Question

“For bonds selling at a discount, the yield to maturity should be greater than the current yield and the coupon rate.” Is the statement true or false? Explain why.

Answer 1

The given statement is TRUE. Now let us understand why with an example.

Bonds selling at a price below its par value are called discount bonds. Suppose the par value of the bond is $ 100 and its coupon rate (i.e. annual interest paid by bond) is 5%, and the bond is trading at a discount from its par value (say at $ 95), then in that case, the current yield would be =Coupon paid by bond/Market price of bond * 100 = (100*5%)/95 = 5.26%. Yield to maturity of a bond can be understood as its IRR i.e. the rate at which present value of outflow from the bond ($95 purchase price) would equate with present value of all future inflows from the bond (coupon of $ 5 each year till maturity + $ 100 at maturity). Here we assume there are 5 years to maturity. This YTM could be found using trial and error method of finding IRR. If we do so, we get YTM = 6.19%. This example here proves that YTM should be greater than current yield and coupon rate for a bond selling at a discount. This relationship between YTM, Coupon rate and Current Yield always holds. One must not forget the inverse relationship of bond price with YTM, higher YTM would imply lower bond prices (which is nothing but bond with lower market value than its par value.