Question

1 (a) Determine the approximate percentage change in price for a bond whose coupon rate changes from 10% to 12% if the duration is -6.76%.
(b) What would be the new price if the old price was GHS5.78?               

2.      A 10-year, 7% coupon bond with a face value of $1,000 is currently selling for $871.65. Compute your rate of return if you sell the bond next year for $880.10.

3. One-year interest rate over the next five years are expected to be 15%, 16%, 17%, 18% and 19%.
Required:
i. Determine the interest rate on one to five-year bonds today.         
ii.   investors have preference for holding short-term bonds so their liquidity premium for holding one-to five-year bonds are 0%, 0.25%, 0.50%, 0.75% and 1%. Determine the interest rate on one to five-year bonds today.                   

Answer 1

Question 1

a) Determination of change in price

Step 1: Calculation of Modified Duration

Modified Duration = Duration / (1+Yield To Maturity)

= -6.76 / 1.1

= -6.15

*Since YTM is not provided in question, current interest rate is taken as YTM.

Step 1: Calculation of percentage change in price

Percentage change in price = Modified Duration * percentage change in YTM

= -6.15 * (12%-10%)

= -6.15 * 2

= -12.30%

(b) Calculation of new price

Old price = 5.78

New price = 5.78 + 5.78 * 12.30%

= 6.49

*In this case bond have negative duration. That means the direction of change in interest rate and bond price is same. When interest rate increases, price also increases and vice-versa.