Time Value of Money Tutorial

Time Value of Money Tutorial

Prepared byRonald Moy

Tobin College of BusinessSt. John’s University

Solving Time Value of Money Problems

• To solve a time value of money problem, you need to ask yourself a number of questions in order to determine which formula you will be using.

Let’s Begin*

* Please view as a slideshow

Type of Cash Flow

• Is the amount one lump sum of money?

Yes No

Present or Future Value

• Are you trying to determine what something is worth in the future or what some future amount is worth today?

Worth Today Worth in the Future

Previous slideBeginning of tutorial

Annuity or Multiple Cash Flow

• Will you be paying (or receiving) an equal sum of money made at equal intervals?

Yes No

Previous slideBeginning of tutorial

Ordinary Annuity or Annuity Due?

• Is the first cash flow at the beginning of the period or at the end of the period?

Beginning End

Previous slide Beginning of tutorial

Present or Future Value

• You are finding the value of multiple cash flows. Are you looking for the value of these cash flows in the future or the value today?

Value in the Future Value Today

Previous slide Beginning of tutorial

Future Value of Multiple Cash Flows

• The future value of multiple cash flows is

Previous slide ExampleBeginning of tutorial

)()3(3

)2(2

)1(1 )1(...)1()1()1( tt

tttt rCrCrCrCFV

Annuity Due

• You are dealing with an annuity due. Are you looking for the value of the annuity in the future or what the annuity is worth today?

Worth in the Future Worth Today

Previous slide Beginning of tutorial

Present Value of Multiple Cash Flows

• You are finding the present value of multiple cash flows

Previous slide ExampleBeginning of tutorial

tt

33

221

)r1(

C...

)r1(

C

)r1(

C

)r1(

CPV

Ordinary Annuity

• You are dealing with an ordinary annuity. Are you looking for the value of the annuity in the future or what the annuity is worth today?

Worth in the Future Worth Today

Previous slide Beginning of tutorial

Present Value of Ordinary Annuity• You are looking for the present value of an

ordinary annuity. The present value of an annuity formula is,

Previous slide ExampleBeginning of tutorial

r)r1(

11

CPVt

Present Value of Annuity Due• You are looking for the present value of an

annuity due. The present value of an annuity formula is,

Previous slide ExampleBeginning of tutorial

r1r)r1(

11

CPVt

Future Value of Ordinary Annuity

• You are looking for the future value of an ordinary annuity. The formula for the future value of an annuity is

Previous slide ExampleBeginning of tutorial

r

1)r1(CFV

t

Future Value of Annuity Due

• You are looking for the future value of an annuity due. The formula for the future value of an annuity is

Previous slide ExampleBeginning of tutorial

r1r

1)r1(CFV

t

Present Value of a Lump Sum• You are looking for the present value of a lump

sum. The present value for a lump sum is

Previous slidePresent value example

Beginning of tutorial

t)r1(

FVPV

Future Value of a Lump Sum

• You are looking for the future value of a lump sum. The future value of a lump sum is,

Previous slide Future Value exampleBeginning of tutorial

t)r1(PVFV

Future Value a Lump Sum Example

• Find the future value in 10 years of $100 received today, if the interest rate is 8%.

Previous slide FV CalculatorBeginning of tutorial Timeline example

89.215$)08.1(100$FV 10

Future Value Time Line

• Previous slide Beginning of tutorial

19

0 1 2 3 4 10

$215.89 $100

. . .

Present Value of a Lump Sum Example

• Find the present value of $1,000 received 5 years from today if the interest rate is 9%.

Previous slide Calculator exampleBeginning of tutorial Timeline example

93.649$)09.1(

000,1$PV

5

Present Value Time Line

Previous slide Beginning of tutorial

0 1 2 3 4 5

$1,000

$649.93

Present Value of an Ordinary Annuity

• You can afford to make monthly car payments of $500 per month for 48 months. If the interest rate is 12% (1% per month). How much can you afford to spend on a car? Assume that the first car payment will be made in one month.

