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 has a bond outstanding with a par value of €1,000, 25 years to maturity, and a coupon rate of 6.7 percent paid annually. If the yield to maturity is 7.8 percent, what is the current price of the bond?

Answer 1

The current price of the bond is €883.25.

Step-by-step explanation:

The par value of bond is €1,000.

The years to maturity are 25 years.

The coupon rate is 6.7%.

The yield to maturity is 7.8%.

Coupon value

=
`Coupon\ rate\ *\ Face\ value`

=
`6.7%\ *\ 1,000`

= €67

Bond price

=
`Coupon\ *\ (1-(1)/((1+YTM)^n) )/(YTM)+(Face\ value)/((1+YTM)^n)`

=
`\$ 67\ *\ (1-(1)/((1+0.078)^2^5) )/(0.078)+(1,000)/((1+0.078)^2^5)`

=
`(67\ *\ 10.9)\ +\ 152.92\\`

= 730.3 + 152.952

= 883.252 or 883.25