Corporate convertible bonds

Convertible corporate bonds are very similar to convertible preferred stocks, with a few key differences. Here are the main 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 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 conversion concepts work the same way.

Conversion logistics

A few examples will make the mechanics clear.

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 the starting point 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 can skip that step because it already tells you how many shares you receive upon conversion.

Sometimes you’ll be asked to work backward.

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 switch places.

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 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 profits from conversion if the common stock price rises above $45. Conceptually, the investor is buying a “20-pack” of shares for $900. On a per-share basis:

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

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

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

If the market price of the common stock rises above $45, converting 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 these bonds with lower interest rates. As a result, they tend to trade at lower yields (higher prices) than comparable non-convertible bonds.

How do you know when conversion makes sense? Just like in the preferred stock chapter, parity prices help you compare the bond’s conversion terms to the stock’s market price. The formulas are essentially the same.

The stock parity price is the effective price per share you’re paying for the common stock if you buy the bond 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 of common stock works out to $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 gain.

Try one 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?

Bond parity price can also help you decide whether it makes sense to buy a convertible bond and convert immediately. This time, you start with the stock’s market price and work toward the bond’s value based on conversion.

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 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?

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 situation, 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.

Conversion becomes profitable if the stock price rises above $25.

Issuers and their employees generally don’t like conversions because conversion creates new shares of common stock. That increases the number of shares outstanding and can dilute the ownership percentage (and value) of existing common stockholders, including officers and directors.

A forward stock split (more shares outstanding at a lower market price) can reduce the value of the conversion feature if the conversion terms don’t adjust.

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 doubles the number of shares outstanding, and each share trades at half the original price. If the conversion ratio stays at 40:1, the conversion value falls from $1,000 to $500. That’s dilution from the convertible bondholder’s perspective.

Anti-dilution covenants are designed to prevent this outcome by requiring the issuer to adjust the conversion terms.

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 conversion value of only $200. The anti-dilution covenant requires the issuer to adjust the conversion price and ratio so the conversion value stays at the original $800.

Start with the conversion ratio. Multiply the original conversion ratio (20) by the stock split factor (4).

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

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

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?

That covers the main convertible bond calculations you’ll see: conversion ratio, conversion price, parity prices, and anti-dilution adjustments.

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
• $\text{PPoCS}=\frac{\text{bond market price}}{\text{Conversion ratio}}$

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