Question

A ten-year par value $20,000 4% bond with quarterly coupons is bought to yield 6% convertible quarterly. Determine the practical dirty and clean values of the bond one month after the twelfth coupon payment using the 30/360 rule.

Answer 1

Solution:

Dirty price is the present value of future coupon payments and maturity value of the bond.

Dirty Price=Price of bond at the last coupon date*(1+YTM)^no. of days since last coupon date/total no. of days in coupon period

No. of payments left=(1*4*10)-12=28 payments

YTM=6%

Coupon amount=$800

Day since last coupon payment=30 days

total no. of days in coupon period=90 days

Price of bond at the last coupon date=Coupon amount*Present valueAnnuity factor @6% for 28th period+Par value*Present value factor@ 6% for 28th period

=$800*13.4062+$20000*.1956

=$10724.96+$3912

=$14,636.96

Dirty Price=$14,636.96*(1+0.06)^30/90

=$14921.13

Accrued Interest=Coupon Amount*Days since last payment/Toatl no. of days between coupon payment

=$800*30/90

=$266.67

Clean price=Dirty Price-Accrued Interest

=$14921.13-$266.67

=$14654.46