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FINE 3010-01 Financial Management

FINE 3010-01 Financial Management. Instructor: Rogério Mazali Lecture 05: 09/23/2011. 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 05: 09/23/2011

  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 • Perpetuities • Annnuities • Ordinary Annuities • Delayed Annuities • Annuities-Due • Effective Annual Interest Rates and Inflation • Real vs. Nominal Cash Flows • Inflation and Interest Rates • Valuing Real Cash Payments • Real or Nominal?

  4. Perpetuities and Annuities • Streams of equal cash flows: • Home mortgage • Car loans • Student loans • Coupon paying Government Bonds • Coupon paying Corporate Bonds • Annuity: any sequence of equally spaced, level cash flows • Example: fixed-rate mortgage • Perpetuity: any sequence of equally spaced, level, everlasting cash flows • Example: Consols (British Government Bonds that pay a yearly coupon forever

  5. Perpetuities • A perpetuity will pay a constant cash flow CFt = C forever C C C C C C C … 0 1 2 3 4 5 6 7

  6. Perpetuities • How to evaluate the PV of a perpetuity?

  7. Perpetuities

  8. Perpetuities • Perpetuity Formula: • Example: British consols that promise to pay £100 as interest yearly (Take r = 10% yearly): PV0 = C/r

  9. Delayed Perpetuities • Consider that you work for a company who has just sold your business in the UK to a British company • It will take two years to finish the deal • You will be paid in British Consol bonds that will pay a total of £3 million in coupons (regular payments). • What is the value of the deal today? £ 3M £ 3M £ 3M £ 3M £ 3M … 0 1 2 3 4 5 6 7

  10. Delayed Perpetuities • We know how to find the value of our bonds when we receive them: • Once we have that, we can find the consols value at today:

  11. Growing Perpetuities • Annual payments grow at a constant rate g

  12. Growing Perpetuities

  13. Example • What is PV if C = $100, r = 10%, and g = 2%?

  14. Example • An investment in a growing perpetuity costs $5000, it is expected to pay $200 next year. • If the interest is 10%, what is the growth rate of the annual payment? • A: we have C = $200, r = 10%, and PV = $5,000; g = ? • Note: this formula only works if g < r

  15. Annuities • An annuity is a series of equal payments made at fixed intervals for a specific length of time • Ordinary Annuity: payments occur at the end of each period • Annuity Due: payments occur at the beginning of each period C C C C C 0 1 2 3 4 5 6 7

  16. Annuities • How to find the PV of an annuity? • Consider, for example, a 3-year annuity C C C 0 1 2 3 4 5 6 7

  17. Ordinary Annuities • Now consider the following strategy: • Buy today perpetuity paying C starting at t=1; • Issue perpetuity at t = 3 promising to pay C starting at t = 4; • Payoffs are: C C C C C C C … … 0 1 2 3 4 5 6 7 C C C C

  18. Ordinary Annuity

  19. Ordinary Annuity • PV of an ordinary annuity paying C dollars every year, for t years:

  20. Example 1 • Compute the present value of a 3-year ordinary annuity with payments of $100 at r=10%

  21. Example 2 • You agree to lease a car for 4 years at $300 per month, payable at the end of the month. If the discount rate is 0.5% per month, what is the cost of the lease?

  22. Delayed Annuity • The Problem: No payment for 5 years… • Then pay 4-year annuity of Example 1 $100 $100 $100 0 1 2 3 4 5 6 7 8

  23. Delayed Annuity • Step 1: Calculate the PV at time 5 using the following formula • Step 2: Determine the PV at time zero:

  24. Example 3 • What is the value today of a 10-year annuity that pays $300 a year (at yearend) if the annuity’s first cash flow starts at the end of year 6 and the interest rate is 15% for years 1 through 5 and 10% thereafter? • Steps: • Get value of annuity at t= 5 (year end) • Bring value in step 1 to t=0

  25. Annuities Due • Annuity and Perpetuity formulas: payment at the end of period • What if payments are made in the beginning of the period? • Often, cash payments start immediately • A level stream of payments starting immediately (beginning of period) is known as annuity due.

  26. Annuity Due • Annuity-Due PV formula:

  27. Future Value of an Annuity • Example: if you save $3,000 a year, at 8% interest rate, how much you would have at the end of 4 years?

  28. Future Value of an Annuity • With many cash flows, calculation can be hard • However, cash flows are the same as annuities’.

  29. Future Value of an Annuity • Future Value of an Annuity paying C dollars for t years: • Future Value of an Annuity-Due paying C dollars for t years:

  30. Inflation and the Time Value of Money • Inflati0n erodes the purchase power of money • So far we have computed PVs and FVs disregarding this issue • Inflation: GENERAL increase in prices, effect of money’s loss of value • Measure of Inflation: Consumer Price Index (CPI)

  31. Inflation and the Time of Money • Nominal vs. Real Values • Nominal Values: actual numbers of dollars of the day • Real Values: amount of purchasing power; stated in number of dollars of reference period • Example: 6% interest rate and 6% inflation rate => you gain NOTHING! • Approximation commonly used:

  32. Inflation and the Time Value of Money • Discounting Cash Flows: $100 to be received 1 year from today when annual interest rate is 10%: • Discounting $100 to be received 1 year from today when real interest rate is 2.8% and inflation is expected to be 7%. • Note: • NOMINAL cash flows discounted using NOMINAL interest rates • REAL cash flows must be discounted using REAL interest rates

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