Ch.9 The basic tools of finance
Definition of finance: the field that studies how people make decision regarding
the allocation of resources over time and the handling of financial risk.
Measuring the time value of money
•
Having money in your pocket today is more valuable having the same
amount in your pocket in the future.
•
For example, I would very much rather have 10 000$ today than in 10
years.
•
However, would I prefer 10 000$ today or 15 000$ in 10 years? Not clear.
•
Prefer 10 000$ because I could then lend the money at a 0.05 rate and
get 16 300$ five years from now.
•
What if the prevailing rate is 4%? PV= 10 133.46$. therefore I should
prefer to take the 15 000 now.
•
The point is that economists need tools to compare the value of money
over time.
Future Value
•
Suppose you put Y dollars in the bank today at an interest rate “r” (e.g.,
r=0.05). Assume no tax.
•
Suppose that interest is paid annually and that the interest – a process
called compounding.
•
Question: What is the future value (FV) of Y after N years?
•
After 1 year: Y + rY = Y(1+r)
•
After 2 years: Y(1+r)+ rY(1+r)= Y(1+r)(1+)= Y(1+r)
2
•
After 3 years: Y(1+r)
2
+ r Y(1+r)
2
= Y(1+r)
2
(1+r) = Y(1+r)
3
•
So if the prevailing interest is r, the value of Y dollars N years from now is:
FN= Y(1+r)
N
Present Value
•
PV refers to the amount of money today that would be needed to produce
using prevailing interest rates, a given future amount of money.
•
PV= FV/ (1+r)
N
Compounding factor or
PV= FV (1/(1+r)
N
Discounting factor
•
Question: What is the PV of 15 000$ in 10 years if the prevailing interest
rate is 5%?
•
PV= FV/(1+r)
N
= 15 000/ (1.05)
10
= 9 803.92$
•
The concept of present value demonstrates the following:
1.
Receiving a given sum of money in the present is preferred to
receiving the same sum in the future.
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 Fall '09
 KOPPEL
 Time Value Of Money

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