Convertible bonds

We first learned about convertible securities in the preferred stock chapter. Both preferred stock and corporate bonds can be convertible into common stock of the same issuer. For example, a convertible Ford bond would allow the bondholder to convert the bond into Ford common stock.

A conversion feature gives the investor an additional way to earn a return:

• The bond’s interest payments provide income.
• If the investor converts to stock and the stock price has risen, the investor may realize a capital gain.

When a convertible bond is issued, the issuer sets its conversion ratio and conversion price. In plain English, both describe how many shares you receive if you convert the bond. These terms are set when the bond is originally issued and typically remain fixed for the life of the bond.

Conversion ratio and conversion price

The conversion price is mainly used to calculate the conversion ratio.

For example:

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

$\text{Conversion ratio}=\frac{\text{Par}}{\text{conversion price}}$

$\text{Conversion ratio}=\frac{\text{\$1,000}}{\text{\$40}}$

$\text{Conversion ratio}=25:1$

So the conversion ratio is 25:1, meaning one $1,000 par bond can be converted into 25 shares of common stock. For most convertible bond math questions, the conversion ratio is the key number. If the question gives you the conversion price, use the formula above to find the conversion ratio.

If the question provides the conversion ratio, you don’t need to calculate it - you already know exactly how many shares you’ll receive upon conversion.

Sometimes you’ll see the reverse: the question gives 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?

$\text{Conversion price}=\frac{\text{Par}}{\text{conversion ratio}}$

$\text{Conversion price}=\frac{\text{\$1,000}}{\text{20}}$

$\text{Conversion price}=\$50$

This is the same relationship as before - conversion price and conversion ratio simply trade places in the formula.

Profit from converting

Now let’s look at how an investor can earn a capital gain by converting.

A corporate bond has a conversion ratio of 10:1 and is purchased for $900

The investor is effectively buying a “bundle” of 10 shares for $900. On a per-share basis:

$\text{Conversion cost per share}=\frac{\text{bond price}}{\text{conversion ratio}}$

$\text{Conversion cost per share}=\frac{\text{\$900}}{\text{10}}$

$\text{Conversion cost per share}=\$90$

If the market price of the common stock rises above $90, the investor could profit by 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?

Convertible bonds offer this extra potential return. Because of that added benefit, they’re typically issued with lower interest rates and trade at lower yields (higher prices) than comparable non-convertible bonds.

Parity pricing

How do you decide when conversion makes sense? Parity pricing helps you compare the bond and the stock on an equivalent basis.

The stock parity price is the effective price per share you’re paying for the stock if you buy the bond and convert it.

A corporate bond has a conversion ratio of 10:1 and is purchased for $900. What is the parity price of the common stock?

$\text{Stock PP}=\frac{\text{bond market price}}{\text{conversion ratio}}$

$\text{Stock PP}=\frac{\text{\$900}}{\text{10}}$

$\text{Stock PP}=\$90$

If a $900 bond is purchased and immediately converted into 10 shares, the investor is effectively paying $90 per share. If the stock trades above $90, converting and selling the shares could produce a profit. In the earlier example, the stock traded at $120, which is a $30 per share gain.

Let’s try one where you have to find the conversion ratio first:

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?

Bond parity price

Bond parity price works in the opposite direction. Here, you use the stock’s market price to find what the bond would be worth if it were priced exactly in line with its conversion value.

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?

$\text{Bond PP}=\text{stock price x conversion ratio}$

$\text{Bond PP}=\text{\$90 x 10}$

$\text{Bond PP}=\$900$

If the bond trades below $900, an investor could buy the bond, convert immediately, and sell the stock for more than the bond’s purchase price - creating an immediate profit.

Try 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?

Anti-dilution covenants

Earlier, we said the conversion price and conversion ratio typically don’t change. That’s generally true, but most convertible bonds include anti-dilution covenants that protect bondholders if the issuer takes actions that would otherwise reduce the conversion value (similar to convertible preferred stock).

To see why this matters, it helps to review how dilution could happen without that protection.

Assume the following:

$1,000 par convertible bond

Convertible bond market price = $1,000

Conversion ratio = 40:1

Common stock market price = $25

Here, the conversion feature is at breakeven (parity). If an investor buys the bond for $1,000, converts into 40 shares, and sells those shares for $1,000 total ($25 x 40), there’s no gain or loss.

If the common stock price rises above $25, investors have a strong incentive to convert. Conversion creates new shares of common stock, which dilutes the ownership percentage (and often the value) of existing common stockholders.

Without an anti-dilution covenant, the issuer could take actions that reduce the conversion value. Stock splits and stock dividends are the classic examples.

Again, assume:

$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 doubles the shares outstanding and cuts the price per share in half. If the conversion ratio stayed at 40:1, the conversion value would drop from $1,000 to $500. That reduction is dilution for convertible bondholders.

Now consider a stock dividend:

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)

With a 25% stock dividend, shares outstanding increase by 25%, and the price per share decreases proportionately ($25 / 1.25 = $20). If the conversion ratio stayed at 40:1, the conversion value would fall from $1,000 to $800.

If you need a refresher on how to calculate changes to positions because of stock splits or dividends, please review this section in the common stock chapter.

To prevent this, most convertible securities include an anti-dilution covenant. It requires the issuer to adjust the conversion feature after stock splits or stock dividends by changing:

• the conversion ratio, and
• the conversion price,

so the conversion value is preserved.

Anti-dilution adjustment for a stock split

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?

Start by finding the original conversion ratio.

$\text{CR}=\frac{\text{Par }}{\text{Conversion price}}$

$\text{CR}=\frac{\text{\$1,000}}{\text{\$50}}$

$\text{CR}=\text{20 : 1}$

Initially, the bond converts into 20 shares. With the stock at $40, the conversion value is $800 ($40 x 20).

After a 4:1 stock split, the stock price is expected to fall by a factor of 4.

$\text{New common stock price}=\frac{\text{Current market price}}{\text{Stock split factor}}$

$\text{New common stock price}=\frac{\text{\$40}}{\text{4}}$

$\text{New common stock price}=\text{\$10}$

If the conversion terms didn’t change, the conversion value would drop to $200 (20 shares x $10). The anti-dilution covenant requires an adjustment that keeps the conversion value at $800.

To find the new conversion ratio, multiply the original conversion ratio by the stock split factor.

$\text{New conversion ratio}=\text{20 x 4}$

$\text{New conversion ratio}=\text{80}$

Now the bond converts into 80 shares. At $10 per share, the conversion value is $800 (80 x $10), matching the original value.

With that in mind, what is the new conversion price?

Anti-dilution adjustment for a stock dividend

Anti-dilution adjustments for stock dividends work the same way, but you use the stock dividend factor instead of a stock split factor.

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?

Key points

Convertible bonds

• Converts to common stock of the same issuer
• Investors eligible to make capital gains on stock
• Lower rates of return (vs. non-convertible bonds)

Conversion ratio

• $\text{CR}=\frac{\text{Par}}{\text{conversion price}}$

Conversion price

• $\text{CP}=\frac{\text{Par}}{\text{conversion ratio}}$

Stock parity price

• $\text{SPP}=\frac{\text{bond market price}}{\text{conversion ratio}}$

Bond parity price

• $\text{BPP}=\text{stock price x conv. ratio}$

Arbitrage opportunity

• Instantaneous profit potential on a security

Anti-dilution covenant

• Prevents issuer from performing dilution actions without adjusting the conversion feature
• Involved when stock dividends & splits occur
• Conversion ratio goes up
• Conversion price goes down