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Principles of Finance Part 3

Principles of Finance Part 3. The Time Value of Money. Chapter 9. Requests for permission to make copies of any part of the work should be mailed to: Thomson/South-Western 5191 Natorp Blvd. Mason, OH 45040. Time Value of Money. The most important concept in finance

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Principles of Finance Part 3

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  1. Principles of FinancePart 3

  2. The Time Value of Money Chapter 9 Requests for permission to make copies of any part of the work should be mailed to: Thomson/South-Western5191 Natorp Blvd.Mason, OH 45040

  3. Time Value of Money • The most important concept in finance • Used in nearly every financial decision • Business decisions • Personal finance decisions

  4. 0 1 2 3 k% CF0 CF1 CF2 CF3 Cash Flow Time Lines Graphical representations used to show timing of cash flows Time 0 is todayTime 1 is the end of Period 1 or the beginning of Period 2.

  5. 0 1 2 Year k% 100 Time line for a $100 lump sum due at the end of Year 2

  6. 0 1 2 3 k% 100 100 100 Time line for an ordinary annuity of $100 for 3 years

  7. 0 1 2 3 k% 100 75 50 -50 Time line for uneven CFs - $50 at t = 0 and $100, $75, and $50 at the end of Years 1 through 3

  8. Future Value The amount to which a cash flow or series of cash flows will grow over a period of time when compounded at a given interest rate.

  9. Future Value How much would you have at the end of one year if you deposited $100 in a bank account that pays 5 percent interest each year? FVn = FV1 = PV + INT = PV + PV(k) = PV (1 + k) = $100(1 + 0.05) = $100(1.05) = $105

  10. 0 1 2 3 10% 100 FV = ? Finding FV isCompounding. What’s the FV of an initial $100 after three years if k = 10%?

  11. Future Value After 1 year: FV1 = PV + Interest1 = PV + PV (k) = PV(1 + k) = $100 (1.10) = $110.00. After 2 years: FV2 = PV(1 + k)2 = $100 (1.10)2 = $121.00. After 3 years: FV3 = PV(1 + k)3 = 100 (1.10)3 = $133.10. In general, FVn = PV (1 + k)n

  12. Three Ways to Solve Time Value of Money Problems • Use Equations • Use Financial Calculator • Use Electronic Spreadsheet

  13. Numerical (Equation) Solution Solve this equation by plugging in the appropriate values: PV = $100, k = 10%, and n =3

  14. Financial Calculator Solution There are 4 variables. If 3 are known, the calculator will solve for the 4th.

  15. 3 10 -100 0 ? N I/YR PV PMT FV 133.10 INPUTS OUTPUT Financial Calculator Solution Here’s the setup to find FV: Clearing automatically sets everything to 0, but for safety enter PMT = 0. Set: P/YR = 1, END

  16. Spreadsheet Solution Set up Problem Click on insert function and choose Financial/FV

  17. Spreadsheet Solution Reference cells: Rate = interest rate, k Nper = number of periods interest is earned Pmt = periodic payment PV = present value of the amount

  18. Present Value • Present value is the value today of a future cash flow or series of cash flows. • Discountingis the process of finding the present value of a future cash flow or series of future cash flows; it is the reverse of compounding.

  19. 0 1 2 3 10% PV = ? 100 What is the PV of $100 due in three years if k = 10%?

  20. What is the PV of $100 duein three years if k = 10%? Solve FVn = PV (1 + k )n for PV: This is the numerical solution to solve for PV.

  21. 3 10 ? 0 100 N I/YR PV PMT FV -75.13 INPUTS OUTPUT Financial Calculator Solution Either PV or FV must be negative. Here PV = -75.13. Invest $75.13 today, take out $100 after 3 years.

  22. Spreadsheet Solution

  23. If sales grow at 20% per year,how long before sales double? Solve for n: FVn = 1(1 + k)n 2 = 1(1.20)n The numerical solution is somewhat difficult.

  24. ? 20 -1 0 2 N I/YR PV PMT FV 3.8 INPUTS FV 2 OUTPUT 3.8 1 Year 0 1 2 3 4 Financial Calculator Solution GraphicalIllustration:

  25. Spreadsheet Solution

  26. Future Value of an Annuity • Annuity: A series of payments of equal amounts at fixed intervals for a specified number of periods. • Ordinary (deferred) Annuity: An annuity whose payments occur at the end of each period. • Annuity Due: An annuity whose payments occur at the beginning of each period.

  27. 0 1 2 3 k% PMT PMT PMT 0 1 2 3 k% PMT PMT PMT Ordinary Annuity Versus Annuity Due Ordinary Annuity Annuity Due

  28. 0 1 2 3 10% 100 100 100 110 121 FV = 331 What’s the FV of a 3-year Ordinary Annuity of $100 at 10%?

  29. Numerical Solution:

  30. INPUTS 3 10 0 -100 ? 331.00 N I/YR PV PMT FV OUTPUT Financial Calculator Solution

  31. Spreadsheet Solution

  32. Present Value of an Annuity • PVAn= the present value of an annuity with n payments. • Each payment is discounted, and the sum of the discounted payments is the present value of the annuity.

  33. 0 1 2 3 10% 100 100 100 90.91 82.64 75.13 What is the PV of this Ordinary Annuity? 248.69 = PV

  34. Numerical Solution

  35. N I/YR PV PMT FV 3 10 ? 100 0 -248.69 INPUTS OUTPUT Financial Calculator Solution We know the payments but no lump sum FV, so enter 0 for future value.

  36. Spreadsheet Solution

  37. 0 1 2 3 10% 100 100 100 Find the FV and PV if theAnnuity were an Annuity Due.

  38. Numerical Solution

  39. N I/YR PV PMT FV 3 10 ? 100 0 -273.55 INPUTS OUTPUT Financial Calculator Solution Switch from “End” to “Begin”. Then enter variables to find PVA3 = $273.55. Then enter PV = 0 and press FV to find FV = $364.10.

  40. Spreadsheet Solution

  41. 0 1 2 3 4 k = ? - 864.80 250 250 250 250 Solving for Interest Rates with Annuities You pay $864.80 for an investment that promises to pay you $250 per year for the next four years, with payments made at the end of each year. What interest rate will you earn on this investment?

  42. Numerical Solution Use trial-and-error by substituting different values of k into the following equation until the right side equals $864.80.

  43. N I/YR PV PMT FV 4 ? -846.80 250 0 7.0 INPUTS OUTPUT Financial Calculator Solution

  44. Spreadsheet Solution

  45. 3 ? -100 0 125.97 8% INPUTS N I/YR PV PMT FV OUTPUT What interest rate would cause $100 to grow to $125.97 in 3 years? $100 (1 + k)3 = $125.97.

  46. Spreadsheet Solution

  47. Uneven Cash Flow Streams • A series of cash flows in which the amount varies from one period to the next: • Payment (PMT) designates constant cash flows—that is, an annuity stream. • Cash flow (CF) designates cash flows in general, both constant cash flows and uneven cash flows.

  48. 1 2 3 100 300 300 4 0 10% -50 90.91 247.93 225.39 530.08 = PV -34.15 What is the PV of this Uneven Cash Flow Stream?

  49. Numerical Solution

  50. Financial Calculator Solution • Input in “CF” register: • CF0 = 0 • CF1 = 100 • CF2 = 300 • CF3 = 300 • CF4 = -50 • Enter I = 10%, then press NPV button to get NPV = 530.09. (Here NPV = PV.)

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