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# Chapter 12

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1. Chapter 12 Capital Budgeting: Decision Criteria

2. Topics • Overview • Methods • NPV • IRR, MIRR • Profitability Index • Payback, discounted payback • Unequal lives • Economic life

3. Capital Budgeting: • Analysis of potential projects • Long-term decisions • Large expenditures • Difficult/impossible to reverse • Determines firm’s strategic direction

4. Steps in Capital Budgeting • Estimate cash flows (Ch 13) • Assess risk of cash flows (Ch 13) • Determine r = WACC for project (Ch10) • Evaluate cash flows – Chapter 12

5. Independent versus Mutually Exclusive Projects • Independent: • The cash flows of one are unaffected by the acceptance of the other • Mutually Exclusive: • The acceptance of one project precludes accepting the other

6. Cash Flows for Projects L and S

7. n CFt . ∑ NPV = (1 + r)t t = 0 n CFt ∑ - CF0 NPV = (1 + r)t t = 1 NPV: Sum of the PVs of all cash flows. NOTE: t=0 Cost often is CF0 and is negative

8. Project S’s NPV

9. Project L’s NPV

10. TI BAII+: Project L NPV DisplayYou Enter ' C001000S!# C01100 !# F011 !# C02300 !# F021 !# C03400 !# F031 !# C04600 !# F041 !# ( I 10 !# NPV% 49.18 Cash Flows: CF0 = -1000 CF1 = 100 CF2 = 300 CF3 = 400 CF4 = 600

11. Rationale for the NPV Method • NPV = PV inflows – Cost • NPV=0 → Project’s inflows are “exactly sufficient to repay the invested capital and provide the required rate of return.” • NPV = net gain in shareholder wealth • Choose between mutually exclusive projects on basis of higher NPV • Rule: Accept project if NPV > 0

12. NPV Method • Meets all desirable criteria • Considers all CFs • Considers TVM • Can rank mutually exclusive projects • Value-additive • Directly related to increase in VF • Dominant method; always prevails

13. Using NPV method, which franchise(s) should be accepted? Project S NPV = \$78.82 Project L NPV = \$49.18 • If Franchise S and L are mutually exclusive, accept S because NPVs > NPVL • If S & L are independent, accept both; NPV > 0

14. Internal Rate of Return: IRR • IRR = the discount rate that forces • PV inflows = cost •  Forcing NPV = 0 • ≈ YTM on a bond • Preferred by executives 3:1

15. n CFt ∑ = NPV (1 + r)t t = 0 n CFt ∑ = 0 (1 + IRR)t t = 0 NPV vs IRR NPV: Enter r, solve for NPV IRR: Enter NPV = 0, solve for IRR

16. Franchise L’s IRR

17. TI BAII+: Project L IRR DisplayYou Enter ' C001000S!# C01100 !# F011 !# C02300 !# F021 !# C03400 !# F031 !# C04600 !# F041 !# ( I 10 !# IRR % 11.79 Cash Flows: CF0 = -1000 CF1 = 100 CF2 = 300 CF3 = 400 CF4 = 600

18. Decisions on Projects S and L per IRR • Project S IRR = 14.5% • Project L IRR = 11.8% • Cost of capital = 10.0% • If S and L are independent, accept both: IRRS > r and IRRL > r • If S and L are mutually exclusive, accept S because IRRS > IRRL

19. Construct NPV Profiles • Enter CFs in CFLO and find NPVL and NPVS at different discount rates:

20. NPV Profile

21. To Find the Crossover Rate • Find cash flow differences between the projects. • Enter these differences in CFLO register, then press IRR. • Crossover rate = 7.17%, rounded to 7.2%. • Can subtract S from L or vice versa • If profiles don’t cross, one project dominates the other

22. Finding the Crossover Rate

23. NPV (\$) IRR > r and NPV > 0 Accept r > IRR and NPV < 0. Reject r (%) IRR NPV and IRR: No conflict for independent projects

24. Mutually Exclusive Projects r > 7.2% NPVS> NPVL IRRS > IRRL NO CONFLICT r < 7.2% NPVL> NPVS IRRS > IRRL CONFLICT NPV L IRRS S % 7.2 IRRL

