1. Net Present Value and Other Investment Rules

2. Percent of CFOs who say they use the following rules to evaluate projects 2

3. 3 What Makes for a Good Investment Rule? 1. Recognize the time value of money 2. Should rely solely on expected future cash flows and the opportunity cost of capital -Manager discretion & accounting numbers, are easy to manipulate 3. Want to be able to rank projects, and evaluate portfolios of projects

4. 4 Potential Investment Criteria Payback Period Average Accounting Return IRR NPV

5. 5 Payback Period Definition: The number of years before the project’s cumulative future cash flows equal the initial investment.  How long does it take the project’s to pay for itself? Decision rule: Accept projects whose payback period is less than a manager determined cut-off

6. 6 Payback Example Assume Payback cut-off is 1 year Which project do we take ProjectYear 0Year 1Year 2PBNPV @ 10% A-10100 Cum. CF B-10015 Cum. CF 0 -10 0 5 2 1-0.91 2.40 -10

7. 7 The Payback Period Method Disadvantages: 1. Biased against long-term projects Ignores cash flows after the payback period 2. Requires an arbitrary acceptance criteria 3. Ignores the time value of money A “Good” project may destroy value Advantages: 1. Easy to understand 2. Biased toward liquidity

8. 8 The Discounted Payback Period Cash flows are discounted before payback period is calculated  Effectively pick positively NPV project Very conservative → only very valuable projects accepted STILL ignores cash flows after the payback period

9. 9 Average Accounting Return Decision Rule: If the calculated value is above a benchmark (Ex. the firm’s current return on book or the industry average) accept the project. Fatally Flawed because:  Based on Accounting Numbers

10. 10 AAR Example A project has net income of $1,200, and $1,600 a year over its 2-year life. The initial cost of the project is $5,000, which will be depreciated using straight-line depreciation to a book value of zero over the life of the project. What is the AAR for this project?

11. 11 AAR example A project has net income of $1,200, and $1,600 a year over its 2-year life. The initial cost of the project is $5,000, which will be depreciated using straight-line depreciation to a book value of zero over the life of the project. What is the AAR for this project? AAR = 1,400 / 2,500 = 0.56 = 56% 012Ave NI BV 5,000 1,2001,6001,400 02,500

12. 12 Average Accounting Return Disadvantages: 1. Uses accounting numbers instead of cash flows 2. Ignores the time value of money 3. The benchmark is arbitrary. Advantages: 1. The accounting information is easy to obtain 2. Easy to calculate

13. 13 Internal Rate of Return (IRR) Definition: It is the discount rate that makes a project’s NPV equal 0. Decision Rule: Accept all projects with IRR’s greater than the opportunity cost of capital.

14. 14 IRR’s Underlying Assumptions All intermediate cash flows can be reinvested at the IRR  Is this reasonable? That short-term interest rates are equal to long- term interest rates  Does not address which to use if they are not equal

15. 15 IRR Notes To find the IRR of a project lasting t years, solve the following equation:  C 0 +C 1 /(1+IRR)+C 2 /(1+IRR) 2 +….+C t /(1+IRR) t =0 NPV > 0 implies that IRR > Op Cost IRR > Op Cost DOES NOT IMPLY that NPV > 0 IRR assumes that causality goes both ways

16. 16 IRR & NPV Investment Example A firm has a project that requires an initial investment of $10m. In the first year, it will return $12m, what is the IRR?  N = 1, I/Y= ???, PV = -10, PMT=0, FV=12  I/Y = 20% → IRR = 20% If r=10% do we accept the project based on IRR and NPV?  IRR > Op cost → Accept  NPV = -10 + 12/1.1 = $0.91m → Accept

17. 17 Internal Rate of Return (IRR) Disadvantages: 1. No distinction between investing and borrowing 2. May have multiple IRR’s, or no IRR 3. Problems with mutually exclusive investments 4. Scale Problem 5. Timing Problem Advantages: 1. Easy to understand and communicate

18. 18 Loan Example According to IRR which project do we pick?  Both What about NPV?  A creates value  B destroys value C0C0 C1C1 IRRNPV @ 10% Project A-1020100% Project B10-20100% -10+20/1.1=8.18 10+(-20/1.1)=-8.18

19. 19 No IRR Example of No IRR

20. Multiple IRR If cash flows switch signs more than once then there exists multiple IRR’s  There will be as many IRRs as there are sign changes  Which IRR do we use? $200 $800 -$200 - $800

21. 21 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?

