Session2 Time Value Of Money (2)

[object Object],The Time Value of Money

[object Object],[object Object],Today Future

[object Object],? If we can MEASURE this opportunity cost, we can: Today Future

[object Object],[object Object],? ? If we can MEASURE this opportunity cost, we can: Today Future Today Future

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

Future Value - single sums If you deposit $100 in an account earning 6%, how much would you have in the account after 1 year? ,[object Object],[object Object],[object Object],[object Object],0 1 PV = -100 FV =

Future Value - single sums If you deposit $100 in an account earning 6%, how much would you have in the account after 1 year? ,[object Object],[object Object],[object Object],[object Object],0 1 PV = -100 FV = 106

Future Value - single sums If you deposit $100 in an account earning 6%, how much would you have in the account after 1 year? ,[object Object],[object Object],[object Object],[object Object],[object Object],0 1 PV = -100 FV = 106

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

Future Value - single sums If you deposit $100 in an account earning 6%, how much would you have in the account after 5 years? ,[object Object],[object Object],[object Object],[object Object],0 5 PV = -100 FV =

Future Value - single sums If you deposit $100 in an account earning 6%, how much would you have in the account after 5 years? ,[object Object],[object Object],[object Object],[object Object],0 5 PV = -100 FV = 133. 82

Future Value - single sums If you deposit $100 in an account earning 6%, how much would you have in the account after 5 years? ,[object Object],[object Object],[object Object],[object Object],[object Object],0 5 PV = -100 FV = 133. 82

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

[object Object],[object Object],[object Object],[object Object],Future Value - single sums If you deposit $100 in an account earning 6% with quarterly compounding , how much would you have in the account after 5 years? 0 20 PV = -100 FV =

[object Object],[object Object],[object Object],[object Object],Future Value - single sums If you deposit $100 in an account earning 6% with quarterly compounding , how much would you have in the account after 5 years? 0 20 PV = -100 FV = 134. 68

[object Object],[object Object],[object Object],[object Object],[object Object],Future Value - single sums If you deposit $100 in an account earning 6% with quarterly compounding , how much would you have in the account after 5 years? 0 20 PV = -100 FV = 134. 68

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

[object Object],[object Object],[object Object],[object Object],Future Value - single sums If you deposit $100 in an account earning 6% with monthly compounding , how much would you have in the account after 5 years? 0 60 PV = -100 FV =

[object Object],[object Object],[object Object],[object Object],Future Value - single sums If you deposit $100 in an account earning 6% with monthly compounding , how much would you have in the account after 5 years? 0 60 PV = -100 FV = 134. 89

[object Object],[object Object],[object Object],[object Object],[object Object],Future Value - single sums If you deposit $100 in an account earning 6% with monthly compounding , how much would you have in the account after 5 years? 0 60 PV = -100 FV = 134. 89

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

[object Object],[object Object],[object Object],[object Object],Future Value - continuous compounding What is the FV of $1,000 earning 8% with continuous compounding , after 100 years? 0 100 PV = -1000 FV =

Future Value - continuous compounding What is the FV of $1,000 earning 8% with continuous compounding , after 100 years? ,[object Object],0 100 PV = -1000 FV = Mathematical Solution: FV = PV (e in ) FV = 1000 (e .08x100 ) = 1000 (e 8 ) FV = $2,980,957. 99

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

[object Object],[object Object],[object Object],[object Object],Present Value - single sums If you will receive $100 one year from now, what is the PV of that $100 if your opportunity cost is 6%? 0 1 PV = FV = 100

[object Object],[object Object],[object Object],[object Object],Present Value - single sums If you will receive $100 one year from now, what is the PV of that $100 if your opportunity cost is 6%? 0 1 PV = -94. 34 FV = 100

[object Object],[object Object],[object Object],[object Object],[object Object],Present Value - single sums If you will receive $100 one year from now, what is the PV of that $100 if your opportunity cost is 6%? 0 1 PV = -94. 34 FV = 100

Present Value - single sums If you will receive $100 5 years from now, what is the PV of that $100 if your opportunity cost is 6%? 0 ? PV = FV =

[object Object],[object Object],[object Object],[object Object],Present Value - single sums If you will receive $100 5 years from now, what is the PV of that $100 if your opportunity cost is 6%? 0 5 PV = FV = 100

Present Value - single sums If you will receive $100 5 years from now, what is the PV of that $100 if your opportunity cost is 6%? ,[object Object],0 5 PV = FV = 100 Calculator Solution: P/Y = 1 I = 6 N = 5 FV = 100 PV = -74.73

[object Object],[object Object],[object Object],[object Object],[object Object],Present Value - single sums If you will receive $100 5 years from now, what is the PV of that $100 if your opportunity cost is 6%? 0 5 PV = -74. 73 FV = 100

