Créer une présentation
Télécharger la présentation

Télécharger la présentation
## Chapter 3 - The Time Value of Money

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**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 duetoopportunity costs. The opportunity cost of receiving $1 in the future is theinterestwe could have earned if we had received the $1 sooner.**If we can measure this opportunity cost, we can:**• Translate $1 today into its equivalent in the future(compounding).**Today**Future ? If we can measure this opportunity cost, we can: • Translate $1 today into its equivalent in the future(compounding).**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).**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).**Future Value - single sumsIf you deposit $100 in an account**earning 6%, how much would you have in the account after 1 year?**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**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**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**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**Future Value - single sumsIf you deposit $100 in an account**earning 6%, how much would you have in the account after 5 years?**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**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**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**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**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?**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 ?**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**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**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**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?**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 ?**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**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**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**Future Value - continuous compoundingWhat is the FV of**$1,000 earning 8% with continuous compounding, after 100 years?**Future Value - continuous compoundingWhat is the FV of**$1,000 earning 8% with continuous compounding, after 100 years? PV = FV = 0 ?**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**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**Present Value - single sumsIf you receive $100 one year from**now, what is the PV of that $100 if your opportunity cost is 6%?**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 ?**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**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**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**Present Value - single sumsIf you receive $100 five years**from now, what is the PV of that $100 if your opportunity cost is 6%?**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 ?**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**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**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**Present Value - single sumsWhat is the PV of $1,000 to be**received 15 years from now if your opportunity cost is 7%?**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%?**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**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**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**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?