Question

Assume that you are considering the purchase of a 15-year bond with an annual coupon rate of 9.5%. The bond has face value of $1,000 and makes semiannual interestpayments. If you require an 11.0% nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?

Answer 1

Assume that you are considering the purchase of a 15-year bond with an annual coupon rate of 9.5%. The bond has face value of $1,000 and makes semiannualinterest payments. If you require an 11.0% nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for thebond?
answer:$ 891

Answer 2

Bond price = Coupon 1/(1+ytm)² + Coupon 2/(1+ytm)² + ……+ (coupon 30+ Maturity value)/(1+ytm)³⁰

Here, maturity value = $1,000; Coupons 1 till 30 = $1000 x 9.5% x 6/12 è $47.5

Number of coupons = 15 years x 2 coupons per year = 30

Annual yield to maturity = 11%; therefore semi-annual yield to maturity = 11%/2 = 5.5%

Bond price = 47.5/(1+.055)¹ + 47.5/(1+.055)² + ……….+ (47.5+1000)/(1+.055)³⁰

è $891.00