###### Backward Induction

Backward induction involves working backward from maturity to time 0 to determine a... **Read More**

When the underlying share price is well below the conversion price, the convertible bond exhibits mostly bond risk-return characteristics and is described as a ** busted convertible**. Therefore, the bond will be sensitive to interest rate movements and credit spreads, just like a straight bond.

Zinhle Inc. issued a 6% annual coupon convertible bond on 31 March 2020 at an issue price of $ 1,000. The bond’s option-free value is $1,100, while its stock price is $25.00. The bond matures four years from the issue date, and its conversion ratio is 30.

The conversion price of the bond is:

$$ \begin{align} \text{Conversion price} & = \frac{\text{Issue price}}{\text{ Conversion ratio}} \\ \\ & = \frac{1000}{30} =$33.33 \end{align} $$

The underlying share price ($25.00) is well below the conversion price ($33.33). Therefore, the convertible bond exhibits mostly * bond risk-return characteristics* and is known as a busted convertible.

Conversely, when the underlying share price is well above the conversion price, a convertible bond exhibits mostly ** stock risk-return characteristics**. In this case, the convertible bond price is mainly affected by movements in the share price but least affected by factors such as interest rate movements and credit spreads that influence the value of an otherwise identical straight bond.

Zinhle Inc issued a 6% annual coupon convertible bond on 31 March 2020 at an issue price of $ 1,000. The bond’s option-free value is $1,100, while its stock price is $39.50. The bond matures four years from the issue date, and its conversion ratio is 30.

The conversion price of the bond is:

$$ \begin{align} \text{Conversion price} & = \frac{\text{Issue price}}{\text{ Conversion ratio}} \\ \\ & = \frac{1000}{30} =$33.33 \end{align} $$

Notice that the underlying share price ($39.50) is well above the conversion price ($33.33). Thus, the convertible bond exhibits mostly ** stock risk-return characteristics**. A fall in the stock price will result in a decrease in the convertible bond price and vice versa. However, the convertible bond price change is less than the change in the stock price because the convertible bond has a floor, which is the value of the straight (option-free) bond.

Ultimately, a convertible bond trades like a hybrid security in between bond and stock extremes.

## Question

Snap Co. has issued a 10% annual coupon convertible bond at an issue price of $ 1,000. The bond’s option-free value is $900, while its stock price is $40.00. The bond matures five years from the issue date, and its conversion ratio is 35. Two years after the bond issue, the interest rates increase. All else equal, the price of Snap Co’s convertible bond

most likely:

- Decreases significantly.
- Increases significantly.
- Does not change significantly.

Solution

The correct answer is C.The conversion price of the bond is:

$$ \begin{align} \text{Conversion price}& = \frac{\text{Issue price}}{\text{Conversion ratio}} \\ \\ &= \frac{1000}{35} =$28.57 \end{align} $$

Notice that the underlying share price ($40) is well above the conversion price ($28.57). Thus, the convertible bond exhibits mostly stock risk-return characteristics.

This implies that the underlying share price mainly influences the bond. Therefore, the increase in interest rates will have little impact on the convertible bond price.

Reading 30: Valuation and Analysis of Bonds with Embedded Options

*LOS 30 (q) Compare the risk-return characteristics of a convertible bond with the risk-return characteristics of a straight bond and the underlying common stock.*