Textbook

Convertible corporate bonds are carbon copies of convertible preferred stocks with only a few exceptions. First, the similarities; both:

- Can be converted into common stock of the same issuer
- Provide the investor with capital appreciation potential
- Sets of formulas are essentially the same

The biggest difference? The par values. Preferred stocks typically maintain $100 par values, while bonds usually reflect $1,000 par values. Beyond that, the concepts are essentially the same.

Let’s go through a few examples to understand convertible bonds better:

A convertible bond has a conversion price of $40. What is the conversion ratio?

$Conversion ratio=conversion pricePar $

$Conversion ratio=$40$1,000 $

$Conversion ratio=25:1$

Doing some quick math provides a *conversion ratio of 25:1 (1 bond can be converted into 25 shares of common stock). The conversion ratio is vital for any convertible bond math-based question. If a test question provides the conversion price, use the formula above to find the conversion ratio. If the question provides the conversion ratio, then there’s no need to do the conversion ratio formula. It tells you exactly how many shares are received at conversion.

You may encounter a question providing the conversion ratio and asking for the conversion price. For example:

A convertible bond has a conversion ratio of 20:1. What is the conversion price?

$Conversion price=conversion ratioPar $

$Conversion price=20$1,000 $

$Conversion price=$50$

As you can see, it’s very similar to the conversion ratio formula. Conversion price trades places with conversion ratio, and that’s it!

Let’s switch gears and learn how an investor may make a capital gain from converting their bond.

A corporate bond has a conversion ratio of 20:1 and is purchased for 90*.

**As we learned in the previous chapter, 90 represents a percentage of par quote. This bond is trading at 90% of the bond’s $1,000 par value, or $900.*

The investor could profit from the conversion if the common stock price rose above $45. They’re basically buying a “20-pack of stocks” for $900. Break it down on a per-share basis:

$Conversion cost per share=conversion ratiobond price $

$Conversion cost per share=20$900 $

$Conversion cost per share=$45$

If the market price of the common stock rises above $45, the investor profits from converting.

A corporate bond has a conversion ratio of 20:1 and is purchased for 90. After a few years, the common stock price rises to $60. What is the profit if the bond is converted and the common shares are sold?

Can you figure it out?

(spoiler)

Step 1: factor in bond purchase

$Bond purchase=$900$

Step 2: find the conversion value

$Conversion ratio=20:1$

$Conversion value=20 shares x $60$

$Conversion value=$1,200$

Step 3: compare conversion value to the original purchase

$Profit=conv. value - original purchase$

$Profit=$1,200 - $900$

$Profit=$300$

Convertible bonds provide added return potential because of their conversion features. Therefore, these securities are issued with lower interest rates and traded at lower yields (higher prices) in the market.

How does an investor know when to convert their bond? Just like we explored in the preferred stock chapter, parity prices help determine when a conversion is profitable. Good news - the formulas are essentially the same! The **stock parity price** describes the equivalent cost of the common stock if an investor buys a bond and converts it.

A corporate bond has a conversion ratio of 20:1 and is purchased for 90. What is the parity price of the common stock?

$Stock PP=conversion ratiobond market price $

$Stock PP=20$900 $

$Stock PP=$45$

A $900 bond converted into 20 shares of common stock results in a $45 common stock cost per share. If the stock trades in the market at any price above $45, the investor realizes a profit. In the example above, the stock’s market price was $60, which provided a $15 per share profit.

Let’s see if you can work through an example on your own:

A 10%, $1,000 par convertible corporate bond with a conversion price of $20 is purchased at 110. The common stock is currently trading at $25. What is the parity price of the stock?

Can you figure it out?

(spoiler)

Answer = **$22**

The first step is calculating the conversion ratio.

$Conversion ratio=conversion pricePar $

$Conversion ratio=$20$1,000 $

$Conversion ratio=50:1$

Now, we can calculate the stock’s parity price by using the market price of the bond ($1,100) and the conversion ratio (50:1).

$Stock PP=conversion ratiobond market price $

$Stock PP=50$1,100 $

$Stock PP=$22$

This question does not require two pieces of information: the coupon (10%) and the stock’s market price ($25). Although it’s not essential to answer the question, we can use the stock’s market price to tell us if buying the bond and immediately converting would be profitable.

Buying a bond for $1,100 and converting it into 50 shares of common stock costs $22 per share (the parity price). With the stock price currently at $25, there is an arbitrage opportunity. The investor could buy 50 shares for an effective price of $22 per share, then sell those shares for a $3 profit per share.

**Bond parity price** can also determine if conversion is profitable. This time, we’ll use the stock’s market price to determine if a convertible bond should be purchased and converted immediately.

A corporate bond has a conversion ratio of 10:1 and is purchased, while the common stock trades at $90. What is the parity price of the bond?

$Bond PP=stock price x conversion ratio$

$Bond PP=$90 x 10$

$Bond PP=$900$

If the bond trades in the market at any price below $900, then the bond should be purchased and converted immediately. An investor could sell the shares for a higher value than the bond’s purchase price, providing an immediate profit (arbitrage).

Let’s see if you can do one on your own:

A 7%, $1,000 par convertible corporate bond with a conversion price of $10 is purchased at 95. The common stock is currently trading at $8. What is the parity price of the bond?

