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I. FIRST PRINCIPLES OF VALUATION
Always remember: A dollar (euro) in the hand today is worth more than a dollar
(euro) promised some time in the future, i.e., money has time value!
If you have it today, you can invest it or use it.
It is rather difficult to invest or use a
promise of some future funds.
A.
Future Value and Compounding
•
Investing for single period
FV = P(1+r),
where P = principal invested, and r = the
interest rate on the investment.
What is the FV of $500 invested for one year at 10%; FV = $500(1.10)
= $550.
•
Investing for more than one period
FV = P(1+r)
t,
where t = the number of periods in the
future
What is the FV of $500 invested for 2 years at 10%; FV = $500(1.10)
2
= $500(1.21) = $605
Note: there are two elements in the $105 interest;
o
There is the interest on the principal; $50 each year (total
$100), and
o
There is the interest on the first year’s interest; $50 x .10 = $5
This is the result of compounding.
For example, the same $500 left on
deposit for 5 years, at simple and compound interest would be, after 5
years:
Simple interest: $750
Compound interest: $805
How does one calculate the factor (1+r)
t
?
You can do it manually,
using your calculator, your computer or the Future Value Tables
(found, along with Present Value and Annuity Tables, in most basic
financial management textbooks).
•
The Financial Tables
o
For any interest rate and time period, the table will give the
value of $1 for that number of periods in the future.
1
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View Full Document B.
Present Value and Discounting
•
What is Present Value?
It is the current value of a future cash flow(s), discounted at an
appropriate discount factor (or interest rate).
This follows the same
principle as compounding.
Alternatively:What will we need today, invested at that same rate, to
give us an amount equal to the future cash flow?
Recall that FV = P(V)(1+r)
t
; let’s do some simple algebra, then
PV = FV/(1+r)
t
,
where r is the discount rate for t periods of time
in the future
•
Let’s look at a single period example:
An antique auto dealer can buy a “mint condition” 1928 Bugatti auto
for $60,000.
He is certain
that he can resell the car in one year for
$70,000.
He also has the opportunity to make a wellcollateralized
loan to an acquaintance for one year at 12% (assume essentially no
risk).
What should he do?
Before solving this problem, let’s introduce the concept of
“Opportunity Cost
.”
Opportunity cost is simply the best alternative
financial opportunity that exists, at the same risk level as the one
under consideration.
In the auto example, it is the 12% certain, that
he can earn on the loan.
Therefore, the appropriate discount rate is
12%.
PV = $70,000/(1+0.12) = $62,500 vs. the $60,000 that he must pay for
the car today.
If he made the loan, then his PV (at 12%, of course) is
$60,000.
(If he makes the loan to his acquaintance, he will receive in
one year $67,200 – his $60,000 plus the 12% interest, or $7200.
$67,200/1.12) = $60,000.)
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This note was uploaded on 11/16/2011 for the course ECO 2023 taught by Professor Rush during the Spring '08 term at University of Florida.
 Spring '08
 Rush
 Macroeconomics

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