C
HAPTER
14
T
IME
V
ALUE
OF
M
ONEY
14.1
I
NTEREST
, C
OMPOUNDING
,
AND
C
ASH
F
LOW
D
IAGRAMS
*
S
IMPLE
I
NTEREST
& C
OMPOUND
I
NTEREST
The two most basic parameters affecting the real value of money is
interest rate and time.
You've heard the comment "…all it takes is time
and money…" Well, they go together.
The value of money is time
dependent; value is always changing with time.
The key is to determine
the equivalent value of alternatives at a common point in time.
Or, some
present value is equal to some future sum of payments.
This is called
equivalenc
e.
Equivalence is the basis of the preceding examples where
investors were deciding whether to invest in your company or to allow an
improvement to increase productivity in an existing company, putting
values to the same point in time as impacted by inflation, loan interest
rates, or required rates of return.
First, what is
interest
? Interest is defined as the return on an
investment or the fee charged by a lender by a borrower for the use of
borrowed money, and which definition you use depends on whether you
are in the position of the lender or the borrower.
Most commonly the
interest is expressed as a percentage of the borrowed money, and a
compounding period is also specified.
An example of this would be 8%
interest compounded monthly.
The interest if there are no compound
periods is called
simple interest
and interest over multiple compound
periods is called
compound
interest
.
The interest rate applicable in an economic transaction is affected by
the perceived risk or probability of nonpayment in the transaction.
A
bank may lend money to a low risk customer at 7.5%, but an
entrepreneur may have to borrow money at much higher rates from
potential investors, since high risk and bank loans are mutually
exclusive.
An interest rate has three components:
1.
A riskfree component based on an economic concept called the
marginal productivity of capital.
Many economists believe this
1
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Chapter 14  Time Value of Money
rate is about 3 or 4 percent in a riskfree and inflation free
environment.
2.
A risk component to compensate for uncertainty or the
possibility of nonpayment.
3.
An inflation component applicable in periods of inflation.
In
periods of inflation, lenders demand higher rates of return to
compensate for the decline in purchasing power between the
time money is lent and the time it is paid.
Simple Interest
Simple interest is interest earned only on the original principal.
The
formula for calculating simple interest or earnings is
n
i
P
E
⋅
⋅
=
where,
E = simple interest or earnings
P = principal (amount borrowed or lent)
i = interest rate per year
n = number of years or fraction thereof
Example 14.1 – simple interest
If you borrow $100 for one year at 10% per annum, the interest for
the year is
E = ($100)(0.10)(1) = $10
If you borrow $100 for 3 months at 10%, the interest is (note the
assumption is made of 10% per annum, so 3 months is 3/12 or 0.25).
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 Spring '09
 Timmons
 Interest Rates

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