Chapter 5 - The Time Value of Money

# Chapter 5 - The Time Value of Money

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## Chapter 5 - The Time Value of Money

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1. Chapter 5 - The Time Value of Money  2005, Pearson Prentice Hall

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 Future ? 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).

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?