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FINANCE 2. Foundations

FINANCE 2. Foundations. Solvay Business School Université Libre de Bruxelles Fall 2007. Interest rates and present value: 1 period. Suppose that the 1-year interest rate r 1 = 5% €1 at time 0 → €1.05 at time 1 €1/1.05 = 0.9523 at time 0 → €1 at time 1

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FINANCE 2. Foundations

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  1. FINANCE2. Foundations Solvay Business School Université Libre de Bruxelles Fall 2007

  2. Interest rates and present value: 1 period • Suppose that the 1-year interest rate r1 = 5% • €1 at time 0 → €1.05 at time 1 • €1/1.05 = 0.9523 at time 0 → €1 at time 1 • 1-year discount factor: DF1 = 1 / (1+r1) • Suppose that the 1-year discount factor DF1 = 0.95 • €0.95 at time 0 → €1 at time 1 • € 1 at time 0 → € 1/0.95 = 1.0526 at time 1 • The 1-year interest rate r1 = 5.26% • Future value of C0 : FV1(C0) = C0 ×(1+r1) = C0 / DF1 • Present value of C1: PV(C1) = C1 / (1+r1) = C1 × DF1 • Data: r1 → DF1 = 1/(1+r1) or Data: DF1→ r1 = 1/DF1 - 1 MBA 2007 02 Foundations

  3. 125 1 0 -100 Using Present Value • Consider simple investment project: • Interest rate r = 5%, DF1 = 0.9523 MBA 2007 02 Foundations

  4. NFV = +125 - 100  1.05 = 20 = + C1 - I (1+r) Decision rule: invest if NFV>0 Justification: takes into cost of capital cost of financing opportunity cost Net Future Value +125 +100 0 1 -100 -105 MBA 2007 02 Foundations

  5. Net Present Value • NPV = - 100 + 125/1.05 = + 19 • = - I + C1/(1+r) • = - I + C1 DF1 • = - 100+125  0.9524 • = +19 • DF1 = 1-year discount factor • a market price • C1 DF1 =PV(C1) • Decision rule: invest if NPV>0 • NPV>0  NFV>0 +125 +119 -100 -125 MBA 2007 02 Foundations

  6. 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 = Profit/Investment = (C1 - I)/I • In our example: IRR = (125 - 100)/100 = 25% • The Rate of Return Rule: Invest if IRR > r • 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 MBA 2007 02 Foundations

  7. Economic foundations of net present value Euros next year I. Fisher 1907, J. Hirshleifer 1958 210 Perfect capital markets Separate investment decisions from consumption decisions 157.5 Y1 105 Slope = - (1 + r) = - (1 + 5%) 52.5 Euros now 150 50 100 200 Y0 MBA 2007 02 Foundations

  8. Net Present Value Consider the following investment project: Initial cost: I (50) Future cash flow: C1 (60) NPV = -I + DF1 C1 = -50 + 0.9524  60 = 7.14 Budget constraint with project: MBA 2007 02 Foundations

  9. Fisher Separation Theorem Euros next year I. Fisher 1907, J. Hirshleifer 1958 Perfect capital markets Investment decision independent of:- initial allocation- preferences (utility functions) 165 105 Slope = - (1 + r) = - (1 + 5%) NPV -50 Euros now 50 100 200 207.14 MBA 2007 02 Foundations

  10. Enterprise Valuation Suppose an all equity financed company is created for this project. Market Cap. Cash flows Step 1: Creation t = 0 t = 1-50 +60 NPV = Assets 0 Equity 0 Step 2: Equity offering + investment I+NPV = t = 0 t = 1 +60 Assets 50 Equity 50 MBA 2007 02 Foundations

  11. Slope = -(1+r) C1 -I 0 NPV Market value of company MBA 2007 02 Foundations

  12. Entreprise Value Maximisation Numerical example Euros next year Investment opportunities Investment NPV 0 Euros today Market value of company MBA 2007 02 Foundations

  13. Arbitrage and the Law of One Price Risk-free interest rate : 5% If bond price = $940 If bond price = $960 MBA 2007 02 Foundations

  14. No Arbitrage Price of a Security MBA 2007 02 Foundations

  15. Valuing a Portfolio: Value Additivity MBA 2007 02 Foundations

  16. No-Arbitrage Price of a Risk-free Security You observe the following data: What is the price of Bond C? Consider the following replicating portfolio: nA = 0.50 nB = 0.50 => Price of Bond C = 0.50 x 101 + 0.50 x 98 = 99.50 MBA 2007 02 Foundations

  17. Looking for discount factors No-Arbitrage & Law of One Price  there exist discount factors DF1 and DF2 such that for any security: Price(Bond)=DF1x CashFlow1+ DF2x CashFlow2 What are the underlying discount factors? Bootstrap method 101.00 = DF1 106 98.00 = DF1 4 + DF2 104 DF1 = 101/106 = 0.9528 DF2 = (98 – 4 x 0.9528)/104 =0.9057 MBA 2007 02 Foundations

  18. MBA 2007 02 Foundations

  19. Risky securities Price of risk 50% 50% Risk-free bond: Risk-free return = risk-free interest rate = Market index: Expected payoff = Expected return = Market index’s risk premium = 10% - 4%= 6% MBA 2007 02 Foundations

  20. No-Arbitrage Price of a Risky Security Price calculation using replicating portfolio: MBA 2007 02 Foundations

  21. Risk is Relative to the Overall Market 600 0 B MBA 2007 02 Foundations

  22. Risk and Risk Premiums for Different Securities MBA 2007 02 Foundations

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