Time Value of Money Concepts
BASIC ANNUITIES
There are many accounting transactions that require the payment of a specific amount each
period. A payment for a auto loan or a mortgage payment are examples of this type of
transaction. If the interval between periods is constant and the amount is always the same, this is
called an annuity.
Because an annuity is a stream of payments over a period of time, our
previous discussion of the time value of money would indicate that there must be an interest
factor involved. In the language of annuities, the payments are called
Rents
(the symbol R is
used to designate the amount of Rents).
If the rent is paid at the end of each period the annuity is
called an
Ordinary Annuity
. If the rent is paid at the beginning of each period the annuity is
called an
Annuity Due
.
FUTURE VALUE OF AN ORDINARY ANNUITY
An example of an ordinary annuity is contributions to a 401-k retirement plan.
At the end of
each month a certain sum is deducted from the employee’s paycheck (or paid by the employer)
and placed in an investment account.
The algebraic formula for the future value of an ordinary annuity is:
FVOA
=
R
*
[FVOA, n, i]
Let’s assume that Spencer Company has agreed to contribute $60,000 to an employee retirement
plan at the end of each year.
The investment yields a 12% annual return.
If we assume that
contributions will be made for 10 years then the following reflects the Future Value of the
retirement plan contributions.
FVOA
=
R
*
[FVOA, n, i]
FVOA
=
60,000
*
[FVOA, n=10, i=12%]
FVOA
=
60,000
*
17.54874
FVOA
=
1,052,924
PRESENT VALUE OF AN ORDINARY ANNUITY
The algebraic formula for the present value of an ordinary annuity is:
PVOA
=
R
*
[PVOA, n, i]
In many cases business enterprises offer some kind of long-term benefits to employees after they
retire.
If Spencer Company has agreed to make semiannual contributions of $60,000 to a post-
retirement medical insurance plan for 10 years and the investment vehicle earns 5% per annum
what is the present value of this contribution schedule?
Using the above formula we can
calculate the present value of this ordinary annuity as follows:
PVOA
=
R
*
[PVOA, n, i]
PVOA
=
60,000
*
[PVOA, n=20, i=2.5%]
PVOA
=
60,000
*
15.58916
PVOA
=
935,350
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