Mortgage Constant Formula
The mortgage constant formula is used in the estimation of the property loan payment installment that the
borrower will be required to pay over a given period.
The mortgage constant reflects the periodic (monthly, quarterly, or annual) cost of financing as percent of total loan amount. The term mortgage actually is exclusive to the real estate industry, as it refers to a loan that uses property as collateral. Thus, the mortgage constant is extremely useful to professionals in the real estate industry, since borrowing is most common practice when acquiring property for two reasons.First because property purchases require large amounts of capital. Second, borrowing can help increase real estate investment returns, provided that certain conditions are met.
The mortgage constant is applicable only to fixed-rate loans and represents the percentage of the original amount borrowed by the investor that needs to be paid periodically in order to completely repay the principal (the original loan amount) and interest over the term of the loan. The mortgage constant formula for a fixed-rate loan is:
Mortgage Constant = Interest Rate/[1- [1/(1+Interest Rate) n]]
Once the mortgage constant for specific period (quarterly, annual,etc.) is calculated, then then loan payment for the respective period can be calculated as:
Periodic Loan Installment= Mortgage Constant X Loan Amount
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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. This effect is referred to in the real estate industry as positive leverage. 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.
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