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Capital Budgeting Techniques

Capital Budgeting Techniques. How do firms make decisions about whether to invest in costly, long-lived assets? How does a firm make a choice between two acceptable investments when only one can be purchased? How are different capital budgeting techniques related?

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Capital Budgeting Techniques

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  1. Capital Budgeting Techniques • How do firms make decisions about whether to invest in costly, long-lived assets? • How does a firm make a choice between two acceptable investments when only one can be purchased? • How are different capital budgeting techniques related? • Which capital budgeting methods do firms actually use?

  2. Capital Budgeting • Introduction to Capital Budgeting • Payback Period—traditional and discounted • Net Present Value (NPV) • Internal Rate of Return (IRR) • Modified IRR • Comparison of NPV and IRR • NPV/IRR Ranking Conflicts/Cautions

  3. Compute Given Capital Budgeting • Capital Budgeting Basics and Techniques • r—firm’s required rate of return • CF—cash flows generated by an investment • Capital Budgeting—cash flows and risk • r—firm’s required rate of return • CF—cash flows generated by an investment

  4. Capital Budgeting Basics • Importance of capital budgeting decisions • long-term effect—capital, or long-term funds, raised by the firms are used to invest in assets that enable the firm to generate revenues several years into the future. • timing of a decision is important—decisions impact the firm for several years. • Generating ideas for capital budgeting • employees, customers, suppliers, and so forth • based on needs and experiences of the firm and these groups

  5. Capital Budgeting Basics • Project classifications—replacement decisions versus expansion decisions • replacement decision—intended to maintain existing levels of operations • expansion decision—a decision concerning whether the firm should expand operations • Project classifications—independent projects versus mutually exclusive projects • independent project—accepting one independent project does not affect the acceptance of any other project • mutually exclusive projects—only one project can be purchased

  6. Capital Budgeting Basics—Capital Budgeting Versus Asset Valuation • Value of an asset = PV of the cash flows the asset is expected to generate during its life: • An asset is an acceptable investment if the cost of the asset is less than its value: • Acceptable if: PV of CFs > Cost

  7. Capital Budgeting Techniques • Payback period • Net present value • Internal rate of return

  8. Year Cash Flow, Capital Budgeting TechniquesIllustrative Investment 0(7,000) 12,000 21,000 35,000 43,000 r = 15%

  9. 0 1 2 3 4 S PV = 7,498.11 498.11 = Capital Budgeting Example Cash Flow Time Line 15% (7,000.00) 2,000 1,000 5,000 3,000 1,739.13 756.14 3,287.58 1,715.26

  10. Capital Budgeting TechniquesPayback Period Number of years it takes to recapture the initial investment. YearCash FlowCumulative CF 0$(7,000)$(7,000) 12,000 (5,000) 21,000 (4,000) 35,000 1,000 43,000 4,000 }2<Payback<3

  11. YearCash FlowCumulative CF 0 $(7,000) $(7,000) 1 2,000 (5,000) 2 1,000 (4,000) 3 5,000 1,000 4 3,000 4,000 }2<Payback<3 $4,000 = + 2 $5,000 = 2.80 years Capital Budgeting TechniquesPayback Period $ investment remaining # of years before to be recaptured Payback = + full recovery of period $ cash flow in original investment year of payback

  12. Capital Budgeting TechniquesPayback Period Accept the project if Payback, PB < some number of years established by the firm PB = 2.8 years is acceptable if the firm has established a maximum payback of 4.0 years

  13. Capital Budgeting TechniquesPayback Period Advantages: • Simple • Cash flows are used • Provides an indication of the liquidity of a project Disadvantages: • Does not use time value of money concepts • Cash flows beyond the payback period are ignored

  14. Capital Budgeting TechniquesPayback Period YearCash FlowCumulative CF 0$(7,000)$(7,000) 12,000 (5,000) 21,000 (4,000) 35,000 1,000 43,000 4,000 YearCash FlowCumulative CF 0$(7,000)$(7,000) 12,000 (5,000) 21,000 (4,000) 35,000 1,000 43,000 4,000 51,000,0001,004,000 }PB = 2.80 yrs

  15. Ù Ù Ù CF CF CF 1 2 n = + + + + NPV CF L 0 1 2 n + + + (1 r) (1 r) (1 r) Ù n CF å t = t + (1 r) t = 0 Capital BudgetingNet Present Value (NPV) NPV = present value of future cash flows less the initial investment An investment is acceptable if NPV > 0

  16. $2,000 $1,000 $5,000 $3,000 = - + + + + NPV $7,000 1 2 3 4 (1.15) (1.15) (1.15) (1.15) $756.14 + $1,715.26 = - + + + $7,000 $1,739.13 $3,287.58 = $498.11 Capital Budgeting—NPV NPV = $498.11 > 0, so the project is acceptable

