types Capital Budgeting Decision Criteria Net Present Value (NPV) Payback Period Internal Rate of Return (IRR) Profitability Index (PI) Equivalent Annual Cost Capital Rationing 1
Learning Objectives Understand how to calculate and use capital budgeting decision techniques: Payback, NPV, IRR, & PI. Understand the advantages and disadvantages of each technique. Understand which project to select when there is a ranking conflict between NPV and IRR. Think about this as we cover Chapter 7 Investment Criteria. Which of the following investment opportunities would you prefer? #1) Give me $1 now and I ll give you $2 at the end of class. #2) Give me $100 now and I ll give you $150 at the end of class. Project Types Independent Projects don t affect acceptance of other projects Mutually Exclusive Projects interact with other projects or accomplish the same objective Normal Projects -only one sign change in sequence of cash flows Non-normal Projects - multiple sign changes in cash flow series. 2
Our Case Study We want to help Marge Simpson, Inc. analyze the following business opportunities by using the following cash flow information. Assume Marge's opportunity cost of capital is 12%. Time Falafel-Full How 'Bout A Pretzel? 0 (20,000) (20,000) 1 15,000 2,000 2 15,000 2,500 3 13,000 3,000 4 3,000 50,000 Net Present Value Net Present Value - Present value of cash flows minus initial investments. Opportunity Cost of Capital - Expected rate of return given up by investing in a project Net Present Value NPV = PV - required investment NPV Ct = C0 + ( 1+ r) t NPV C1 C2 Ct = C0 + + +... + 1 2 t ( 1+ r) ( 1+ r) ( 1+ r) 3
Net Present Value Net Present Value Rule Managers increase shareholders wealth by accepting all projects that are worth more than they cost. Therefore, they should accept all projects with a positive net present value. Marge s NPVs: r = 12% Time Falafel-Full PV(CF) How 'Bout A Pretzel? PV(CF) 0 (20,000) (20,000) (20,000) (20,000) 1 15,000 13,393 2,000 1,786 2 15,000 11,958 2,500 1,993 3 13,000 9,253 3,000 2,135 4 3,000 1,907 50,000 31,776 NPV 16,510 17,690 Calculator Steps. Falafel-Full: CF0 = -20,000, C01 = 15,000, F01 = 2, C02 = 13,000, F02 = 1, C03 = 3,000. NPV: I = 12, CPT NPV = 16,510 Pretzel: CF0 = -20,000, C01 = 2,000, F01=1, C02 = 2,500, F02=1, C03 = 3,000, F03=1, C04 = 50,000. NPV: I = 12, CPT NPV = 17,690 Excel and NPV: Why Microsoft deserves its legal troubles. Excel s NPV function is goofed up. =NPV(r, range of cash flows) Assumes first cash flow in range occurs at t = 1. See spreadsheet. Solution to this spreadsheet problem: exclude initial cost (t = 0 cash flow) from NPV cell range and add initial cost (if already negative) to the NPV function. 4
Marge s NPV Decision If projects are independent? If the projects are mutually exclusive? Payback Period (PB) Measures how long it takes to recovers a project s cost. Easy to calculate and a good measure of a project s risk and liquidity. Decision Rule: Accept if PB < some maximum period of time. Marge s Payback (Assume Marge s max is 2 years) Time Falafel-Full Cumulative CF How 'Bout A Pretzel? Cumulative 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 Falafel PB = 1 + 5000/15,000 = 1.33 Pretzel PB = 3 + 12,500/50,000 = 3.25 General form PB = last year of negative cumulative cash flow + unrecovered cost from that year/next year s cash flow Marge should choose Falafel using Payback Period. 5
Problems with Payback Ignores time value of money! Ignores cash flows beyond payback period. Not a good investment decision technique. Internal Rate of Return (IRR) Internal Rate of Return is a project s expected rate of return on its investment. IRR is the interest rate where the PV of the project s cash flows equals its cost. In other words, the IRR is the rate where a project s NPV = 0. C t /(1 + IRR) t = Cost Decision Rule: Accept if IRR > r (opportunity cost of capital). Non-normal projects have multiple IRRs. Don t use IRR to decide on non-normal projects. Marge s IRRs Time Falafel-Full How 'Bout A Pretzel? 0 (20,000) (20,000) 1 15,000 2,000 2 15,000 2,500 3 13,000 3,000 4 3,000 50,000 Best to use calculator. Calculator Steps. Falafel-Full: CF0 = -20,000, C01 = 15,000, F01 = 2, C02 = 13,000, F02 = 1, C03 = 3,000. Press IRR, then CPT: IRR = 54.7% Pretzel: CF0 = -20,000, C01 = 2,000, F01=1, C02 = 2,500, F02=1, C03 = 3,000, F03=1, C04 = 50,000. Press IRR, then CPT: IRR = 33.3% r = 12%. If independent projects? Mutually exclusive? 6
Profitability Index (PI) The ratio of the net present value of a project s cash flows to its cost. PI = NPV/Cost Decision Rule: Accept if PI > 0 CAUTION: PI can rank mutually exclusive projects that have different initial costs differently than NPV. Marge s PIs: r = 12% Time Falafel-Full PV(CF) How 'Bout A Pretzel? PV(CF) 0 (20,000) (20,000) (20,000) (20,000) 1 15,000 13,393 2,000 1,786 2 15,000 11,958 2,500 1,993 3 13,000 9,253 3,000 2,135 4 3,000 1,907 50,000 31,776 NPV 16,510 17,690 Comparison of NPV & IRR For normal independent projects, all three methods give same accept/reject decision. NPV > 0 yields IRR > r in order to lower NPV to 0. However, these methods can rank mutually exclusive projects differently. What to do, then? 7
