We first learned about convertible securities in the preferred stock chapter. Both preferred stock and corporate bonds can be convertible into stock of the same issuer. For example, a convertible Ford bond would allow the bondholder to convert their bond into Ford stock at any time.
Conversion features provide the investor with another way to make money on their bond. The bond’s yield provides a return, and additionally, the investor can make capital gains on the stock if they convert.
When a convertible bond is issued, the issuer sets its conversion ratio and conversion price. In plain English, both tell the investor how many shares of stock are received if the bond is converted. They are set when the issuer originally sells the bond and typically stay fixed through the life of the bond.
The conversion price is only useful in finding the conversion ratio. For example:
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 (one bond can be converted into 25 shares of common stock). The conversion ratio is important for any convertible bond math-based question. If the conversion price is provided in the question, 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 when the bond is converted.
However, it’s possible you see a question that provides the conversion ratio and asks 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 10:1 and is purchased for $900
The investor could make a profit on the conversion if the common stock price were to rise above $90. They’re basically buying a “pack of 10 stocks” for $900. Break it down on a per share basis:
Conversion cost per share=conversion ratiobond price
Conversion cost per share=10$900
Conversion cost per share=$90
If the market price of the common stock rises above $90, the investor would make a profit from converting.
A corporate bond has a conversion ratio of 10:1 and is purchased for $900. After a few years, the common stock price rises to $120. If the bond is converted and the common shares are sold, what is the profit?
Can you figure it out?
(spoiler)
Step 1: factor in bond purchase
Bond purchase=$900
Step 2: find conversion value
Conversion ratio=10
Conversion value=10 shares x $120
Conversion value=$1,200
Step 3: compare conversion value to the original purchase
Profit=conv. value - original purchase
Profit=$1,200 - $900
Profit=$300
As you can see, convertible bonds provide an extra potential for return. Because of this, convertible bonds are sold with lower interest rates and traded at lower yields (higher prices) in the market.
How does an investor know when to convert their bond? Parity pricing helps determine when profit can be made from conversion. Good news - the formulas we learned in the preferred stock chapter are essentially the same! The stock parity price describes the equivalent price of the stock if a bond is bought and converted.
A corporate bond has a conversion ratio of 10:1 and is purchased for $900. What is the parity price of the common stock?
Stock PP=conversion ratiobond market price
Stock PP=10$900
Stock PP=$90
If a $900 bond is purchased and immediately converted into 10 shares of common stock, the investor is paying the equivalent of $90 per share for the stock. If the stock trades in the market at any price above $90, the investor could realize a profit. In the example above, the stock’s market price was $120, which provided a $30 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 to calculate the conversion ratio, which is not provided in the question.
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
There are two pieces of information that are not required in this question - the coupon (10%) and the stock’s market price ($25). Although it’s not important 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.
The parity price of $22 is another way of saying buying a bond for $1,100 and converting it into 50 shares of common stock costs $22 per share. With the stock price currently at $25, there actually is an arbitrage opportunity. The investor could buy 50 shares for an effective price of $22 per share (through buying the bond and converting), then sell those shares for a $3 profit per share.
Bond parity price also exists and can be used to determine if a profit can be made by converting a bond. 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. This allows the investor to sell the stock for a higher value than the purchase price of the bond, providing an immediate profit.
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 to calculate the conversion ratio, which is not provided in the question.
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
There are two pieces of information that are not required in this question - the coupon (7%) and the bond’s market price ($950). Although it’s not important to answer the question, we can use the bond’s market price to tell us if buying the bond and immediately converting would be profitable.
The parity price of $800 is another way of saying a bond that’s convertible into 100 shares of common stock currently trading at $8 per share should be worth at least $800. With the bond price currently at $950, there is no arbitrage opportunity. Arbitrage would only exist if the bond could be purchased for less than $800, which would allow the investor to buy the bond (for less than $800), convert it into stock, and sell that stock for a total of $800.
At the beginning of this section, we discussed how the conversion price and ratio typically do not change. While this is true, convertible bonds usually have anti-dilution covenants that prevent the issuer from diluting the conversion value of the bond (similar to convertible preferred stock). Before we discuss how the anti-dilution covenant protects convertible bondholders, let’s refresh on how they could be diluted without it.
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). If an investor buys the bond at $1,000, converts it into 40 shares of common stock, and sells those shares for $1,000 overall ($25 x 40), they will not make or lose any money.
