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Aswath Damodaran
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Present Value
Aswath Damodaran
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Intuition Behind Present Value
n
There are three reasons why a dollar tomorrow is worth less than a
dollar today
•
Individuals
prefer present consumption to future consumption. To
induce people to give up present consumption you have to offer them
more in the future.
•
When there is
monetary inflation, the value of currency decreases over
time. The greater the inflation, the greater the difference in value between
a dollar today and a dollar tomorrow.
•
If there is any
uncertainty (risk) associated with the cash flow in the
future, the less that cash flow will be valued.
n
Other things remaining equal, the value of cash flows in future time
periods will decrease as
•
the preference for current consumption increases.
•
expected inflation increases.
•
the uncertainty in the cash flow increases.
Aswath Damodaran
3
Discounting and Compounding
•
The mechanism for factoring in these elements is the discount rate.
•
Discount Rate:
The discount rate is a rate at which present and future
cash flows are traded off. It incorporates 
(1) Preference for current consumption (Greater .
...Higher Discount Rate)
(2) expected inflation (Higher inflation
....
Higher Discount Rate)
(3) the uncertainty in the future cash flows (Higher Risk.
...Higher Discount Rate)
•
A higher discount rate will lead to a lower value for cash flows in the
future.
•
The discount rate is also an opportunity cost, since it captures the returns
that an individual would have made on the next best opportunity.
•
Discounting future cash flows converts them into cash flows in present
value dollars. Just a discounting converts future cash flows into present
cash flows,
•
Compounding converts present cash flows into future cash flows.
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Present Value Principle 1
n
Cash flows at different points in time cannot be compared and
aggregated. All cash flows have to be brought to the same point in
time, before comparisons and aggregations are made.
Aswath Damodaran
5
Cash Flow Types and Discounting Mechanics
n
There are five types of cash flows 
•
simple cash flows,
•
annuities,
•
growing annuities
•
perpetuities and
•
growing perpetuities
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I.Simple Cash Flows
n
A simple cash flow is a single cash flow in a specified future time
period.
Cash Flow:
CF
t
_______________________________________________
Time Period:
t
n
The present value of this cash flow is
PV of Simple Cash Flow = CF
t
/ (1+r)
t
n
The future value of a cash flow is 
FV of Simple Cash Flow = CF
0
(1+ r)
t
Aswath Damodaran
7
Application 1:
The power of compounding 
Stocks, Bonds and Bills
n
Ibbotson and Sinquefield, in a study of returns on stocks and bonds
between 192692 found that stocks on the average made 12.4%,
treasury bonds made 5.2% and treasury bills made 3.6%.
n
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This note was uploaded on 03/01/2012 for the course FINS 3641 taught by Professor Hyip during the Three '11 term at University of New South Wales.
 Three '11
 hyip

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