# Debt to Income Ratio

Debt to income ratio is the proportion of a person's income that goes into servicing debt. It is calculated by dividing the monthly debt payments by monthly gross income multiplied by 100.

Debt to income ratio is one of the criteria that lenders use to assess a person's current debt level relative to income and determine whether she is able to take on additional debt. A lower debt to income ratio is better and vice versa.

There are two variants of the debt to income ratio: (a) the front-ent debt to income ratio (also called housing ratio) and (b) back-end debt to income ratio (or total debt to income ratio).

FHA specifies a threshold (currently 43%) for debt to income ratio which you are usually required to meet in order to get a qualified mortgage.

## Formula

The front-end debt to income ratio (i.e. housing ratio) is calculated using the following formula:

$$ \text{Housing Ratio}=\frac{\text{Monthly Mortgage Payments}}{\text{Monthly Gross Income}} $$

The monthly mortgage payments include the monthly payment on mortgage and associated insurance fees.

The total debt to income ratio (the back-end DTI) can be calculated using the following formula:

$$ \text{Debt to Income Ratio}=\frac{\text{Monthly Debt Payments}}{\text{Monthly Gross Income}} $$

Monthly debt payments are the debt payments that recur every month on all of the loans. These include payment on mortgages (both the principal and interest portion), auto loans, minimum payment on credit card, etc. It also includes any other recurring payment obligations such as child support payments, etc.

Monthly gross income is the monthly income before tax and any other deductions.

Back-end DTI is higher or equal to the front-end DTI.

## Example

In July 20X3, Alex Noriega earned $5,000 in monthly gross income. During the month he paid $900 on account of his mortgage ($300 interest and $600 principal repayment), minimum monthly payment on credit card of $200, property tax of $80, auto loan installment of $300. Further, he contributed $200 to a charity and paid advance of $500 to a furniture vendor for production of customized furniture. Find his debt to income ratio.

Monthly recurring payments in this scenario sum up to $1,480 [= $900 + $200 + $80 + $300]. Contribution to charity and advance for furniture are non-recurring payments that are not related to loans, so they excluded.

$$ \text{Debt to Income Ratio}=\frac{\text{\$1,480}}{\text{\$5,000}}=\text{29.6%} $$

Alex has relatively low debt to income ratio which is a good thing because it enables him to raise additional financing easily if needed.

by Obaidullah Jan, ACA, CFA and last modified on