Time Value of Money
Business and personal financial decisions that involve cash flows occur at different points
in time require an understanding of the time value of money. The concepts introduced
here are important for solving business financial problems as well as personal financial
problems.
Mastering this topic is a prelude to tackling other topics in finance.
These
other topics include: (1) valuation of securities and other assets; (2) capital budgeting; (3)
cost of capital.
The basic concept of the time value of money is that you must compensate lenders for the
use of their money by paying them interest.
For instance, if I said to you "Lend me
$1000 for one year and in one year I will pay you $1000", you would not agree to this.
You would expect to be paid something
greater
than $1000.
You need to be
compensated for giving up the use of your money for one year.
So that the amount I
would have to pay you back
must
be greater than the amount I borrowed.
Put another way:
Future Value must always be greater than Present Value
and
Present Value must always be less than Future Value
Future Value
is the value of some amount at some point of time in the future
Present Value
is the value of something
today
.
So let's see explicitly what we mean:
I.
In borrowing or lending money, the amount due can be calculated using simple
interest or compound interest.
A.
The principal is the amount of money borrowed or invested, the term of a
loan is the length of time or number of periods the loan is outstanding, and
the rate of interest is the percent of the principal the borrower pays the
lender per time period.
B.
Simple interest is the interest paid on the principal sum only:
I = PV
0
*
i
*
n
where I = simple interest in dollars, PV
0
= present value which is principal
amount at time 0, i = interest rate per time period, and n = number of time
periods.
1
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The future value (amount due at time n) using simple interest is:
FV
n
= PV
0
+ I
FV
n
= PV
0
+ (PV
0
* i * n) = PV
0
[1 + (i * n)]
II.
Compound interest refers to process where interest earned on principal is
converted into interestearning principal.
That is, the interest that was earned in
previous compounding periods is part of the principal on which interest is earned.
The amount of interest due each period is the interest rate times the principal
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 Spring '11
 Spencer
 Time Value Of Money, Interest

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