1 1000 points volue Even though most corporate bonds in the

1 10,00 points volue: Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of 1,000, 25 years to maturity, and a coupon rate of 7.1 percent paid annualy If the yield to maturity is 8.2 percent, what is the current price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16 Price

Solution

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

Maturity of bond = 25 years

Number of annual coupon payments = n = 25

Annual coupon payments = €1,000 * 7.1% = €71

Annual effective interest rate = r = 8.2% = 0.082

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

Present value of annual coupon payments = €71 * (1-1.082^-25)/0.082 = €745.14

Present value of face value of bond = $1000/1.082²⁵ = €139.42

Price of bond = €745.14 + €139.42 = €884.56