Question

You own a 10-year, 5% semi-annual coupon bond with $100 face value. If its yield to maturity is 5.3%, what percentage of its value comes from coupon payments?

Answer 1

Number of periods = 10 * 2 = 20

Semi annual coupon = (5% of 100) / 2 = 2.5

Rate = 5.3% / 2 = 2.65%

Present value of coupon = Annuity * [1 - 1 /(1 + r)^n] / r

Present value of coupon = 2.5 * [1 - 1 /(1 + 0.0265)^20] / 0.0265

Present value of coupon = 2.5 * [1 - 0.592681]/ 0.0265

Present value of coupon = 2.5* 15.370532

Present value of coupon = 38.42633

Present value of face value = Future value / (1 + r)^n

Present value of face value = 100 / (1 + 0.0265)^20

Present value of face value = 100 / 1.687249

Present value of face value = 59.268089

Total value = 38.42633 + 59.268089 = 97.694419

Percentage of value from coupons = (38.42633 / 97.694419) * 100

Percentage of value from coupons = 39.33%