If the common stock price rises any further, there’s a big incentive for investors to begin converting their bonds. You can safely assume some employee of the issuer (likely the Chief Financial Officer) is keeping a close eye on this. While the issuer had to obtain stockholder approval to issue the convertible bond, it doesn’t mean they’ll be thrilled if a significant amount of bonds start converting. Remember, conversion results in brand new shares of common stock, which dilutes the value and ownership level of every common stockholder (which likely includes the officers and directors of the issuer).
The issuer could do several things to manipulate the price of the common stock downward, resulting in the conversion feature having less value. In particular, stock splits and stock dividends would do the job. Again, 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)
A 2:1 stock split concludes with twice as many shares outstanding with each share trading at half its original value. This results in the conversion value being cut in half. Before the stock split, the conversion netted $1,000 of common stock ($25.00 x 40), but after it only nets $500 of common stock ($12.50 x 40) At this point, it’s not likely any conversions occur. This is an example of dilution for convertible bondholders.
Assuming the same example, let’s look at what would happen if a stock dividend occurred:
25% stock dividend
Pre-split common stock price = $25.00
Pre-split conversion value = $1,000 ($25.00 x 40)
Post-split common stock price = $20.00
Post-split conversion value = $800 ($20.00 x 40)
Again, an issuer action reduced the value of the conversion feature. With a 25% stock dividend, the number of shares outstanding increases by 25%, while the price per share decreases proportionately ($25 / 1.25 = $20). Before the stock dividend, the conversion netted $1,000 of common stock ($25.00 x 40), but after it only nets $800 of common stock ($20.00 x 40).
To avoid this problem, nearly every convertible security issued comes with an anti-dilution covenant. It’s a promise to the convertible security owner that the issuer will make adjustments to the conversion feature if a stock split or dividend occurs. Specifically, the issuer will change the conversion price and ratio to offset the dilution. Let’s explore this idea with a 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. If the bond contains an anti-dilution covenant, what is the adjustment to the conversion price and ratio?
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. Prior to 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 falls to $200 if it doesn’t adjust (can convert into 20 shares worth $10 each). With the anti-dilution covenant, the issuer will make an appropriate adjustment to 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
Because the issuer created 4 times the number of common shares outstanding, the bondholders should receive 4 times the original amount received at conversion. If the investor converts now, they’ll receive 80 shares of common stock worth $10 each. This represents a conversion value of $800 (80 x $10), matching the original value.
With that being said, 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. To find the new conversion price, you’ll need to divide the original conversion price ($50) by the stock split factor (4).
New conversion price=4$50
New conversion price=$12.50
The other way can only be used if the new conversion ratio has been 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 way is more comfortable for you.
Anti-dilution adjustments for stock dividends are very similar. The only difference is using the stock dividend factor instead of the stock split factor. Let’s see if you calculate this one on your own:
An investor purchases a $1,000 par, 6% convertible bond with a conversion price of $10. The common stock is currently trading at $12. The issuer performs a 25% stock dividend on the common stock. If the convertible bond contains an anti-dilution covenant, what is the adjustment to the conversion price and ratio?
(spoiler)
Answers:
New conversion ratio: 125 : 1
New conversion price: $8
First, let’s figure out the original conversion ratio:
CR=Conversion pricePar
CR=$10$1,000
CR=100 : 1
In the beginning, the bond can be converted into 100 shares of common stock. With the common stock currently trading at $12 per share, the conversion feature is currently worth $1,200 (100 x $12). Now, the issuer performs a 25% stock dividend, which will drive down the price of the common stock. The anti-dilution covenant will force the issuer to make adjustments to the conversion price and ratio.
Let’s start with the conversion ratio first. With a stock dividend of 25%, the stock dividend factor is 1.25 (1 + 0.25). To find the new conversion ratio, multiply the original ratio by the stock dividend factor:
New conversion ratio=100 x 1.25
New conversion ratio=125 : 1
When bondholders convert now, they’ll receive 125 shares of common stock, which will be worth $9.60 per share after the split ($12 / 1.25). This results in a conversion value of $1,200 (125 x $9.60), which matches the original value.
To find the new conversion price, we can divide the original conversion price by the stock dividend factor:
New conversion price=1.25$10
New conversion price=$8
You could also use the new conversion ratio to find the same answer:
New CP=New conversion ratioPar
New CP=125$1,000
New CP=$8
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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