(spoiler)

Answer = **$800**

The first step is calculating the conversion ratio.

$Conversion ratio=conversion pricePar $

$Conversion ratio=$10$1,000 $

$Conversion ratio=100:1$

Now, we can calculate the bond’s parity price by using the market price of the stock ($8) and the conversion ratio (100:1).

$Bond PP=stock price x conversion ratio$

$Bond PP=$8 x 100$

$Bond PP=$800$

Two pieces of information are not required in this question - the coupon (7%) and the bond’s market price ($950). Although it’s not essential to answer the question, we can use the bond’s market price to determine if converting would be profitable.

Buying a bond for $1,100 and converting it into 50 shares of common stock costs $22 per share (the parity price)

A bond convertible into 100 shares of common stock currently trading at $8 per share should be worth at least $800 (the parity price). Therefore, a bond market price of $950 does not offer an arbitrage opportunity. Arbitrage only exists if the bond can be purchased for less than $800, allowing the investor to buy the bond (for less than $800), convert it into stock, and sell the shares for a total of $800.

Like convertible preferred stock, convertible bonds are typically issued with anti-dilution covenants. Let’s explore what it looks like:

Assume the following:

$1,000 par convertible bond

Convertible bond market price = $1,000

Conversion ratio = 40:1

Common stock market price = $25

In this circumstance, the conversion feature is at breakeven (parity). An investor purchasing the bond for $1,000, converting it into 40 shares of common stock, and selling those shares for $1,000 overall ($25 x 40) will not make or lose any money.

Converting the bond becomes profitable if the stock price rises above $25. Issuers and their employees are not thrilled when their securities are converted. Remember, conversion results in brand new shares of common stock, which dilutes the value and ownership level of every common stockholder (including the issuer’s officers and directors).

A forward stock split, which results in more outstanding shares at a lower market price, could result in conversion features losing value.

Assume the following:

$1,000 par convertible bond

Convertible bond market price = $1,000

Conversion ratio = 40:1

Common stock market price = $25

**2:1 stock split**

- Pre-split common stock price = $25.00
- Pre-split conversion value = $1,000 ($25.00 x 40)
- Post-split common stock price = $12.50
- Post-split conversion value = $500 ($12.50 x 40)

*Stock splits were covered in the common stock chapter. Follow this link if you need a refresher.*

A 2:1 stock split results in twice as many outstanding shares, with each share trading at half its original value. At this point, the conversion value is cut in half. Before the stock split, the conversion netted $1,000 of common stock ($25.00 x 40), but after, it only netted $500 of common stock ($12.50 x 40). This is an example of dilution for convertible bondholders.

Anti-dilution covenants prevent this problem from materializing. Let’s explore how it works with bonds using this question:

An investor purchases a $1,000 par, 5% convertible bond with a conversion price of $50. The common stock is currently trading at $40. The issuer performs a 4:1 stock split on the common stock. What are the conversion price and ratio adjustments if the bond contains an anti-dilution covenant?

Let’s walk through this one together. The first step is to find the original conversion ratio.

$CR=Conversion pricePar $

$CR=$50$1,000 $

$CR=20:1$

In the beginning, the bond is convertible into 20 shares of common stock worth $40 each. Before the stock split, the conversion feature is worth $800 ($40 x 20). If a 4:1 common stock split occurs, the share price will fall significantly.

$New common stock price=Stock split factorCurrent market price $

$New common stock price=4$40 $

$New common stock price=$10$

With the common stock’s price falling to $10 per share, the conversion feature’s value declines to $200 if it doesn’t adjust (converts into 20 shares worth $10 each). The anti-dilution covenant requires the issuer to appropriately modify the conversion price and ratio. Remember, they must make the proper change to retain the original conversion value of $800. Let’s start first with the conversion ratio.

To find the new conversion ratio, simply multiply the current conversion ratio (20) by the stock split factor (4).

$New conversion ratio=20 x 4$

$New conversion ratio=80$

The issuer created 4 times the number of common shares outstanding. Therefore, the bondholders should receive 4 times the original amount received at conversion. If the investor converts now, they’ll receive 80 shares worth $10 each, representing a conversion value of $800 (80 x $10). The original conversion value is now matched.

Do you know what the new conversion price would be?

(spoiler)

Answer = **$12.50**

You can find this one of two ways. First, let’s only use the stock split factor. A 4:1 stock split results in a stock split factor of 4 (4/1). We multiplied this number times the conversion ratio to find the new conversion ratio. You’ll need to divide the original conversion price ($50) by the stock split factor (4) to discover the new conversion price.

$New conversion price=4$50 $

$New conversion price=$12.50$

The other way can be used if the new conversion ratio is already calculated. We know the new conversion ratio is 80, so we could simply do the traditional conversion price formula:

$CP=Conversion ratioPar $

$CP=80$1,000 $

$CP=$12.50$

Either way works! Feel free to use whichever method is more comfortable for you.

Whew! You made it through another set of convertible security questions. Good news - there are no more convertible securities to learn. If it all made sense to you, great! You’ll do well when you see questions on this material. If it felt overwhelming, hang in there! With convertible securities, practice makes perfect. Be sure to work through enough questions to feel comfortable.

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