Question

Consider a $1000 par value two-year 8% bond with semiannual coupons bought at t = 0 to yield 6% convertible semiannually. Assuming the market yield rate does not change, compute the flat price, accrued interest, and market price five months after purchase of the bond using the theoretical method.

Answer: 1063.04, 33.25, 1029.79

Note: Please elaborate as much as you can and don't use TVM calculator

Answer 1

A two-year bond paying coupon semi-annually

Coupon paid every 6 months = (8%/2)*1000 = 40

Yield to maturity = 6% pa convertible semi-annually = 3% semi-annually = 0.03

FP: Flat price of bond

MV = discounted value of all cash flows

MV = 148.684+888.487 = 1037.171

This is the market price at t =0

Therefore the market price at t = 5 months

Market price = 1037.171*(1+3%)^(5/6) = 1063.036 = 1063.04

Accrued interest on the 4% coupon for 5 months

Days in 5 months: 31(jan)+28(feb)+31(mar)+30(apr)+31(may) = 151 days

Days in 6months = 151 + 30(jun) = 181days

Accrued interest = (151/181)*40 = 33.37 (note the value of 33.25 can be derived only if the actual dates or any particular day convention is given)

Flat price = 1063.4 - 33.37 = 1030.03