22. 22 Mutually Exclusive Projects Choosing between projects  RANK all alternatives, and select highest IRR  IRR ignore the amount of wealth generated Which project should we take according to IRR?  INDIFFERENT Which project do investors prefer?  A, creates more wealth C0C0 C1C1 IRRNPV @ 10% Project A-10015050%36.36 Project B-7512050%34.09

23. 23 Resource constraint The firm has $100 to invest, what should it buy? IRR: NPV: ProjectC0C0 C1C1 C2C2 IRRNPV 10% A-10030050216%$210 B-5050200156%$160 C-5050150130%$120

24. 24 Resource constraint The firm has $100 to invest, what should it buy? IRR: A NPV: ProjectC0C0 C1C1 C2C2 IRRNPV 10% A-10030050216%$210 B-5050200156%$160 C-5050150130%$120

25. 25 Resource constraint The firm has $100 to invest, what should it buy? IRR: A NPV: B & C  160+120 = 280 > 210 ProjectC0C0 C1C1 C2C2 IRRNPV 10% A-10030050216%$210 B-5050200156%$160 C-5050150130%$120

26. 26 Verdict on IRR Gives the same result as NPV if:  Flat term structure  Conventional cash flows  Independent projects Otherwise IRR can lead to BAD decisions

27. 27 The Profitability Index (PI) Minimum Acceptance Criteria:  Accept if PI > 1 Ranking Criteria:  Select alternative with highest PI

28. 28 Selection Example Which projects do we take? Projects C0C0 C1C1 C2C2 NPV @ 10%PI A-10030050214 B-5050200161 C-5050150119

29. 29 Selection Example Which projects do we take? Projects C0C0 C1C1 C2C2 NPV 10% PI A-10030050214314/100=3.14 B-5050200161 C-5050150119

30. 30 Selection Example Which projects do we take? Projects C0C0 C1C1 C2C2 NPV 10% PI A-10030050214314/100=3.14 B-5050200161211/50=4.22 C-5050150119

31. 31 Selection Example Which projects do we take? Take the projects with the highest PI: B, then C Projects C0C0 C1C1 C2C2 NPV 10% PI A-10030050214314/100=3.14 B-5050200161211/50=4.22 C-5050150119169/50=3.38

32. 32 The Profitability Index Disadvantages: 1. Problems when there are additional constraints Use linear or integer programming Advantages: 1. When funds limited (Capital Rationing), provides better rankings than NPV 2. Easy to understand and communicate

33. 33 The Net Present Value (NPV) Rule Net Present Value (NPV) = Total PV of future CF’s + Initial Investment Estimating NPV: 1. Estimate future cash flows: how much? and when? 2. Estimate discount rate 3. Estimate initial costs Minimum Acceptance Criteria: Accept if NPV > 0 Ranking Criteria: Choose the highest NPV

34. 34 Why We Love NPV NPV recognizes the time value of money NPV depends only on future cash flows and the opportunity cost of capital Present value, can be added up, thus allowing us to evaluate “packages of projects” or a single project Accepting positive NPV projects, increases wealth

35. 35 Capital Budgeting in Practice Varies by industry The most frequently used technique for large corporations are: IRR or NPV  However, many companies also consider payback

36. Real World Capital Budgeting 36

37. 37 Example of Investment Rules Compute the Payback Period, NPV, and PI 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

38. 38 Example of Investment Rules Project AProject B CF 0 -$200.00-$150.00 PV 0 of CF 1-3 $241.92$240.80 Payback = NPV = PI = 1 241.92/200 1.2096 $41.92 240.80/150 1.6053 $90.80 2

39. 39 Summary – Discounted Cash Flow Net present value  Accept the project if the NPV is positive  Has no serious problems  Yields the best decision Internal rate of return  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  Take investment if PI > 1  Cannot be used to rank mutually exclusive projects  Should be used to rank projects in the presence of capital rationing

40. 40 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

41. 41 Summary – Accounting Criterion Average Accounting Return  Measure of accounting profit relative to book value  Similar to return on assets measure  Take the investment if the AAR exceeds some specified return level  Serious problems and should not be used

42. 42 Quick Quiz Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9%, and payback cutoff is 4 years.  What is the payback period?  What is the discounted payback period?  What is the NPV?  What is the IRR?  Should we accept the project? What method should be the primary decision rule? When is the IRR rule unreliable?

43. Why We Care Help you develop your finance intuition Showing you common mistakes, so that you won’t make those mistakes 43