Market Interest Rate

The market interest rate is the rate of interest that lenders and investors require, at a given time, on a loan or debt security with a particular level of risk and maturity. It is also called the effective rate, the yield or the discount rate. It differs from the stated rate, also called the coupon or contractual interest rate, which is written into the bond or note and fixes the cash interest paid. When the two rates differ, the debt is issued or traded at a price above or below its face value.

Market rates are shaped by general interest rates in the economy, including central bank policy rates such as the federal funds rate, by inflation expectations, by the length of the loan, and by the borrower's credit risk. A risky company must offer a higher rate than the government, which typically borrows close to the risk-free rate.

The price of a bond is the present value of its future cash flows, discounted at the market rate:

• $C$ is the cash interest payment each period, set by the stated rate.
• $r$ is the market interest rate per period.
• $F$ is the face value repaid at maturity.
• $n$ is the number of periods.

If the market rate is higher than the stated rate, investors pay less than face value and the bond sells at a discount. If the market rate is lower, they pay more and it sells at a premium. If the two are equal, it sells at par. The market rate at which an investor buys and holds to maturity is the bond's yield to maturity.

A company issues $1,000,000 of five-year bonds with a stated rate of 5 percent, paying $50,000 of interest a year. On the issue date, the market rate for similar bonds is 6 percent. The present value of the five interest payments at 6 percent is about $210,618, and the present value of the $1,000,000 repayment is about $747,258, so the bonds sell for about $957,876. The company records cash of $957,876, a discount on bonds payable of $42,124, and bonds payable of $1,000,000.

In year one, interest expense is 6 percent of the carrying amount, or about $57,473, while cash paid is $50,000. The $7,473 difference amortizes the discount and raises the carrying amount. This is the effective interest rate method, required under IFRS and preferred under US GAAP. If the market rate had been 4 percent, the bonds would have sold at a premium, and the premium would be reduced over time as described in the entry on amortization of bond premium.

• Notes with no or unusually low stated interest: US GAAP requires the note to be recorded at present value using a market rate, with the difference recognized as imputed interest.
• Leases: lessees discount lease payments at the rate implicit in the lease or, if that cannot be determined, their incremental borrowing rate, a form of market rate.
• Fair value: debt investments carried at fair value are remeasured using current market rates, so prices fall when rates rise.
• Pensions: defined benefit obligations are discounted using market yields on high-quality corporate bonds.

Once a bond is issued, its interest expense is locked in at the market rate on the issue date, even if market rates change later. However, changes in market rates move the bond's trading price: when rates rise, existing bonds fall in value, which is the core of interest rate risk. Companies may disclose the fair value of their debt in the notes to show what it would cost to settle at current rates. A common mistake is to use the stated rate to calculate interest expense on debt issued at a discount or premium, which misstates both the liability and profit.