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Learning Center Experience
By Jerry Taylor, Full-Time Faculty, Kaplan University Published March 2015
At the heart of finance, accounting,
economics, business, government, and families is MONEY. I do not mean it is the
value system, the faith, or the reason for living. I’m talking strictly about
the measurement system. Finance, accounting, and economics measure it or
measure with it for their very existence as disciplines. Business, government,
and families achieve whatever programs or adventures they wish to pursue
generally with it. Business builds new plants or creates new product;
government pursues the next best boondoggle; and families feed, clothe,
shelter, educate, and entertain with it.
We focus on many financial matters
in our classes including financial markets. Many of you may think the financial
market sounds like a formidable place and that the concept must be terribly
complicated. Actually it is amazingly simple. A financial
market is a place where people come together to lend and borrow MONEY
(people who need money meet up with people who have money). This
is then the first characteristic or function of a financial market—it is a
conduit between those participants who might want to lend (or invest) money at
a particular time point and those who might want to borrow money at the same
point. The lending and borrowing of money extend the financial market into the
dimensions of time and uncertainty.
The basic second function of
financial markets is setting the market interest rate, the price of money.
Interest is a payment by the borrower to the lender for the use of the lender’s
money during a period of time. Time is the first challenge to both parties:
those who have funds and no preference to spend these funds NOW, and those
without funds who find it appropriate, for whatever reason, to spend these
funds NOW. The first party needs a place to protect their resources from
inflation so that their money maintains value while they are not using it for
consumption. The second party has a priority that makes the paying of some
interest for the time they will use the resources worthwhile to them. The
longer the borrower wants to use the lender’s funds the more compensation the
lender will seek … generally.
Next the market (and lender) must
consider the nature or the opportunity (the borrower) taking into consideration
all sorts of variable to determine the risk
(uncertainty) involved in the financial event. What is risk? It is the chances
the lender will not recover his money?
When determining interest rates
lenders consider two factors: (1) the risk free rate and (2) the risk premium. The
formula for determining the interest rate is:
(i) = Risk free rate (Rf) + Risk Premium (Rp)
Time can also play a role in
determining the Rf and Rp. The most "risk-less" investments in our
economy are U.S. government securities. The pricing of these securities
contemplates time (you frequently hear quotes on 5-, 10-, and 30-year
government bonds.) Time is what differentiates the interest rate on these
investments as they are viewed as risk free. The Rp can also include additional
"charges" for time risk.
So let’s move on to some math, the
Time Value of Money.
Let’s assume that:
PV is a present value or the initial amount of loan
FV is a future amount (future value)
i equals the interest rate per time period
n is the number of time periods
If you borrow $200 for 1 year and
agree to repay the lender $220 at the end of the year, the interest cost of
borrowing is $20.
The formula to calculate the rate of
interest (i) is:
= .10 or 10% per year.
All the mechanics of compound
interest are illustrated in this simple example. There are two cash flows of
importance here, the initial inflow of cash of $200 and the payment, 1 year
later of $220. So using our variables, this example could be expressed as:
= PV + interest payment
And since the interest payment is
usually expressed as a rate or percent (i) of the amount borrowed (PV) then:
= PV + (PV x i)
Which can be rearranged (simplified)
= PV (1 + i)
= 200 (1 + .10)
= 200 + 20
Now we can calculate the compounding
over time by simply adding the "n" as an exponent to the equation.
= PV (1 + I)n
Now you can determine any one of
these variables if you know the others. If you know the future value and the
term (number of years or periods) and the interest rate you can determine the
PV, initial or present value. It is the same with all the variables. Try it out
with our example expanding the period to 3 years.
= $200 (1 + 10%)^3
First let’s do the exponent portion
(1 + .10)3 that is 1.1 x 1.1 x 1.1 = 1.331, multiply that times $200
and you get $266.20. Why isn’t it $260? Because you get interest on the
interest that is owed you. That is the nature of compounded interest
versus simple interest. You can now insert any interest rate, term, and initial
value to determine a future value.
You can calculate the present value
(our initial value) of a future payment buy rearranging the same formula.
= FV / (1 + i)n .... FV divided by (1 + i)n
In our example:
= $266.20 / 1.331 = $200
All methods of time value analysis
have their roots in this simple formula. Today calculators and computers do
these calculations and the more complex events with monthly, quarterly, or
yearly cash flows. This formula is at the heart of the computer formula and the
other payment schedules.
One more easy adjustment. We have
been calculating values "compounding annually," meaning the interest
is calculated once per year. Many times today financial instruments compound
quarterly, or monthly, or even daily. The adjustment to our formula is easy. You
divide "i" by the number of periods in the year—for example,
quarterly is by 4, monthly by 12, daily by 365—and you multiply "n"
by the same factor.
So in our 3 year 10% example, if
interest were compounded quarterly we would divide 10% by 4 = 2.5% and multiply
3 years by 4 = 12 periods. So instead of charging 10% interest for 3 years we
would be charging 2.5% interest for 12 periods. So:
= $200 (1 + 2.5%)^12
= $200 x 1.34489
The added compounding generated
$2.77 more interest over the 3 years. Not much, unless we were talking about
$200 million and of course in the big picture we often are. Try doing the compounding
monthly yourself and let's see what you get.
Here too, PV = FV/(1+i)^n ... try it
PV = 268.97/1.34489 = $200, so the present value of $268.97 paid to you in 3
years if the discount rate was 10% compounded quarterly would be $200. On a
Time Value of Money basis these two amounts $200 and $268.97 would be equal to
one another if the $200 was paid to you today versus the $268.97 was to be paid
to you in 3 years if the interest rate environment was 10% compounded
Internal rate of return and net present value
functions that determine the value of companies in acquisitions and the market,
and the financial priority of vast numbers of capital projects in corporations
all over the world are deeply rooted in this formula. They are all based on the
time value of money.
Jerry Taylor is a full-time faculty member at Kaplan University.
The views expressed in this article are solely those of the author and do not
represent the view of Kaplan University.
By Cynthia Waddell, PhD, CPA, CFE
By Geoffrey Vanderpal, Full-Time Faculty
By Richard Carter, PhD
By Stanley W. Self, CFE
By Jerry Taylor
By Rachel Byers, Full-Time Faculty, School of Business
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