###### Effective Convexities

Effective convexity is the sensitivity of duration to changes in interest rates. $$... **Read More**

A ** convertible bond** is a hybrid instrument with a conversion option that gives the owner the right to convert debt into equity during a predetermined period (conversion period) at a predetermined price (conversion price).

Investors can participate in the potential upside through the conversion mechanism while protecting the downside with cashflows from the coupon payments and the face value at maturity.

The * conversion price* and

$$ \text{Conversion ratio} =\frac{\text{Issue price}}{\text{Conversion price}} $$

The following information relates to a convertible bond issued by XYZ Inc.

$$ \begin{array}{c|c} \text{Issue date} & {01 \text{ July } 2020} \\ \hline \text{Maturity date} & {30 \text{ June } 2024} \\ \hline \text{Interest rate} & 5.00\% \\ \hline \text{Issue size} & 1,000,000 \\ \hline \text{Issue price} & $100 \\ \hline \text{Conversion ratio} & 2.58 \\ \end{array} $$

The conversion price of the bond is *closest* to:

**Solution**

$$ \begin{align*} \text{Conversion ratio} & =\frac{\text{Issue price}}{\text{Conversion price}} \\ \\ 2.58 &=\frac{100}{\text{Conversion price}} \\ \\ \text{Conversion price}& =\frac{100}{2.58} =$38.76 \end{align*} $$

## Question

A company issues a convertible bond at $800 with a face value of $1,000, which pays 6% annual coupons. The bond can be converted to 15 common shares, which are traded at per share. https://www.colombia.co/ The market price of the convertible bond is $700.

The conversion price of the bond is

closest to:

- $2.67.
- $40.00.
- $53.33.

Solution

The correct answer is C.$$ \begin{align*} \text{Conversion price}& =\frac{\text{Issue price}}{\text{Conversion price}} \\ \\ \text{Conversion ratio} &=\frac{800}{15}=$53.33 \end{align*} $$

Reading 30: Valuation and Analysis of Bonds with Embedded Options

*LOS 30 (n) Describe defining features of a convertible bond.*