Question

This problem illustrates how to [1] determine the payments of an interest rate swap, [2] value the swap, [3] and hedge with the swap. The problem is based on the WSJ article “School District, Bank in Swap clash”.

The setting: The local school district was planning to build a new high school. The estimated cost of the building was around $100M. To finance the building the school district needed to issue a bond for about $58M. It had two choices:

[1] Issue a fixed rate bond or

[2] issue a floating-rate bond and enter into a swap to receive floating and make fixed payments.

Question 1: Calculate the payments (cashflows) of a fixed-rate 10-year bond with face value $58M, coupon rate 4% that will be sold at face value.

Question 2: Calculate the payments (cashflows) of a floating-rate 10-year bond with face value $58M that will be sold at face value.

[a] after the bond is sold the short-term interest rate increases to 5.5% per year and is expected to stay at that level.

[b] after the bond is sold the short-term interest rate decreases to 2% and is expected to remain at 2% for the next 5 years. After 5 years the interest rate is expected to increase to 4% and remain stable.

Question 3: The school district signed a swap agreement to pay 3.884% on $58M and receive the floating rate. What are the payments associated with this swap for [a] and [b] from Question 2?

[a]

[b]

Question 4. Suppose that the school district issues the floating rate bond and enters the swap. What are the net cashflows for scenarios [a] and [b]?

[a]

[b]

Question 5. Compare the cashflows from the fix-rate bond and the combined floating-rate bond and the swap. What is the risk and cost of the two alternatives?

Question 6. The State College School district entered the swap but did not issue the bond. This position is called a “naked swap”. When interest rates plummeted in 2008 the school district lost a lot of money. How can you explain that?

Question 7. Suppose that the school district had entered the swap in January 2007. Now it is January 2008 and interest rates have fallen to 0% and are expected to remain at 0% for the next 10 years. The school district issues the $58M bond with zero coupons and sells it at face value. What is the value of the swap? How much did the school district save by issuing the bond when the interest rates were 0% vs when the interest rate was 4%?

Question 8. Big picture. This problem implicitly assumes that the school district dislikes risk and prefers fixed rates, all other things equal. However, the district’s income comes from local real estate and income taxes. What is the correlation between interest rates and taxes paid? Does the district really need fixed bond payments?

Answer 1

We received 58 million i year 0. Every year we pay 58million*4% = 2.32 million. At last we also pay 58million back.

I can only answer one question at a time. For separate questions, ask separately. Thanks