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McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. NPV, Internal Rate of Return (IRR), and the Profitability Index (PI) Module 2.3

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The Internal Rate of Return IRR: the discount rate that sets NPV to zero IRR the rate that yields a break-even NPV Minimum Acceptance Criteria: Accept if the IRR exceeds the required return Ranking Criteria: Select alternative with the highest IRR Reinvestment assumption: All future cash flows are assumed to be reinvested at the IRR

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5-2 Internal Rate of Return (IRR) Disadvantages: IRR may not exist There may be multiple IRRs Problems with mutually exclusive investments Advantages: Easy to understand and communicate

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5-3 IRR: Example Consider the following project: 0123 $50$100$150 -$200 The internal rate of return for this project is 19.44%

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5-4 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. FVrtPV Initial Investment =-200 NPV = E-05

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5-5 NPV Payoff Profile If we graph NPV versus the discount rate, we can see the IRR as the x-axis intercept. IRR = 19.44%

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5-6 Calculating IRR with Spreadsheets You 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

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Problems with IRR Multiple IRRs The Scale Problem The Timing Problem

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5-8 Mutually Exclusive vs. Independent Mutually 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

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5-9 Multiple IRRs There are two IRRs for this project: $200 $800 -$200 - $ % = IRR 2 0% = IRR 1 Which one should we use?

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5-10 The Scale Problem Would 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?

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5-11 The Timing Problem $10,000 $1,000$1,000 -$10,000 Project A $1,000 $1,000 $12,000 -$10,000 Project B

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5-12 The Timing Problem 10.55% = crossover rate 16.04% = IRR A 12.94% = IRR B

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5-13 Note on interest rate sensitivity See 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 valuation Bonds 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

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5-14 Calculating the Crossover Rate Compute the IRR for either project “A-B” or “B-A” 10.55% = IRR

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5-15 NPV versus IRR NPV and IRR will generally give the same decision. Exceptions: Non-conventional cash flows – cash flow signs change more than once Mutually exclusive projects Initial investments are substantially different Timing of cash flows is substantially different

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

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5-17 The Profitability Index Disadvantages: Problems with mutually exclusive investments Advantages: May be useful when available investment funds are limited Easy to understand and communicate Correct decision when evaluating independent projects Obviously a close cousin to the NPV

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5-18 Example of Investment Rules Compute 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

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5-19 Example of Investment Rules Project AProject B CF 0 -$ $ PV 0 of CF 1-3 $241.92$ NPV =$41.92$90.80 IRR = 0%, 100% 36.19% PI = Payback =1 year (3?)2 years

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5-20 Project A Project B ($200) ($100) $0 $100 $200 $300 $ %0%15%30%45% 70%100% 130% 160%190% Discount rates NPV IRR 1 (A) IRR (B) NPV profiles of both projects IRR 2 (A) Cross-over Rate

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The Practice of Capital Budgeting Varies 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)

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5-22 Summary – Discounted Cash Flow Net present value Difference between market value and cost Accept the project if the NPV is positive Has no serious problems Preferred decision criterion Internal rate of return Discount rate that makes NPV = 0 Take the project if the IRR is greater than the required return Same decision as NPV with conventional cash flows IRR is unreliable with non-conventional cash flows or mutually exclusive projects Profitability Index Benefit-cost ratio Take investment if PI > 1 Cannot be used to rank mutually exclusive projects May be used to rank projects in the presence of capital rationing

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5-23 Summary – Payback Criteria Payback period Length of time until initial investment is recovered Take the project if it pays back in some specified period Does not account for time value of money, and there is an arbitrary cutoff period Discounted payback period Length of time until initial investment is recovered on a discounted basis Take the project if it pays back in some specified period There is an arbitrary cutoff period

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