Floating Rate Coupon Structure

A bond’s coupon payment is the periodic interest payment that the issuer promises to pay the holder. A coupon can be structured in numerous ways. Although the majority of bonds pay fixed coupons annually or semi-annually, some bonds pay a variable-rate coupon that fluctuates based on a formula. Below are the most common structures of floating coupons:

Straight Floating Rate Coupon: A bond with a floating rate coupon will make a periodic payment derived from a formula that incorporates a reference market interest rate. The coupon rate is set at the beginning of each payment interval based on the prevailing reference rate. The set coupon is paid by the issuer of the bond on the payment date at the end of the payment interval. Below is the formula for a basic floating rate coupon:

Consider the following example: A bond with a floating rate coupon makes a semi-annual coupon payment equal to the London Interbank Offered Rate (LIBOR) plus 150 basis points. The prevailing LIBOR on January 1, 2002 is 3.75%. The June 30, 2002 coupon payment is calculated as follows:

Floating Rate Coupon = 3.75% + 150bps = 5.25%

Inverse Floating Rate Coupon: Inverse floating rate coupons are similar to traditional floaters. However, an inverse floater’s coupon rate will move inversely to its reference market interest rate. If the market interest rate rises, the coupon payment will decrease and vice versa. Below is the formula for an inverse floater:

Consider the following example: A bond’s coupon is structured as an inverse floater to pay an interest payment equal to 10% less the prevailing London Interbank Offered Rate. The prevailing LIBOR on January 1, 2003 is 4.25%. The June 30, 2003 coupon payment is calculated as follows:

Inverse Floating Rate Coupon = 10% - 4.25% = 5.75%

De-Leveraged Floating Rate Coupon: A de-leveraged floating rate coupon is a floater with an added variable: a multiple of less than 1.0 that effectively decreases the leverage of the market interest rate. Examine the following formula:

Consider the following example: A bond with a floating rate coupon makes a semi-annual coupon payment equal to the London Interbank Offered Rate (LIBOR) plus 150 basis points. The coupon contains a de-leveraging multiple of 0.50x. The prevailing LIBOR on January 1, 2002 is 4.00%. The June 30, 2002 coupon payment is calculated as follows:

Floating Rate Coupon = (4.00%)(0.50) + 150bps = 3.50%

Non-Interest Rate Floating Coupons: A bond’s coupon can be structured as a floater that is not derived from a market interest rate. For example, a Treasury Inflation Protection Security (T.I.P.S.) is a government bond with a coupon rate that is indexed to the present level of inflation. The following is the basic formula of a T.I.P.S:

Consider the following example: A T.I.P.S. offers a coupon payment equal to 1.5% plus the rate of inflation. The latest Consumer Price index suggests inflation is 3.3%. What is the value of the coupon? 

T.I.P.S. Coupon Rate = 3.3% + 1.5% = 4.8%

Caps, Floors & Collars

A problem with floating coupons is that their coupon rates can fluctuate substantially when their reference interest rates increase or decrease. A dramatic rise in a floater’s reference interest rate would create a significant expense for the issuer (in the form of higher coupon payments). In contrast, a significant decline in the reference interest rate would deteriorate an investor’s return. To maintain a reasonable range of rates, most floaters incorporate caps and floors. A cap is the highest rate that a floating coupon will pay in periods of increasing interest rates. A floor is the lowest rate that a coupon will pay in periods of decreasing interest rates. Used collectively, a cap and floor are known as a collar.

Practice Questions:

1.  A $10,000 face value bond with a floating rate coupon makes a semi-annual coupon payment equal to LIBOR plus 225 basis points. The prevailing LIBOR on January 1, 2000 was 4%. By June 30, 2000 LIBOR increased 110 basis points to 5.1%. Calculate the coupon payment to be dispersed on June 30, 2000.

1. $625
2. $375
3. $735
4. $725

2.  A $5,000 face value bond is structured to pay a semi-annual inverse floater equal to 7% less the prevailing LIBOR. LIBOR on July 1, 2003 was 3.5%. LIBOR increased to 4% by December 31, 2003. What is the value of the coupon to be paid on December 31, 2003?

1. $100
2. $500
3. $175
4. $150

3.  A $1,000 face value bond is structured to pay a semi-annual de-leveraged floater equal to 9% less .50x the prevailing LIBOR. Libor on January 1, 2003 was 5.0%. What is the value of the coupon to be paid on June 30, 2003?

1. $90
2. $65
3. $45
4. $50

4.  A $1,000 face value bond is structured to pay a semi-annual floating rate coupon equal to 4% plus LIBOR. LIBOR on January 1, 2001 was 3%. The bond has a cap of 6%. What is the value of the coupon to be paid on June 30, 2001?

1. $800
2. $600
3. $80
4. $60

5.  A bond is structured with to pay a semi-annual floating rate coupon equal to LIBOR + 3%. Although the bond does not have a cap or floor, what is the minimum coupon rate the bond will pay during periods of declining interest rates?

1. LIBOR – 3%
2. LIBOR
3. 3%
4. 6% semi-annually

6.  A T.I.P.S. pays a coupon rate indexed to the rate of:

1. 6-Month T-Bills
2. LIBOR
3. Interest
4. Inflation

Answers:

1.    A

2.    C

3.    B

4.    D

5.    C

6.    D

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