?? 1ù???÷ By Vincent Kok??There is a relationship between bond prices and interest rates, and the maturity of a bond has an impact on its pricesensitivity to interest rates. This article examines the relationship.??A dollar today is worth more than a dollar in the future, simply because a dol-lar today can be deposited into a bank ac-count to earn interest. If one-year interest rates are 5%, the $1 received today and deposited into the bank account would be worth $1.05 in a year's time.??$1 today is also known as the present value of the $1.05 expected in a year, given the one-year interest rates of 5% relationship between present value, future value and interest rates is given by the simple discounting formula :-??Present Value = sum of future cashflows / (1 interest rate)??In our earlier example, the present val-ue of $1 was therefore obtained from:-????=$1.05/ (1 5%) =$1.00??A bond holder receives a stream of interest, or coupons for owning the bond and gets back his principal on maturity of the bond. In order to receive these streams of future cashflows, the pros-pective bond holder pays a price to the issuer of the bond. The price paid upfront is the present value of all the future cash-flows of coupons and principal on matu-rity, discounted at the appropriate interest rate, which is also known as the yield to maturity (YTM) of the bond.??The YTM is the current market interest rates, which could differ from the fixed interest or coupon rate paid by each bond. The YTM is determined by (among other factors) inflation, demand and supply of funds and Central Bank policy. On the other hand, the bonds coupon or fixed in-terest rate is determined at the launch of the bond and stays fixed during the bond's lifetime.??The following examples will illustrate how changes in YTM or market interest rates affect bond prices.??Let's calculate the price of a two-year bond, which pays annual coupons of 8%, if the current interest rates or YTM is 5%. Note that this bond pays a higher coupon than the prevailing interest rates of 5%, which therefore makes the bond attractive to investors. Applying the present value formula to obtain the price of the bond:-??Present Value = ?2$8/(1 5%) ?3 ?2$8 $100/(1 5%)2.?3= $105.58??A very important point to note is the inverse relationshipbetween yield (deno-minator) and price. A rise in interest rates will reduce the price, or present value of all the future cashflows, of the bond. Conversely, a fall in interest rates will in-crease the price, or present value ofall future cashflows of the bond. For in-stance, if the interest rates or yields rise to 6%, the new price of the bond will now only be:-??Present Value = ?2$8/(1 6%)?3 ?2$8 $100/(1 6%)2.?3= $103.67