NPV Profiles A graph which shows a project s NPV at different interest rates (opportunity cost of capital). Can illustrate ranking conflicts between NPV and IRR. Below is a table of NPVs for Marge s projects. r Falafel-Full How 'Bout A Pretzel? 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 Projects Marge's NPV Profiles NPV 40,000 30,000 20,000 IRR(P) IRR(F) 10,000 0-10,000 0% 10% 20% 30% 40% 50% 60% -20,000 Cost of Capital (r) Falafel-Full How 'Bout A Pretzel? Determining NPV/IRR Conflict Range For each year, subtract one project s cash flows from the other. If there is a change of signs of these cash flow differences, a ranking conflict exists. Find IRR of these cash flow differences to find rate where the two projects have the same NPV = crossover rate. At a cost of capital less than this crossover rate, a ranking conflict between NPV and IRR exists. 8
Determining Marge s NPV/IRR Conflict range Marge s Projects Marge's NPV Profiles NPV 40,000 30,000 20,000 10,000 0 IRR(P) -10,000 0% 10% 20% 30% 40% 50% 60% -20,000 Cost of Capital (r) IRR(F) Falafel-Full How 'Bout A Pretzel? Which project is best for Marge? Think back to my indecent proposal. Which of the following investment opportunities would you prefer? #1) Give me $1 now and I ll give you $2 at the end of class. #2) Give me $100 now and I ll give you $150 at the end of class. 9
Reconciling NPV/IRR Ranking Conflicts Shareholder Wealth Maximization: Want to add more value to the firm than less. Result: Choose project with highest NPV when NPV/IRR ranking conflict exists for mutually exclusive projects. Also, IRR has the multiple IRR problem for non-normal projects like the following. Acme, Inc. Rocket-Powered Roller Blade Project Acme is considering the following project which would market these roller blades to coyotes trying to catch road runners. Acme expects a cash inflow in the year 1, but an outflow in the 2 nd (last) year of the project due to liability claims from injured cartoon coyotes. Acme s opportunity cost of capital is 13%. Year 0 1 2 Cash Flow (5) 30 (30) NPV = -1.95 IRR = 26.8% NPV 4-6 Rocket-Powered Roller Blade NPV Profile -1 0% 50% 100% 150% 200% 250% 300% 350% 400% 450% 500% 550% At Acme s 13% opportunity cost of capital, the project has a negative NPV even though the IRRs is greater than 13%. Because of this conflict, don t use IRR to make decisions for non-normal projects! (or look for a first IRR that is less than cost of capital) 10
Comparing Projects with unequal lives To replace the Budweiser sign that the ferret dropped in the frog pond, Louie the Lizard is evaluating two new signs. Louie must purchase and care for a replacement sign indefinitely. Here are the annual costs for the two replacement signs. Which sign should Louie choose given an opportunity cost of capital of 11%? Year Frying Frogs Lizards Leaping over Frogs 0 4,000 6,000 1 1,000 900 2 1,000 700 3 700 4 700 Equivalent Annual Cost Equivalent Annual Cost - The cost per period with the same present value as the cost of buying and operating a machine. Equivalent annual cost = present value of costs annuity factor Louie The Lizard s Decision, r = 11% Year Frying Frogs Lizards Leaping over Frogs 0 4,000 6,000 1 1,000 900 2 1,000 700 3 700 4 700 Frying Frogs (FF) PV of costs = 5713 Lizards Leaping (LL) PV of costs = 8352 FF EAC: 5713=PV, 11=I/Y, 2=N, 0=FV, CPT PMT = 3336 LL EAC: 8352=PV, 11=I/Y, 4=N, 0=FV, CPT PMT = 2692 Louie should choose the Lizards Leaping over Frogs sign because of its lower cost on an annual basis. 11
Capital Rationing Capital Rationing - Limit set on the amount of funds available for investment. Soft Rationing - Limits on available funds imposed by management. Hard Rationing - Limits on available funds imposed by the unavailability of funds in the capital market. Profitability Index (PI) The ratio of the net present value of a project s cash flows to its cost. PI = NPV/Cost Decision Rule: Accept if PI > 0 PI can be used to rank projects under capital rationing conditions. Accept highest PI projects under the capital constraint to maximize NPV. CAUTION: PI can rank mutually exclusive projects that have different initial costs differently than NPV. Summary of Capital Budgeting Methods Want a method the uses the time value of money with all project cash flows: NPV, PI, IRR. IRR can give erroneous decision for non-normal projects. Overall, NPV is the best and preferred method. However, under capital rationing (budget restraint), ranking projects by PI can be useful in helping to maximize NPV under capital constraint. 12