Previous slide Calculator exampleBeginning of tutorial

98.986,18$01.)01.1(1

1500$PV

48

Present Value of an Annuity Due Example

• You can afford to make monthly car payments of $500 per month for 48 months. If the interest rate is 12% (1% per month). How much can you afford to spend on a car? Assume that the first car payment will be made today.

Previous slide Calculator exampleBeginning of tutorial

85.176,19$)01.1(01.)01.1(1

1500$PV

48

Future Value of an Ordinary Annuity Example

• Suppose you want to start saving next year for your retirement. You save $1,000 per year for the next 40 years. If the interest rate is 10%, how much will you have in your account after you make the last deposit?

Previous slide Calculator exampleBeginning tutorial

56.592,442$10.

1)10.1(000,1$FV

40

Future Value of an Annuity Due Example

• Suppose you want to start saving today for your retirement. You save $1,000 per year for the next 40 years. If the interest rate is 10%, how much will you have in your account after you make the last deposit?

Previous slide Calculator exampleBeginning of tutorial

82.851,486$)10.1(10.

1)10.1(000,1$FV

40

Present Value of Multiple Cash Flows Example

• You are considering an investment that will pay you $1,000 in one year, $2,000 in two years and $3,000 in three years. If you want to earn 10% on your money, how much would you be willing to pay?

Previous slide Calculator exampleBeginning of tutorial Timeline example

93.815,4$)10.1(

000,3$

)10.1(

000,2$

)10.1(

000,1$PV

32

PV Time Line – Multiple Cash Flows

Previous slide Beginning of tutorial27

0 1 2 3 4

1,000 2,000 3,000909.09

1,652.89

2,253.94

4,815.92

Future Value of Multiple Cash Flows Example

• Suppose you invest $500 in a mutual fund today and $600 in one year. If the fund pays 9% annually, how much will you have in two years?

Previous slide Timeline exampleBeginning of tutorial

05.248,1$)09.1(600$)09.1(500$ 2 FV

FV Time Line – Multiple Cash Flows

Previous slideBeginning of

tutorial

29

$500

0 1 2 3 4 5

$600

$654.00

$594.05

$1,248.05

PV Calculator• Calculator solution

Previous slide Beginning of tutorial

N I/Y PMT PV FV

5 9 1000

CPT PV 649.93

FV Calculator• Calculator solution

Previous slide Beginning of tutorial

N I/Y PMT PV FV

10 8 -100

CPT FV 215.89

Calc Ex. PV Ordinary Annuity• Calculator solution• Make sure calculator is set for “END”

– Set by 2nd BGN 2nd Enter

Previous slide Beginning of tutorial

N I/Y PMT PV FV

48 1 500

CPT PV 18,986.98

Calc Ex PV Annuity Due

• Calculator solution• Make sure calculator is set for “BEG”

– Set by 2nd BGN 2nd Enter

Previous slide Beginning of tutorial

N I/Y PMT PV FV

48 1 500

CPT PV 19,176.85

Calc Ex FV Ordinary Annuity

• Calculator solution• Make sure calculator is set for “END”

– Set by 2nd BGN 2nd Enter

Previous slide Beginning of tutorial

N I/Y PMT PV FV

40 10 1000

CPT FV 442,592.56

FV Annuity Due• Calculator solution• Make sure calculator is set for “BEG”

– Set by 2nd BGN 2nd Enter

Previous slide Beginning of tutorial

N I/Y PMT PV FV

40 10 1000

CPT FV 486,851.82

PV Multiple Cash Flows

• In this case, you will use the Cash Flow Worksheet on the calculator.– CF– CF0 – CF01 1000 Enter– F01 – CF02 2000 Enter– F02 – CF03 3000 Enter – F03 – NPV 10 Enter– CPT 4,815.93 Previous slide Beginning of tutorial