NPV, Internal Rate of Return (IRR), and the Profitability Index (PI) - PowerPoint Presentation

1. NPV, Internal Rate of Return (IRR), and the Profitability Index (PI)Module 2.3

2. 5.4 The Internal Rate of ReturnIRR: the discount rate that sets NPV to zeroIRR the rate that yields a break-even NPV Minimum Acceptance Criteria: Accept if the IRR exceeds the required returnRanking Criteria: Select alternative with the highest IRRReinvestment assumption: All future cash flows are assumed to be reinvested at the IRR

3. Internal Rate of Return (IRR)Disadvantages:IRR may not existThere may be multiple IRRs Problems with mutually exclusive investmentsAdvantages:Easy to understand and communicate

4. IRR: ExampleConsider the following project:0123$50$100$150-$200The internal rate of return for this project is 19.44%

5. IRR example (spreadsheet)I used ‘Goal Seek’ to change the rate cell, such that my target cell (NPV cell) is equal to zero.My pink rate cell is the cell that I ask to change in Goal Seek. I set the other rate cells to change with the pink rate cell.FVrtPV500.194377042141.862827431000.194377042270.099852821500.194377042388.03734124  Initial Investment =-200      NPV = 2.14811E-05

6. NPV Payoff ProfileIf we graph NPV versus the discount rate, we can see the IRR as the x-axis intercept.IRR = 19.44%

7. Calculating IRR with SpreadsheetsYou start with the same cash flows as you did for the NPV.You may use the IRR function:You first enter your range of cash flows, beginning with the initial cash flow.You can enter a guess, but it is not necessary.The default format is a whole percent – you will normally want to increase the decimal places to at least two.Again, I prefer to not use the IRR function, and instead use “goal seek” to find IRR, but using the IRR function is fine

8. 5.5 Problems with IRRMultiple IRRsThe Scale ProblemThe Timing Problem

9. Mutually Exclusive vs. IndependentMutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g., acquiring an accounting system. RANK all alternatives, and select the best one.Independent Projects: accepting or rejecting one project does not affect the decision of the other projects.Must exceed a MINIMUM acceptance criteria

10. Multiple IRRsThere are two IRRs for this project: 0 1 2 3$200 $800-$200- $800100% = IRR20% = IRR1Which one should we use?

11. The Scale ProblemWould you rather make 100% or 50% on your investments?What if the 100% return is on a $1 investment, while the 50% return is on a $1,000 investment?

12. The Timing Problem0 1 2 3$10,000 $1,000 $1,000-$10,000Project A0 1 2 3$1,000 $1,000 $12,000-$10,000Project B

13. The Timing Problem10.55% = crossover rate16.04% = IRRA12.94% = IRRB

14. Note on interest rate sensitivitySee on prior slide that NPV of project B is more sensitive to interest rates. This is because it’s cash flows are more heavily weighted in the future.We will see this concept again with bond valuationBonds with longer maturity (or more heavy weight of cash flows going to holder in the future) will have valuations more sensitive to interest rate changes

15. Calculating the Crossover RateCompute the IRR for either project “A-B” or “B-A”10.55% = IRR

16. NPV versus IRRNPV and IRR will generally give the same decision.Exceptions:Non-conventional cash flows – cash flow signs change more than onceMutually exclusive projectsInitial investments are substantially differentTiming of cash flows is substantially different

17. 5.6 The Profitability Index (PI)Minimum Acceptance Criteria: Accept if PI > 1Ranking Criteria: Select alternative with highest PI

18. The Profitability IndexDisadvantages:Problems with mutually exclusive investmentsAdvantages:May be useful when available investment funds are limitedEasy to understand and communicateCorrect decision when evaluating independent projectsObviously a close cousin to the NPV

19. Example of Investment RulesCompute the IRR, NPV, PI, and payback period for the following two projects. Assume the required return is 10%. Year Project A Project B 0 -$200 -$150 1 $200 $50 2 $800 $100 3 -$800 $150

20. Example of Investment Rules Project A Project BCF0 -$200.00 -$150.00PV0 of CF1-3 $241.92 $240.80NPV = $41.92 $90.80IRR = 0%, 100% 36.19%PI = 1.2096 1.6053 Payback = 1 year (3?) 2 years

21. Project AProject B($200)($100)$0$100$200$300$400-15%0%15%30%45%70%100%130%160%190%Discount ratesNPVIRR 1(A)IRR (B)NPV profiles of both projectsIRR 2(A)Cross-over Rate

22. 5.7 The Practice of Capital BudgetingVaries by industry:A few firms may use payback if they are in need of cash (liquidity).The most frequently used technique for large corporations is a combination of NPV and IRR.It is common to build out NPV profiles (which incoporates IRRs) and conduct sensitivity analysis (covered in module 3)

23. Summary – Discounted Cash FlowNet present valueDifference between market value and costAccept the project if the NPV is positiveHas no serious problemsPreferred decision criterionInternal rate of returnDiscount rate that makes NPV = 0Take the project if the IRR is greater than the required returnSame decision as NPV with conventional cash flowsIRR is unreliable with non-conventional cash flows or mutually exclusive projectsProfitability IndexBenefit-cost ratioTake investment if PI > 1Cannot be used to rank mutually exclusive projectsMay be used to rank projects in the presence of capital rationing

24. Summary – Payback CriteriaPayback periodLength of time until initial investment is recoveredTake the project if it pays back in some specified periodDoes not account for time value of money, and there is an arbitrary cutoff periodDiscounted payback periodLength of time until initial investment is recovered on a discounted basisTake the project if it pays back in some specified periodThere is an arbitrary cutoff period