Problem:
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 15-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 4 percent. Because Joi is just starting out, she does not have $500,000 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 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.
Requirement:
Question 1: What is the monthly mortgage payment on Mike's mortgage?
Question 2: What is the most significant risk Joi faces in this deal?
Question 3: How can Joi hedge this risk?
Question 4: Suppose that in the next three months the market rate of interest rises to 6 percent.
Question 5: How much will Ian be willing to pay for the mortgage?
Question 6: What will happen to the value of Treasury bond futures contracts? Will a long or short position increase in value?
Question 7: Suppose that in the next three months the market rate of interest falls to 3 percent.
Question 8: How much will Ian be willing to pay for the mortgage?
Question 9: What will happen to the value of T-bond futures contracts? Will a long or short position increase in value?
Question 10: Are there any possible risks Joi faces in using Treasury bond futures contracts to hedge her interest rate risk?
Note: Explain all calculation and formulas.