The worked solutions are included for this question but I need an explanation for the worked solution.

Why must the equation of step 2 include the 1/1.0246956^20?

Bond “ABC” is a 10-year, $1,000 par value bond which pays a 6% coupon with quarterly payments during its first five years (you receive $15 a quarter for the first 20 quarters). During the remaining five years the security has an 8% quarterly coupon (you receive $20 a quarter for the second 20 quarters). At the end of 10 years (40 quarters) you will also receive the par value.

Bond “DEF” is another 10-year bond issued by the same company, and it has a 10% semiannual coupon. This bond is selling at its par value $1,000 and has the same risk as the bond “ABC”. Given this information, what should be the price of the bond “ABC”?

Worked Solution:

Step 1: Find the periodic interest rate on “ABC”.

Since the securities are of equal risk and maturity, they must have the same effective annual rate. Since “DEF” is a 10-year bond is selling at par, its nominal yield is 10%, the same as its coupon rate. DEF’s effective annual rate is (1 + 0.10/2)2 – 1 = 10.25%. Since “ABC” has quarterly payments, its periodic rate = (1.1025)0.25 – 1 = 2.4695%

Step 2: Price of ABC Price of “ABC” = PV of Annuity (20 payments of $15) + PV of Annuity (next 19 payments of $20) + PV of (last $20 + $1,000) = 15/0.024695 (1 ? 1/1.024695^20 ) + 1/1.024695^20 { 20/0.024695 (1 ? 1/1.024695^19 )} + 1020/1.024695^40

= 234.51 + 184.42 + 384.42 = $ 803.36

The final answer is $803.36

Why must the equation of step 2 include the 1/1.0246956^20?

Are you overwhelmed by an intense schedule and facing difficulties completing this assignment? We at GrandHomework know how to assist students in the most effective and cheap way possible. To be sure of this, place an order and enjoy the best grades that you deserve!

Post Homework