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Chapter 3 - The Time Value of Money

Chapter 3 - The Time Value of Money. The Time Value of Money. Compounding and Discounting Single Sums. Today. Future. We know that receiving $1 today is worth more than $1 in the future. This is due to opportunity costs .

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Chapter 3 - The Time Value of Money

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  1. Chapter 3 - The Time Value of Money

  2. The Time Value of Money Compounding and Discounting Single Sums

  3. Today Future We know that receiving $1 today is worth more than $1 in the future. This is duetoopportunity costs. The opportunity cost of receiving $1 in the future is theinterestwe could have earned if we had received the $1 sooner.

  4. If we can measure this opportunity cost, we can:

  5. If we can measure this opportunity cost, we can: • Translate $1 today into its equivalent in the future(compounding).

  6. Today Future ? If we can measure this opportunity cost, we can: • Translate $1 today into its equivalent in the future(compounding).

  7. Today Future ? If we can measure this opportunity cost, we can: • Translate $1 today into its equivalent in the future(compounding). • Translate $1 in the future into its equivalent today(discounting).

  8. Today Today Future Future ? ? If we can measure this opportunity cost, we can: • Translate $1 today into its equivalent in the future(compounding). • Translate $1 in the future into its equivalent today(discounting).

  9. Compound Interest and Future Value

  10. Future Value - single sumsIf you deposit $100 in an account earning 6%, how much would you have in the account after 1 year?

  11. Future Value - single sumsIf you deposit $100 in an account earning 6%, how much would you have in the account after 1 year? PV = FV = 0 1

  12. Future Value - single sumsIf you deposit $100 in an account earning 6%, how much would you have in the account after 1 year? Calculator Solution: P/Y = 1 I = 6 N = 1 PV = -100 FV = $106 PV = -100 FV = 0 1

  13. Future Value - single sumsIf you deposit $100 in an account earning 6%, how much would you have in the account after 1 year? Calculator Solution: P/Y = 1 I = 6 N = 1 PV = -100 FV = $106 PV = -100 FV = 106 0 1

  14. Future Value - single sumsIf you deposit $100 in an account earning 6%, how much would you have in the account after 1 year? Mathematical Solution: FV = PV (FVIF i, n) FV = 100 (FVIF .06, 1) (use FVIF table, or) FV = PV (1 + i)n FV = 100 (1.06)1 = $106 PV = -100 FV = 106 0 1

  15. Future Value - single sumsIf you deposit $100 in an account earning 6%, how much would you have in the account after 5 years?

  16. Future Value - single sumsIf you deposit $100 in an account earning 6%, how much would you have in the account after 5 years? PV = FV = 0 5

  17. Future Value - single sumsIf you deposit $100 in an account earning 6%, how much would you have in the account after 5 years? Calculator Solution: P/Y = 1 I = 6 N = 5 PV = -100 FV = $133.82 PV = -100 FV = 0 5

  18. Future Value - single sumsIf you deposit $100 in an account earning 6%, how much would you have in the account after 5 years? Calculator Solution: P/Y = 1 I = 6 N = 5 PV = -100 FV = $133.82 PV = -100 FV = 133.82 0 5

  19. Future Value - single sumsIf you deposit $100 in an account earning 6%, how much would you have in the account after 5 years? Mathematical Solution: FV = PV (FVIF i, n) FV = 100 (FVIF .06, 5) (use FVIF table, or) FV = PV (1 + i)n FV = 100 (1.06)5 = $133.82 PV = -100 FV = 133.82 0 5

  20. Future Value - single sumsIf you deposit $100 in an account earning 6% with quarterly compounding, how much would you have in the account after 5 years?

  21. Future Value - single sumsIf you deposit $100 in an account earning 6% with quarterly compounding, how much would you have in the account after 5 years? PV = FV = 0 ?

  22. Future Value - single sumsIf you deposit $100 in an account earning 6% with quarterly compounding, how much would you have in the account after 5 years? Calculator Solution: P/Y = 4 I = 6 N = 20 PV = -100 FV = $134.68 PV = -100 FV = 0 20

  23. Future Value - single sumsIf you deposit $100 in an account earning 6% with quarterly compounding, how much would you have in the account after 5 years? Calculator Solution: P/Y = 4 I = 6 N = 20 PV = -100 FV = $134.68 PV = -100 FV = 134.68 0 20

  24. Future Value - single sumsIf you deposit $100 in an account earning 6% with quarterly compounding, how much would you have in the account after 5 years? Mathematical Solution: FV = PV (FVIF i, n) FV = 100 (FVIF .015, 20) (can’t use FVIF table) FV = PV (1 + i/m) m x n FV = 100 (1.015)20 = $134.68 PV = -100 FV = 134.68 0 20

  25. Future Value - single sumsIf you deposit $100 in an account earning 6% with monthly compounding, how much would you have in the account after 5 years?

  26. Future Value - single sumsIf you deposit $100 in an account earning 6% with monthly compounding, how much would you have in the account after 5 years? PV = FV = 0 ?

