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, 23 years to maturity, and a coupon rate of 5.8 percent paid annually. If the yield to maturity is 4.7 percent, what is the current price of the bond?
Bond Value = PV of the Coupons + PV of the Face Amount
[C ×(1-1/(1+r)^t )/r]+[F/(1+r)^t ]=[(0.058×1,000)×(1-1/(1.047)^23 )/0.047]+[1,000/(1.047)^23 ]
[58×(1-0.3477)/0.047]+1,000/2.8759=804.94+347.72=$1,152.66 nion Local School District has a bond outstanding with a coupon rate of 3.7 percent paid semiannually and 16 years to maturity. The yield to maturity on this bond is 3.9 percent, and the bond has a par value of $5,000. What is the price of the bond?
Present value of par value of bonds = Par value of bonds [1/ (1+r)^t]
= $5,000 x [1/ (1+0.0195)^32]
=$5,000 x 0.5390
=$2,695
Present value of interest payments = Interest payable x [{1-1/(1+r)^t}/r]
= ($5,000 x (3.7/100) x (1/2))) x [{1-(1/(1+0.0195)^32)}/0.0195]
=$92.5 x 23.64
=$2,186.70
Current price of bonds = (Present value of par value of bonds + Present value of interest payments)
= $2,695 + $2,186.70
=$4,881.70
So the current price of the bond is $4,881.70.