Net Present Value and Other Investment Criteria

1. 9 Net Present Value and Other Investment Criteria

2. Key Concepts and Skills • Be able to compute payback and discounted payback and understand their shortcomings • Understand accounting rates of return and their shortcomings • Be able to compute the internal rate of return and understand its strengths and weaknesses • Be able to compute the net present value and understand why it is the best decision criterion

3. What is capital budgeting? • Process of planning and evaluating expenditures on asset whose cash flows are beyond 1 year. • Decide which are acceptable investments • Decide which actually should be purchased (or invested) • Long-term decisions; involve large expenditures. • Very important to firm’s future.

4. Good Decision Criteria • We need to ask ourselves the following questions when evaluating capital budgeting decision rules • Does the decision rule adjust for the time value of money? • Does the decision rule adjust for risk? • Does the decision rule provide information on whether we are creating value for the firm?

5. Main criteria • The Payback • The Discounted Payback • Net Present Value • The Internal Rate of Return • The Profitability Index • The Average Accounting Return

6. What is the payback period? The number of years required to recover a project’s cost, or how long does it take to get the business’s money back?

7. Payback for Franchise L(Long: Most CFs in out years) 2.4 0 1 2 3 CFt -100 10 60 100 80 Cumulative -100 -90 -30 0 50 PaybackL = 2 + 30/80 = 2.375 years

8. Franchise S (Short: CFs come quickly) 1.6 0 1 2 3 CFt -100 70 100 50 20 Cumulative -100 -30 0 20 40 PaybackS = 1 + 30/50 = 1.6 years

9. Payback Period • Computation • Estimate the cash flows • Subtract the future cash flows from the initial cost until the initial investment has been recovered • Decision Rule – Accept if the payback period is less than some preset limit • If the cut-off point is 2 years, which project should be accepted, which should be rejected?

10. Strengths and weaknesses of payback • Strengths • Provides an indication of a project’s risk and liquidity. • Easy to calculate and understand. • Weaknesses • Ignores the time value of money. • Ignores CFs occurring after the payback period. • requires an arbitrary cut-off point

11. Discounted Payback Period • Compute the present value of each cash flow and then determine how long it takes to payback on a discounted basis • Compare to a specified required period • Decision Rule - Accept the project if it pays back on a discounted basis within the specified time

12. Discounted Payback: Uses discounted rather than raw CFs. Project L 0 1 2 3 10% CFt -100 10 60 80 PVCFt -100 9.09 49.59 60.11 Cumulative -100 -90.91 -41.32 18.79 Discounted payback 2 + 41.32/60.11 = 2.7 yrs = Recover invest. + cap. costs in 2.7 yrs.

13. Discounted payback period (project S) • Uses discounted cash flows rather than raw CFs. 3 0 1 2 10% CFt -100 70 50 20 PV of CFt -100 63.64 41.32 15.03 Cumulative -100 -36.36 19.99 4.96 Disc PaybackS = 2 + / = 1.88 years = 36.36 41.32

14. Advantages Includes time value of money Easy to understand Disadvantages Requires an arbitrary cutoff point Ignores cash flows beyond the cutoff point Advantages and Disadvantages of Discounted Payback

15. Net Present Value • The difference between the market value of a project and its cost • How much value is created from undertaking an investment? • The first step is to estimate the expected future cash flows. • The second step is to estimate the required return for projects of this risk level. • The third step is to find the present value of the cash flows and subtract the initial investment.

16. NPV: Sum of the PVs of inflows and outflows. Cost often is CF0 and is negative.

17. NPV – Decision Rule • If the NPV is positive, accept the project • A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners. • Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal.

18. What’s Franchise L’s NPV? Project L: 0 1 2 3 10% -100.00 10 60 80 9.09 49.59 60.11 18.79 = NPVL

19. Calculator Solution Enter in CFLO for L: -100 10 60 80 10 CF0 CF1 CF2 CF3 I NPV = 18.78 = NPVL

20. What’s Franchise S’s NPV? Project S: 0 1 2 3 10% -100.00 70 50 20 63.64 41.32 15.03 19.98 = NPVS

21. Calculator Solution Enter in CFLO for S: -100 70 50 20 10 CF0 CF1 CF2 CF3 I NPV = 19.98 = NPVS

22. Decision Criteria Test - NPV • Does the NPV rule account for the time value of money? • Does the NPV rule account for the risk of the cash flows? • Does the NPV rule provide an indication about the increase in value? • Should we consider the NPV rule for our primary decision rule?

23. Internal Rate of Return • This is the most important alternative to NPV • It is often used in practice and is intuitively appealing • It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere • Project A: cost $1000, PV of all future cash flows = $1500. What is NPV of A? • Project B: cost $1,000,000, PV of all future cash flows = $1,500,000. What is NPV of B? • We might need a rate of return in this case.

24. Internal Rate of Return: IRR 0 1 2 3 CF0 CF1 CF2 CF3 Cost Inflows IRR is the discount rate that forces PV inflows = cost. This is the same as forcing NPV = 0.

25. NPV: Enter r, solve for NPV. IRR: Enter NPV = 0, solve for IRR.

26. What’s Franchise L’s IRR? 0 1 2 3 IRR = ? -100.00 10 60 80 PV1 PV2 PV3 0 = NPV Enter CFs in CFLO, then press IRR: IRRL = 18.13%. IRRS = 23.56%.

