MORTGAGE CONSTANT FORMULA

The mortgage constant formula (or loan constant formula) is used for the estimation of the mortgage loan payment that the borrower will be required to pay over a given period. The main inputs in the mortgage constant calculation are the mortgage rate and the loan term. See here summary of the latest mortgage rate forecast.

The term morgage actually is exclusive to the real estate industry, as it refers to a loan that uses property as collateral. The main sources of property loans are conventional or non-conventional mortgage lenders and brokers. The most important factors in the mortgage constant formula are the mortgage rate and the term of the loan. This formula actually calculates the periodic (monthly, quarterly, or annual) cost (including principal and interest payments) of financing as percent of total loan amount.

The mortgage constant formula is the following:

MC = i / [ 1 -(1/(1 + i)ⁿ) ]

where

MC = mortgage constant
i = mortgage interest rate
n = number of periods equal to the term of the loan

MORTGAGE CONSTANT EXAMPLE

Notice that the mortgage constant formula has nothing to do with the amount of the loan, just the rate and the duration of the loan. The term interest rate refers to interest rate of the loan obtained by the borrower, while n refers to the term (duration) of the loan in number of periods. Thus, the number of periods (the value of n) in the mortgage constant formula will depend on two factors: a) the length of the period we want the annual constant to refer to, which can be month, quarter or year typically, and b) the term of the loan. For example, if we want to estimate a quarterly mortgage constant, which will reflect the quarterly cost of financing as percent of the total loan amount, and the term of the loan is 10 years then the n in the formula will have the value of 40 (4 quarters per year times 10). If one wants to estimate the monthly mortgage constant, n would represent the term of the loan in months and in our example of a 10-year loan it would have the value of 120.

For a loan at an interest rate of 6% and term of 20 years, the annual mortgage constant would be: Mortg. Const = 6%/ [1-[1/(1.06)²⁰]]= 8.72%

If the investor borrows $100,000 then the annual payment will be:

Annual Payment = 100,000 X 0.0872 = $8,720

MORTGAGE CONSTANT AND INVESTMENT RETURN

A major usefulness of mortgage constant is that it provides a measure that real estate investors can use to evaluate whether borrowing will have a positive or a negative impact on investment return. In other words, assess whether borrowing will help increase the return on a property investment compared to the return that would be obtained if no borrowing is used for the acquisition of the property.

According to Wurtzebach and Miles (1994), borrowing will help the investor achieve a higher rate of return if the mortgage constant associated with the specific loan (as it is defined by its term/duration and interest rate) is smaller than the unleveraged return offered by the property. The unleveraged return is the return provided by the property if it is acquired without using borrowed money. For example, if the annual mortgage constant is 7% and the property’s return, if purchased without borrowing, is 8% then acquiring the property by borrowing a significant percentage of the purchase price will further increase the return on investment. On the contrary, if the property’s expected return when purchased with no borrowed funds is 6%, then borrowing will result in an even lower (than 6%) return. This effect is referred to in the real estate industry as negative leverage.

It should be noted though that the use of the mortgage constant for evaluating whether borrowing will have a positive effect on the investment is a rather quick and simplistic technique and can not account for changing cash flows through time as well as the impact of capital gains on holding-period returns. For this reason accurate evaluation of the impact of borrowing on returns requires the use of the discounted cash flow model (DCF model) and estimation of returns under alternative financing structures.

MATH FOR PROPERTY INVESTORS
AND
REALTORS
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