Slide 1Ocean CarriersSensitivity, Scenario, and Breakeven analysis.Internal Rate of ReturnIRR – “Normal” Cash Flow PatternIRR – NPV Profile DiagramThe Merit to the IRR ApproachPitfalls of the IRR ApproachPitfalls of IRR cont…Pitfalls of IRR cont…Pitfalls of IRR cont…Mutually Exclusive Projects and IRRProject Scale and the IRRSummary of IRR vs. NPVSlide 16Dealing With InflationCash Flow and InflationSlide 19Slide 20Brief Introduction to Real OptionsThe Deferral OptionThe Option to AbandonThe Option to AbandonThe Option to AbandonCapital Budgeting ApplicationsImplementing the NPV RuleOcean CarriersJanuary 2001, Mary Linn of Ocean Carriers is evaluating the purchase of a new capesize carrier for a 3-year lease proposed by a motivated customer.Ocean Carriers owns and operates capesize dry bulk carriers that mainly carry iron ore and coal worldwide.Ocean Carriers’ vessels were commonly chartered on a time charter basis for 1-, 3-, or 5-year periods, however the spot charter market was also used.Sensitivity, Scenario, and Breakeven analysis.The NPV is usually dependent upon assumptions and projections. What if some of the projections are off?Breakeven analysis asks when do we see zero NPV?One example we will see is IRR.Sensitivity analysis considers how NPV is affected by our forecasts of key variables.Examines variables one at a time. Consider for example a one standard deviation change in expected inflation.Scenario analysis accounts for the fact that some variables are related.In a recession, the selling price and the units sold may both be lower than expected.Simulation is the granddaddy of them all, you will learn about this technique in your Ops course.Internal Rate of ReturnDefinition: The discount rate that sets the NPV of a project to zero is the project’s IRR.Conceptually, IRR asks: “What is the project’s rate of return?”Standard Rule: Accept a project if its IRR is greater than the appropriate market based discount rate, reject if it is less. Why does this make sense?This is where the term “hurdle rate” comes from.IRR is completely internal to the project. To use the rule effectively we compare the IRR to a market rate.For independent projects with “normal cash flow patterns” IRR and NPV give the same conclusions.IRR – “Normal” Cash Flow PatternConsider the following stream of cash flows:Calculate the NPV at different discount rates until you find the discount rate where the NPV of this set of cash flows equals zero.That’s all you do to find IRR.0 1 2 3-$1,000$400 $400 $400IRR – NPV Profile DiagramEvaluate the NPV at various discount rates:Rate NPV 0 $20010 -$5.320 -$157.4At r = 9.7%, NPV = 0The Merit to the IRR ApproachThe IRR is an approximation (assumes reinvestment of payouts at the IRR) for the return generated over the life of a project on the initial investment.The IRR is based on all incremental cash flows and (by comparison to the appropriate discount rate, r) takes proper account of the time value of money (and risk).In short, it can be useful.Pitfalls of the IRR ApproachMultiple IRRsThere can be as many solutions to the IRR definition as there are changes of sign in the time ordered cash flow series.Consider:This can (and does) have two IRRs.0 1 2-$100 $230 -$132Pitfalls of IRR cont…Pitfalls of IRR cont…-0.500.511.522.530 10 15 20 40Discount RateNPVPitfalls of IRR cont…Mutually exclusive projects:IRR can lead to incorrect conclusions about the relative worth of projects.Ralph owns a warehouse he wants to fix up and use for one of two purposes:A. Store toxic waste.B. Store fresh produce.Let’s look at the cash flows, IRRs and NPVs.Mutually Exclusive Projects and IRRProject Year 0 Year 1 Year 2 Year 3A -10,000 10,000 1,000 1,000B -10,000 1,000 1,000 12,000Project NPV @0%NPV @10%NPV@15%IRRA $2000 $669 $109 16.04%B $4000 $751 -$484 12.94%At low discount rates, B is better. At high discount rates, A is better.But A always has the higher IRR. A common mistake to make is choose A regardless of the discount rate.Simply choosing the project with the larger IRR would be justified only if the projects’ intermediate cash flows could be reinvested at the IRR instead of the actual market rate, r, for the life of the project.Project Scale and the IRRBecause the IRR puts things in terms of a “rate” it may not tell you what really interests you; which investment will create the most “wealth”.Example:ProjectInvestmentTime 1 IRR NPV at 10%A -$1,000 +$1,500 50% $363.64B -$10,000 +$13,000 30% $1,1818.18Summary of IRR vs. NPVIRR analysis can be misleading if you don’t fully understand its limitations.For individual projects with normal cash flows NPV and IRR provide the same conclusion.For projects with inflows followed by outlays, the decision rule for IRR must be reversed.For Multi-period projects with several changes in sign of the cash flows multiple IRRs exist. Must compute the NPVs to see what decision rule is appropriate.IRR may give incorrect evaluation when comparing projects.Suffers from a reinvestment assumption.I recommend NPV analysis, using others as a way to communicate if necessary.NPV and Microeconomics One ‘line of defense’ against bad decision making is to think about NPV in terms of the underlying economics.NPV is the present value of the project’s future ‘economic profits’. Economic profits are those in excess of the ‘normal’ return on invested capital (i.e. the opportunity cost of capital).In ‘long-run competitive equilibrium’ all projects and firms earn zero economic profits.In what way does the proposed project differ from the theoretical ‘long run competitive equilibrium’? If no plausible answers emerge, any positive NPV is likely to be illusory.Dealing With InflationInterest rates and inflation:The general formula (complements of Irving Fisher) is:(1 + rNom) = (1 + rReal)  (1 +rInf)Rearranging:Example:Nominal Interest Rate=10%Inflation Rate=6%rReal = (1.10/1.06) - 1 = 0.038=3.8%111InfNomRealrrrCash Flow and InflationCash flows are called nominal if they are expressed in terms of the actual dollars to be received or paid out. A cash flow is called real if expressed in terms of a common date’s purchasing power.The big question: Do we discount real or nominal