Mortgages Analyzed
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Debt To Income Ratio (Back-end Ratio)

What is Debt To Income Ratio?

Debt To Income Ratio

Debt To Income (DTI) ratio is the monthly debt obligation amount expressed as a percentage of gross monthly income. It reflects the proportion of borrower’s income that is dedicated towards making loan related payments.

The purpose of DTI is to assess the availability of income to meet loan repayment. Borrower’s income is the primary source of repayment from which the borrower makes payments for mortgage and other loans. In the event the borrower losses the income, then the lender falls back on the collateral (foreclosure process).

DTI is calculated by dividing the monthly debt obligation by gross monthly income. Monthly debt obligation includes monthly mortgage payment, property taxes, insurance premium, and other debt payments. Other debt payments may include payments for credit card loans, student loans, and auto loans. Monthly mortgage payment includes the payment for principal and interest. Insurance includes premium for homeowner’s insurance and private mortgage insurance (PMI). The debt obligation also includes homeowners association fee, condominium fee, and coop fee. Gross monthly income refers to income before taxes.

DTI is also known as the Back-end Ratio, Total Coverage Ratio, Total Debt Service Ratio, and Household Debt Service Ratio.

Source :www.MortgagesAnalyzed.com

Debt To Income Ratio is a Measure of Risk

Lenders use DTI as a measure of risk. DTI measures the proportion of income that is available for meeting the mortgage and other debt obligations. The higher the DTI, the higher is the risk the borrower may default on the loan. With lower DTI the borrower has greater ability to meet unexpected decline in income. Also, the borrower may also use surplus cash flow to maintain and build reserves that may be used to meet temporary decline in income.

Lenders usually cap the maximum DTI that they are willing to lend up to. Some lenders limit loans with a maximum DTI of 36%, while others may allow higher with greater credit requirements such as higher credit score or lower LTV.

DTI is not used in isolation. Housing ratio is used along with DTI to determine the ability of the borrower to meet monthly debt obligations. Lenders also use additional risk indicators such as LTV, CLTV, and credit score, to assess the overall level of risk.

Source :www.MortgagesAnalyzed.com

Formula for Debt To Income Ratio

DTI is calculated by dividing the monthly debt obligation by gross monthly income. It can be expressed using the formula below.

DTI =  
Monthly Debt Obligation Gross Monthly Income

Monthly debt obligation equals monthly mortgage payment, property taxes, insurance premium, and other loan payments.

The formula can be rewritten as:

DTI =  
(Principal + Interest + Taxes + PMI + Other Loan Payments) Gross Monthly Income

Or,

DTI =  
(PITI + Loan Payment) Y
Source :www.MortgagesAnalyzed.com

Where,

DITI  =  Debt To Income Ratio
PITI  =  Principal + Interest + Taxes + PMI
Y  =  Gross Monthly Income
Source :www.MortgagesAnalyzed.com

Examples for Debt To Income Ratio Calculations

Example 1: Fully Amortizing Loan

Roland obtains a 30 year fully amortizing loan for $75,000 at an interest rate of 6% per annum. Roland’s monthly income is $3,000. The property taxes are 1% per annum. The property insurance premium per annum is $480. His monthly payment for credit card loan is $80.

In this case,

Gross Monthly Income (Y)  =  $3,000
Monthly Payment (P&I)  =  $449.66
Monthly Property Taxes(T)  =  1% × 75,000 = $62.50
Monthly Insurance Premium (I)  =  480/12 = $40
Other Loan Payments  =  $80
Monthly Debt Obligation  =  449.66 + 62.50 + 40 + 80 = $632.16
DTI =  
632.16 3,000
= 21.07%
Source :www.MortgagesAnalyzed.com

Example 2: Fully Amortizing Loan with PMI

Roland obtains a 30 year fully amortizing loan for $75,000 at an interest rate of 6% per annum. Roland’s monthly income is $3,000. The property taxes are 1% per annum. The property insurance premium per annum is $480. Roland has to pay $25.25 as monthly premium for PMI. His monthly payment for credit card loan is $80.

