Question

Joi Chatman recently received her finance degree and has decided to enter the mortgage broker

business. Rather than working for someone else, she will open her own shop. Her cousin Mike

has approached her about a mortgage for a house he is building. The house will be completed in

three months, and he will need the mortgage at that time. Mike wants a 25-year, fixed-rate

mortgage in the amount of $400,000 with monthly payments.

Joi has agreed to lend Mike the money in three months at the current market rate of 6 percent.

Because Joi is just starting out, she does not have $400,000 available for the loan; she

approaches Ian Turnbell, the president of IT Insurance Corporation, about purchasing the

mortgage from her in three months.

Ian has agreed to purchase the mortgage in three months, but he is unwilling to set a price on the

mort-gage. Instead, he has agreed in writing to purchase the mortgage at the market rate in three

months. There are Treasury bond futures contracts available for delivery in three months. A

Treasury bond contract is for $100,000 in face value of Treasury bonds.

1. What is the monthly mortgage payment on Mike’s mortgage?

2. What is the most significant risk Joi faces in this deal?

3. Treasury bond prices have a __________ relationship with interest rates.

a. positive

b. negative

4. As interest rates rise, Treasury bonds become _________.

a. less valuable

b. more valuable

5. Since Joi will _____ when interest rates rise.

a. loss money

b. gain money

6.

In order to protect Joi from decreases in the price of Treasury bonds, she

should take a _____ position in Treasury bond futures to hedge the risk.

a.

Long

b.

Short

7. Suppose that in the next three months the market rate of interest falls to 5 percent. a.

How much will Ian be willing to pay for the mortgage?

Answer 1

The multiple choice questions are a series of questions and contain explanation within the answer. Therefore, further explanation has not been given.

_______

Part 1)

The value of monthly mortgage payment on Mike's mortgage can be calculated with the PMT (Payment) function/formula of EXCEL/Financial Calculator. The function/formula for PMT is PMT(Rate,Nper,PV,FV) where Rate = Interest Rate, Nper = Period, PV = Present Value and FV = Future Value.

Here, Rate = 6%/12, Nper = 25*12 = 300, PV = $400,000 and FV = 0

Using these values in the above function/formula for PMT, we get,

Monthly Mortgage Payment = PMT(6%/12,300,400000,0) = $2,577.21

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Part 2)

In the given case, the most signifcant risk faced by Joi is "Interest Rate Risk". It is because an increase in interest rate during the period of 3 months starting from today and the actual date on which the mortgage is sold would cause a decrease in the fair value of mortgage which in turn would result in lesser value of loan getting granted to Mike (as Ian wouldn't be willing to lend more than the fair value of mortgage.

______

Part 3)

Treasury bonds have a negative relationship with interest rates. (which is Option b)

______

Part 4)

As interest rates rise, Treasury bonds become less valuable. (which is Option a)

______

Part 5)

Since Joi will lose money when interest rates rise. (which is Option a)

______

Part 6)

In order to protect Joi from decreases in the price of Treasury bonds, she should take a short position in Treasury bond futures to hedge the risk. (which is Option b)

[As the size of each contract is $100,000, Joi would be required to short 4 contracts of $100,000 to hedge the interest rate risk.]

______

Part 7)

The maximum amount Ian be willing to pay for the mortgage can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate, Nper = Period, PMT = Payment and FV = Future Value.

Here, Rate = 5%/12, Nper = 25*12 = 300, PMT = $2,577.21 and FV = 0

Using these values in the above function/formula for PV, we get,

Present Value (Maximum Amount Ian Would be Willing to Pay for the Mortgage) = PV(5%/12,300,2577.21,0) = $440,856.91