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

[object Object],[object Object],[object Object],[object Object],Present Value - single sums What is the PV of $1,000 to be received 15 years from now if your opportunity cost is 7%? 0 15 PV = FV = 1000

[object Object],[object Object],[object Object],[object Object],Present Value - single sums What is the PV of $1,000 to be received 15 years from now if your opportunity cost is 7%? 0 15 PV = -362. 45 FV = 1000

[object Object],[object Object],[object Object],[object Object],[object Object],Present Value - single sums What is the PV of $1,000 to be received 15 years from now if your opportunity cost is 7%? 0 15 PV = -362. 45 FV = 1000

Present Value - single sums If you sold land for $11,933 that you bought 5 years ago for $5,000, what is your annual rate of return? 0 ? PV = FV =

[object Object],[object Object],[object Object],[object Object],Present Value - single sums If you sold land for $11,933 that you bought 5 years ago for $5,000, what is your annual rate of return? 0 5 PV = -5,000 FV = 11,933

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Present Value - single sums If you sold land for $11,933 that you bought 5 years ago for $5,000, what is your annual rate of return?

Present Value - single sums Suppose you placed $100 in an account that pays 9.6% interest, compounded monthly. How long will it take for your account to grow to $500? 0 PV = FV =

[object Object],[object Object],[object Object],[object Object],Present Value - single sums Suppose you placed $100 in an account that pays 9.6% interest, compounded monthly. How long will it take for your account to grow to $500? 0 ? PV = -100 FV = 500

Present Value - single sums Suppose you placed $100 in an account that pays 9.6% interest, compounded monthly. How long will it take for your account to grow to $500? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],Hint for single sum problems:

[object Object],[object Object],The Time Value of Money 0 1 2 3 4

[object Object],Annuities 0 1 2 3 4

[object Object],[object Object],Examples of Annuities:

Future Value - annuity If you invest $1,000 at the end of the next 3 years, at 8%, how much would you have after 3 years? 0 1 2 3

[object Object],[object Object],[object Object],[object Object],Future Value - annuity If you invest $1,000 at the end of the next 3 years, at 8%, how much would you have after 3 years? 1000 1000 1000 0 1 2 3

[object Object],[object Object],[object Object],Future Value - annuity If you invest $1,000 at the end of the next 3 years, at 8%, how much would you have after 3 years?

[object Object],[object Object],[object Object],[object Object],[object Object],Future Value - annuity If you invest $1,000 at the end of the next 3 years, at 8%, how much would you have after 3 years?

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Future Value - annuity If you invest $1,000 at the end of the next 3 years, at 8%, how much would you have after 3 years?

Present Value - annuity What is the PV of $1,000 at the end of each of the next 3 years, if the opportunity cost is 8%? 0 1 2 3

[object Object],[object Object],[object Object],[object Object],Present Value - annuity What is the PV of $1,000 at the end of each of the next 3 years, if the opportunity cost is 8%? 1000 1000 1000 0 1 2 3

[object Object],[object Object],[object Object],Present Value - annuity What is the PV of $1,000 at the end of each of the next 3 years, if the opportunity cost is 8%?

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Present Value - annuity What is the PV of $1,000 at the end of each of the next 3 years, if the opportunity cost is 8%?

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Present Value - annuity What is the PV of $1,000 at the end of each of the next 3 years, if the opportunity cost is 8%?

Other Cash Flow Patterns 0 1 2 3

[object Object],[object Object],Perpetuities

[object Object],Present Value of a Perpetuity

[object Object],PV = PMT (PVIFA i, n ) Present Value of a Perpetuity

[object Object],[object Object]

[object Object],[object Object],1 - 1 (1 + i) n i

[object Object],[object Object],[object Object],1 - 1 (1 + i) n i

When n gets very large, this becomes zero. So we’re left with PVIFA = 1 - 1 (1 + i) n i 1 i

[object Object],PMT i PV = Present Value of a Perpetuity

[object Object],= $125,000 PMT i PV = = $10,000 .08

Ordinary Annuity vs. Annuity Due $1000 $1000 $1000 4 5 6 7 8

Begin Mode vs. End Mode 1000 1000 1000 4 5 6 7 8

year year year 5 6 7 Begin Mode vs. End Mode 1000 1000 1000 4 5 6 7 8

year year year 5 6 7 Begin Mode vs. End Mode 1000 1000 1000 4 5 6 7 8 PV in END Mode

year year year 5 6 7 Begin Mode vs. End Mode 1000 1000 1000 4 5 6 7 8 PV in END Mode FV in END Mode

year year year 6 7 8 Begin Mode vs. End Mode 1000 1000 1000 4 5 6 7 8

year year year 6 7 8 Begin Mode vs. End Mode 1000 1000 1000 4 5 6 7 8 PV in BEGIN Mode

year year year 6 7 8 Begin Mode vs. End Mode 1000 1000 1000 4 5 6 7 8 PV in BEGIN Mode FV in BEGIN Mode

