Time Value of Money

***Rashmi Chaudhary***

Lawrence Gitman


Which is more Valuable?

1000 $ now

1000 $ after 2 years


Money NOW

is worth more than

money LATER!


Future Value Versus Present Value

Financial decisions are based on either future value or present value

• Future value- cash you will receive

at a future date

• Present value- cash

in hand today


Time Line

Horizontal line on which time

zero appears at the left most

end and future periods are

marked from left to right

Used to depict investment cash

flows


Time Line


• Future value- value at future date of a

present amount deposited and earning

specified interest rate. (Compounding)

• Present value-The current value of a

future amount. The amount that have to be

invested today at a given interest rate over

a specified period for a future amount.

(Discounting)


Types of

Cash Flows

Single Amounts

Annuities

(a stream of equal

periodic cash flows)

Mixed Stream

(a stream of

unequal cash

flows )


Future value of Single Amount

The General equation for the future value at end of period n is

FVn= PV X (1+i)n

Where,FVn= Future value at the end of

period n

PV= Present Value

i= annual rate of interest paid

n= number of periods that money is left

for deposits


Example

Jane places $800 in a saving account paying 6% interest compounded annually. She wants to know how much money will be in account at the end of 5 years.


Now in this example

PV = $800, i = 0.06, n = 5

So,

FVn= PV X (1+i)n

FV5= $800 X (1+0.06)5=$1070.40


Future value Relationship (Interest rates, time periods, and future value

of one dollar)


Present Value of a Single

Amount

The process of finding present

value is often referred as

discounting cash flow

Inverse of compounding


Example

Pam wishes to find the present value of $1700 that will be received 8 years from now. Opportunity cost is 8%

We know,FVn= PV X (1+i)n

so,PV= FVn = $1700 = $918.42

(1+i)n (1+8)8


Comparing Present Value and

Future Value


Types of Annuities

• Ordinary Annuity -

cash flows occur at

the end of each

period

• Annuity Due- cash

flows occur at the

beginning of each

period.


Future Value of an Ordinary

Annuity

FVAn=PMT X (FVIAi,n)


Frank wishes to determine how much money he will have at the end of 5 years if he chooses annuity A. i=7%


Present Value of an ordinary

annuity

PVAn= PMT X (PVIFAi,n)


Braden wants to know what

should it most pay to receive $700

at the end of each year


Annuity Due

Future value of an annuity due

FVIAi,n(Annuity due)= FVIAi,n X (1+i)

Present value of an annuity due

PVIFAi,n(annuity due)= PVIFAi,n X (1+i)


Future value of a Mixed Stream

Shrell expects a stream of mixed cash flows over the next five years and expects to earn 8%. What will be earned after five years if cash flows are immediately invested.


Present value of a mixed stream

Frey has an opportunity of receving mixed stream cash flows over 5 years. If he must earn 9%, what is the most he should pay.


Application of time Value

Determining deposits needed to

accumlate a future amount

Determination of equal periodic

loan payments

EMI’s

Finding interest rates

Finding an unknown number of

periods


Have a nice Day…………….

Time Value of Money

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