Explain how a firm that has issued a floating-rate bond with a coupon equal to the LIBOR rate can use swaps to convert that bond into a synthetic fixed-rate bond.

To understand how a firm can use swaps to convert a floating-rate bond into a synthetic fixed-rate bond, let's break it down into several steps:

Step 1: Understand the concept of a floating-rate bond and LIBOR
A floating-rate bond is a debt instrument whose interest rate can change over time based on a reference rate, such as the London Interbank Offered Rate (LIBOR). LIBOR is the average interest rate at which major banks can borrow from one another in the London interbank market. The coupon rate of a floating-rate bond is typically set as the reference rate (e.g., LIBOR) plus a spread.

Step 2: Determine the motivation for converting to a fixed-rate bond
Firms may wish to convert a floating-rate bond into a fixed-rate bond due to various reasons, such as reducing interest rate risk or securing a known future interest payment.

Step 3: Using an interest rate swap
To convert a floating-rate bond into a synthetic fixed-rate bond, the firm can utilize an interest rate swap. An interest rate swap is a financial derivative that allows two parties to exchange cash flows based on different interest rate benchmarks.

Step 4: Enter into an interest rate swap agreement
The firm enters into an interest rate swap agreement with another counterparty (often a bank or financial institution) that agrees to exchange interest payments with the firm. In this case, the firm wants to convert the floating-rate payments of the bond into fixed-rate payments.

Step 5: The swap structure
The interest rate swap agreement typically involves the following elements:
- Notional principal: This represents the face value of the bond, on which the interest payments are calculated.
- Payment frequency: The agreed-upon interval at which interest payments will be exchanged (e.g., quarterly or semi-annually).
- Swap rate: The fixed interest rate at which payments will be exchanged.
- Floating-rate index: The reference rate used to calculate the floating-rate payments (e.g., LIBOR).

Step 6: Calculating cash flows
Under the swap agreement, the firm receives fixed-rate payments based on the agreed-upon swap rate and pays floating-rate payments based on the LIBOR rate. By doing so, the floating-rate bond's coupon payments are effectively converted into fixed-rate payments.

Step 7: Synthetic fixed-rate bond
As a result of the interest rate swap, the firm effectively converts its floating-rate bond into a synthetic fixed-rate bond. The firm now receives fixed interest payments from the interest rate swap counterparty and no longer has exposure to fluctuations in the LIBOR rate.

Note: It's important to remember that executing interest rate swaps involves certain risks, such as counterparty risk, interest rate risk, and basis risk. Engaging in such financial transactions should be done carefully, and it is advisable to seek guidance from financial professionals.