1 / 35

Capital Budeting with the Net Present Value Rule

Capital Budeting with the Net Present Value Rule. Professor André Farber Solvay Business School Université Libre de Bruxelles. Time value of money: introduction. Consider simple investment project: Interest rate r = 10%. 121. 1. 0. -100. NFV = +121 - 100  1.10 = 11

stephenflores
Télécharger la présentation

Capital Budeting with the Net Present Value Rule

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles Vietnam 2004

  2. Time value of money: introduction • Consider simple investment project: • Interest rate r = 10% 121 1 0 -100 Vietnam 2004

  3. NFV = +121 - 100  1.10 = 11 = + C1 - I (1+r) Decision rule: invest if NFV>0 Justification: takes into cost of capital cost of financing opportunity cost Net future value +121 +100 0 1 -100 -110 Vietnam 2004

  4. Net Present Value • NPV = - 100 + 121/1.10 • = + 10 • = - I + C1/(1+r) • = - I + C1 DF1 • DF1 = 1-year discount factor • a market price • C1 DF1 =PV(C1) • Decision rule: invest if NPV>0 • NPV>0  NFV>0 +121 +110 -100 -121 Vietnam 2004

  5. Internal Rate of Return • Alternative rule: compare the internal rate of return for the project to the opportunity cost of capital • Definition of the Internal Rate of Return IRR : (1-period) IRR = (C1 - I)/I • In our example: IRR = (121 - 100)/100 = 21% • The Rate of Return Rule: Invest if IRR > r Vietnam 2004

  6. IRR versus NPV • In this simple setting, the NPV rule and the Rate of Return Rule lead to the same decision: • NPV = -I+C1/(1+r) >0 •  C1>I(1+r) •  (C1-I)/I>r •  IRR>r Vietnam 2004

  7. The Internal Rate of Return is the discount rate such that the NPV is equal to zero. -I + C1/(1+IRR)  0 In our example: -100 + 121/(1+IRR)=0  IRR=21% IRR: a general definition Vietnam 2004

  8. Extension to several periods • Investment project: -100 in year 0, + 150 in year 5. • Net future value calculation: NFV5 = +150 - 100  (1.10)5 = +150 - 161 = -11 <0 Compound interest • Net present value calculation: NPV = - 100 + 150/(1.10)5 = - 100 + 150  0.621 = - 6.86 0.621 is the 5-year discount factor DF5 = 1/(1+r)5 a market price Vietnam 2004

  9. NPV: general formula • Cash flows: C0 C1C2 … Ct … CT • t-year discount factor: DFt = 1/(1+r)t • NPV = C0 + C1 DF1 + … + Ct DFt + … + CT DFT Vietnam 2004

  10. NPV calculation - example • Suppose r = 10% Vietnam 2004

  11. IRR in multiperiod case • Reinvestment assumption: the IRR calculation assumes that all future cash flows are reinvested at the IRR • Disadvantages: • Does not distinguish between investing and financing • IRR may not exist or there may be multiple IRR • Problems with mutually exclusive investments • Advantages: • Easy to understand and communicate Vietnam 2004

  12. Constant perpetuity Proof: PV = C d + C d² + C d3 + … PV(1+r) = C + C d + C d² + … PV(1+r)– PV = C PV = C/r • Ct =C for t =1, 2, 3, ..... • Examples: Preferred stock (Stock paying a fixed dividend) • Suppose r =10% Yearly dividend = 50 • Market value P0? • Note: expected price next year = • Expected return = Vietnam 2004

  13. Growing perpetuity • Ct=C1 (1+g)t-1 for t=1, 2, 3, .....r>g • Example: Stock valuation based on: • Next dividend div1, long term growth of dividend g • If r = 10%, div1 = 50, g = 5% • Note: expected price next year = • Expected return = Vietnam 2004

  14. Constant annuity • A level stream of cash flows for a fixed numbers of periods • C1 = C2 = … = CT = C • Examples: • Equal-payment house mortgage • Installment credit agreements • PV = C * DF1 + C * DF2 + … + C * DFT+ • = C * [DF1 + DF2 + … + DFT] • = C * Annuity Factor • Annuity Factor = present value of €1 paid at the end of each T periods. Vietnam 2004

  15. Growing annuity • Ct = C1 (1+g)t-1 for t = 1, 2, …, T r ≠ g • This is again the difference between two growing annuities: • Starting at t = 1, first cash flow = C1 • Starting at t = T+1 with first cash flow = C1 (1+g)T • Example: What is the NPV of the following project if r = 10%? Initial investment = 100, C1 = 20, g = 8%, T = 10 NPV= – 100 + [20/(10% - 8%)]*[1 – (1.08/1.10)10] = – 100 + 167.64 = + 67.64 Vietnam 2004

  16. Review: general formula • Cash flows: C1, C2, C3, … ,Ct, … CT • Discount factors: DF1, DF2, … ,DFt, … , DFT • Present value: PV = C1×DF1 + C2×DF2 + … + CT×DFT If r1 = r2 = ...=r Vietnam 2004

