Question

A twelve-year corporate bond has a coupon rate of 9%, a face value of $1,000, and a yield to maturity of 11%. Assume annual interest payments. (i) (2 pts) What is the current price? (ii) (3 pts) What is the duration (Macaulay’s)? (iii) (2 pts) Compare this bond to a eight-year zero coupon bond. Which has more interest-rate risk (which bond price changes more given a 1 percentage point change in the interest rate)? (iv) (2 pts) Using duration, what is the change in price of the bond if there was a parallel shift in interest rates and rates rose 3 percentage points? (v) (2 pts) What is the true current price if interest rates rose 3 percentage points? (vi) (2 pts) Why are the answers different?

Answer 1

Bond Maturity = 12 years, Coupon Rate = 9 %, Face Value = $ 1000, Yield to Maturity = 11 %

(i) Let the market price of the bond be P(m)

Annual Coupon Payment = Annual Coupon Rate x Face Value = 0.09 x 1000 = $ 90

Therefore, P(m) = 90 x (1/0.11) x [1-{1/(1.11)^(12)}] + 1000 / (1.11)^(12) = $ 870.1528 or $ 870.153 approximately.

(ii)

(iii) The duration (Macaulay's) of a zero coupon bond is always equal to its period of maturity and hence would be 8 years in this case. The bond under consideration has a Macaulay's Duration of 7.4928 and Modified Duration of 6.7503 which is lesser than that of the ZCB. As the duration of a bond is a measure of its sensitivity to interest rate risk, the ZCB will have more interest rate risk.

(iv) Change in Bond Price = Change in Yield (in basis points) x Modified Duration x Bond Price (before yield change) = [(14 - 11) / 100] x 6.75028 x 870.15 = $ 176.213 approximately.

NOTE: Please raise a separate query for solutions to the remaining sub parts.