Question

A bond that has a face value of $2,500 and coupon rate of 4.80% payable semi-annually was redeemable on July 1, 2021. Calculate the purchase pric of the bond on February 10, 2015 when the yield was 5.30% compounded semi-annually. Round to the nearest cent

Answer 1

Due to multiple questions asked, as HOMEWORKLIB's policy only the first question is answered.

Given information

Face value F = $2500

coupon rate = C = 4.8% payable seminannually = 4.8%*2500 *1/2 = $60

Since the bond is redeemable on July 1 2021. This is the maturity date of the bond.

We are asked to calculate purchase price on Feb 10,2015.

Solution:

We will first determine the duration /number of months between Feb 10, 2015 till July 1 2021. The duration is 6 years, 4 months and 28 days. The last coupon payment was on Jan 1, 2015 and we are in between the two coupon dates.Jan 1 and July 1. We will first calculate the clean price using the bond pricing formula and then add the accrued interest from Jan 1 till Feb 10 i.e. 40 days.

The formula to calculate bond price is as follows: C is the coupon payment and r is the yield till maturity

Bond Clean price = C/(1+r) + C/(1+r)² + C/(1+r)³ + C/(1+r)⁴ + ........ + C/(1+r)ⁿ + F/(1+r)ⁿ

This can be simplified as   

Bond Clean price = C * [(1-(1+r)^-n ) / r] + F/(1+r)ⁿ

C = $60

F = $2500

n = 6 years = 6*2 = 12 periods (since coupon is paid semi annually)

yield r = 5.3% per annum = 5.3/2 = 2.65%

Substitute these values in the formula above

Bond Clean price = 60*((1-(1+2.65%)^-12)/2.65%)+2500/(1+2.65%)¹² = 2436.4674

Now we will calculate accrued interest:

Accrued interest = coupon payment * number of days since last payment / number of days between payments

= 60 * 40/181 = 13.2597

Hence bond price = bond clean price + accrued interest = 2436.4674 + 13.2597 = $2,449.73