Question

Java Spirit Ltd. intends to issue a new series of bonds on July 1, 2023, with a $1,000 par value. They are expected to mature in 32 years and will have a coupon rate of 5%, paid semi-annually. We would like to find the expected price of the bond on December 31, 2029, if interest rates were 12%? Bond Valuation Formula What values should we use in the above formula for C, i and n?

Answer 1

To calculate the expected price of a Java Spirit Ltd. bond with semi-annual coupon payments on December 31, 2029, you need to determine C ($25), i (6% per period), and n (13 periods). Given that the coupon rate is less than the market interest rate, the bond's price will be below its face value.

Step-by-step explanation:

To calculate the expected price of a bond, we use the bond valuation formula which considers the present value of future coupon payments and the present value of the par value at maturity. In the case of Java Spirit Ltd., which intends to issue a bond with a $1,000 par value, a coupon rate of 5%, and semi-annual payments, the bond valuation formula requires values for C (the coupon payment), i (the market interest rate per period), and n (the total number of periods until maturity).

For this bond:

• C = $1,000 par value x 5% coupon rate / 2 (because the interest is paid semi-annually) = $25 per period.
• i = 12% market annual interest rate / 2 = 6% per period.
• n = Number of years to December 31, 2029 (6.5 years from issuance) x 2 = 13 periods remaining.

Given that interest rates rise to 12%, the present value of the coupon payments and the face value must be discounted using the market rate. Therefore, the price of the bond will be lower than its face value, because the coupon rate is less than the market interest rate.