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

To determine the current price of a bond, we can use the present value formula to calculate the present value of future cash flows.

Step-by-step explanation:

To determine the current price of the bond, we need to calculate the present value of the future cash flows. The bond has a par value of €1,000, a maturity of 20 years, and a coupon rate of 7.8% paid annually. We can use the present value formula to calculate the price of the bond:

Price = Coupon Payment * (1 - (1 + Interest Rate)^-Number of Periods) / Interest Rate + Par Value / (1 + Interest Rate)^Number of Periods

Plugging in the values, we get:

Price = €78 * (1 - (1 + 0.078)^-20) / 0.078 + €1,000 / (1 + 0.078)^20

Solving this equation will give us the current price of the bond.

Answer 2

Market Price $985.01

Step-by-step 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 * (1-(1+r)^(-time) )/(rate) = PV\\`

`78 * (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

`(Principal)/((1 + rate)^(time) = Present Value)`

`(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.