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FINE 3010-01 Financial Management

FINE 3010-01 Financial Management. Instructor: Rogério Mazali Lecture 03: 09/16/2011. FINE 3010-01 Instructor: Rogério Mazali. Chapter 5 : The Time Value of Money. Fundamentals of Corporate Finance Sixth Edition Richard A. Brealey Stewart C. Myers Alan J. Marcus McGraw Hill/Irwin.

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FINE 3010-01 Financial Management

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  1. FINE 3010-01Financial Management Instructor: RogérioMazali Lecture 03: 09/16/2011

  2. FINE 3010-01Instructor: RogérioMazali Chapter 5: The Time Value of Money Fundamentals of Corporate Finance Sixth Edition Richard A. Brealey Stewart C. Myers Alan J. Marcus McGraw Hill/Irwin

  3. Agenda • Future Values and Present Value • The One-Period Case • The Multi-Period Case • Compounding Periods • Perpetuities • Annuities • Inflation

  4. BASIC QUESTION • Is a dollar today worth more or less than a dollar in the future? • Why?

  5. Future Values: One-Period Case • Interest • Definition: Amount that your investment earns • Future Value (FV) • Definition: Amount to which an investment will grow after earning interest

  6. Future Values: One-Period Case • Let’s assume: • you have $100 in a bank account (defined as Initial Investment or C0) • current interest rate 6% per year • Question: • How much will you have in one year? Year 0 Year 1 $100 FV???

  7. Future Values: One-Period Case • Interest: Interest = Initial Investment * Int. Rate Interest = $100 * 0.06 = $6 • Future Value (FV): FV1 = Initial Investment + Interest = $100 + $6 = $100 + $100 * 0.06 = 100 * (1+ 0.06) = $106

  8. Future Values: One-Period Case • General formula (1-period):

  9. Present Values: One-Period Case • Suppose you need to buy a new computer that costs $1,060 one year from today. • Suppose you will have no income next year • How much money do you need to have today in order to be able to purchase the computer? Year 0 Year 1 PV??? $1,060

  10. Present Values: One-Period Case Discount Factor Present value of a $1 future payment. Present Value (PV) Value today of a future cash flow. Discount Rate Interest rate used to compute present values of future cash flows.

  11. Present Values: One-Period Case

  12. Present Values: One-Period Case

  13. Example • What is the value today of $1 dollars in one year? • r=10% • r=5% • r=15% • What is the value today of $400 dollars in one year if we know DF = 0.85?

  14. Note on Discount Rates • The discount rate to be used is the opportunity cost of capital – the rate of return offered by comparable investment opportunities. • The discount rate should take into account: • Time value of money • Riskiness of cash flow

  15. Future Values: Multi-Period Case • Let’s assume: • you have $100 in a bank account (defined as Initial Investment or C0) • current interest rate 6% per year • Question: • How much will you have in two years? Year 0 Year 1 Year 2 $100 FV???

  16. Simple Interest • Interest earned on initial investment ONLY • Equivalently: FV1 = PV0 × (1 + r) FV2 = PV1 + PV0 × r = PV0 × (1 + 2r) Year 0 Year 1 Year 2 Interest 1 = 0.06 × $100 = $6 Interest 2 = 0.06 × $100 = $6 $100 FV??? Interest = $ 6 Principal = $100 Total = $106 Interest = $ 6 Principal = $106 Total = $112

  17. Compound Interest • Interest earned on initial inv. AND on interest • Equivalently: FV1 = PV0 × (1 + r) FV2 = PV1 + PV1 × r = PV0 × (1 + r)2 Year 0 Year 1 Year 2 Interest 1 = 0.06 × $100 = $6 Interest 2 = 0.06 × $106 = $6.36 $100 FV??? Interest = $ 6 Principal = $100 Total = $106 Interest = $ 6.36 Principal = $106.00 Total = $112.36

  18. Compound vs. Simple Interest • Compound Interest: • Simple Interest: • We will use the Compound Rule as long as it is not noted.

  19. Future Values and Compound Interest • Example: Manhattan Island Sale: • Peter Minuit bought Manhattan Island for $24 in 1626. Was this a good deal? • To answer, determine $24 is worth in the year 2008, compounded at 8% (how to choose the right interest rate will be seen in later chapters). The value of Manhattan Island land is well below this figure.

  20. Valuing Long-Lived Assets • You cannot compare cash flows at two different points in time, let’s say, t=2 and t=1!! Compare them at Today, or compare them at t=1! t = 0 t = 1 t = 2 $100/(1+r)2 $100 t = 0 t = 1 $100/(1+r) $100

  21. Examples • What is the value today of $15,000 in 5 years at r=10% • What is $100 today worth in 3 years at r=10%?

  22. General Formulae • Future Value: • Present Value: • Given any three, you can solve for the fourth • Present value PV • Future value FV (or future cash flow Ct) • Time period t • Discount rate r

  23. Examples • How much must you deposit today to have $1 million in 25 years? (r=12%) PV? • If a $58,823.31 investment yields $1 million in 25 years, what is the rate of interest? r? • How many years will it take $58,823.31 to grow to $1 million if r=12%? t? • What will $58,823.31 grow to after 25 years if r=12%? FV?

  24. Example • Puerto Rico Borrows Some Cash • In 2007, Puerto Rico needed to borrow about $2.6 billion for up to 47 years. It did so by selling IOUs (bonds), each of which simply promised to pay the holder $1,000 at the end of that time. The market interest rate at the time was 5.15%. How much would have been prepared to pay for one of these IOUs?

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