# How to Price Bonds With Floating Rates

The par value of a bond is 100. This is its face value -- the principal amount the bond will pay at maturity -- quoted as a percentage of face value. A bond’s coupon period is the interval between interest payments, and floating-rate bonds normally reset on the payment date. Because coupon rates on floating-rate bonds reset to market rates, each bond should carry a price that is close to par.

## Bond Conventions

The price of a bond is the invoice price -- the amount you pay to buy it, not counting commissions or accrued interest -- divided by its face value. For example, the price of a \$1,000 face value bond selling for \$950 is quoted as 95, which is \$950 divided by \$1,000 expressed as a percentage. Many bonds pay interest semiannually, so that their coupon payments are equal to one-half of the coupon rate times the bond’s face value.

## Beginning of Period

On the coupon payment date, a floater‘s new coupon rate is reset to a reference rate such as the London Interbank Offer Rate, or LIBOR, plus a fixed percentage increment. For example, a floating-rate bond might annually pay LIBOR plus 1 percent in semiannual payments. If the annualized LIBOR rate is 2.5 percent, the new bond annual rate is 3.5 percent. On a \$1,000 face value, this equals a seminannual payment of \$1,000 times 0.5 year times 3.5 percent per year, or \$17.50. The price of the bond at the start of the coupon period should be 100, because the coupon rate is reset to reflect prevailing market rates.

## The Price Formula

Prevailing interest rates might change during the coupon period. The price of the floater will become par after the period ends, so the current price must equal par plus the upcoming coupon payment, adjusted for the time until payment. The formula for floater’s price is a fraction. The numerator is par plus the coupon amount as a percentage of face value. The denominator is a factor raised by an exponent. The factor is 1 plus the prevailing interest rate, divided by the number of months in each coupon period, divided by 12 months. The exponent is the time until the next payment rate, expressed as a fraction of the coupon period.

## Price Formula Example

Suppose LIBOR rises to 3 percent one month before the payment date of the floating-rate bond. This makes the prevailing annual market rate 4 percent, which is LIBOR plus the 1 percent increment. The numerator of the price equation is 101.75, which is (the face value of \$1,000 plus the upcoming \$17.50 coupon) divided by the \$1,000 face value, on a percentage basis. The denominator is (1 plus (0.5 year times 4 percent annual market rate)) raised to the power of 1/6. The exponent of 1/6 reflects the fact that one month remains in the six-month coupon period. The result is a price of 101.4147 for the floating-rate bond.

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#### About the Author

Based in Chicago, Eric Bank has been writing business-related articles since 1985, and science articles since 2010. His articles have appeared in "PC Magazine" and on numerous websites. He holds a B.S. in biology and an M.B.A. from New York University. He also holds an M.S. in finance from DePaul University.

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