EBS – Bond Pricing, YTM, Forward Interest Rates Bond pricing and yield to maturity Pricing the bond The bond price is obtained by discounting the bond cash flows by the set of spot rates covering the timing of the cash flows. If you have a 9% coupon, 5 year bond, the cash flows will be 9, 9, 9, 9, 109. The 9 is the interest that the bondholder gets each year (this is 9% of the par or face value, which will be 100). The 109 at the end is the repayment of the original 100 plus the last coupon payment of 9. If the set of spot rates for the next 5 years is 6%, 6.25%, 6.5%, 6.95% and 7.5% what is the bond price? The bond price is the discounted value of the bond’s cash flows, so the calculation would be: Bond price = 9 (1.06) + 9 + 9 + 9 + 109 (1.0625)2 (1.065)3 (1.0695)4 (1.075)5 Bond price = 106.72 The bond price is the present value of the bond’s cash flows, discounted by the set of spot rates. Terminology Face value: also known as ‘Par value’ or ‘Nominal value’. This is usually the issue price of the bond. In the UK this will be £100, in the US and Europe it will be $1000 or €1000. Coupon: this is the income return that the bondholder receives. The coupon is usually expressed as a percentage, for example, 6%. This is the coupon rate. The income that a 6% bond would deliver in the UK would be £6 and in the US and Europe, $60 or €60. The bondholder will receive this every year through until the maturity of the bond. Maturity: this is when the bond is due for repayment, for example, the 6% bond above might have a seven year maturity. What that means is that the company has to pay back the sum borrowed originally (ie the face value of the bond for all the bondholders of that bond issue). The redemption value of the bond is the same as the face value of the bond (£100, $1000, or €1000). Market price of bond: the bond will be sold at face value (£100, $1000, or €1000), but once it is on the market, the bond price may move away from that face value. Why would it do