Question

. Jim has an annual income of $300,000.

Jim is looking to buy a house with monthly property taxes of $140 and monthly homeowner’s insurance of $70.

Jim has $178 in monthly student loan payments.

Apple bank has a maximum front end DTI limit of 28% and a maximum back end DTI limit of 36%. Both limits must be satisfied.

Apple bank is offering a fully amortizing 30 year FRM at an annual rate of 4.5%, with monthly payments, compounded monthly.

Apple Bank allows a maximum LTV of 80%.

How much is the most expensive house Jim can buy?

Answer 1

Maximum front end DTI limit is 28%.

Front end DTI = (monthly mortgage payment + monthly tax + monthly insurance) / monthly gross income.

28% = (monthly mortgage payment + $140 + $70) / ($300,000 / 12)

monthly mortgage payment = $6790.

Maximum back end DTI is 36%.

Back end DTI = (monthly mortgage payment + monthly tax + monthly insurance + other debt payments) / monthly gross income.

36% = (monthly mortgage payment + $140 + $70 + $178) / ($300,000 / 12)

monthly mortgage payment = $8612.

The maximum monthly mortgage payment to satisfy both ratios is $6790 (lower of the two).

With a monthly mortgage payment of $6790, the loan amount is calculated using PV function in Excel :

rate = 4.5% / 12 (converting annual rate into monthly rate)

nper = 30 * 12 (30 year loan with 12 monthly payments each year)

pmt = -6790 (Monthly payment. This is entered with a negative sign because it is a cash outflow)

PV is calculated to be $1,340,082.

The maximum loan is $1,340,082.

The maximum LTV is 80%.

LTV = loan amount / value of house

Maximum value of house =  $1,340,082 / 80%

Maximum value of house =  $1,675,103