NOMINAL
AND EFFECTIVE INTEREST RATES
Banks, credit unions and other lenders commonly quote the interest rate
charged on the loan as an annual nominal rate, for
example, 12% per annum nominal.
Nominal in this case means "not exactly" so that the valuer
analyzing the rate for comparison purposes should adjust it to an effective
or "real" rate. This is done by using the payment period as follows:
EXAMPLE
If
a bank quotes the lending rate as 12% per annum but the repayments are
made monthly, the effective monthly rate is (12/12)% or 1% per month.
CONVERTING TO AN EFFECTIVE ANNUAL RATE
It
is common practice for valuers to use annual capitalization rates even
though the income and/or payments from investment properties are
generally, monthly. Therefore, the capitalization rate can be analyzed
from comparable sales on a monthly basis and then converted to an
annual equivalent to value the subject property on an annual net income.
EXAMPLE
An
analyzed sale shows an effective monthly rate of 1% per month. The
effective annual equivalent must be more than 12% because the monthly
income attracts monthly compound interest during the year. The
effective annual rate is found by determining how much 100 invested at
the beginning of the year will amount to at the end of the year if it
compounds at the effective monthly rate. The capital of 100 is then
subtracted from the accumulated amount so that the remainder is the
effective annual rate.
The future value (FV) formula is used is follows:
FV(100) = 100 * (1+i)n
Where:
FV(100) = the future value of 100
i
= interest rate per period as a decimal
n = the number of periods per year
Substituting for the above example:
FV(100) = 100 * (1+0.01)12 = 112.683
Therefore, the effective annual rate is 112.683 - 100.000 = 12.683%
The capitalization rate of 12.683% can now be used to value comparable
investment properties using annual net incomes. For the example above,
the future value of the net annual income in arrears is:
FV.PMT(1000) = ((1.0112-1)/0.01) * 1000 = 12 683
per annum
Capitalise at 12.683% per annum:
12682.5 * 100/12.683 = 99 996 say 100 000
(error due to rounding)