A convertible is a bond with an option for the holder to exchange the bond into new shares of common stock of the issuing company under specified terms and conditions. These include the conversion period and the conversion ratio. The conversion period is the period during which the bond may be converted into shares. The conversion ratio is the number of shares received per convertible. The conversion price, which is the effective price paid for the common stock, is the ratio of the face value of the convertible and the conversion ratio. Convertibles almost always have a call provision built in.


Special types of convertibles are: mandatory convertible bonds, exchangeable bonds, and liquid yield option notes [LYONS].


A convertible is much like a bond with a warrant attached. However, this concept is not very useful for valuation purposes. An important problem is that the exercise price of the warrant (the conversion price) is paid by surrendering the accompanying bond. Therefore the exercise price changes through time. The fact that most convertibles are callable creates another valuation problem. Brennan and Schwartz (1980) have developed a model which takes all these factors into account.


Motives For The Issuance Of Convertibles

Motives for the issuance of convertibles can be divided into traditional and modern motives.


Traditional Motives

Traditional motives are that convertibles are:

  • a deferred sale of stock at an attractive price; and
  • a cheap form of capital (Brigham, 1966)

These motives are criticized by Brennan and Schwartz (1988). The first motive is based on the fact that normally the conversion price is above the market price of the underlying stock at the issuance date.

However, the conversion price should in fact be compared to the underlying stock price at the exercise date:

  • If the underlying stock price is higher than the conversion price, the company suffers an opportunity loss.
  • If it is lower than the conversion price, the conversion right will not be exercised.


The second motive is based on the fact that the coupon rate of a convertible is lower than the coupon rate of an ordinary bond. However, if the cost of the conversion right is taken into account it can be demonstrated that the cost of convertibles is relatively high.

The cost of convertibles is neither a reason to issue, nor a reason to refrain from issuing convertibles. Its cost is just an adequate compensation for the risk involved in its investment.


Modern Motives for The Issuance of Convertibles

Modigliani and Miller [M&M] have demonstrated that in perfect markets the financing decision of the firm is irrelevant for its market value. Therefore, modern motives for the issuance of convertibles are based on market imperfections. Brennan and Schwartz (1988) argue that convertibles are relatively insensitive to the risk of the issuing company. If the risk increases, the value of the bond part decreases, but the value of the warrant part increases, because the value of a warrant is an increasing function of the volatility. This makes it easier for bond issuers and purchasers to come to terms when they disagree about the riskiness of the firm.

Because of the insensitivity towards risk, convertibles may result in lower agency costs between share and bondholders. Bond-holders are less concerned about the possibility that shareholders attract risky projects. Because of their conversion right they also participate in the value created if risky projects are undertaken (Green, 1984).

Other motives, based on imperfections, include the reduction of flotation costs compared to the case where the firm raises debt now and equity later, and the possibility to ”polish” the company’s financial accounts by recording the convertible as debt on the balance sheet (Veld, 1992).

With regard to the optimal moment to call convertibles, Ingersoll (1977) has demonstrated that this moment occurs when the conversion value, this is the value of the common stock to be received in the conversion exchange, equals the call price. However, in an empirical study he finds that in practice the calls show a delay. On average the conversion value of the bonds was 43.9 percent above the call price.


Exchangeable Bonds

An exchangeable bond may be converted into existing shares of the same or an alternative company. It is much like a convertible, except that in a convertible, the bond may be converted into “new” shares. Analogously, the conversion right of an exchangeable bond is equivalent to a covered warrant. An example of a large issue of exchangeable debt is the IBM US$300 million offering in January 1986, which is convertible into the common stock of Intel Corporation. An analysis of exchangeable debt is made by Ghosh et al. (1990).


Liquid Yield Option Notes [LYONS]

Liquid yield option notes (LYONS) are zero-coupon, callable, puttable convertibles. This security was created by Merrill Lynch in 1985. It was first issued by Waste Management Inc. in spring 1985. A number of subsequent issues were made in the United States. McConnell and Schwartz (1986) have developed a valuation model, which takes all the above mentioned characteristics of LYONS into account.


Mandatory Convertible Bonds

Mandatory convertible bonds are convertibles which may be converted during the conversion period and which are automatically converted at the end of the conversion period.



Ghosh, C., Varma, R. & Woolridge, J. R. (1990). An analysis of exchangeable debt offers.

Journal of Financial Economics, 19, 251–63. Green, R. C. (1984). Investment incentives, debt, and warrants. Journal of Financial Economics, 13, 115–36.

Ingersoll, J. (1977). An examination of corporate call policies on convertible securities. The Journal of Finance, 32, 463–78.

Brennan, M. J. & Schwartz, E. S. (1980). Analyzing convertible bonds. Journal of Financial and Quantitative Analysis, 4, 907–29. 80

Brennan, M. J. & Schwartz, E. S. (1988). The case for convertibles. Journal of Applied Corporate Finance, Summer, 55–64.

Brigham, E. F. (1966). An analysis of convertible debentures: theory and some empirical evidence. The Journal of Finance, 21, 35–54.

McConnell., J. J. & Schwartz, E. S. (1986). LYON taming. The Journal of Finance, 41, 561–76. Veld, C. (1992). Analysis of equity warrants as investment and finance instruments. Tilburg, Netherlands: Tilburg University Press.