## Bond Valuation

### Learning Outcomes

• Determine the items that impact the selling price of a bond

It would be nice if bonds were always issued at the par or face value of the bonds. But, certain circumstances prevent the bond from being issued at the face amount. We may be forced to issue the bond at a discount or premium. This video will explain the basic concepts and then we will review examples:

You can view the transcript for “Bond Interest Rates” here (opens in new window).

## Bond prices and interest rates

The price of a bond issue often differs from its face value. The amount a bond sells for above face value is a premium. The amount a bond sells for below face value is a discount. A difference between face value and issue price exists whenever the market rate of interest for similar bonds differs from the contract rate of interest on the bonds. The effective interest rate (also called the yield) is the minimum rate of interest that investors accept on bonds of a particular risk category. The higher the risk category, the higher the minimum rate of interest that investors accept. The contract rate of interest is also called the stated, coupon, or nominal rate is the rate used to pay interest. Firms state this rate in the bond indenture, print it on the face of each bond, and use it to determine the amount of cash paid each interest period. The market rate fluctuates from day to day, responding to factors such as the interest rate the Federal Reserve Board charges banks to borrow from it; government actions to finance the national debt; and the supply of, and demand for, money.

Market and contract rates of interest are likely to differ. Issuers must set the contract rate before the bonds are actually sold to allow time for such activities as printing the bonds. Assume, for instance, the contract rate for a bond issue is set at 12%. If the market rate is equal to the contract rate, the bonds will sell at their face value. However, by the time the bonds are sold, the market rate could be higher or lower than the contract rate.

Market Rate = Contract Rate Bond sells at par (or face or 100%) Bonds sells at premium (price greater than 100%) Bond sells at discount (price less than 100%)

As shown above, if the market rate is lower than the contract rate, the bonds will sell for more than their face value. Thus, if the market rate is 10% and the contract rate is 12%, the bonds will sell at a premium as the result of investors bidding up their price. However, if the market rate is higher than the contract rate, the bonds will sell for less than their face value. Thus, if the market rate is 14% and the contract rate is 12%, the bonds will sell at a discount. Investors are not interested in bonds bearing a contract rate less than the market rate unless the price is reduced. Selling bonds at a premium or a discount allows the purchasers of the bonds to earn the market rate of interest on their investment.

Computing long-term bond prices involves finding present values using compound interest. Buyers and sellers negotiate a price that yields the going rate of interest for bonds of a particular risk class. The price investors pay for a given bond issue is equal to the present value of the bonds.

Issuers usually quote bond prices as percentages of face value—100 means 100% of face value, 97 means a discounted price of  97% of face value, and 103 means a premium price of 103% of face value. For example, one hundred $1,000 face value bonds issued at 103 have a price of$103,000 (100 bonds x \$1,000 each x 103%). Regardless of the issue price, at maturity, the issuer of the bonds must pay the investor(s) the face value (or principal amount) of the bonds.