  17. 0 1 2 3 4 15% (7,000.00) 2,000 1,000 5,000 3,000 1,739.13 756.14 3,287.58 1,715.26 498.11 = NPV Capital Budgeting Example Cash Flow Time Line

  18. Capital Budgeting—NPV Advantages: • Cash flows rather than profits are analyzed • Recognizes the time value of money • Acceptance criterion is consistent with the goal of maximizing value Disadvantage: • Detailed, accurate long-term forecasts are required to evaluate a project’s acceptance

  19. Solving for NPV • Numerical (equation) solution • Financial Calculator solution • Spreadsheet solution

  20. $2,000 $1,000 $5,000 $3,00 = - + + + + NPV $7,000 1 2 3 4 (1.15) (1.15) (1.15) (1.15) $756.14 + $1,715.26 = - + + + $7,000 $1,739.13 $3,287.58 = $498.11 Solving for NPVNumerical Solution

  21. Solving for NPVFinancial Calculator Solution • Input the following into the cash flow register: CF0=-7,000 CF1=2,000 CF2=1,000 CF3=5,000 CF4=3,000 • Input I = 15 • Compute NPV = 498.12

  22. Capital BudgetingDiscounted Payback Period Payback period computed using the present values of the future cash flows. Cumulative YearCash FlowPV of CF @15% PV of CF 0$(7,000)$(7,000.00)$(7,000.00) 12,000 1,739.13(5,260.87) 21,000 756.14(4,504.73) 35,000 3,287.58(1,217.14) 43,000 1,715.26 498.12 }PBdisc= 3.71 A project is acceptable if PBdisc < project’s life

  23. Capital BudgetingInternal Rate of Return (IRR) • If NPV>0, project’s return > r • Example: Initial investment = $7,000.00 PV of future cash flows = $7,498.12 IRR > 15% NPV = $498.12 r = 15% • If IRR = project’s rate of return • IRR = the rate of return that causes the NPV of the project to equal zero, or where the present value of the future cash flows equals the initial investment.

  24. Ù Ù Ù CF CF CF 1 2 n = + + + + = NPV CF 0 L 0 1 2 n + + + (1 IRR) (1 IRR) (1 IRR) Ù Ù Ù CF CF CF 1 2 n = + + + CF L 0 1 2 n + + + (1 IRR) (1 IRR) (1 IRR) Capital BudgetingInternal Rate of Return (IRR) A project is acceptable if its IRR > r

  25. 2,000 1,000 5,000 3,000 = - + + + + = NPV 7,000 0 1 2 3 4 + + + + (1 IRR) (1 IRR) (1 IRR) (1 IRR) $2,000 $1,000 $5,000 $3,000 = + + + $7,000 1 2 3 4 + + + + (1 IRR) (1 IRR) (1 IRR) (1 IRR) Capital BudgetingInternal Rate of Return (IRR)

  26. 0 1 2 3 4 (7,000) 2,000 1,000 5,000 3,000 S of PVs = 7,000 0 = NPV Internal Rate of Return (IRR)Cash Flow Time Line IRR = ?

  27. Capital Budgeting—IRR Advantages: • Cash flows rather than profits are analyzed • Recognizes the time value of money • Acceptance criterion is consistent with the goal of maximizing value Disadvantages: • Detailed, accurate long-term forecasts are required to evaluate a project’s acceptance • Difficult to solve for IRR without a financial calculator or spreadsheet

  28. $2,000 $1,000 $5,000 $3,000 = + + + $7,000 1 2 3 4 + + + + (1 IRR) (1 IRR) (1 IRR) (1 IRR) Solving for IRRNumerical Solution Using the trial-and-error method plug in values for IRR until the left and right side of the following equation become equal.

  29. Solving for IRRNumerical Solution Rate of Return NPV 15%498.12 16327.46 17162.72 183.62 19(150.08) }18<IRR<19

  30. Solving for IRRFinancial Calculator Solution • Input the following into the cash flow register: CF0=-7,000 CF1=2,000 CF2=1,000 CF3=5,000 CF4=3,000 • Compute IRR = 18.02%

  31. NPV versus IRR • When NPV > 0, a project is acceptable because the firm will increase its value, which means the firm earns a return greater than its required rate of return (r) if it invests in the project. • When IRR > r, a project is acceptable because the firm will earn a return greater than its required rate of return (r) if it invests in the project. • When NPV > 0, IRR > r for a project—that is, if a project is acceptable using NPV, it is also acceptable using IRR.

