Chapter 8: Mortgage Mathematics

The Residential Mortgage Financial Process

Application - central doc. in the financing process. Designed to detect info about the financial ability of the applicant and the property's value. The application is prepared and forwarded electronically by a mortgage broker for review by underwriting department.

Appraisal and Credit Check - the lender reviews the application, applies loan qualification ratios and considers the income stability and future prospects. An appraiser or bank rep. may inspect the property to ensure it meets lender criteria. A credit check is usually performed to verify financial stability of the applicant. 

Commitment - a letter from the lender agreeing to make the loan. Such a letter has little, if any, stature.

 

The Commercial Mortgage Financing Process

• Feasibility (осуществимость) Report - report on economic, market and physical characteristics of the venture.
• Construction and Site Analysis - complete documentation regarding the property, architecture, construction plans, landscaping, utilities etc.
• Borrower Info - past projects, financial statements for the past 2-3 years, credit check and background of the company/individual.
• Estimated Income/Operating Expenses

Mortgage Qualification

Involves 2 factors:

• Downpayment - required cash recourses from the borrower. Typically represent total liquid assets minus purchasing costs (ex. fees and adjustments).
• Mortgage Qualification - lender requirements (gross debt service ratio / total debt service ratio) for approval of the mortgage principal.

Affordability Index - measures the cost of homeownership. Assumes 25% downpayment and a 5-year loan amortized over 25 years.

Gross Debt Service Ratio (GDS) - represents the max % of borrower's gross income to be allocated to principal, interest and tax payments (PIT). May include heating costs.

ex. Max's Income = $50000   GDS ratio = 30%   

max PIT payment (50k x 0.30) = $15000

Annual taxes (T) on property = $1500

Remaining PI payments availavle - $13500

Max Monthly PI Payment Available ($13500 / 12) = $1125

If Max requires a $140000 mortgage at 6.5% 25 years, the payment is: 6.698238 x 140000 = $937.75. Max meets lender's requirements.

GDS Ratio - Condo

Includes a portion of the common share expenses.

ex. Max's gross income = $58000    Downpayment = $50000   Condo Purchase = $170000   Taxes = $4120   Maintainance = $325 per month (3900 year) 

Max requires $120000 conventional mortgage for 25 years with a 5 year term. Current rates are 7.5% and the monthly payment factor per $1000 - 7.315549

Monthly Mortgage Payment: 120000 / 1000 x 7.315549 = $877.87 | Annual: 877.87 x 12 = $10534.44 | + Taxes and Maint. fee: 10534.44 + 4120 + (3900 x 0.5) = 16604.44

GDS = (Principal and Interest + Taxes + Maint. (50%)) / Gross Income = 16604.44 / 58000 = 28.63% (Max meets the max 30% limit for this particular lender. 

Total Debt Service Ratio (TDS)

Includes charges for principal, interest, and taxes, plus other debts including personal. 

Calculating  Loan Payments

Max's Income = $55000   Lender req. 30% GDS   PIT = GDS x Buyer Income | 55000 x 0.30 = $16500

Calculating GDS 

Max's income = $65000   PIT = $20960 GDS = PIT / Income | 20960 / 65000 = 0.32246 (32.25%)

Calculating Required Income 

PIT = $29000    30% GDS   Income = PIT / GDS | 29000 / 0.30 = 96700

 

Calculating Maximum Mortgage

1. Establish Buyer Income                                 $60000
2. Determine Lender GDS Ratio                       30%
3. Calculate Available PIT Ratio                        18000 (60000 x 0.30)
4. Establish Annual Property Taxes (T)            $2000
5. Calculate Remaining PI Payments               $16000 (18000 - 2000)
6. Calculate Monthly PI payment                     $1333.33 (16000 / 12)
7. Insert Current Mortgage Rate                       6.5%             
8. Insert Amortization Period                            25 years
9. Obtain Mortgage Payment Factor               6.698238
10. Calculate Mortgage Principal                        $199056.83 = (1333.33 / 6.698238) x 1000

Mortgage Interest

Calculating Simple Interest 

Interest payable for a specified period of time at a given rate with no compounding. Short term financing or small personal loan may involve simple interest. 

Interest (I) = Principal (P) x Rate (R) x Time (T)

Calculating Compound Interest 

Interest charged at specific intervals (daily, weekly ...). Compound Interest earned during each period is reinvested and continues to earn interest. 

Compound Amount (A) = P x (1 + i (interest rate per period))n

Nominal vs. Effective Interest Rates

The nominal rate is stated rate ex. 12%. The effective takes into account any compounding ex. 12.6485 or 12.64%.

Monthly Mortgage Payment = Monthly Payment Factor x Loan Value (in 1thousands)

$150000 mortgage, 25-year amortization, 6.5% interest | 6.698238 x 150 = $1004.74