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)