Question

Three $1,000 face value, 10-year, noncallable, bonds have the same amount of risk, hence their YTMs are equal. Bond 8 has an 8% annual coupon, Bond 10 has a 10% annual coupon, and Bond 12 has a 12% annual coupon. Bond 10 sells at par. Assuming that interest rates remain constant for the next 10 years, which of the following statements is CORRECT?
a. Bond 8’s current yield will increase each year.
b.Since the bonds have the same YTM, they should all have the same price, and since interest rates are not expected to change, their prices should all remain at their current levels until maturity.
c.Bond 12 sells at a premium (its price is greater than par), and its price is expected to increase over the next year.
d.Bond 8 sells at a discount (its price is less than par), and its price is expected to increase over the next year.e.Over the next year, Bond 8’s price is expected to decrease, Bond 10’s price is expected to stay the same, and Bond 12’s price is expected to increase.

Answer 1

Answer:

D is the correct answer

Explanation:

In this question, we are trying to evaluate the options and see which is correct.

As stated, option. D is correct.

From the analysis in the question, we can see that although the three bonds have the same risk amount, it can be seen that they have different annual coupons with a constant interest rate over the next ten years.

Now, we were made to understand that the Bond 10 sells at par. Comparing its annual coupon to Bond 8, we can deduce that Bond 8 actually sells at a lower annual coupon. Since Bond 10 is at par, it means that bond 8 is selling less than the par value and as such it is selling at a discount.

Now, to meet up with the par value over the next year, it is expected that the price of Bond 8 is expected to increase

Answer 2

Answer: E) Over the next year, Bond 8’s price is expected to decrease, Bond 10’s price is expected to stay the same, and Bond 12’s price is expected to increase.

Explanation:

In the question, it is clear that the face value of all three bonds is $1000. Bond 10, also in the question sells at par meaning it sells at the $1000 face value. To determine the interest rate of any bond, one has to know the bond's coupon rate. As given in the question, the coupon rate of bond 10 is 10%. Therefore, the interest rate of bond 10 is coupon rate  × face value. Which means, 10% of $1000 = $100. For bond 8, same procedure goes and its interest rate is $80. This figure is below par which means it is at a discount of $20. For bond 12, same procedure goes and its interest rate is $120. This figure is above par which means it is at a premium of $20.

At this stage, bond 8's price is expected to decrease since it yields a much lower interest rate than the other two bonds. Bond 10's price is expected to remain the same because it's face value was sold at par. There wasn't any discounts or premiums discovered. For bond 12, its price is expected to increase since it yielded much more interest rate than the rest.