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, 20 years to maturity, and a coupon rate of 7.8 percent paid annually. what is the current price of the bond?

Answer 1

Answer:

Market Price $985.01

Explanation:

We have to convert the US semiannually rate to annually.

$(1 + 0.078/2)^{2} -1 = 0.079521$

Now this is the annual rate spected for a similar US Bonds

So we are going to calculate the present value using this rate.

Present value of an annuity of 78 for 20 years at 7.9521%

$C * \frac{1-(1+r)^{-time} }{rate} = PV$

$78 * \frac{1-(1+0.079521)^{-20} }{0.079521} = PV$

PV = 768.55

And we need to add the present value ofthe 1,000 euros at this rate

$\frac{Principal}{(1 + rate)^{time} = Present Value}$

$\frac{1,000}{(1 + 0.079521)^{20} = Present Value }$

Present Value = 216.4602211

Adding those two values together

$985.01

The reasoning behind this is that an american investor will prefer at equal price an US bonds because it compounds interest twice a year over the German Bonds.