Convertible Bonds
What you'll learn
- LOS 25.nDescribe defining features of a convertible bond.
- LOS 25.oCalculate and interpret the components of a convertible bond’s value.
- LOS 25.pDescribe how a convertible bond is valued in an arbitrage free framework.
- LOS 25.qCompare the risk−return characteristics of a convertible bond with the risk−return characteristics of a straight bond and of the underlying common
The owner of a convertible bond has the right to convert the bond into a fixed number of common shares of the issuer during a specified timeframe (conversion period) and at a fixed amount of money (conversion price). Convertibles allow investors to enjoy the upside on the issuer’s stock, although this comes at a cost of lower yield. The issuer of a convertible bond benefits from a lower borrowing cost, but existing shareholders may face dilution if the conversion option is exercised.
The conversion ratio is the number of common shares for which a convertible bond can be exchanged. For example, a convertible bond issued at par with an initial conversion ratio of 10 allows its holder to convert one $1,000 par bond into 10 shares of common stock. Equivalently, the conversion price of the bond is $1,000 / 10 shares = $100.
For bonds not issued at par, the conversion price is the issue price divided by the conversion ratio. Offer documents will indicate how the initial conversion ratio would be modified to account for corporate actions such as stock splits or stock dividends.
Offer documents may also provide a contingent put option in the event of any change of control events such as mergers. Such a contingent put option can be exercised for a specific period of time after the change of control. Alternatively, a lower conversion price may be specified in the event of a change of control.
The conversion ratio may also be adjusted upward if the company pays a dividend in excess of a specified threshold dividend. This adjustment protects the convertible bondholders in the event that the company pays out an unusually large dividend (which will cause the ex dividend price of the stock to decline). Other put options exercisable during specific periods may also be embedded with a convertible.
These put options can be hard puts (i.e., redeemable for cash) or soft puts (i.e., the issuer decides whether to redeem the bond for cash, stock, subordinated debentures, or a combination of the three).
The conversion value of a convertible bond is the value of the common stock into which the bond can be converted. The conversion ratio is the number of shares the holder receives from conversion for each bond. Conversion value is calculated as:
The straight value, or investment value, of a convertible bond is the value of the bond if it were not convertible, the present value of the bond’s cash flows discounted at the return required on a comparable option free issue.
The minimum value of a convertible bond is the greater of its conversion value or its straight value. This must be the case, or arbitrage opportunities would be possible. For example, if a convertible bond were to sell for less than its conversion value, it could be purchased, immediately converted into common stock, and the stock could be sold for more than the cost of the bond.
Business Supply Company, Inc. operates retail office equipment stores in the United States and Canada. Consider a BSC convertible bond with a 7% coupon that is currently selling at $985 with a conversion ratio of 25 and a straight value of $950.
Suppose that the value of BSC’s common stock is currently $35 per share, and that it pays $1 per share in dividends annually. What is this bond’s minimum value?
Solution
The conversion value of this bond is 25 × $35 = $875. Since the straight value of $950 is greater than the conversion value of $875, the bond is worth at least $950.
The market conversion price, or conversion parity price, is the price that the convertible bondholder would effectively pay for the stock if she bought the bond and immediately converted it. The market conversion price is given as:
Compute and interpret the market conversion price of the BSC bond.
Solution
The market conversion price is: $985 / 25 = $39.40. This can be viewed as the stock price at which an investor is indifferent between selling the bond and converting it.
The market conversion premium per share is the difference between the market conversion price and the stock’s current market price:
Compute and interpret the market conversion premium per share of the BSC bond.
Solution
Since BSC is selling for $35 per share, the market conversion premium per share for the BSC bond is: $39.40 − $35 = $4.40. This can be interpreted as the premium that investors are willing to pay for the opportunity to profit should the market price of the stock rise above the market conversion price. This is done with the assurance that even if the stock price declines, the value of the convertible bond will not fall below its straight value.
Market conversion premium per share is usually expressed as a ratio, appropriately called the market conversion premium ratio. Its formula is:
Compute the market conversion premium ratio of the BSC bond.
Solution
The BSC bond market conversion premium ratio is:
The convertible bond investor’s downside risk is limited by the bond’s underlying straight value because the price of a convertible bond will not fall below this value regardless of what happens to the price of the issuer’s common stock.
This downside risk is measured by the premium over straight value, which is calculated as:
Compute and interpret the BSC bond’s premium over straight value.
Solution
The premium over straight value for the BSC bond is:
All else equal, the greater the premium over straight value, the less attractive the convertible bond.
We need to recognize an obvious flaw with the premium over straight value metric, the straight value is not constant. It varies with changes in interest rate and with the credit spread of the bond.
Investing in a noncallable/nonputable convertible bond is equivalent to buying:
an option free bond, and a call option on an amount of the common stock equal to the conversion ratio.
The value of a noncallable/nonputable convertible bond can be expressed as:
Most convertible bonds are callable, giving the issuer the right to call the issue prior to maturity. Incorporating this feature into the valuation of a convertible bond results in the following expression:
To further complicate the situation (just for fun), consider a convertible bond that is both callable and putable. The expression for value then becomes:
stock.
Buying convertible bonds instead of stocks limits downside risk; the price floor set by the straight bond value provides this downside protection. The cost of the downside protection is reduced upside potential due to the conversion premium. Keep in mind though, that just like investing in nonconvertible bonds, convertible bond investors must be concerned with credit risk, call risk, interest rate risk, and liquidity risk.
Consider the following two examples based on our previous BSC example.
Calculate the return on the convertible bond and the common stock if the market price of BSC common stock increases to $45 per share.
Solution
The return from investing in the convertible bond is:
The return from investing directly in the stock is:
The lower return from the convertible bond investment is attributable to the fact that the investor effectively bought the stock at the market conversion price of $39.40 per share.
Calculate the return on the convertible bond and on the common stock if the market price of BSC common stock falls to $30 per share.
Solution
Recall that the bond will trade at the greater of its straight value or its conversion value. The conversion value in this scenario is 25 × $30 = $750. Assuming the straight value of the bond does not change, the bond will trade at $950.
So, the return from investing in the convertible bond is:
The return from investing directly in the stock is:
The loss is less for the convertible bond investment because we assumed that the straight value of the bond did not change. Even if it had changed, the loss would probably still be less than the loss on the straight stock investment, thus emphasizing how the straight value serves as a floor to cushion a decline, even if it is a moving floor.
The following comparisons can be made between ownership of the underlying stock and the risk return characteristics of the convertible bond:
When the stock’s price falls, the returns on convertible bonds exceed those of the stock, because the convertible bond’s price has a floor equal to its straight bond value. As the stock’s price approaches zero, the convertible’s value will move toward the present value of estimated recovery. When the stock’s price rises, the bond will underperform because of the conversion premium.
This is the main drawback of investing in convertible bonds versus investing directly in the stock. If the stock’s price remains stable, the return on a convertible bond may exceed the stock return due to the coupon payments received from the bond, assuming no change in interest rates or credit risk of the issuer.
Sometimes the price of the common stock associated with a convertible issue is so low that it has little or no effect on the convertible’s market price, and the bond trades as though it is a straight bond. When this happens, the convertible security is referred to as a fixed income equivalent or a busted convertible.
Other times, the price of the stock may be high enough that the convertible behaves as though it is an equity security. When this happens, the convertible issue is referred to as a common stock equivalent. Most of the time, however, the convertible behaves as a hybrid security with the characteristics of both equity and a fixed income security.