Question

Emma Jones is planning to move this coming summer to Oxford, MS to start her new job at a technology firm. She has not yet decided whether she wants to rent or buy a property in Oxford and she is asking your team to help her make this financial decision. Her monthly housing budget is $1,800.  This budget must cover housing expenses including rent or owner’s costs (example: mortgage, hazard insurance, property taxes, and Home Owner Association fees, if any). A good start of the analysis is to apply financial concepts such as the “time value of money.”

Estimate the maximum house value Emmacan afford to buy. Assume the mortgage is fixed rate, 30-year maturity, 80% LTV, with no points. The interest rate that she was quoted is 3.5% with monthly payments. The property tax rate in the city of Oxford is 0.7% per year based on property value; the hazard insurance premium is 0.5% per year based on property value, and that on average you should consider $50 per month for maintenance. Determine the required monthly payment for the mortgage and the maximum house value she can afford if she buys

Answer 1

Let the property value be x.

Then, loan taken = property value*LTV = x*80% = 0.8x

Monthly mortgage payment = Loan taken*monthly interest rate/[1-(1+monthly interest rate)^-number of payments]

= 0.8x*(3.5%/12)/[1-(1+3.5%/12)^-(30*12)] = 0.0035924x

Property tax per month = annual property tax/12 = 0.7%*x/12 = 0.0006x

Hazard insurance premium per month = annual premium/12 = 0.5%*x/12 = 0.0004x

Maintenance per month = $50

Monthly housing budget = $1,800

So,

monthly mortgage payment + property tax per month + hazard insurance premium per month + maintenance per month = monthly housing budget

0.0035924x + 0.0006x + 0.0004 + 50 = 1,800

x = 1,750/0.004592 = 381,067.89

Property value = 381,067.89

Monthly mortgage payment = 0.0035924*381,067.89 = 1,368.93