Question

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 6.3 percent paid annually.

If the yield to maturity is 7.4 percent, what is the current price of the bond?

Please break down step by step

Answer 1

Bond price is the present value of all the coupon payments and the face value/maturity value of the bond. Present value of coupon payments are done using present value annuity formula.

Bond Price = C*PVIFA (r%,n) + FV*PVIF(r%,n)

C = 6.3%*1000 = 63

r% = 7.4%

FV = 1000

n = 25

Bond Price = C* [ 1 - ( 1+ r)^-n ] / r + FV / ( 1+ r)ⁿ

Bond Price = 63 * [ 1 - ( 1+ 0.074)^-25 ] / 0.074    + 1000/(1+ 0.074)²⁵

Bond Price = 63 * [ 1- 0.167839 ] / 0.074 + 1000 / 5.95809

Bond Price = 63 * 11.24542 + 167.839

Bond Price = 708.4614 + 167.839

Bond Price = € 876.3004

Current price of the bond is € 876.30