What is the monthly mortgage payment on Mike’s mortgage
Chatman
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 $500,000
with monthly payments.
Joi has agreed to lend Mike the money in three months at the current market rate of 8
percent. Because Joi is just starting out, she does not have $500,000 available for the
loan; so 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 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 Mike’s mortgage (Hint: Use time value
of money you have learned to solve this problem ?
2. What is the most significant risk Joi faces in this deal?
3. How can Joi hedge this risk? Should Joe use a long hedge or short hedge?
4. Suppose that in the next three months the market rate of interest rises to 9 percent.
a. How much will Ian be willing to pay for the mortgage?
b. What will happen to the value of Treasury bond futures contracts? Will the
futures position Joe takes increase or decrease in value?
5. Suppose that in the next three months the market rate of interest falls to 7 percent.
a. How much will Ian be willing to pay for the mortgage?
b. What will happen to the value of T-bond futures contracts? Will the futures
position Joe takes increase or decrease in value?
6. What is the major risk Joi faces in using Treasury bond futures contracts to hedge
her interest rate risk?
Solution preview
The Monthly Mortage Pay is given by the Mortgage amount divided by the Discount Factor
That is:
Monthly Mortage Pay = Mortgage amount / Discount Factor
The Discount factor = [{(1 + i) ^n} – 1] / [i (1 + i) ^n]
Where i=8/12 and n 25*12, thus i=0.0067% and n=300
Thus the discount factor = [{(1 + 0.0067%) ^300} – 1] / [0.0067% (1 + 0.0067%) ^300]
Discount factor = $129.56452
Therefore, the monthly payment amount………………………
APA
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