Question

Acme Inc. just issued a bond with a​ $10,000 face value and a coupon rate of​ 7%. If the bond has a life of 30​ years, pays semi−annual coupons, and the yield to maturity is​ 9%, what will the bond sell​ for?

Answer 1

Market value of bond = Present value of coupon payments + Present value of face value of bond

Maturity of bond = 30 years

Number of semi-annual coupon payments = n = 30 years * 2 = 60

Semi-annual coupon payments = $10,000*7%*1/2 = $350

Semi-annual effective interest rate = r = 9%/2 = 4.5% = 0.045

Present value of annuity = Annuity amount*{1-(1+r)^-n}/r

Present value ofsemi- annual coupon payments = $350 * (1-1.045^-60)/0.045 = $7,223.31

Present value of face value of bond = $10,000/1.045⁶⁰ = $712.89

Price of bond = $7,223.31 + $712.89 = $7,936.20