# Hanoi April 20001 Capital budeting decisions with the Net Present Value rule 1. Foundations Professor André Farber Solvay Business School University of.

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Hanoi April 20001 Capital budeting decisions with the Net Present Value rule 1. Foundations Professor André Farber Solvay Business School University of Brussels, Belgium

Hanoi April 20002 Time value of money: introduction Consider simple investment project: Interest rate r = 10% 121 -100 0 1

Hanoi April 20003 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

Hanoi April 20004 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

Hanoi April 20005 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

Hanoi April 20006 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

Hanoi April 20007 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%

Hanoi April 20008 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

Hanoi April 20009 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

Hanoi April 200010 NPV calculation - example Suppose r = 10%

Hanoi April 200011 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 200012 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%

Hanoi April 200013 NPV Profiles

Hanoi April 200014 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 200015 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 200016 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 200017 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 200018 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 200019 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 200020 Interest-bearing debt: definition +Long-term debt +Current maturities of long term debt +Notes payable to banks

Hanoi April 200021 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

Hanoi April 200022 (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 )

Hanoi April 200023 Free cash flow FCF = (NI +DEP -  WCR) - (INV) = CF op + CF inv From the statement of cash flows FCF = - (SI +  D - DIV) +  CASH

Hanoi April 200024 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

Hanoi April 200025 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 200026 Scenario 1: no inflation

Hanoi April 200027 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 200028 Scenario 2 : Inflation = 100% Nominal discount rate: (1+10%) x (1+100%) = 2.20 Nominal rate = 120% NPV now negative. Why?

Hanoi April 200029 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

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