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Problem 7. Suppose that a corporation has semi-annual coupon bond trading in the United States with a YTM of 6.25% and an annual coupon bond traded in Europe with a YTM of 6.3%. Which has the greater yield?

User Randhir
by
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1 Answer

5 votes

Answer:

the bond with the greater yield is the semi-annual coupon bond trading in the United States.

Step-by-step explanation:

To determine which bond has the greater yield, we need to compare the effective annual yields of both bonds.

For the semi-annual coupon bond trading in the United States with a YTM (yield to maturity) of 6.25%, the semi-annual yield is simply the YTM divided by 2, since it pays coupons twice a year. Therefore, the semi-annual yield is 6.25% / 2 = 3.125%.

To calculate the effective annual yield of the semi-annual coupon bond, we use the formula:

1

+

Effective Annual Yield

=

(

1

+

Semi-Annual Yield

)

2

1+Effective Annual Yield=(1+Semi-Annual Yield)

2

Let's substitute the value of the semi-annual yield into the formula:

1

+

Effective Annual Yield

=

(

1

+

0.03125

)

2

1+Effective Annual Yield=(1+0.03125)

2

Simplifying the equation:

1

+

Effective Annual Yield

=

1.0312

5

2

1+Effective Annual Yield=1.03125

2

1

+

Effective Annual Yield

=

1.063416015625

1+Effective Annual Yield=1.063416015625

Effective Annual Yield

=

1.063416015625

1

Effective Annual Yield=1.063416015625−1

Effective Annual Yield

=

0.063416015625

Effective Annual Yield=0.063416015625 or 6.3416%.

For the annual coupon bond traded in Europe with a YTM of 6.3%, the yield is already given as an annual yield, so the effective annual yield is simply 6.3%.

Comparing the effective annual yields, we find that the semi-annual coupon bond in the United States has an effective annual yield of 6.3416%, while the annual coupon bond in Europe has an effective annual yield of 6.3%.

Therefore, the bond with the greater yield is the semi-annual coupon bond trading in the United States.

User Bublik
by
8.6k points