Digicel Jamaica has raised financing by issuing 25-year bonds on January 1, 2009. They mature on December 31, 2033
and have a par value of $1,000 and a coupon rate of 8%. Coupon
payments are made semi-annually.
a)What is interest rate risk?
Which bond has more interest
rate risk? Why?
b)What would the value of the bonds be on June 30, 2027, if interest rates had risen to 12%?
c)What would be their value on
December 31, 2023, if interest rates had fallen to 6%?
d) If the bonds had a value of $925.00 on December 31, 2028, what would be their yield to maturity on that date?
You're taking a class called UWI? Strange class! As for your question, I recommend you read your textbook to find the answers.
i have the same question lol this is so funny
a) Interest rate risk refers to the potential for the value of a bond to change due to fluctuations in interest rates. When interest rates rise, bond prices tend to fall, and when interest rates fall, bond prices tend to rise. This is because when interest rates rise, newer bonds with higher coupon rates become more attractive, reducing the demand for existing bonds with lower coupon rates and causing their prices to decrease. The longer the maturity of a bond, the more sensitive it is to changes in interest rates, resulting in higher interest rate risk.
In this case, both bonds have the same maturity of 25 years, but they may differ in their interest rate risk based on their coupon rate. A bond with a lower coupon rate would have more interest rate risk because if interest rates rise, its fixed coupon rate becomes less attractive compared to the prevailing market rates, leading to a greater decrease in its value. Therefore, to determine which bond has more interest rate risk, we need to compare their coupon rates.
b) To calculate the value of the bonds on June 30, 2027, if interest rates had risen to 12%, we need to discount the future cash flows generated by the bonds back to the present value using the new interest rate. Given that the bonds have a coupon rate of 8% and semi-annual coupon payments, we can use the following steps:
1. Determine the number of years and semi-annual periods until June 30, 2027, from the issuance date of January 1, 2009.
Number of years = 2027 - 2009 = 18 years
Number of semi-annual periods = 18 * 2 = 36 semi-annual periods
2. Calculate the present value of the future coupon payments using the new interest rate of 12%.
Coupon payment = 8% * $1,000 / 2 = $40 (semi-annual coupon payment)
Present value of coupon payments = Σ(Coupon payment / (1 + (12%/2))^n, from n=1 to 36
3. Calculate the present value of the final payment (par value) on December 31, 2033.
Present value of final payment = $1,000 / (1 + (12%/2))^72
4. Add the present values of the coupon payments and the final payment to get the total estimated value on June 30, 2027.
c) To calculate the value of the bonds on December 31, 2023, if interest rates had fallen to 6%, we follow similar steps as in part b) but using the new interest rate of 6% instead of 12%.
d) To determine the yield to maturity (YTM) of the bonds on December 31, 2028, when their value is $925.00, we need to solve for the discount rate (YTM) that equates the present value of the bond's future cash flows (coupon payments and final payment) to its current market value of $925.00. This involves using the bond pricing formula and solving for YTM through an iterative process since there is no direct formula to calculate it.
We can use various financial calculators or spreadsheet programs with bond pricing functions to find the YTM given the bond's current market value, coupon rate, time to maturity, and payment frequency.