Question

A 1000 face value, 8% coupon annual pay bond is issued on Feb. 28 at par.

Calculate the accrued interest on the bond on 31 My; accrued interest on 31 July, dirty price on the bond 31 May and the dirty price on 31 July. The first coupon will be paid on Feb. 28 of the next year. The bond is quoted on each of the following dates at clean prices noted:

31 May at $1080

31 July at $1110

A) 40, 66.67, 1100, 1143.33

B) 20, 33.33, 1100, 1143.33

C) 20, 33.33, 1120, 1143.33

D) 40, 66.67, 1120, 1143.33

Answer 1

Solution:

Let's first understand the meaning of clean prices and dirty prices with regards to bond pricing mechanisms. Please consider the following example:

Example:

• A bond is issued on 1st January for $100 per bond having 10% interest rate payable annually. It means that the bondholders would receives the first interest of $10 after one year. As time passes during the year, the interest income related to the bond is getting accrued which will be received at the end of the year.
• If a bondholder sells his bond at any time during the year, he is also giving up the income that has been accrued to him so far. So if a bondholder sells his bonds on 30th June, i.e. 6 months into the year, he is also giving up the 6 months worth of interest income that belongs to him (as held the bond during those 6 months).
• In order to ensure that the bond holder is compensated for that 6 months worth of interest income, the market price of the bond goes up accordingly such that the buyer pays for the market value of bond as well as the 6 months worth of interest to the bond seller.

Hence, the dirty price refers to the total value of bond including any accrued interest for the year that has not yet been paid and will be received later by the bond buyer when it becomes due. On the contrary, clean price refers to the value of bond excluding the accrued interest.

Given case:

The period of accrued interest is 3 months for 31st May and 5 months for 31st July (i.e. period from march to 31stMay/31st July)

Accrued interest (31st May)= 1,000*8%*3/12 = $20

Accrued interest (31st July)= 1,000*8%*5/12 = $33.33

Dirty price (31st May)= Clean price (31st May) + Accrued interest (31st May) = 1,080 + 20 = $1,100

Dirty price (31st July)= Clean price (31st July) + Accrued interest (31st July) = 1,110 + 33.33 = $1,143.33

Therefore, the correct option is Option B.