finance

Question 1

Kim borrows $950,000 to purchase a $1,000,000 home from the Bank of Moncton. To make life easy, suppose that the loan has a one year term and a 5% interest rate. So after one year, she will owe $950,000 * 1.05 = 997,500. BoM has required that Kim pay for mortgage insurance from a private insurer. The insurer has a discount rate of 5%, and believes that Kim will default at term (one year from now) with 2% probability, and that if there is a default, the lender will only be able to recover $650,000 so the insurer will then owe the lender the difference between $997,500 and $650,000.

How much should the insurer charge to cover this loan, given their beliefs and their discount rate? This premium will be charged immediately. Answer with a decimal that represents a dollar amount (not a % of the home's value). You can round to the nearest dollar.

Question 2

Pat borrows $550,000 to purchase a $1,000,000 home from the Bank of Moncton. BoM does not require mortgage insurance, but Pat must also borrow $400,000 from the Really Beautiful Corporation (RBC) to make the deal work. RBC also does not require Pat to borrow mortgage insurance. There is no chance that Pat will default on her loan from BoM, which charges 4% interest, and therefore has a balance due of 572,000.Like the mortgage insurer above, they think there is a 2% probability that Pat will default, and if so, then the lenders will be able to recover only $650,000. In that event, BoM is entitled to $572,000, and RBC recovers only the remaining $78,000. In all other states of the world, RBC expects that they will be paid in full (given the interest rate you find below). RBC's discount rate for this loan is 4%.

What interest rate will leave RBC with a zero NPV loan? That is if they receive in one year $78,000 with 2% probability, and $400,000*(1+r) with 98% probability, what is r to set the NPV to zero on a $400,000 loan? You can round to the nearest .1%, and write your number as a decimal.

Question 3

Kim and Pat both borrow $950,000 to purchase $1,000,000 homes from the Bank of Moncton. To make life easy, suppose that each loan has a one year term and a 5% interest rate. So after one year, they will each owe $950,000 * 1.05 = 997,500. Suppose now that everyone thinks that there is a 10% probability that Kim will default at term (one year from now), and that if there is a default, the lender will only be able to recover $750,000. There is no mortgage insurance in this problem. (Note: I have increased both the recovery amount and probability of default from the first question). Suppose that they believe the same thing about Pat: 10% probability of default, and $750,000 recovery in the event of default.

Now suppose that BoM sells the loans to two investors. Investor A gets a senior claim on the mortgage repayment. This investor pays $1,710,000, or 90% of the initial loan proceeds of 2*$950,000 = 1,900,000. A junior investor ("B") funds the remaining 10% or $190,000.

Suppose that investor A discounts her repayment at 4%, and suppose that investor A believes that the defaults are independent events. That is, she believes neither loan will default with 81% probability, Kim only will default with 9% probability, Pat only will default with 9% probability, and both Pat and Kim will default with 1% probability. Investor A is entitled to the lesser of: (i) (1+r)*1,710,000 or (ii) the total amount recovered by BoM in principal and interest and/or default recovery. Under these conditions, what is the lowest interest rate r that investor A can accept and still have a non-negative NPV? You can round to the nearest tenth of a percent (e.g. .041, .042, ... .983, etc.)? Note that the investment occurs immediately, and the repayment occurs in one year.

Question 4

MOSTLY THE SAME QUESTION AS THE LAST ONE...

Kim and Pat both borrow $950,000 to purchase $1,000,000 homes from the Bank of Moncton. To make life easy, suppose that each loan has a one year term and a 5% interest rate. So after one year, they will each owe $950,000 * 1.05 = 997,500. Suppose now that everyone thinks that there is a 10% probability that Kim will default at term (one year from now), and that if there is a default, the lender will only be able to recover $750,000. Suppose that they believe the same thing about Pat: 10% probability of default, and $750,000 recovery in the event of default.

Now suppose that BoM sells the loans to two investors. Investor A gets a senior claim on the mortgage repayment. This investor pays $1,710,000, or 90% of the initial loan proceeds of 2*$950,000 = 1,900,000. A junior investor ("B") funds the remaining 10% or $190,000.

EXCEPT NOW:

Suppose that investor A discounts her repayment at 4%, and suppose that investor A believes that the defaults are perfectly correlated events. That is, she believes neither loan will default with 90% probability, Kim only will default with 0% probability, Pat only will default with 0% probability, and both Pat and Kim will default with 10% probability. Investor A is entitled to the lesser of: (i) (1+r)*1,710,000 or (ii) the total amount received by BoM in principal and interest and/or default recoveries. Under these conditions, what is the lowest interest rate r that investor A can accept and still have a non-negative NPV? You can round to the nearest tenth of a percent (e.g. .041, .042, ... .983, etc.)? Note that the investment occurs immediately, and the repayment occurs in one year.