Assumptions Inherent in TVOM Calculations
There are several important assumptions underlying the
TVOM equations and it would not be prudent to perform
calculations without being fully aware of their influence:
- Money is always invested and always productive so
that returns can be reinvested at a rate equal
(This assumption is illustrated and discussed in the
example problem #23.)
- The yield curve is flat so that short term interest
rates are equivalent to long term interest rates.
- Time periods are all of equal length.
- Payments are all equal and either all inflows or all outflows.
- The interest rate is constant throughout the term.
- Annuities are simple, certain, discrete and ordinary.
This last assumption requires further explanation:
- Annuity-Certain - one with a fixed number of
payments and the assurance that the payments will be made
(i.e., they are not contingent on any event that cannot
be entirely foretold)
- Discrete Annuity - one with equal intervals
between successive payment dates
- Simple annuity - one with payments and interest
conversions on the same date
- Ordinary annuity - one in which all the payments
are made at the end of the period
(But see annuity-due for
an alternative arrangement.)
Dealing with Restrictions Imposed by the Assumptions
Often you'll find in real-life that problems don't
fit neatly into formulas and assumptions that
have been derived from theory.
Fortunately, there are 'work-arounds'
for many of the restrictions imposed by the
A very versatile approach to overcoming the
restrictions of overburdening assumptions is
to borrow from John Locke's epistemology,
one of the basic tenets of which is that
complex things are built from combinations
of simpler things.
In other words, break the problem up into smaller pieces.
Uneven payments? Changing interest rates?
Unequal time periods?
All of these issues violate the basic assumptions
However, they can all be handled quite easily.
Remember, any annuity can be broken up into a series of
individual single sums. Likewise, a single sum
with a large term can be broken down
into a series of smaller single sums with shorter terms.
In either case, the 'aggregate' present or future value
is simply the summation of all the individual pieces.
An example of how this can be done in practice
is illustrated in Example Problem #12.
A Flat Yield Curve Will Not Persist
Another key assumption that can cause practical
problems is that the yield curve is flat.
In other words, there is no difference between long and
short term interest rates.
This is almost never the case.
In choosing the right interest rate, the time horizon exerts
a powerful influence.
At a minimum, the interest rate
should always be adjusted for the time to maturity.
Other factors that may need to be considered are: credit risk,
inflation, taxes, options or unusual contractual terms, the
nature and type of investment, alternative investments,
and anticipated economic activity.
The need for precision is also a significant
factor to consider when deciding
on a interest rate.
See Interest Rates
for more information on choosing
an appropriate value for i.
The terminology used with TVOM calculations is
For example, in practice the term interest rate,
discount rate, yield,
and rate of return are often used
In an effort to avoid equivocation, here are some basic
definitions that may be helpful:
Money that is loaned earns money for the lender and
such money is called interest.
The amount of money which is owed and upon which
the interest is earned is called principal.
The rate of interest in a given interval is
numerically equal to the interest earned in
one interval on a unit of principal per
unit of time.
The term is the interval extending from
beginning of the first compounding period to the
end of the last compounding period.
Compound interest is interest charged on
The nominal rate of interest is the stated
annual rate of interest not taking into account
The effective rate of interest is the
actual annual rate of interest taking into
account the effect of compounding.
An annuity is a series of periodic payments.
The accumulated value of an annuity is
the total accumulated values of all payments
and interest as of the end of the annuity term.
A coupon bond is a bond that makes periodic
(usually semi-annual) interest payments.
A discount bond (a.k.a. zero-coupon bond)
is a bond that does not make periodic
Instead it is sold at a 'discount' and
the difference between its face value and
the price paid is the equivalent of a
single interest payment made at maturity.
T-Bills are an example of a discount bond.
The Interest Rates page
provides a more detailed discussion on the distinction
among the various types of interest rates.