  27. Future Value - single sumsIf you deposit $100 in an account earning 6% with monthly compounding, how much would you have in the account after 5 years? Calculator Solution: P/Y = 12 I = 6 N = 60 PV = -100 FV = $134.89 PV = -100 FV = 0 60

  28. Future Value - single sumsIf you deposit $100 in an account earning 6% with monthly compounding, how much would you have in the account after 5 years? Calculator Solution: P/Y = 12 I = 6 N = 60 PV = -100 FV = $134.89 PV = -100 FV = 134.89 0 60

  29. Future Value - single sumsIf you deposit $100 in an account earning 6% with monthly compounding, how much would you have in the account after 5 years? Mathematical Solution: FV = PV (FVIF i, n) FV = 100 (FVIF .005, 60) (can’t use FVIF table) FV = PV (1 + i/m) m x n FV = 100 (1.005)60 = $134.89 PV = -100 FV = 134.89 0 60

  30. Future Value - continuous compoundingWhat is the FV of $1,000 earning 8% with continuous compounding, after 100 years?

  31. Future Value - continuous compoundingWhat is the FV of $1,000 earning 8% with continuous compounding, after 100 years? PV = FV = 0 ?

  32. Future Value - continuous compoundingWhat is the FV of $1,000 earning 8% with continuous compounding, after 100 years? Mathematical Solution: FV = PV (e in) FV = 1000 (e .08x100) = 1000 (e 8) FV = $2,980,957.99 PV = -1000 FV = 0 100

  33. Future Value - continuous compoundingWhat is the FV of $1,000 earning 8% with continuous compounding, after 100 years? Mathematical Solution: FV = PV (e in) FV = 1000 (e .08x100) = 1000 (e 8) FV = $2,980,957.99 PV = -1000 FV = $2.98m 0 100

  34. Present Value

  35. Present Value - single sumsIf you receive $100 one year from now, what is the PV of that $100 if your opportunity cost is 6%?

  36. Present Value - single sumsIf you receive $100 one year from now, what is the PV of that $100 if your opportunity cost is 6%? PV = FV = 0 ?

  37. PV = FV = 100 Present Value - single sumsIf you receive $100 one year from now, what is the PV of that $100 if your opportunity cost is 6%? Calculator Solution: P/Y = 1 I = 6 N = 1 FV = 100 PV = -94.34 0 1

  38. PV = -94.34 FV = 100 0 1 Present Value - single sumsIf you receive $100 one year from now, what is the PV of that $100 if your opportunity cost is 6%? Calculator Solution: P/Y = 1 I = 6 N = 1 FV = 100 PV = -94.34

  39. PV = -94.34 FV = 100 0 1 Present Value - single sumsIf you receive $100 one year from now, what is the PV of that $100 if your opportunity cost is 6%? Mathematical Solution: PV = FV (PVIF i, n) PV = 100 (PVIF .06, 1) (use PVIF table, or) PV = FV / (1 + i)n PV = 100 / (1.06)1 = $94.34

  40. Present Value - single sumsIf you receive $100 five years from now, what is the PV of that $100 if your opportunity cost is 6%?

  41. Present Value - single sumsIf you receive $100 five years from now, what is the PV of that $100 if your opportunity cost is 6%? PV = FV = 0 ?

  42. PV = FV = 100 0 5 Present Value - single sumsIf you receive $100 five years from now, what is the PV of that $100 if your opportunity cost is 6%? Calculator Solution: P/Y = 1 I = 6 N = 5 FV = 100 PV = -74.73

  43. PV = -74.73 FV = 100 0 5 Present Value - single sumsIf you receive $100 five years from now, what is the PV of that $100 if your opportunity cost is 6%? Calculator Solution: P/Y = 1 I = 6 N = 5 FV = 100 PV = -74.73

  44. PV = -74.73 FV = 100 0 5 Present Value - single sumsIf you receive $100 five years from now, what is the PV of that $100 if your opportunity cost is 6%? Mathematical Solution: PV = FV (PVIF i, n) PV = 100 (PVIF .06, 5) (use PVIF table, or) PV = FV / (1 + i)n PV = 100 / (1.06)5 = $74.73

  45. Present Value - single sumsWhat is the PV of $1,000 to be received 15 years from now if your opportunity cost is 7%?

  46. PV = FV = 0 15 Present Value - single sumsWhat is the PV of $1,000 to be received 15 years from now if your opportunity cost is 7%?

  47. PV = FV = 1000 0 15 Present Value - single sumsWhat is the PV of $1,000 to be received 15 years from now if your opportunity cost is 7%? Calculator Solution: P/Y = 1 I = 7 N = 15 FV = 1,000 PV = -362.45

  48. PV = -362.45 FV = 1000 0 15 Present Value - single sumsWhat is the PV of $1,000 to be received 15 years from now if your opportunity cost is 7%? Calculator Solution: P/Y = 1 I = 7 N = 15 FV = 1,000 PV = -362.45

  49. PV = -362.45 FV = 1000 0 15 Present Value - single sumsWhat is the PV of $1,000 to be received 15 years from now if your opportunity cost is 7%? Mathematical Solution: PV = FV (PVIF i, n) PV = 100 (PVIF .07, 15) (use PVIF table, or) PV = FV / (1 + i)n PV = 100 / (1.07)15 = $362.45

  50. Present Value - single sumsIf you sold land for $11,933 that you bought 5 years ago for $5,000, what is your annual rate of return?

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