Problem #3 (20 points)

You are a loan analyst in the mortgage department of a bank in Chicago. A customer applies for a loan to buy a house with 80% debt (and 20% equity). The price of the house is constant, equal to $500,000 and will remain constant. The penalty for re-financing or pre-payment is so high that in practice re-financing is not an option.

Assume the loan is a fixed-monthly-payment type. You do the math and the customer fixed payment is supposed to pay $2000 per month for 30 years (i.e. 360 months), no matter how much the future interest rates are.

You are doing a risk analysis because the bank worries that following an expansionary monetary policy the interest rates may drop. What is the lowest threshold for the interest rates to potentially trigger a voluntary (strategic) default on this mortgage loan? For simplicity, assume there are no additional costs associated with default. (hint: Calculate the present value of customer's payments and compare it with the value of her house. Play with Excel to find the threshold rate.)