Question

2) Please solve for the value of the following bonds and briefly explain your results:

A) A U.S. Government Treasury Strip is quoted in the Wall Street Journal at a market price of 87:19 (87 and 19/32). If the strip is scheduled to mature in May 2025, what is the annual interest rate for this bond?

B) Xenor Corporation introduced a bond in 2001 that offered a coupon rate of 8 1/2%, resulting in coupon payments of $8.50. The bond is scheduled to mature in 2030. If the current going interest rate in the market is 6 3/4%, what is the market price (please calculate the interest and the principal due to get this value) of this bond today? What is the bond selling for in the market relative to its initial value at the time the bond was introduced and what is the common term used to describe a bond that is selling at this price?

C) A bond offers a coupon that makes annual payments of $87.50. The bond was originally set to mature in 17 years. A quote for this bond, obtained 15 years after the original issue date, listed the market price as $1,070.00. What is the YTM for this bond?

Answer 1

Part A:

Market price of the STRIP= 87+19/32= 87.59375% of face value = $87.59375

Time to maturity= 5 years (till May 2025)

Annual interest rate=[(100/87.59375)^(1/5)]-1 = 1.141634^(1/5)-1 = 2.684614%

Part B:

Given,

Time to maturity in 2030= 10 years

Amount of coupon= $8.50    YTM at the time of issue= 8.5% or, 0.085

Face value= 8.50/0.085= $100.

Since the amount of coupon is given as $8.50 for a coupon rate of 8.5%, frequency is annual.

Number of coupon payments in future=10

Present value of future coupon payments with YTM at 6.75%= $55.155531 as follows:

Present value of Redemption value= FV/1+YTM)^10 = 100/(1+6.75%)^10 = 100/ 1.92167 =$ 52.03807

Current Market price= PV of interest + PV of Face value= $$55.155531+$52.03807 = $107.1936

Since the coupon rate and YTM were equal, the bond was issued at par ($100) initially. Current value is 107.19% of issue price. Bond selling at this price is commonly called Premium Bond.

Part C:

YTM of the bond= 4.986107% as follows: