Solution 11280: Calculating Qualifying Loan Amount (QLA) for Buyer Qualification the BA Real Estate™.
How does the BA Real Estate calculate QLA (qualifying loan amount)?
The loan qualification equations come from the basic Time-Value-of-Money equations:
FV = -PV*(1+i)N - PMT*(1+i*BGN)*((1+i)N - 1)/i
FV = Future Value
PV = Present Value
PMT = Payment
i = Interest rate in decimal (not percent)
N = Number of periods (number of years * PPY)
BGN = 1 if payments are at the beginning of the period
BGN = 0 if payments are at the end of the period (BGN is normally set to 0)
If solving for FV, PMT, PV or N, then I% must be converted to i using the formula:
i = [1 + I% / (100*CPY)]CPY/PPY - 1
I% = Interest rate / year
CPY = Compounding periods / year
PPY = Payments / year
Solve for PV:
PV = PMT*(1+i*BGN)*((1+i)-N-1/i - FV*(1+i)-N
PV (Loan Amount) is the unknown. FV is normally zero, but doesn't have to be.
PMT is the payment, which only includes interest and principal (not taxes and insurance).
First calculate PITI = principal + interest + taxes + insurance on a monthly basis, based on the monthly income of the buyer, the debt of the buyer, and the income / debt ratio.
PITI = - min (INCOME*INC% / 100, INCOME*DEBT% / 100 - DEBT)
Since PITI is negative, tax and insurance have to be added to get PMT. i.e.,
PMT = PITI + PRC*(tax%+debt%) / (100*PPY), where PRC is the total price of the house (PV + down payment).
Now the user has the option of entering the tax and insurance (tax&ins) and the down payment as a dollar amount. This makes computing easier, because then PMT = PITI - tax&ins$ and PRC = PV + DN$. The tricky part comes when the tax and insurance values are given as percentages. Then, the PMT equation has the PRC variable in it and PMT can't be directly computed. Instead PRC should be substituted with the following:
PRC = PV + DN$ = PV / (1-DN% / 100)
Now PRC is replaced into the PMT equation, and the PMT equation is replaced into the PV equation, thus:
PMT = PITI + (PV / (1-DN% / 100))*(tax%+debt%) / (100*PPY)
PV = PMT*(1+i*BGN)*((1+i)-N - 1) / i - FV*(1+i)-N
= [PITI + (PV / (1-DN%/100))*(tax%+debt%) / (100*PPY)] *(1+i*BGN)*((1+i)-N - 1) / i - FV*(1+i)-N
Solve for PV, and get the maximum loan amount.
Please see the BA Real Estate guidebook for additional information.