1. Vietnam 20041 Capital Budeting with the Net Present Value Rule Professor André Farber Solvay Business School Université Libre de Bruxelles

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

3. Vietnam 2004 |3|3 Net future value NFV = +121 - 100  1.10 = 11 = + C 1 - I (1+r) Decision rule: invest if NFV>0 Justification: takes into cost of capital – cost of financing –opportunity cost -100 +100 +121 -110 01

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

5. Vietnam 2004 |5|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 = (C 1 - I)/I In our example: IRR = (121 - 100)/100 = 21% The Rate of Return Rule: Invest if IRR > r

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

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

8. Vietnam 2004 |8|8 Extension to several periods Investment project: -100 in year 0, + 150 in year 5. Net future value calculation: NFV 5 = +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 DF 5 = 1/(1+r) 5 a market price

9. Vietnam 2004 |9|9 NPV: general formula Cash flows: C 0 C 1 C 2 … C t … C T t-year discount factor: DF t = 1/(1+r) t NPV = C 0 + C 1 DF 1 + … + C t DF t + … + C T DF T

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

11. 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

12. Vietnam 2004 | 12 Constant perpetuity C t =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 = Proof: PV = C d + C d² + C d3 + … PV(1+r) = C + C d + C d² + … PV(1+r)– PV = C PV = C/r

13. Vietnam 2004 | 13 Growing perpetuity C t =C 1 (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%, div 1 = 50, g = 5% Note: expected price next year = Expected return =

14. Vietnam 2004 | 14 Constant annuity A level stream of cash flows for a fixed numbers of periods C 1 = C 2 = … = C T = C Examples: Equal-payment house mortgage Installment credit agreements PV = C * DF 1 + C * DF 2 + … + C * DF T + = C * [DF 1 + DF 2 + … + DF T ] = C * Annuity Factor Annuity Factor = present value of €1 paid at the end of each T periods.

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

16. Vietnam 2004 | 16 Review: general formula Cash flows: C 1, C 2, C 3, …,C t, … C T Discount factors: DF 1, DF 2, …,DF t, …, DF T Present value:PV = C 1 × DF 1 + C 2 × DF 2 + … + C T × DF T If r 1 = r 2 =...=r

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

18. Vietnam 2004 | 18 IRR and NPV - Example Compute the IRR and NPV for the following two projects. Assume the required return is 10%. YearProject AProject B 0-$200-$150 1$200$50 2$800$100 3-$800$150 NPV 42 91 IRR0%, 100%36%

19. Vietnam 2004 | 19 NPV Profiles

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

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

27. 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:  SE = STOCK ISSUE + RETAINED EARNINGS = SI + NET INCOME - DIVIDENDS  FA = INVESTMENT - DEPRECIATION (INV - DEP) +  WCR +  CASH = (SI + NI - DIV) +  D

28. Vietnam 2004 | 28 (NI +DEP -  WCR) - (INV) + (SI +  D - DIV) =  CASH  Net cash flows from operating activities (CF op )  Cash flow from investing activities (CF inv )  Cash flow from financing activities (CF fin )

29. Vietnam 2004 | 29 Free cash flow FCF = (NI +DEP -  WCR) - (INV) = CF op + CF inv From the statement of cash flows FCF = - (SI +  D - DIV) +  CASH

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

31. 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%

32. Vietnam 2004 | 32 Scenario 1: no inflation

33. 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

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

35. 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