In this case,

Gross Monthly Income (Y)  =  $3,000
Monthly Payment (P&I)  =  $449.66
Monthly Property Taxes(T)  =  1% × 75,000 = $62.50
Monthly Insurance Premium (I)  =  (480/12) + 25.25 = $65.25
Other Loan Payments  =  $80
Monthly Debt Obligation  =  449.66 + 62.50 + 65.25 + 80 = $657.41
DTI =  
577.41 3,000
= 21.91%
Source :www.MortgagesAnalyzed.com

Example 3: Calculating Max Loan Amount Using DTI

Roland wants to obtain a 30 year fully amortizing loan at an interest rate of 6% per annum. The lender provides loans with a maximum DTI of 36%. Roland’s monthly income is $3,000. The property taxes are $1,200 per annum. The property insurance premium is $480. His monthly payment for credit card loan is $80. What is the maximum amount that Roland can borrow?

In this case,

Gross Monthly Income (Y)  =  $3,000
Monthly Property Taxes(T)  =  1200/12 = $100
Monthly Insurance Premium (I)  =  480/12 = $40
Periodic interest rate (i)  =  6%/12 = 0.005
Number of periods (n)  =  12 × 30 = 360
Other Loan Payments  =  $80
Debt to Income Ratio (DTI)  =  36%
Source :www.MortgagesAnalyzed.com
Maximum Debt Obligation = Y × DTI = 3000 × 36% = $1,080

Max monthly payment (P&I) = 1,080 - 40 - 100 - 80 = $960
Monthly Payment (P&I) =  
[ P × i × (1+i)^n ] [ (1+i)^n – 1 ]

 

Solving for P, maximum principal loan amount = $160,119.95

This is a simple example that shows how much Roland can borrower based on lenders guidelines for DTI. Typically, the affordability calculator is performed by using both housing ratio and DTI. Use the Affordability Calculator for your loan scenario to determine the maximum loan amount.

Source :www.MortgagesAnalyzed.com

Example 4: Calculating Maximum Loan Amount Using DTI and Housing Ratio

Roland wants to obtain a 30 year fully amortizing loan at an interest rate of 6% per annum. The lender provides loans with a maximum housing ratio of 28% and maximum DTI of 36%. Roland’s monthly income is $3,000. The property taxes are $1,200 per annum. The property insurance premium is $480. His monthly payment for credit card loan is $80. What is the maximum amount that Roland can borrow?

In this case,

Gross Monthly Income (Y)  =  $3,000
Monthly Property Taxes(T)  =  1200/12 = $100
Monthly Insurance Premium (I)  =  480/12 = $40
Periodic interest rate (i)  =  6%/12 = 0.005
Number of periods (n)  =  12 × 30 = 360
Housing Ratio (HR)  =  28%
Debt To Income Ratio (DTI)  =  36%
Source :www.MortgagesAnalyzed.com

Based on Housing Ratio

Maximum monthly obligation = Y × HR = 3000 × 28% = $840

Max monthly payment (P&) = 840 - 40 - 100 = $700
Monthly Payment (P&I) =  
[ P × i × (1+i)^n ] [ (1+i)^n – 1 ]

 

Solving for P, maximum principal = $116,754.13

Based on DTI

Maximum Debt Obligation = Y × DTI = 3000 × 36% = $1,080

Max monthly payment (P&) = 1,080 - 40 - 100 - 80 = $960
Monthly Payment (P&I) =  
[ P × i × (1+i)^n ] [ (1+i)^n – 1 ]

 

Solving for P, maximum principal = $160,119.95

Lower of maximum loan amount = $116,754.13

The maximum loan amount calculated using housing ratio is lower than the amount calculated using DTI. Therefore, Roland can obtain a loan with maximum loan amount of $116,754.13.

Source :www.MortgagesAnalyzed.com

Updated: Nov 24, 2013

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DTI is calculated by dividing the monthly debt obligation by gross monthly income
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