LOS d: Identify the relationship among the price of a callable bond, the price of an option-free bond, and the price of an embedded call option.

Q1. Jori England, CFA candidate, is studying the value of callable bonds. She has the following information: a callable bond with a call option value calculated at 1.75 (prices are quoted as a percent of par) and a straight bond similar in all other aspects priced at 98.0. Which of the following choices is closest to what England calculates as the value for the callable bond?

A)   99.75.

B)   96.25.

C)   98.75.

Q2. Which of the following statements about the relationship between the value of a callable bond, the value of an option-free bond, and the value of the embedded call option is TRUE?

A)   Value of a callable bond = value of an option-free bond ? value of an embedded call option.

B)   Value of a callable bond = present value of the interest payments + present value of the principal at maturity.

C)   Value of a callable bond = value of an option-free bond + value of an embedded call option.

Q3. As part of his job at an investment banking firm, Damian O’Connor, CFA, needs to calculate the value of bonds that contain a call option. Today, he must value a 10-year, 7.5% annual coupon bond callable in five years priced at 96.5 (prices are stated as a percentage of par). A straight bond that is similar in all other aspects as the callable bond is priced at 99.0. Which of the following is closest to the value of the call option?

A)   2.5.

B)   4.2.

C)   3.5.

Q4. If the volatility of interest rates increases, which of the following will experience the smallest price increase resulting from lower rates?

A)   Putable bond.

B)   Zero-coupon option-free bond.

C)   Callable bond.

Q5. When market rates were 6% an analyst observed a $1,000 par value callable bond selling for $950. At the same time the analyst also observed an identical non-callable bond selling for $980. What would the analyst estimate the value of the call option on the callable bond to be worth?

A)   $20.

B)   $80.

C)   $30.

Q6. Which of the following statements about the value of a callable bond is FALSE?

A)   The value of the callable bond is less than the value of an option-free bond in an amount equal to the value of the call option.

B)   The value of a callable bond equals the value of the bond without the option plus the option value.

C)   When yields rise, the value of a callable bond may exhibit less of a price change than a noncallable bond.

Q7. Which of the following statements about a callable bond is TRUE?

A)   A bondholder usually loses if a bond is called by being forced to reinvest the proceeds at a lower interest rate.

B)   Callable bonds follow the standard inverse relationship between interest rates and price.

C)   The call option on a bond trades separately from the bond itself.

LOS d: Identify the relationship among the price of a callable bond, the price of an option-free bond, and the price of an embedded call option.fficeffice" />

Q1. Jori ffice:smarttags" />England, CFA candidate, is studying the value of callable bonds. She has the following information: a callable bond with a call option value calculated at 1.75 (prices are quoted as a percent of par) and a straight bond similar in all other aspects priced at 98.0. Which of the following choices is closest to what England calculates as the value for the callable bond?

A)   99.75.

B)   96.25.

C)   98.75.

Correct answer is B)

To calculate the callable bond value, use the following formula:

Value of callable bond = Value of straight bond – Call option value
Value of callable bond = 98.0 – 1.75 = 96.25.

Remember: The call option is of value to the issuer, not the holder.

Q2. Which of the following statements about the relationship between the value of a callable bond, the value of an option-free bond, and the value of the embedded call option is TRUE?

A)   Value of a callable bond = value of an option-free bond ? value of an embedded call option.

B)   Value of a callable bond = present value of the interest payments + present value of the principal at maturity.

C)   Value of a callable bond = value of an option-free bond + value of an embedded call option.

Correct answer is A)

Because the bondholder has given something of value to the issue of a callable bond, the value of the embedded call option should be subtracted from the value of the straight bond.

Q3. As part of his job at an investment banking firm, Damian O’Connor, CFA, needs to calculate the value of bonds that contain a call option. Today, he must value a 10-year, 7.5% annual coupon bond callable in five years priced at 96.5 (prices are stated as a percentage of par). A straight bond that is similar in all other aspects as the callable bond is priced at 99.0. Which of the following is closest to the value of the call option?

A)   2.5.

B)   4.2.

C)   3.5.

Correct answer is A)

To calculate the option value, rearrange the formula for a callable bond to look like:

Value of embedded call option = Value of straight bond – Callable bond value
Value of call option = 99.0 – 96.5 = 2.5.

Remember: The call option is of value to the issuer, not the holder.

Q4. If the volatility of interest rates increases, which of the following will experience the smallest price increase resulting from lower rates?

A)   Putable bond.

B)   Zero-coupon option-free bond.

C)   Callable bond.

Correct answer is C)

For a callable bond the issuer has the option to call the bond if the interest rate decreases during its call period. The issuer will call the bond if interest rates have decreased in order to obtain cheaper financing elsewhere. If the interest rate volatility increases the chance the it is optimal for the issuer to call the bond increases, making the call option more valuable. Therefore, the bond price is depressed by an increase in interest rate volatility.

Q5. When market rates were 6% an analyst observed a $1,000 par value callable bond selling for $950. At the same time the analyst also observed an identical non-callable bond selling for $980. What would the analyst estimate the value of the call option on the callable bond to be worth?

A)   $20.

B)   $80.

C)   $30.

Correct answer is C)

The noncallable bond has the traditional PY shape. The callable bond bends backwards. The difference between the two curves is the value of the option. 980 ? 950 = $30.

Q6. Which of the following statements about the value of a callable bond is FALSE?

A)   The value of the callable bond is less than the value of an option-free bond in an amount equal to the value of the call option.

B)   The value of a callable bond equals the value of the bond without the option plus the option value.

C)   When yields rise, the value of a callable bond may exhibit less of a price change than a noncallable bond.

Correct answer is B)

The value of the call option is subtracted from the value of the bond without the option because the option is of value to the issuer, not the holder.
As interest rates decrease, the issuer values the call option more because the company has the potential to call the bond and replace existing debt with lower-coupon (and thus lower cost) debt. Also, it is more likely that the bond will be called. The other choices are true.

Q7. Which of the following statements about a callable bond is TRUE?

A)   A bondholder usually loses if a bond is called by being forced to reinvest the proceeds at a lower interest rate.

B)   Callable bonds follow the standard inverse relationship between interest rates and price.

C)   The call option on a bond trades separately from the bond itself.

Correct answer is A)

A bondholder will most likely lose if a bond is called because a bond is most likely to be called in a declining interest rate environment. The issuer will likely call the bond and replace it with lower cost (lower coupon debt). The holder faces prepayment and reinvestment risk, because he must reinvest the bond cash flows into lower-yielding current investments.
In bond trading, the call option is bundled with the bond and is not traded separately. The price of a callable bond does not follow the standard inverse relationship. As yields fall, the call option becomes more valuable to the issuer. With a decrease in interest rates, the value of a callable bond can only increase to approximately the call value. Straight bonds will continue to exhibit the inverse relationship between yields and prices as there is no ceiling call price. When yields rise, the value of callable bond may not fall as much as that of a similar straight bond because of the embedded call option feature.

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