How to Calculate the Loan Constant (Cost of Capital)

How to Calculate the Loan Constant (Cost of Capital)

The cost of capital for a property is called the Loan Constant (Constant) or Mortgage Constant. All loans have a certain interest rate and, unless there is an interest-only portion to the loan, all loans will require a principal and interest payment. The principal is calculated based upon the amortization of the loan. Thus, if the loan has a 30-year amortization, which is equal to 360 months, the principal must be paid in 360 installments so the loan is paid in full on the last loan payment.

The quoted interest rate of a loan is strictly the amount of interest that loan accrues. The loan constant, on the other hand, is expressed as an interest rate that incorporates both the interest and principal repayment of a loan. The formula is:

Loan Constant = [Interest Rate / 12] / (1 - (1 / (1 + [interest rate / 12]) ^ n))

n = the number of months in the loan term

Example 1: Suppose an investor received a loan for $4,000,000 at a 5.50% interest rate with a 30-year amortization. We can calculate the required annual loan payments once the loan constant is known.

Constant = [.055 / 12] / (1 - (1 / (1 + (.055 / 12]) ^ 360))

Constant = .06813 x 100 = 6.813% (rounded)

Annual payments = $4,000,000 * .06813 = $272,520

While the property has an interest rate of 5.50% the investor's actual cost of capital for the loan is 6.813% once the principal payment has been factored. If the above loan scenario has a 1.25x debt service coverage ratio (DSCR) requirement then an investor knows that the property must have at least the following NOI to support the loan:

$272,520 x 1.25 = $340,650

Consider that the reverse also holds true. A borrower can factor his potential debt service loan with the loan constant as long as he knows the NOI.

Example 2: A borrower wants to refinance his loan. His NOI is $560,000 and he has heard that his local bank will give him an interest rate of 6.25% for 25 years with a minimum DSCR of 1.25. What is the maximum loan he can borrower subject to an appraisal?

Constant = [.0625 / 12] / (1 - (1 / (1 + (.0625 / 12]) ^ 300))

Constant = .07916 x 100 = 7.916% (rounded)

Since the borrower knows the Debt Service Coverage Ratio must be 125% more than annual debt payments he can calculate the annual payments as the following:

$560,000 = $448,000

1.25

With $448,000 of the property's net operating income available to service the debt payments, his maximum possible mortgage based on debt service would be:

$448,000 = $5,659,424

.07916

As illustrated, the loan constant is a tool that can help a borrower easily understand the potential debt service associated with a property based upon a certain net operating income. Any borrower should make sure they check the loan constant with their lender to ensure that it matches his assumptions. For example, FHA multifamily mortgages have a mortgage insurance premium that is also factored into the loan constant which raises a property's cost of capital. A few other items to remember are:

Shortcoming #1: The constant only works for fixed rate loans. For adjustable rate mortgages that have changing monthly interest rates lenders will typically underwrite the maximum possible interest rate for that loan. Find out from your lender what is appropriate when modeling debt assumptions.

Shortcoming #2: The constant changes based upon the amortization of the mortgage. While not necessarily a shortcoming, it is important to understand the terms of any loan quote you receive from a lender or if your loan assumptions are accurate for a particular property or market. The shorter the amortization period of a loan, the higher the property's cost of capital.

Shortcoming #3: The constant does not factor interest-only periods. In the current lending environments, most lenders use an amortizing constant. When modeling cash flow it is important to note an interest only periods but although it will increase the cash-on-cash returns, it will not change the loan amount.

Robert Prouty is Co-Founder of Apartment Analytics Software, LLC [http://apartmentanalyticssoftware.com] one of the real estate industry's leading apartment investment software firms dedicated to providing investors with powerful and easy-to-use analytical tools enabling them to crunch the numbers with ease and make smart real estate investments with total confidence. Learn more by visiting [http://apartmentanalyticssoftware.com]

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