Question

Ashes Divide Corporation has bonds on the market with 16 years to maturity, a YTM of 7.8 percent (APR), and a current price of $1,326.50. The bonds make semiannual payments. What must the coupon rate be on these bonds (as an APR)? Note: first find the semi-annual payment. Then convert it into an annual payment and use this annual payment to find the coupon rate as an APR. (Do not round your intermediate calculations.)

• 17.25%

• 11.51%

• 22.88%

• 11.41%

• 8.60%

Answer 1

Price of bond = pv of coupon payments at YTM + Present value of Face value at maturity period.

1326.5 = Semi annual Coupon payment * PVAF(3.9%,32 periods) + 1000 * PVF(3.9%,32 periods)

1326.5 = Semi annual Coupon payment * ( 1 - ( 1.039)^-32) / 0.039) + 1000 * 1 / (1.039)³²

1326.5 = Semi annual Coupon payment * PVAF(3.9%, 32 periods) + $ 293.969638393

1326.5 - 293.969638393 = Semi annual Coupon payment * 18.10334

Semi annual Coupon payment = $ 57.03534336827

Annual coupon payment= $ 57.03534336827 * 2 =$ 57.03534336827

Coupon rate= Annual copon amount / Face value = ($ 57.03534336827 / 1000)* 100 = 0.1140706867

Coupon rate = 11.41%