Question

Problem #1: A bond issued on February 1, 2004 with face value of $48400 has semiannual coupons of 5%, and can be redeemed for par (face value) on February 1, 2021. What is the accrued interest and the market price (the “clean” price) of the bond on November 15, 2006, if the bond's yield on that date is to be 8%? (use actual/actual for accrued interest). Problem #1: 702.79,36069.82 accrued interest and market price in that order), separated with a comma both answers correct to 2 decimals Just Save Submit Problem #1 for Grading Attempt #3 Attempt #4 Attempt #5 Problem #1 Your Answer: Attempt #1 806.67, 36177.58 0/4x Attempt #2 702.79, 36069.82 0/4X Your Mark:

Answer 1

Semi-annual Coupon Payments = 48,400*5%*0.5 = $1,210

No. of semi-annual periods left as on 1^st Aug,2006 = 29

Semi-annual yield = 8%/2 = 4%

We need to work out the bond value as at the last coupon date i.e. 1 August, 2006

= Present value of future coupon payments and maturity value of the bond discounted at the current yield

= 1,210*PVIFA(4%,29) + 48,400*PVIF(4%,29)

= 1,210*16.9837 + 48,400*0.3207

= $36,072.16

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To get to a value as at Nov 15, 2006, we must compound the above value by the fraction of t/T. Where t is the number of days since last coupon period i.e. 106 and T is the total number of days in a coupon period i.e. 180.

Dirty Price of the bond as on Nov 15,2006 = 36,072.16*(1 + 8%/2)^(106/180)

= 36,072.16 * (1.04^0.588889)

= 36,072.16*1.0233654

= $36,915.

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Clean Price = Dirty Price – Accrued Interest

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Accrued Interest = F ×	C	×	D
	m		T

Where F is the face value, C is the total annual coupon rate, m is the coupon payments per year, D is the days since last payment date and T is the total number of days between coupon payments.

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Accrued Interest = 48,400*(5%/2)*[(180-74)/180]

= 48,400*2.5%*106/180

=48,400*2.5%*0.588889

= $714.03

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Therefore, Clean Price of the Bond on Nov 15,2006 = 36,915-714.03

= $36,200.97

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So ,the answer is $714.03 , $36,200.97