Suppose a bank has to make a decision about two residential mortgage applications.

QUESTION

Suppose a bank has to make a decision about two residential mortgage applications. Applicant A wants to borrow $525,000 to purchase a property for $600,000. Applicant B wants to borrow $385,000 to purchase a property for $400,000.(a) What is the LTV (loan-to-value ratio) for the two applications?(b) Consider a situation, in which the bank grants both applicants a 30-year interest-only loan with a lockout period of two years and a note rate of 9% for the full amount that the applicants desire to borrow. Suppose that within the first two years house prices have depreciated by 10 percent (that is, after two years a house previously worth $100,000 is now worth $90,000). Assume that both applicants default on their mortages after two years and that the bank will repossess the properties and sell it for the current market value. What percentage can the bank recover from each of the two loans?(c) Taking into account your answers to (a) and (b), which application should the bank(d) How does your answer to part (b) change if both applicants are granted a standard 30-year mortgage with a note rate of 9% for the full amount that they desire to borrow?(Standard refers to a fixed-rate mortgage contract with level payments.)(e) Does the change in the terms of the mortgage contract from part (b) to part (d) affect the banks decision which application it should have denied in the first place?
(a) For applicant A, For applicant B, (b) As the loan is an interest-only loan with a lockout period of two years, the outstanding balance of the loan after two years is the same as the outstanding balance at the moment of origination. So, As mortgage balance is still $525,000 and Bs mortgage balance is still $385,000. With regard to As property, the bank can sell it for 0.9$600,000=$540,000. As the outstanding balance ($525,000) is less than the sales price of the house ($540,000), the bank will recover all of the originally lent money. It will even be able to distribute $25,000 back to A. With regard to Bs property, the bank can sell it for 0.9$400,000=$360,000. This means that the bank will only recover of the originally lent amount. (c) A high LTV exposes the bank to the risk that it will not be able to recover all the originally lent money if house prices depreciate. Therefore, the bank should have denied Bs application in the first place. (d) In order to find the outstanding balance at the end of 2 years (24 months) use the

wing formula: where n: number of months of the mortgage loan, i: note rate divided by 12, MB0: original mortgage balance, MBt: mortgage balance after t months. It follows that the outstanding mortgage balance for A after 24 months is The bank still sells As property for $540,000. It will therefore still be able to recover all of the originally lent money. The amount that it redistributes to A is now $22,510.03. The outstanding mortgage balance for B after 24 months is With regard to Bs property, the bank can still sell it for $360,000. This means that the bank will only recover which is slightly higher than the recovery rate from part (b). (e) The assessment from part (c) is unchanged.

ANSWER:

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