3 TVM Damodaran.ppt - The Tools of Corporate Finance...

Aswath Damodaran
The Tools of Corporate Finance
Present Value
Financial Statement Analysis
Fundamentals of Valuation

Aswath Damodaran
Present Value
Aswath Damodaran

Aswath Damodaran
Intuition Behind Present Value

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.

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.

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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.

Aswath Damodaran
Present Value Principle 1

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.

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Time Lines
0 1 2 3
4
$ 100 $ 100 $ 100 $ 100
Figure 3.1: A Time Line for Cash Flows: $ 100 in Cash Flows Received
at the End of Each of Next 4 years
Cash Flows
Year

Aswath Damodaran
Cash Flow Types and Discounting Mechanics

There are five types of cash flows -

simple cash flows,

annuities,

growing annuities

perpetuities and

growing perpetuities

Aswath Damodaran
I.Simple Cash Flows

A simple cash flow is a single cash flow in a specified future time
period.
Cash Flow: CF
t
_______________________________________________|
Time Period: t

The present value of this cash flow is-
PV of Simple Cash Flow = CF
t
/ (1+r)
t
 The future value of a cash flow is -
FV of Simple Cash Flow = CF
0
(1+ r)
t

Aswath Damodaran
Application: The power of compounding -
Stocks, Bonds and Bills

Between 1926 and 1998, Ibbotson Associates found that stocks on the
average made about 11% a year, while government bonds on average
made about 5% a year.