A 10,000 par value bond with coupons at 8%, convertible semiannually, is being sold three years and four months before the bond

Question

3 years ago

13

A 10,000 par value bond with coupons at 8%, convertible semiannually, is being sold three years and four months before the bond

matures. The purchase will yield 6%convertible semiannually to the buyer. The price at the most recent coupon date, immediately after the coupon payment, was 5,640.Calculate the market (quoted) price of the bond.

Business

1 answer:

konstantin123 [22] · Answer 1 · 2022-09-08T02:40:35+03:00

Answer:

$9,124.94

Explanation:

the clean price of the bond two months ago was $5,640.

Currently, interest rate have changed and the price of the bond has changed:

the semiannual yield is 4%, that means that the bimonthly yield = 1.04 = (1 + r)³

1 + r = 1.0132

r = 0.0132

the current price of the bond:

PV of face value = $10,000 / (1 + 0.0132)²⁰ = $7,693.01

PV of coupon payments = ($300 x {[1 - (1 + 0.04)⁻⁶] / 0.04}) / (1 + 0.0132)² = $1,572.64 / (1 + 0.0132)² = $1,531.93

minus accrued interests (dirty price) = $300 x 1/3 = $100

Market value of bond = $9,124.94