Question

# Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere...

 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

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

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