Jennifer Williamson recently received her MBA and has decided to enter the mortg

Question

Jennifer Williamson recently received her MBA and has decided to enter the mortgage brokerage business. Rather than work for someone else, she has decided to open her own shop. Her cousin, Jerry has approached her about a mortgage for a house he is building. He house will be completed in 3 month, and he will need a mortgage at that time. Jerry wants a 25-year, fixed-rate mortgage in the amount of $500,000 with monthly payments.

Jennifer agreed to lend Jerry the money in three months at the current market rate of 5.5%. Because Jennifer is just starting out, she does not have $500,000 available for the loan, so she approaches Max Cabell, the president of MC Insurance Corp about purchasing the mortgage in three months. Max has agreed to purchase the mortgage in three months, but he is unwilling to set a price on the mortgage. 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 Jerrys mortgage?

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

3.      How can Jennifer hedge this deal?

4.      Suppose that the next three months the market rate of interest rises to 6.2%.

a.       How much will Max be willing to pay for the mortgage?

b.      What will happen to the value of Treasury bonds future contracts? Will he long or short position increase in value?

5.      Suppose that in the next three months the market rate of interest falls to 4.6%.

a.       How much will Max be willing to pay for the mortgage?

b.      What will happen to the value of Treasury bonds futures contracts? Will the long or short position increase in value?

6.      Is there any possible risk Jennifer faces in using Treasury bond futures contracts to hedge her interest rate risk?

__Please don't answer unless you actually know what you're talking about- Thanks

Explanation / Answer

Hi. We interacted & you indicated that you want answer for 5 & 6 only. SO I am giving you answer for 5&6 as below.

1.Jerry%u2019s mortgage payments form a 25-year annuity with monthly payments, discounted at the long-

term interest rate of 5.5%. We can solve for the payment amount so that the present value of the

annuity equals $500,000, the amount of principal that he plans to borrow. The monthly mortgage

payment will be: nper = 25*12=300

$500,000 = PMT(PVIFA5.5%/12,300)

ie 500,000 = PMT*162.5270

SO PMT = $3,076.41

5.

a. If the market interest rate is 4.6% on the date that Jennifer meets with the Max, the fair value

of the mortgage is the present value of an annuity that makes monthly payments of $3,076.41 for 25 years, discounted at 4.6%:

So Mortgage value = $3,076.41(PVIFA4.6%/12,300)

Mortgage value = $3,076.41*178.8130

ie Mortgage value = $550,102.10

b. An increase in the interest rate will cause the value of the Treasury bond futures contracts to

increase. The long position will gain and the short position will lose. Since Jennifer is short in

the futures, the futures lose will be offset by the gain in value of the mortgage.

6.

The biggest risk is that the hedge is not a perfect hedge. If interest rates change, the fact that

Treasury bond interest is semiannual, while the mortgage payments are monthly, may affect the

relative value of the two. Additionally, while a change in one of the interest rates will likely coincide with a change in the other interest rate, the change does not have to be the same. For example, the

Treasury rate could increase 20 basis points, and the mortgage rates could increase by 40 basis

points. The fact that this is not a perfect hedge simply means that the gain/loss from the futures

contracts may not exactly offset the loss/gain in the mortgage. We would expect, especially given the short-term nature of the hedge, that the loss in one instrument would be similar to the gain in the

other instrument.

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