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Capital Budeting with the Net Present Value Rule

Understand the Time Value of Money, NPV, IRR, & Perpetuities in investment decisions. Learn to evaluate projects for value creation. Practical examples and calculations.

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Capital Budeting with the Net Present Value Rule

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  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

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