Download - Time Value of Money
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***Rashmi Chaudhary***
Lawrence Gitman
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***Rashmi Chaudhary***
Which is more Valuable?
1000 $ now
1000 $ after 2 years
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***Rashmi Chaudhary***
Money NOW
is worth more than
money LATER!
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***Rashmi Chaudhary***
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
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***Rashmi Chaudhary***
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
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***Rashmi Chaudhary***
Time Line
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***Rashmi Chaudhary***
• 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)
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***Rashmi Chaudhary***
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***Rashmi Chaudhary***
Types of
Cash Flows
Single Amounts
Annuities
(a stream of equal
periodic cash flows)
Mixed Stream
(a stream of
unequal cash
flows )
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***Rashmi Chaudhary***
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
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***Rashmi Chaudhary***
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.
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***Rashmi Chaudhary***
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
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***Rashmi Chaudhary***
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***Rashmi Chaudhary***
Future value Relationship (Interest rates, time periods, and future value
of one dollar)
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***Rashmi Chaudhary***
Present Value of a Single
Amount
The process of finding present
value is often referred as
discounting cash flow
Inverse of compounding
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***Rashmi Chaudhary***
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
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***Rashmi Chaudhary***
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***Rashmi Chaudhary***
Comparing Present Value and
Future Value
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***Rashmi Chaudhary***
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***Rashmi Chaudhary***
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***Rashmi Chaudhary***
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.
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***Rashmi Chaudhary***
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***Rashmi Chaudhary***
Future Value of an Ordinary
Annuity
FVAn=PMT X (FVIAi,n)
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***Rashmi Chaudhary***
Frank wishes to determine how much money he will have at the end of 5 years if he chooses annuity A. i=7%
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***Rashmi Chaudhary***
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***Rashmi Chaudhary***
Present Value of an ordinary
annuity
PVAn= PMT X (PVIFAi,n)
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***Rashmi Chaudhary***
Braden wants to know what
should it most pay to receive $700
at the end of each year
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***Rashmi Chaudhary***
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***Rashmi Chaudhary***
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)
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***Rashmi Chaudhary***
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.
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***Rashmi Chaudhary***
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***Rashmi Chaudhary***
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***Rashmi Chaudhary***
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.
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***Rashmi Chaudhary***
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***Rashmi Chaudhary***
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***Rashmi Chaudhary***
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
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***Rashmi Chaudhary***
Have a nice Day…………….
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***Rashmi Chaudhary***