Convertible securities (CSs) combine debt and equity. In option terms, CSs are a call option on a specified number of shares whose exercise price is the debt claim forgone in exchange for the shares. CSs are also like a stock with a put option whose exercise price is the market value of the convertible.
Some critics insist that CSs are uneconomic because they address several habitats of investors at the same time. Others say that they comprise flexible, non-dilutive, easily executed, and cheap finance, which appeals to many professional investors including hedge funds.
Management’s task is to measure the cost of CSs with the formula while allowing for the real world influences that the basic model ignores.
Cost-influencing factors include dividends, tax, and resolution of agency costs.
Convertible securities (CSs) and other equity-linked instruments combine debt and equity. Depending on the terms and the issuer’s future performance, CSs can range from almost pure equity to an option-free bond. In option terms, a CS can be viewed in two ways. It amounts to a straight bond with a call option on a specified number of shares. It is also effectively a share with a put option whose exercise price is the market value of the convertible.
Some iconoclasts persistently argue that CSs and other equity-linked instruments are essentially uneconomic. Classically championed by Tony Merrett and Allen Sykes, critics maintain that by jointly approaching the equity and fixed interest markets a company must offer costly conversion rights to attract the equity investor while giving virtually the same rights to the fixed interest investor who values them less. Likewise, issuers must give fixed interest investors an acceptable income. In short, CSs contradict the advantage of specialization whereby capital-raising is tailored to habitats of investors. The iconoclasts invoke studies like Ammann, Fehr, and Seiz (2006) to the effect that negative equity returns follow the announcement and issue of CS.
Loss of interest on the part of one habitat can lead to greater interest from the other. The mini-boom in convertibles in the spring of 2009 occurred as the reduced value of the equity element led to higher yields becoming available to investors interested in debt. At the same time some straight equity investors crossed over into convertibles attracted by the combination of yield and equity option.
A counterargument is that CSs are flexible, non-dilutive, easily executed, and cheap finance. CSs appeal to professional investors, including hedge funds which exploit arbitrage opportunities.
Rating agencies such as Fitch see sense in both viewpoints and hold that the desirability of CSs depends more strongly than other sources of finance on individual corporate circumstances and market context. Fitch (2006) concludes:
“Issuers must find continuing compelling reasons for such issuance...The lower costs of such issuance compared with the cost of issuing equity are certainly supportive, as are the gradual standardisation, transparency and consistency of documentation, market practice and the activities of the agencies. On the other hand, issuers and their advisers must always strive to satisfy several constituencies, including regulators, legal and tax authorities, the agencies and finally, investors. Investor appetite underpinned the buoyant corporate activity of recent years. However, that appetite arose in an environment of low interest rates that will not persist indefinitely.”
What is the true cost of CSs? Definition is less difficult than measurement. Having defined the parameters and influences on cost, management must frankly ask whether their measurements are so unreliable as to make them a dubious basis for decision-taking. Of course this applies across financial management, but it is particularly acute for the cost of capital.
The Cost Formula
The cost of a CS is a weighted average of the cost of its debt element and the cost of a call option on the issuer’s shares, since the investor in a CS is a lender and the holder of a call option on the value of the firm. The difference between a conversion right and a regular call option is that a CS holder gets new shares upon exercise. It follows that if the price at which the CS holder is entitled to shares is below market price, then the value of all corporate equity, including the convertor’s, is diluted. This explains why a convertible warrant is worth less than a straight call option on the company’s shares whose exercise leaves existing equity intact.
The market will discount each element to the present using appropriate required rates of return. The cost of CS is an average of the rates weighted by each element’s share of total market value.
The starting point is the textbook formula (see, for example, Copeland, Weston and Shastri, 2004, Chapter 15) which can be summarized as follows.
These are the essential terms: kcv is the cost of convertible debt; B is the value of debt element; W is the value of equity element, being the value of a call option on the company’s shares; B + W is the value of the convertible security; kb is the required rate of return on debt; and kc is the required rate of return on a call option on the company’s shares. See below.
Using the capital asset pricing model,
kc = Rf + [E(Rm) − Rf] βc
where kc is the required rate of return on a call option on the company’s shares with the same maturity as the CS; Rf is the risk-free rate of return for a bond with the same maturity as the CS; E(Rm) is the expected rate of return on a portfolio comprising all the shares in the market; βc is the systematic risk of the call option expressing its correlation with the market. βc is computed by reference to the β of an underlying share of the company adjusted to option using the Black–Scholes option pricing programme:
kcv = kb B ÷ (B + W) + kc W ÷ (B + W)
The basic Black–Scholes option pricing scheme assumes that the issuer pays neither dividends nor tax (see, for example, Berk and DeMarzo, 2007, Chapters 21, 22, 23; Brealey and Myers, 2007, Part 6; and packages like the London Business School’s).
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