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Zorluk: Çok zorDebt Securities and Bond Structure

An institutional investor purchases 1010 corporate bonds in the secondary market, each with a par value of $1,000\$1,000 and a stated annual coupon rate of 5.40%5.40\%. Interest is paid semi-annually on March 1 and September 1. The trade is executed at a quoted market price of 97.5097.50 (97.50%97.50\% of par value) and settles on June 1 using the standard 30/36030/360 day-count convention. What is the total dollar amount, including accrued interest, that the investor must pay to settle the purchase of all 1010 bonds?

Cevap: 9885 $

Cevap

The total dollar amount required to settle the purchase of all 1010 bonds, including accrued interest, is $9,885.00\$9,885.00.
To find the total settlement cost for corporate bonds, two components must be computed: the total principal purchase price and the total accrued interest. The principal price per bond is 97.50%97.50\% of $1,000=$975.00\$1,000 = \$975.00, which equals $9,750.00\$9,750.00 for 1010 bonds. Under corporate bond rules (30/36030/360 day-count convention), interest accrues from the most recent coupon date (March 1) through the day before settlement (May 31). That comprises 33 full months of 3030 days each, totaling 9090 days. The annual interest per bond is 5.40%×$1,000=$54.005.40\% \times \$1,000 = \$54.00. Accrued interest per bond is $54.00×(90/360)=$13.50\$54.00 \times (90 / 360) = \$13.50, giving a total accrued interest of $135.00\$135.00 for 1010 bonds. Summing the principal cost ($9,750.00\$9,750.00) and accrued interest ($135.00\$135.00) yields the final settlement amount of $9,885.00\$9,885.00.

Adım Adım Çözüm

1
Calculate the principal purchase price per bond and total principal for the position.
Principal price per bond = $975.00\$975.00; Total principal for 1010 bonds = $9,750.00\$9,750.00.
A bond quoted at 97.5097.50 trades at 97.50%97.50\% of its $1,000\$1,000 par value.
2
Calculate annual interest per bond.
Annual coupon interest = $54.00\$54.00 per bond.
Annual interest is calculated as stated coupon rate times par value (5.40%×$1,0005.40\% \times \$1,000).
3
Determine the number of accrued days using corporate bond 30/36030/360 convention.
Accrued days = 9090 days.
Interest accrues from the last coupon payment date (March 1) up to, but not including, the settlement date (June 1). Under 30/36030/360, March has 3030 days, April has 3030 days, and May has 3030 days (30+30+30=9030 + 30 + 30 = 90 days).
4
Calculate the accrued interest per bond and total position accrued interest.
Accrued interest per bond = $13.50\$13.50; Total accrued interest for 1010 bonds = $135.00\$135.00.
Accrued interest per bond = $54.00×(90/360)=$13.50\$54.00 \times (90 / 360) = \$13.50.
5
Add total principal cost and total accrued interest to find total settlement cost.
Total settlement amount = $9,885.00\$9,885.00.
The buyer must pay the agreed principal price plus the interest earned by the seller up to settlement date.

Anahtar Kavram

Corporate Bond Settlement Price and Accrued Interest Calculation (30/360 Day-Count Convention)
Tahmini Süre:2m 30s
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Debt Securities and Bond Structure

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