Introduction to bonds

A bond is an instrument issued by a company (corporate bond), a country (sovereign debt) or a state/city (municipal bond). They have a finite life, and may make a periodic payment (a coupon) and some final payment (par value). Bonds that do not make a periodic payment are known as zero coupon bonds.

In order to evaluate the price of a bond we need to sum together the present value of future cash flows, evaluated at some required rate of return that reflects the riskiness of those flows. This technique is near identical to the dividend discount model, with a number of noticeable differences:

1. 1. bonds have a finite life; shares are irredeemable and hence have an infinite life

2. 2. bond payments (coupon and par value) are known with certainty, whereas dividends paid on ordinary shares are uncertain

Bond pricing

Bond prices can be communicated in two ways: (i) the price itself, which represents the sum of the present value of these cash flows; and (ii) the interest rate used to determine the price of the bond. The latter is often called a bond's yield to maturity (YTM) and is the interest rate implied by the payment structure.

Let T be the maturity of the bond and C(1), C(2) … C(T) be the future cash flows; the yield to maturity is the rate of return which satisfies:

If the bond pays a constant coupon C and a final payment (the par value) of D at maturity, then the yield to maturity must now solve:

Hopefully it is clear that there is an inverse relationship between the price of a security and its yield to maturity. If the yield to maturity increases, the market price of the bond will decrease.

Example

Consider a bond issued in November 2013 that pays an annual coupon of 1.25%, and expires in November 2017. If it has a par value of €1,000 and the yield to maturity is 1.5%, what is the price of this bond?