Simply put, time value of money proceeds from the notion
that a dollar today is not worth the same as a dollar tomorrow or the day next
(Correia, Flynn, Uliana&Wormald, 2008). Faced with a decision to choose
between receiving $ 1000 today or one year from now, most people will prefer to
receive it today. For one, failing to receive the $1000 now will mean that
there is some consumption that has to be forgone and there is value in that
consumption. Similarly, a business that loses an investment due to a failure to
receive $ 1,000 today incurs opportunity cost. Inflation also acts to reduce
the purchasing power of the $ 1,000. Also important is the fact that opting to
receive money in the future has risks.
Importance to the Financial Manager
Financial managers have to evaluate financial
transactions involved in valuing uncertain future cash flows (Bierman &
Smidt, 2006). Such valuations are complicated by the fact that there is always
a time value to money. Financial managers are, therefore, better able to
evaluate alternative projects using the concept of time value of money. Mangers
can recommend or advise against proceeding with a project depending on their
assessment of the future cash flows. Besides, financial managers must also make
decisions regarding credit terms with their customers and the knowledge of time
value of money becomes very important in setting appropriate interest rates.
Present/Future values and their determination
This is the value in present terms of some future amount
of money when evaluated at a given interest rate. On its part, future value is
the value of an amount today at a future point in time when evaluated at a
given rate. This given rate can be of interest, return or even inflation. It is
easier to understand the determination of future value before moving on to that
of present value.
Future value
For calculations that involves only a single period, the
future value is simply the value of the given amount plus the simple interest
earned on it.
Thus, for a principal amount (P) the Future
Value (FV) at a given interest rate(r) at the end of a single time period (t)
is just P+Simple Interest.
Take the example of $1000 deposited in an interest
earning account at a rate of 5% in one year.
P=$, 1000, r=5%
Thus, FV=$1000+ (1000
0.05)
0.05)
FV=$1,050
Calculating the FV for the next year will
also involve going over the whole process while taking the FV from the first
year as the P.
Thus, FV (second year) =$1050+ (10500.05)
0.05)
FV (Second Year) =$1102.50
It is apparent from the above calculations that even as
the initial $1,000 earns interest the interest on it also earns interest. This
makes the method above to be very cumbersome when one has to do the
calculations over a long period of time. That is why there is a derived formula
for doing the calculations.
FV=P (1+r) t
Recalculating
the FV in the second year using the formula
FV=$1,000(1+0.05)2
=$1,000(1.05)2
=$1,0001.1025
1.1025
FV=$1102.5
The answer is
the same as when one uses the other method only that it is less tedious.
Present
Value
Assuming that P
in the calculation for FV above now stands for Present Value (P),the formula
for P is simply to solve for it in that formula.
Thus 
Using the
formula to get the present value of P=$1,102.5÷1.1025
=$1,000
Annuity
Annuity is
simply a series of payments at fixed intervals for a specified number of
periods. Thus, depositing $1,000 into a bank account at the beginning of every
month for two years is an annuity.
Annuity
future value (FV)
The derived
formula for Future Value of an Annuity (FV ANn)=PMT
Where FV ANn
=Present Value of an annuity
PMT=The Amount
of payment
n = number of
periods
i= interest
rate.
Annuity
Present Value
The present
value is simply to discount (divide) the future value by the discounting
factor.
References
Bierman, H.
&Smidt, S. (2006). The Capital
Budgeting Decision: Economic Analysis of Investment Decisions. New York:
Routledge.
Correia, C.,
Flynn, D., Uliana, E. &Wormald, M. (2008).Financial Management, Sixth Edition. Cape Town, South Africa:
Junta& Co.
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