Question

You want to know the price of a 8% coupon bond that is currently being traded in the bond markets. The maturity of the bond is 3 years, its par value is $1000, and it pays its coupons annually. You do not know the corresponding market interest rates, but you know the YTM of 8 % for the bond.

(1) What is the price of this bond?

(2) Does this mean that YTM is equivalent to the market interest rate determined in the bond market? Why, or why not?

Answer 1

Solution

(1) The price of the bond is the same as its Face value $1000 since the coupon rate and YTM are both the same i.e. 8%

The YTM represents the return that the holder of the bond would earn if he holds the bond till its maturity. Discounting the coupon payments and terminal payment of face value to the present at the YTM gives the valuation or price of the bond. When bond cash flows are discounted at the coupon rate, it always gives the face value of the bond. Hence when YTM and coupon rate are same, we get the face value as the price of the bond.

(2) YTM and market interest rate are not the same thing. YTM is determined from the cash flows and the point in time when the bond is acquired and is the internal rate of return of the bond to the holder till maturity. On the bond market, bonds are often bought and sold before they reach maturity and the market interest rate is an indication of the return from the buying and selling of the bond and not the cash flows (coupon and face value) of the bond from holding.

If the bond is bought to be held to maturity, the YTM is all that matters to the holder but if he is to sell it the implicit market interest rate is what matters to him. Thus, YTM is not equivalent to market interest rate or spot rate determined in the bond market.