SUNNY SIDE OF THE STREET: ANALYSIS OF THE FINANCIAL SYSTEM & THE ECONOMY (part 13)

Interest Rates, Bond Prices, and Present Values

by

Charles Lamson

Although bonds issued by corporations and governments differ in a variety of ways, they really share the following character: they have an original maturity greater than ten years; they have a face or par value (F) of $1,000 per bond, and the issuer (borrower) agrees to make equal periodic interest payments over the term to maturity of the instrument and to repay the face value at maturity. The periodic payments are called coupon payments (C) and are equal to the coupon rate on a bond multiplied by the face value of the bond. As we shall see in a moment, the coupon rate, which usually appears on the bond itself, is not the same thing as the interest rate. The distinction between the coupon rate and the coupon payment and between the coupon rate and the interest rate is often a source of considerable confusion.

So, for example, you buy a bond for Jane for $981.48, you would receive $60 of interest at maturity ($1,000) plus a capital gain of $18.53; the gain is equal to the par value you get back at maturity ($1,000) minus the price you pay at the time of purchase ($981.48). Together the interest and the capital gain ($60 + $1,852 = $78.52). Thus, in this example, you buy the bond at a price below its par value. This is called a discount from par and raises yield on the bond, called the yield to maturity, from 6 to 8 percent. In sum, as the market interest rate rises, the price of existing bonds falls. The lower yield to maturity on existing bonds is unattractive to potential purchasers who can purchase newly issued bonds with higher yields to maturity. Therefore, the yield to maturity on previously issued bonds must somehow rise to remain competitive with the new higher level of prevailing interest rates. The yield on existing bonds rises when their prices fall. 

Suppose that instead of rising from 6 percent to 8 percent the day after Jane buys the bond. The interest rate in the market falls to 4 percent. Jane's bond will rise to $1,019.23. What does this represent?If any of us bought Jane's bond for $1,019.23, we would be paying a price above the par value. This is called a premium above par. At maturity we would get $60 minus a capital loss of $19.23; the loss is equal to what we pay at the time of purchase minus the par value we receive at maturity ($1019.23 - $1,000 = $19.23). The $40.77 ($60 - $19.23 = $40.77) represents a 4 percent yield over the year ($40.77/$1019.23 = .04). Thus, as the market interest rate falls, the prices of existing bonds rise. The reason is that the higher yield to maturity on existing bonds is attractive to potential investors, and as they buy existing bonds, the bond prices rise, reducing their yield to maturity.

In general, then, there is an inverse relationship between the price of outstanding bonds trading in the secondary market and the prevailing level of market interest rates. As a result one can say that if bond prices are rising, then interest rates are falling, and vice versa. These are different ways of saying the same thing, and we need not resort to the formalities of discounting and present value analysis to see the bare essentials of this relationship

*SOURCE: THE FINANCIAL SYSTEM & THE ECONOMY, 3RD ED., 2003,  MAUREEN BURTON & RAY LOMBRA, PGS.  

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