2NPV AnalysisThe recommended approach to any significant capital budgeting decision is NPV analysis.NPV = PV of the incremental benefits – PV of the incremental costs.When evaluating independent projects, take a project if and only if it has a positive NPV.When evaluating interdependent projects, take the feasible combination with the highest total NPV.The NPV rule appropriately accounts for the opportunity cost of capital and so ensures the project is more valuable than comparable alternatives available in the financial market.
3Internal 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?For independent projects with “normal cash flow patterns” IRR and NPV give the same conclusions.IRR is completely internal to the project. To use the rule effectively we compare the IRR to a market rate.
4IRR – “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.123-$1,000$400
5IRR – NPV Profile Diagram Evaluate the NPV at various discount rates:Rate NPV0 $20010 -$5.320 -$157.4At r = 9.7%,NPV = 0
6The Merit to the IRR Approach The IRR is an approximation for the return generated over the life of a project on the initial investment.As with NPV, the IRR is based on incremental cash flows, does not ignore any cash flows, and (by comparison to the appropriate discount rate, r) take proper account of the time value of money and risk.In short, it can be useful.
7Pitfalls of the IRR Approach Multiple IRRsThere 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.12-$100$230-$132
10Pitfalls 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:Store toxic waste.Store fresh produce.Let’s look at the cash flows, IRRs and NPVs.
12At 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 project cash flows could be reinvested at the IRR instead of the actual market rate, r, for the life of the project.This last point explains why the correct decision depends upon cash flow timing and the interest rate. Since we really will only be able to invest cash flows from the project at the market rate not the IRR it matters what the market rate is and how long we invest the intermediate cash flows at the market rate.
13Project Scale and the IRR Because the IRR puts things in terms of a “rate” it may not tell you what interests you; which investment will create the most “wealth”.Example:ProjectInvestmentTime 1IRRNPV at 10%A-$1,000+$1,50050%$363.64B-$10,000+$13,00030%$1,
14Summary of IRR vs. NPVIRR 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 changes in sign of the cash flows, multiple IRRs exist. Must compute the NPVs to see what decision rule is appropriate.IRR can give conflicting signals relative to NPV when ranking projects.I recommend NPV analysis, using others as backup.
15Payback Period RuleFrequently used as a check on NPV analysis or by small firms or for small decisions.Payback period is defined as the number of years before the cumulative cash inflows equal the initial outlay.Provides a rough idea of how long invested capital is at risk.Example: A project has the following cash flowsYear 0 Year 1 Year 2 Year 3 Year 4-$10,000 $5,000 $3, $2,000 $1,000The payback period is 3 years. Is that good or bad?
16Payback Period RuleAn adjustment to the payback period rule that is sometimes made is to discount the cash flows and calculate the discounted payback period.This “new” rule continues to suffer from the problem of ignoring cash flows received after an arbitrary cutoff date.If this is true, why mess up the simplicity of the rule? Simplicity is its one virtue.At times the discounted payback period may be valuable information but it is not often that this information alone makes for good decision-making.
17Economic Profit or EVA EVA and Economic Profit Economic Profit The difference between revenue and the opportunity cost of all resources consumed in producing that revenue, including the opportunity cost of capitalEconomic Value Added (EVA)The cash flows of a project minus a charge for the opportunity cost of capital
18Economic Profit or EVA EVA When Invested Capital is Constant EVA in Period n (when capital lasts forever)where I is the project’s capital, Cn is the project’s cash flow at time n, and r is the cost of capital. (r × I ) is known as the capital charge
19Economic Profit or EVA EVA When Invested Capital is Constant EVA Investment RuleAccept any investment for which the present value (at the project’s cost of capital) of all future EVAs is positive.When invested capital is constant, the EVA rule and the NPV rule will coincide.
20ExampleProblemRalph has an investment opportunity which requires an upfront investment of $150 million.The annual end-of-year cash flows of $14 million dollars are expected to last forever.The firm’s cost of capital is 8%.Compute the annual EVA and the present value of the project.
21Example Solution EVA each year is: The present value of the EVA perpetuity is:
22Economic Profit or EVA EVA When Invested Capital Changes EVA in Period n (when capital depreciates)Where Cn is a project’s cash flow in time period n, In – 1 is the project’s capital at time n – 1, and r is the cost of capitalWhen invested capital changes, the EVA rule and the NPV rule continue to coincide.
23ExampleRalph is considering an investment in a machine to manufacture rubber chickens.It will generate revenues of $20,000 each year for 4 years and cost $60,000. The machine is expected to depreciate evenly over the 4 years.The current interest rate is 5%Should he invest in the machine?
24ExampleUsing the NPV rule we have a cost of $60,000 and benefits that look like a 4 year annuity. The NPV isIndicating that this is a valuable endeavor.
25Example For EVA we calculate The present value of EVA is then: Year 1 1234Capital$60,000$45,000$30,000$15,000$0Cash Flow$20,000Capital Charge($3,000)($2,250)($1,500)($750)Depreciation($15,000)EVAn$2,000$2,750$3,500$4,250