27. Rationale for the IRR Method If IRR > cost of capital (or required return), then the project’s rate of return is greater than its cost-- some return is left over to boost stockholders’ returns. Example: required return = 10%, IRR = 15%. Profitable. If required return = 10%, should we accept or reject L and S?

28. Decision Criteria Test - IRR • Does the IRR rule account for the time value of money? • Does the IRR rule account for the risk of the cash flows? • Does the IRR rule provide an indication about the increase in value? • Should we consider the IRR rule for our primary decision criteria?

29. Advantages of IRR • Knowing a return is intuitively appealing • It is a simple way to communicate the value of a project to someone who doesn’t know all the estimation details • If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task

30. NPV Vs. IRR • NPV and IRR will generally give us 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

31. NPV Vs. IRR • NPV and IRR will generally give us the same decision • NPV>0 and IRR> required return • NPV<0 and IRR< required return • NPV=0 and IRR= required return

32. Project Example Information • You are looking at a new project and you have estimated the following cash flows: • Year 0: CF = -165,000 • Year 1: CF = 63,120; • Year 2: CF = 70,800; • Year 3: CF = 91,080;

33. NPV profile • A graphical representation of the relationship between an investment’s NPV and various discount rates (required return) • IRR = 16.13324% • R = 0, NPV = 60,000 • R = 10, NPV = 19,324 • R = 16.3224, NPV = 0 • R = 18, NPV = -5227 • IRR > R, NPV > 0 • IRR < R, NPV < 0 • Same decision

34. NPV Profile For The Project IRR = 16.13%

35. NPV Vs. IRR • NPV and IRR will generally give us 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

36. NPV Vs. IRR • Non-conventional cash flows – cash flow signs change more than once • Normal (conventional) Time 0 1 2 3 CF -300 150 200 250 sign - + + + • Non-normal (non-conventional) Time 0 1 2 3 CF -90,000 132,000 100,000 -150,000 sign - + + - • More than 1 IRR, if the signs change 2 times, we have 2 IRRs, the signs changes 3 times, we have 3 IRRs

37. IRR and Non-conventional Cash Flows • When the cash flows change sign more than once, there is more than one IRR • When you solve for IRR you are solving for the root of an equation and when you cross the x-axis more than once, there will be more than one return that solves the equation • If you have more than one IRR, which one do you use to make your decision?

38. Example – Non-conventional Cash Flows • Suppose an investment will cost $90,000 initially and will generate the following cash flows: • Year 1: 132,000 • Year 2: 100,000 • Year 3: -150,000 • The required return is 15%. • Should we accept or reject the project?

39. Example – Non-conventional Cash Flows • Calculator: CF0 = -90,000; C01 = 132,000; F01 = 1; C02 = 100,000; F02 = 1; C03 = -150,000; F03 = 1; I = 15; CPT NPV = 1769.54 • Solve for IRR • 0 = -90,000 + 132,000/(1+IRR)1 +100,000/(1+IRR)2 -150,000/(1+IRR)3 • (IRR-0.101102)(IRR-0.426585) = 0 • IRR = 10.1102% and IRR = 42.6585% • If you compute the IRR on the calculator, you get 10.1102% because it is the first one that you come to.

40. Summary of Decision Rules • The NPV is positive at a required return of 15%, so you should Accept • If you use the financial calculator, you would get an IRR of 10.11% which would tell you to Reject • You need to recognize that there are non-conventional cash flows and look at the NPV profile • When you have conflict between NPV and IRR, go with the NPV

41. NPV Profile IRR = 10.11% and 42.66%

42. IRR and Mutually Exclusive Projects • Independent and Mutually exclusive projects • Independent: the decision to accept/reject one project does not affect the decision to accept/reject another. • Mutually exclusive: If you choose one, you can’t choose the other • NPV(L) = 18.79, NPV(S) = 19.98 • If L and S are independent, which project should we accept? • IF L and S are mutually exclusive, which project should we accept? • Intuitively you would use the following decision rules (if mutually exclusive) • NPV – choose the project with the higher NPV • IRR – choose the project with the higher IRR

43. Example With Mutually Exclusive Projects The required return for both projects is 10%. Which project should you accept and why?

44. Period A B A-B 0 -500 -400 -100 1 325 325 0 2 325 200 125 • Cross-over rate is the rate where NPV(A) = NPV(B). It is the IRR of the difference in the cash flows of the 2 projects • IRR (A-B) = cross over rate = 11.8034%

45. NPV Profiles IRR for A = 19.43% IRR for B = 22.17% Crossover Point = 11.8%

46. Example With Mutually Exclusive Projects The required return for both projects is 10%. Which project should you accept and why?

47. Conflicts Between NPV and IRR • NPV directly measures the increase in value to the firm • Whenever there is a conflict between NPV and another decision rule, you should always use NPV • IRR is unreliable in the following situations • Non-conventional cash flows • Mutually exclusive projects

48. Profitability Index • PI = PV of future cash flows/ Intial cost • Measures the benefit per unit cost, based on the time value of money • A profitability index of 1.1 implies that for every $1 of investment, we create an additional $0.10 in value • Can have conflict with NPV in some mutually exclusive projects • This measure can be very useful in situations in which we have limited capital

49. Advantages Closely related to NPV, generally leading to identical decisions Easy to understand and communicate May be useful when available investment funds are limited Disadvantages May lead to incorrect decisions in comparisons of mutually exclusive investments Advantages and Disadvantages of Profitability Index

50. Summary – Discounted Cash Flow Criteria • Net present value • Difference between market value and cost • Take 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