Question

A 20-year maturity bond with par value of $1,000 makes semiannual coupon payments at a coupon rate of 8%. Find the bond equivalent and effective annual yield to maturity of the bondif the bond price is:a. $950b. $1,000c. $1,050

Answer 1

a. $950

yield to maturity = YTM = {40 + [(1,000 - 950)/40]} / [(1,000 + 950)/2] = 41.25 / 975 = 4.23% x 2 = 8.46%

effective yield = [1 + (r/n)]ⁿ - 1 = [1 + (0.08/2)]² - 1 = 8.16%, measures the coupon yield

since the effective yield is lower than the YTM, the bond is sold at a discount

b. $1,000

YTM = 8%, since the bond is sold at par

effective yield = [1 + (r/n)]ⁿ - 1 = [1 + (0.08/2)]² - 1 = 8.16%, measures the coupon yield

since the bond yield semiannual coupons, the effective yield is slightly higher than the YTM

c. $1,050

yield to maturity = YTM = {40 + [(1,000 - 1,050)/40]} / [(1,000 + 1,050)/2] = 38.75 / 1,025 = 3.78% x 2 = 7.56%

effective yield = [1 + (r/n)]ⁿ - 1 = [1 + (0.08/2)]² - 1 = 8.16%, measures the coupon yield

since the effective yield is higher than the YTM, the bond is sold at a premium