Question

Today a bod has a coupon rate of 13.80% par value of $1000,ytm of 8.20% and a semi-annaual coupons with the next coupon due ij 6 months. one year ago, the bonds proce was $1,281.05 and the bond had 4 years until maturity. what is the current yeild of the bond today?

Answer 1

Time to maturity one year ago = 4 years

Time to maturity now = 3 years

Number of coupon payments left = 3 years * 2 = 6 payments

Semi-annual coupon payment = Face value * Coupon rate / 2

= $1,000 * 13.80% / 2 = $69.00

Semi-annual yield = 8.20% / 2 = 4.10%

Current price of the bond = [Semi-annual coupon amount * (1 - (1 + Semi-annual yield)^{-(Number of coupons left)}) / Semi-annual yield] + [Face value / (1 + Semi-annual yield)^{Number of coupons left}]

= [$69 * (1 - (1.041)^-6) / 0.041] + [$1,000 / 1.041⁶]

= $1,146.30

Current yield = Annual coupon payment / Current price of the bond

= ($69 * 2) / $1,146.30

= 12.04%