Bonds are valued in a number of different ways. Generally, the value of a bond is determined by the present value of the bond’s cash flow which includes periodic interest payments and the repayment of principal. Three key factors affect a bond’s price: the par value, the market interest rate and length of maturity, and the investor’s discount rate.

Par Value

When a bond is sold for less than its par value, it is being traded at a discount; when a bond is sold for more than its par value, it is being traded at a premium. The terms premium and discount in this situation refer to the bond’s current market value. Bonds are sold at a discount when the interest rate on the bond is lower than the prevailing market interest rate; bonds are sold at a premium when the interest rate on the bond is higher than the prevailing market interest rate. For example, suppose the market interest rate is 4 percent and the coupon interest rate on a bond is 6 percent. Because this bond pays more interest than the market average, investors will be willing to pay a higher price for this bond; thus, this bond will trade at a premium.

Market Interest Rate and Maturity

A bond’s value fluctuates according to changes in the market interest rate. A bond’s coupon interest rate and par value are fixed over the life of the bond. If the market interest rate increases (i.e., the interest rate increases), the value of the bond will decrease because investors will require a higher return on the bond to make up for the fact that coupon payments are lower than the market return rate. Investors will pay less for the bond to make up for the lower expected return. If the market interest rate decreases, the value of the bond will increase.
The price of a bond is also affected by the bond’s maturity length. The longer a bond takes to mature, the greater the impact of fluctuations in the market interest rate. The less time it takes for a bond to mature, the less the impact of fluctuations in the market interest rate.

Investor’s Required Rate of Return and Price

The value of a bond is related to the investor’s required rate of return, which is the rate of return an investor requires to hold or invest in a bond. If the investor’s required rate increases, the investor will require a higher rate of return on all cash flows. Since the interest rate on bond coupons is generally fixed, the only way an investor can increase a bond’s cash flow is by paying a lower price for the bond. The less an investor is willing to pay for a bond, the more the value of the bond decreases. The reverse is also true. An investor’s required rate of return can change for many reasons:

• The investor perceives a change in the risk associated with the issuer of the bond: As perceived risk of an issuer increases, investors require a higher discount rate to invest in the issuer’s bond.
• The investor perceives a change in the general market interest rate: As the market interest rate increases, investors require a higher discount rate to invest in any bond.
• The investor perceives a change in overall market risk: As the perceived riskiness of the market increases, investors require a higher discount rate to invest in all asset classes.

Note that the investor’s discount rate will vary from one investor to another.

Bond Yields

The bond yield is the total return on a bond investment. The bond yield is not the same as the coupon interest rate. The bond yield is affected by the bond price, which may be more or less than par value. The bond yield is calculated in three different ways: current yield, yield to maturity, and equivalent taxable yield.

• Current yield: Current yield is the ratio of annual interest payments and the bond’s current market price. Current yield is calculated by dividing the total annual interest payment by the market price of the bond.
• Yield to maturity: Yield to maturity is the true yield that the holder receives if the bond is held to maturity; when this yield is calculated, it is assumed that all interest payments can be reinvested at the same interest rate as the coupon rate. Since this calculation involves cash flow, it is best solved with a financial calculator.
• Equivalent taxable yield (ETY): Finding the equivalent taxable yield allows you to calculate the yield you must receive from a taxable security to get the same return you would make on a tax-advantaged security. To solve for the equivalent taxable yield, use the following formula:

ETY = tax-free yield / (1 – marginal tax rate)

Remember, the marginal tax rate is a combination of both state and local taxes. To effectively calculate after-tax returns, you must know the tax benefits of each type of bond (for example, you must know that municipal bonds are free from federal taxes and Treasury debt securities are free from state and local taxes). For help with calculating after-tax returns and equivalent taxable yields, see Learning Tool 26: After-Tax Returns, Equivalent Taxable Yield, and After-Inflation Returns in the Learning Tools directory of this website.