25. Mutually Exclusive Projects CONFLICT r < 7.2% NPVL> NPVS IRRS > IRRL r > 7.2% NPVS > NPVL IRRS > IRRL NO CONFLICT

26. Two Reasons NPV Profiles Cross • Size (scale) differences • Smaller project frees up funds sooner for investment • The higher the opportunity cost, the more valuable these funds, so high r favors small projects • Timing differences • Project with faster payback provides more CF in early years for reinvestment • If r is high, early CF especially good, NPVS > NPVL

27. Issues with IRR • Reinvestment rate assumption • Non-normal cash flows

28. Reinvestment Rate Assumption • NPV assumes reinvest at r (opportunity cost of capital) • IRR assumes reinvest at IRR • Reinvest at opportunity cost, r, is more realistic, so NPV method is best • NPV should be used to choose between mutually exclusive projects

29. Modified Internal Rate of Return (MIRR) • MIRR = discount rate which causes the PV of a project’s terminal value (TV) to equal the PV of costs • TV = inflows compounded at WACC • MIRR assumes cash inflows reinvested at WACC

30. MIRR for Project S: First, find PV and TV (r = 10%)

31. Second: Find discount rate that equates PV and TV • PV = PV(Outflows) = -1000 • FV = TV(Inflows) = 1579.5 • N = 4 • PMT = 0 • CPY I/Y = 12.1063 = 12.1% • EXCEL: =MIRR(Value Range, FR, RR)

32. MIRR versus IRR • MIRR correctly assumes reinvestment at opportunity cost = WACC • MIRR avoids the multiple IRR problem • Managers like rate of return comparisons, and MIRR is better for this than IRR

33. Normal vs. Nonnormal Cash Flows • Normal Cash Flow Project: • Cost (negative CF) followed by a series of positive cash inflows • One change of signs • Nonnormal Cash Flow Project: • Two or more changes of signs • Most common: Cost (negative CF), then string of positive CFs, then cost to close project • For example, nuclear power plant or strip mine

34. 0 1 2 r = 10% -800 5,000 -5,000 Enter CFs, enter I = 10 NPV = -386.78 IRR = ERROR Pavilion Project: NPV and IRR?

35. NPV Profile NPV IRR2 = 400% 450 0 r 100 400 IRR1 = 25% -800 Nonnormal CFs:Two sign changes, two IRRs

36. Multiple IRRs • Descartes Rule of Signs • Polynomial of degree n→n roots • 1 real root per sign change • Rest = imaginary (i2 = -1)

37. Logic of Multiple IRRs • At very high discount rates: • The PV of both CF1 and CF2 are low • CF0 dominates • Again NPV < 0 • At very low discount rates: • The PV of CF2 is large & negative • NPV < 0

38. Logic of Multiple IRRs • In between: • The discount rate hits CF2 harder than CF1 • NPV > 0 • Result: 2 IRRs

39. The Pavillion Project:Non-normal CFs and MIRR: 1 2 0 -800,000 5,000,000 -5,000,000 RR FR PV outflows @ 10% = -4,932,231.40 TV inflows @ 10% = 5,500,000.00 MIRR = 5.6%

40. Profitability Index • PI =present value of future cash flows divided by the initial cost • Measures the “bang for the buck”

41. Project S’s PV of Cash Inflows

42. Profitability Indexs PV future CF \$1078.82 PIS = = Initial Cost \$1000 PIS = 1.0788 PIL = 1.0492

43. Profitability Index • Rule: If PI>1.0  Accept • Useful in capital rationing • Closely related to NPV • Can conflict with NPV if projects are mutually exclusive

44. Profitability Index • Strengths: • Considers all CFs • Considers TVM • Useful in capital rationing • Weaknesses: • Cannot rank mutually exclusive • Not Value-additive

45. Payback Period • The number of years required to recover a project’s cost • How long does it take to get the business’s money back? • A breakeven-type measure • Rule: Accept if PB<Target

46. Payback for Projects S and L

47. Payback for Projects S and L

48. Strengths and Weaknesses of Payback • Strengths: • Provides indication of project risk and liquidity • Easy to calculate and understand • Weaknesses: • Ignores the TVM • Ignores CFs occurring after the payback period • Biased against long-term projects • ASKS THE WRONG QUESTION!

49. Discounted Payback: Use discounted CFs