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

Hanoi April Time value of money: introduction Consider simple investment project: Interest rate r = 10%

Hanoi April Net future value NFV =  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

Hanoi April Net Present Value NPV = /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>

Hanoi April 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 = ( )/100 = 21% The Rate of Return Rule: Invest if IRR > r

Hanoi April 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 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: /(1+IRR)=0  IRR=21%

Hanoi April Extension to several periods Investment project: -100 in year 0, in year 5. Net future value calculation: NFV 5 =  (1.10) 5 = = -11 <0 Compound interest Net present value calculation: NPV = /(1.10) 5 =  = is the 5-year discount factor DF 5 = 1/(1+r) 5 a market price

Hanoi April 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 NPV calculation - example Suppose r = 10%

Hanoi April 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 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 IRR0%, 100%36%

Hanoi April NPV Profiles

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

Hanoi April 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 (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 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 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 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 Scenario 1: no inflation

Hanoi April 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 NPV = (110 x 1.20)/(1.10 x 1.20) = 110/1.10 = 100

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

Hanoi April Decomposition of NPV –EBITD after taxes –Depreciation tax shield –  WCR –Investment –Resale value after taxes –NPV