[object Object],[object Object],[object Object], 1000 1000 1000 Earlier, we examined this “ordinary” annuity: 0 1 2 3

[object Object],[object Object],[object Object],[object Object],1000 1000 1000 What about this annuity? 0 1 2 3

Future Value - annuity due If you invest $1,000 at the beginning of each of the next 3 years at 8%, how much would you have at the end of year 3? 0 1 2 3

[object Object],[object Object],[object Object],[object Object],Future Value - annuity due If you invest $1,000 at the beginning of each of the next 3 years at 8%, how much would you have at the end of year 3? 0 1 2 3 -1000 -1000 -1000

Future Value - annuity due If you invest $1,000 at the beginning of each of the next 3 years at 8%, how much would you have at the end of year 3? ,[object Object],[object Object],[object Object],[object Object],0 1 2 3 -1000 -1000 -1000

Future Value - annuity due If you invest $1,000 at the beginning of each of the next 3 years at 8%, how much would you have at the end of year 3? ,[object Object],[object Object],[object Object]

Future Value - annuity due If you invest $1,000 at the beginning of each of the next 3 years at 8%, how much would you have at the end of year 3? ,[object Object],[object Object],[object Object],[object Object],[object Object],(1 + i)

Future Value - annuity due If you invest $1,000 at the beginning of each of the next 3 years at 8%, how much would you have at the end of year 3? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],(1 + i) (1.08)

Present Value - annuity due What is the PV of $1,000 at the beginning of each of the next 3 years, if your opportunity cost is 8%? 0 1 2 3

[object Object],[object Object],[object Object],[object Object],Present Value - annuity due What is the PV of $1,000 at the beginning of each of the next 3 years, if your opportunity cost is 8%? 0 1 2 3 1000 1000 1000

Present Value - annuity due ,[object Object],[object Object],[object Object]

Present Value - annuity due ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],(1 + i)

Present Value - annuity due ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],(1 + i) (1.08)

[object Object],[object Object],Uneven Cash Flows 0 1 2 3 4 -10,000 2,000 4,000 6,000 7,000

[object Object],Uneven Cash Flows 0 1 2 3 4 -10,000 2,000 4,000 6,000 7,000

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],0 1 2 3 4 -10,000 2,000 4,000 6,000 7,000

Example ,[object Object],0 1 2 3 4 5 6 7 8 0 0 0 0 40 40 40 40 40

[object Object],0 1 2 3 4 5 6 7 8 0 0 0 0 40 40 40 40 40

[object Object],[object Object],[object Object],0 1 2 3 4 5 6 7 8 0 0 0 0 40 40 40 40 40

119,624 0 1 2 3 4 5 6 7 8 0 0 0 0 40 40 40 40 40

[object Object],[object Object],[object Object],[object Object],119,624 0 1 2 3 4 5 6 7 8 0 0 0 0 40 40 40 40 40

119,624 69,226 0 1 2 3 4 5 6 7 8 0 0 0 0 40 40 40 40 40

[object Object],119,624 69,226 0 1 2 3 4 5 6 7 8 0 0 0 0 40 40 40 40 40

Retirement Example ,[object Object],0 1 2 3 . . . 360 400 400 400 400

0 1 2 3 . . . 360 400 400 400 400

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],0 1 2 3 . . . 360 400 400 400 400

Retirement Example If you invest $400 at the end of each month for the next 30 years at 12%, how much would you have at the end of year 30? ,[object Object],[object Object],[object Object]

Retirement Example If you invest $400 at the end of each month for the next 30 years at 12%, how much would you have at the end of year 30? ,[object Object],[object Object],[object Object],[object Object],[object Object]

Retirement Example If you invest $400 at the end of each month for the next 30 years at 12%, how much would you have at the end of year 30? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],House Payment Example

House Payment Example ,[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],0 1 2 3 . . . 360 ? ? ? ?

House Payment Example ,[object Object],[object Object],[object Object]

House Payment Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

House Payment Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],Team Assignment

[object Object],[object Object],[object Object],[object Object],27 28 29 30 31 32 33 34 35 250 250 250 250 250

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],27 28 29 30 31 32 33 34 35 250 250 250 250 250

[object Object],27 28 29 30 31 32 33 34 35 250 250 250 250 250 1,042,466

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],27 28 29 30 31 32 33 34 35 250 250 250 250 250 1,042,466

Session2 Time Value Of Money (2)

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