  17. Review: Shortcut formulas • Constant perpetuity: Ct = C for all t • Growing perpetuity: Ct = Ct-1(1+g) r>g t = 1 to ∞ • Constant annuity: Ct=Ct=1 to T • Growing annuity: Ct = Ct-1(1+g) t = 1 to T Vietnam 2004

  18. IRR and NPV - Example Compute the IRR and NPV 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 NPV 42 91 IRR 0%, 100% 36% Vietnam 2004

  19. NPV Profiles Vietnam 2004

  20. The Payback Period Rule • How long does it take the project to “pay back” its initial investment? • Payback Period = # of years to recover initial costs • Minimum Acceptance Criteria: set by management • Ranking Criteria: set by management Vietnam 2004

  21. The Payback Period Rule (continued) • Disadvantages: • Ignores the time value of money • Ignores CF after payback period • Biased against long-term projects • Payback period may not exist or multiple payback periods • Requires an arbitrary acceptance criteria • A project accepted based on the payback criteria may not have a positive NPV • Advantages: • Easy to understand • Biased toward liquidity Vietnam 2004

  22. The Profitability Index (PI) Rule • PI = Total Present Value of future CF’s / Initial Investment • Minimum Acceptance Criteria: Accept if PI > 1 • Ranking Criteria: Select alternative with highest PI • 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 Vietnam 2004

  23. Incremental Cash Flows • Cash, Cash, Cash, CASH • Incremental • Sunk Costs • Opportunity Costs • Side Effects • Tax and Inflation • Estimating Cash Flows • Cash flows from operation • Net capital spending • Changes in net working capital • Interest Expense Vietnam 2004

  24. Summarized balance sheet • Assets • Fixed assets (FA) • Working capital requirement (WCR) • Cash (Cash) • Liabilities • Stockholders' equity (SE) • Interest-bearing debt (D) • FA + WCR + Cash = SE + D Vietnam 2004

  25. Working capital requirement : definition • + Accounts receivable • + Inventories • + Prepaid expenses • - Account payable • - Accrued payroll and other expenses • (WCR sometimes named "operating working capital") • Copeland, Koller and Murrin Valuation: Measuring and Managing the Value of Companies, 2d ed. John Wiley 1994 Vietnam 2004

  26. Interest-bearing debt: definition • + Long-term debt • + Current maturities of long term debt • + Notes payable to banks Vietnam 2004

  27. The Cash Flow Statement • Let us start from the balance sheet identity: • FA + WCR + CASH = SE + D • Over a period: • FA + WCR + CASH = SE + D • But: DSE = STOCK ISSUE + RETAINED EARNINGS = SI + NET INCOME - DIVIDENDS DFA = INVESTMENT - DEPRECIATION • (INV - DEP) + WCR + CASH = (SI + NI - DIV) + D Vietnam 2004

  28. (NI +DEP - WCR) - (INV) + (SI + D - DIV) = CASH •  • Net cash flows from • operating activities (CFop) •  • Cash flow from • investing activities (CFinv) •  • Cash flow from • financing activities (CFfin) Vietnam 2004

  29. Free cash flow • FCF = (NI +DEP - WCR) - (INV) • = CFop + CFinv • From the statement of cash flows • FCF = - (SI + D - DIV) + CASH Vietnam 2004

  30. Understanding FCF CF from operation + CF from investment + CF from financing = CASH Cash flow from operation Cash flow from financing Cash flow from investment Cash Vietnam 2004

  31. NPV calculation: example • Length of investment : 2 years • Investment : 60 (t = 0) • Resale value : 20 (t = 3, constant price) • Depreciation : linear over 2 years • Revenue : 100/year (constant price) • Cost of sales : 50/year (constant price) • WCR/Sales : 25% • Real discount rate : 10% • Corporate tax rate : 40% Vietnam 2004

  32. Scenario 1: no inflation Vietnam 2004

  33. Inflation • Use nominal cash flow • Use nominal discount rate • Nominal versus Real Rate (The Fisher Relation) (1 + Nominal Rate) = (1 + Real Rate) x (1 + Inflation Rate) • Example: • Real cash flow year 1 = 110 • Real discount rate = 10% • Inflation = 20% • Nominal cash flow = 110 x 1.20 • Nominal discount rate = 1.10 x 1.20 - 1 • NPV = (110 x 1.20)/(1.10 x 1.20) = 110/1.10 = 100 Vietnam 2004

  34. Scenario 2 : Inflation = 100% Nominal discount rate: (1+10%) x (1+100%) = 2.20 Nominal rate = 120% NPV now negative. Why? Vietnam 2004

  35. Decomposition of NPV • EBITDA after taxes 52.07 52.07 • Depreciation tax shield 20.83 7.93 • WCR -3.94 -23.67 • Investment -60 -60 • Resale value after taxes 9.02 9.02 • NPV 17.96 14.65 Vietnam 2004

More Related