Convertible corporate bonds

Convertible corporate bonds are very similar to convertible preferred stocks, with a few key differences.

First, the similarities:

• Both can be converted into common stock of the same issuer
• Both provide the investor with capital appreciation potential
• Both sets of formulas are essentially the same

The biggest difference is the par value. Preferred stock typically has a $100 par value, while bonds usually have a $1,000 par value. Aside from that, the core conversion concepts work the same way.

Conversion logistics

A convertible bond’s conversion terms are usually described using two related numbers:

• Conversion ratio (CR): how many shares you receive if you convert one bond
• Conversion price (CP): the effective price per share you’re paying at conversion

Let’s work through a few examples.

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 1 bond can be converted into 25 shares of common stock.

The conversion ratio is essential for most convertible bond math:

• If a question gives you the conversion price, use the formula above to find the conversion ratio.
• If a question already gives you the conversion ratio, you don’t need to calculate it - you already know how many shares you’ll receive.

Sometimes you’ll be asked to go the other direction.

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 swap places in the formula.

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

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

*As we learned in a 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.

To see when conversion becomes profitable, convert the bond’s cost into a cost per share.

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

$\text{Conversion cost per share}=\frac{\text{\$900}}{\text{20}}$

$\text{Conversion cost per share}=\$45$

This means the investor is effectively paying $45 per share (because $900 buys the right to receive 20 shares). If the common stock rises above $45, conversion creates a profit.

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?

Convertible bonds offer added return potential because of the conversion feature. Because investors are getting that potential upside, issuers can typically offer lower interest rates, and these bonds tend to trade at lower yields (higher prices) than comparable non-convertible bonds.

How do you know when conversion is attractive? Just like we explored in a previous chapter with preferred stock, parity prices help you compare the bond’s conversion terms to the stock’s market price.

The stock parity price is the effective price per share if you buy the bond at its market price and convert 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?

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

$\text{Stock PP}=\frac{\text{\$900}}{\text{20}}$

$\text{Stock PP}=\$45$

A $900 bond converted into 20 shares produces an effective cost of $45 per share. If the stock trades above $45, conversion produces a profit. In the earlier example, the stock traded at $60, which is a $15 per share difference.

Let’s try one you can work through.

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 answers the reverse question: based on the stock’s market price, what should the bond be worth based only on its conversion feature?

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 in the market below $900, an investor could buy the bond, convert it, and sell the shares for more than the bond’s purchase price - an immediate arbitrage profit.

Try one more.

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?

Like convertible preferred stock, convertible bonds are typically issued with anti-dilution covenants. Here’s what that 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). Buying the bond for $1,000, converting into 40 shares, and selling those shares for $1,000 total ($25 x 40) produces no gain or loss.

Conversion becomes profitable if the stock price rises above $25. Issuers and their employees generally don’t like conversions because conversion creates new common shares. That increases the number of shares outstanding and can dilute both ownership percentage and value for existing shareholders (including officers and directors).

A forward stock split increases the number of shares outstanding and lowers the market price per share. If the conversion terms didn’t adjust, the conversion feature could lose 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)

A 2:1 stock split doubles the number of shares outstanding, and each share trades at half its prior price. If the conversion ratio stayed at 40:1, the conversion value would drop from $1,000 to $500. That’s dilution from the convertible bondholder’s perspective.

Anti-dilution covenants are designed to prevent this by requiring the issuer to adjust the conversion terms. Work through this example:

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?

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 feature is worth $800 ($40 x 20).

After a 4:1 stock split, the stock price adjusts downward.

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

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

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

If the conversion terms didn’t change, the bond would still convert into 20 shares, now worth $10 each, for a total of $200. The anti-dilution covenant requires adjustments so the conversion feature keeps the original $800 value.

To adjust the 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 back to $800 (80 x $10).

Do you know what the new conversion price would be?

Key points

Convertible bonds

• Converts to common stock of the same issuer
• Investors eligible to make capital gains on stock
• Sold with lower dividend rates (vs. non-convertible)
  • Higher prices & lower yields

Conversion ratio

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

Conversion price

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

Common stock parity price

• Price paid per common share based on convertible security market price
• $\text{PPoCS}=\frac{\text{Convertible bond market price}}{\text{Conversion ratio}}$

Bond parity price

• Value of bond based only on the conversion feature
• $\text{BPP}=\text{stock price x conv. ratio}$

Anti-dilution covenant

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