Question

A 9-year, 12% coupon bond with face value $1,000 is priced at $856.85. If we know that the price of the same bond is $741.82 when the YTM is 18%, state the range of the YTM for this bond without using any calculation. Justify your answer.

Answer 1

Answer -  

The range of YTM for this bond will be in the range of 12 % to 18 %.

When the bond trades at a discount, its yield to maturity is always higher than its coupon rate. Threfore the YTM will be greater than 12 % coupon rate as it is tradinfg at discount price of $ 856.85 to the original face value of $ 1000. If the Bond price is $ 741.82 at 18 % YTM. The bond price decreases as the YTM increases. Therefore the bond YTM will be less than 18 % as the price of bond is higher ( $ 856.85 > $ 741.82).

We can verify it by calculation

Given

Face value = FV = $ 1000
Present value = PV = $ 856.85
Number of years = N = 9 years
Coupon rate = 12%
Coupon payment = 12 % x $ 1000 = $ 120

YTM = I/Y = ?

YTM = 15 %

Therefore YTM = 15 % which is in the range of 12 % to 18 %