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Capital budeting decisions with the Net Present Value rule 1. Foundations

Capital budeting decisions with the Net Present Value rule 1. Foundations. Professor André Farber Solvay Business School University of Brussels, Belgium. Time value of money: introduction. Consider simple investment project: Interest rate r = 10%. 121. 1. 0. -100.

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Capital budeting decisions with the Net Present Value rule 1. Foundations

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  1. Capital budeting decisions with the Net Present Value rule1. Foundations Professor André Farber Solvay Business School University of Brussels, Belgium Hanoi April 2000

  2. Time value of money: introduction • Consider simple investment project: • Interest rate r = 10% 121 1 0 -100 Hanoi April 2000

  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 Hanoi April 2000

  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 Hanoi April 2000

  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 Hanoi April 2000

  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 Hanoi April 2000

  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 Hanoi April 2000

  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 Hanoi April 2000

  9. NPV: general formula • Cash flows: C0 C1 C2 … Ct … CT • t-year discount factor: DFt = 1/(1+r)t • NPV = C0 + C1 DF1 + … + Ct DFt + … + CT DFT Hanoi April 2000

  10. NPV calculation - example • Suppose r = 10% Hanoi April 2000

  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 Hanoi April 2000

  12. 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% Hanoi April 2000

  13. NPV Profiles Hanoi April 2000

  14. 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 Hanoi April 2000

  15. 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 Hanoi April 2000

  16. 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 Hanoi April 2000

  17. 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 Hanoi April 2000

  18. 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 Hanoi April 2000

  19. 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 Hanoi April 2000

  20. Interest-bearing debt: definition • + Long-term debt • + Current maturities of long term debt • + Notes payable to banks Hanoi April 2000

  21. 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 Hanoi April 2000

  22. (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) Hanoi April 2000

  23. Free cash flow • FCF = (NI +DEP - WCR) - (INV) • = CFop + CFinv • From the statement of cash flows • FCF = - (SI + D - DIV) + CASH Hanoi April 2000

  24. 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 Hanoi April 2000

  25. 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% Hanoi April 2000

  26. Scenario 1: no inflation Hanoi April 2000

  27. 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 Hanoi April 2000

  28. Scenario 2 : Inflation = 100% Nominal discount rate: (1+10%) x (1+100%) = 2.20 Nominal rate = 120% NPV now negative. Why? Hanoi April 2000

  29. Decomposition of NPV • EBITD 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 Hanoi April 2000

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