  32. Accept/Reject Decisions Using NPV, Discounted Payback, and IRR Technique Evaluation Result Acceptable? NPVNPV> 0 IRRIRR>r Discounted PBPBdisc< project’s life YES YES YES

  33. NPV Profile A graph that shows the NPVs of a project at various required rates of return. Rate of Return NPV 15%498.12 16327.46 17162.72 183.62 19(150.08) 20(298.61) 21(442.20)

  34. NPV $5,000 $4,000 $3,000 $2,000 NPV > 0 $1,000 r $0 NPV < 0 5% 10% 15% 20% 25% ($1,000) ($2,000) NPV Profile IRR =18.02%

  35. Cash Flow, Year Project A Capital Budgeting TechniquesIllustrative Projects A & B 0(7,000.00) 12,000.00 21,000.00 35,000.00 43,000.00 Project B 0 12,000.00 21,000.00 35,000.00 43,000.00 Trad PB =2.80 NPV =498.12 IRR =18.02% (8,000.00) 6,000.00 3,000.00 1,000.00 500.00 1.67 429.22 19.03% r = 15%

  36. NPV 5000 Project A 4000 3000 Crossover = 16.15 2000 Project B IRRB = 19.03 1000 r 0 20% 25% 5% 10% 15% -1000 IRRA = 18.02 -2000 NPV Profiles for Projects A & B

  37. Rate of Return NPVA 15% 498.12 16 327.46 17 162.72 18 3.62 19 (150.08) 20 (298.61) 21 (442.20) Rate of Return NPVA 15% 498.12 16 327.46 17 162.72 18 3.62 19 (150.08) 20 (298.61) 21 (442.20) NPVB 429.22 318.71 210.94 105.82 3.26 (96.84) (194.55) NPVB 429.22 318.71 210.94 105.82 3.26 (96.84) (194.55) Rate of Return 15% 16 17 18 19 20 21 NPV Profile—Projects A & B

  38. Cash Flow, Year Project A Project B CFA - CFB Capital Budgeting TechniquesIllustrative Projects A & B 0(7,000)(8,000) 12,0006,000 21,0003,000 35,0001,000 43,000500 1,000 (4,000) (2,000) 4,000 2,500 IRR of (CFA – CFB) Cash Flow Stream = 16.15% At r = 16.15%, NPVA = NPVB = 302.37

  39. NPV/IRR Ranking Conflicts Asset AAsset B Traditional PB 2.80 yrs 1.67 yrs Discounted PB 3.71 yrs 2.78 yrs NPV $498.12 $429.22 IRR 18.02% 19.03% Asset A Traditional PB 2.80 yrs Discounted PB 3.71 yrs NPV $498.12 IRR 18.02% Asset AAsset B Traditional PB 2.80 yrs 1.67 yrs Discounted PB 3.71 yrs 2.78 yrs NPV$498.12 $429.22 IRR 18.02% 19.03% Which asset(s) should be purchased? Asset A, because it has the higher NPV.

  40. NPV/IRR Ranking Conflicts • Ranking conflicts result from: • Cash flow timing differences • Size differences • Unequal lives • Reinvestment rate assumptions • NPV—reinvest at the firm’s required rate of return • IRR—reinvest at the project’s internal rate of return, IRR

  41. Multiple IRRs • Conventional cash flow pattern—cash outflow(s) occurs at the beginning of the project’s life, followed by a series of cash inflows. • Unconventional cash flow pattern—cash outflow(s) occurs during the life of the project, after cash inflows have been generated. • An IRR solution occurs when a cash flow pattern is interrupted; if a cash flow pattern is interrupted more than once, then more than one IRR solution exists.

  42. Multiple IRRs—Example YearCash Flow 0(15,000) 140,150 2(13,210) 3(16,495) IRR1 = 22.5% IRR2 = 92.0%

  43. Modified Internal Rate of Return (MIRR) • Generally solves the ranking conflict and the multiple IRR problem

  44. MIRR—Example YearProject AProject B 0(7,000)(8,000) 12,0006,000 21,0003,000 35,0001,000 43,000500 Discounted PB3.71 yrs2.78 yrs NPV$498.12$429.22 IRR18.02%19.03% 44

  45. MIRR—Example YearProject AProject B 0(7,000)(8,000) 12,0006,000 21,0003,000 35,0001,000 43,000500 Project A—calculator solution: N = 4, PV = -7,000, PMT = 0, FV = 13,114.25; I/Y = 16.99 = MIRRA Project A—calculator solution: N = 4, PV = -7,000, PMT = 0, FV = 13,114.25; I/Y = 16.99 = MIRRA Project B—calculator solution: N = 4, PV = -8,000, PMT = 0, FV = 14,742.75; I/Y = 16.51 = MIRRB 45

  46. Capital Budgeting—The Answers • How do firms make decisions about whether to invest in costly, long-lived assets? • Firms use decision-making methods that are based on fundamental valuation concepts • How does a firm make a choice between two acceptable investments when only one can be purchased? • The decision should be consistent with the goal of maximizing the value of the firm

  47. Capital Budgeting—The Answers • How are different capital budgeting techniques related? • All techniques except traditional payback period (PB) are based on time value of money • Which capital budgeting methods do firms actually use? • Most firms rely heavily on NPV and IRR to make investment decisions

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