# Zero coupon convertibles do not have a zero cost

Convertible bond issuance is at a record high, with companies ‘benefiting’ from low interest rates and high equity volatility. A recent $1.44bn convertible bond issue by Twitter, with a zero coupon and conversion premium of 67%,­ is a good example. Convertibles are not the cheap form of financing that is sometimes claimed, nor do we think that so-called ‘hedging’ transactions, which often accompany convertible issues, create value for investors. We present an interactive model to demonstrate how to calculate the cost of capital for a convertible. Global convertible bond issues have increased significantly over the last year or so. In the US,$106bn of convertibles were issued in 2020, over double the highest annual amount in recent years, and 2021 is on track for even more.

#### US market convertible bond issuance

From an issuer perspective, the attraction of convertibles has been enhanced by low interest rates coupled with high equity volatility. This enables companies to achieve a low interest cost for the bond while obtaining a high conversion premium, hence minimising the potential dilution due to the conversion option. Some claim that the low interest cost and the effective issue of shares at a premium to their current price results in cheap financing compared with straight debt or straight equity.

The most common form of convertible is a fixed rate bond with a maturity of between 3 and 7 years, where the holders have the option to convert into a fixed number of equity shares prior to the maturity of the bond. If the holders do not convert, the bond is redeemed, usually at par. If the conversion option is exercised, additional shares are issued, and no further interest or redemption cash flows are paid.

An investor in a convertible, in effect, purchases two things: a fixed rate bond and an equity call option – the option to give up the bond in exchange for equity shares. The return for the investor depends on the bond coupon received prior to conversion, and the overall debt return if there is no conversion, plus the value of the shares received if conversion takes place. However, the real benefit to the investor, and the key driver of the true cost to the company and existing shareholders, is the optionality.

Investors gain value from being able to choose between the promised debt cash flows or switch into equity if it provides a higher return. This investor benefit due to the call option results in a corresponding cost to the company and existing shareholders.

In exchange for this optionality, convertible bond investors accept a lower debt coupon, compared with straight debt, and a conversion premium compared with straight equity.

• Lower coupon: Adding a valuable conversion option to a bond means that the coupon is generally set significantly below what it would be if straight debt were issued. The reduction of the coupon depends on the conversion premium and the value of the conversion option. Given current low interest rates, this can mean a zero coupon for some convertibles.
• Conversion premium: The conversion premium is the difference between the price at which shares are issued through a convertible (the conversion price) and the current share price. For example, a convertible with an issue price and par value of 1,000 that converts into 100 shares has a conversion price of 10. If the current share price is 6 then the conversion premium is 67%. In effect the shares issued (assuming conversion takes place) from selling this convertible are then sold at a 67% premium compared with the current stock price and the issue price of a straight equity offer.

The coupon and conversion premium interact in the pricing of the convertible and in determining its characteristics. For example, a higher conversion premium reduces the value of the conversion option for investors, which would likely result in a higher coupon. In this case the convertible becomes more bond-like. The characteristics of a convertible may change after issue, largely due to changes to the stock price. If the stock price rises, the convertible behaves more like straight equity. A price fall results in the bond element dominating.

## Cost of capital for a convertible

A convertible bond can be analysed into debt and conversion option components. The debt value is the value of the debt cash flows discounted at the return that investors would require if it were straight debt. Given the reduced coupon this will be less than the face value of the convertible. The remainder of the value of the convertible is attributed to the conversion option. The option can also be directly valued using a suitable option pricing model.1A convertible can also be analysed into two different components. It can be regarded as a holding of equity shares plus a put option – the option to ‘sell’ those shares back to the issuer and instead receive the bond cash flows. A liability plus call option is equivalent to an equity investment plus a put option. Our analysis is based on the more common call option view but could equally be done from the other perspective.

It is important that convertibles are correctly included in cost of capital calculations used in equity valuation. The cost of capital for a convertible reflects its hybrid nature and is the weighted average of the cost of the debt and conversion option components.

The cost of the debt component is simply equal to what the company would pay for comparable straight debt. The cost of the conversion option component is a little more complex. Because the returns on equity call options are closely linked to those of the underlying common equity, the cost of a call option must reflect the cost of that common equity. However, call options have higher risk and volatility, which means that the cost of the call is also higher.

In a CAPM approach to the cost of capital calculation, we need the beta factor for the conversion option.  A call option beta equals the beta factor of the underlying equity multiplied by the relative volatility of the option compared with that of equity. This relative volatility is called the option elasticity, which itself equals the option delta multiplied by the ratio of the share price to the option price.

Betaoption = Betaequity x Option delta x Stock price / Option value

To apply this to a conversion option simply use the value of shares obtained if the convertible were converted (the conversion value) in place of the stock price.

Because option elasticity is always more than 1.0, the beta and cost of capital for the conversion option must always be higher than the equity beta and cost of equity.

When the cost of the conversion option is combined with the cost of the debt component, the resulting overall cost of capital for a convertible lies between the costs of straight debt and equity. In addition, the cost of convertibles changes over time, in part due to changes in the costs of straight debt and equity but also due to the changing characteristics of the convertible, which make the security either more bond-like or closer to equity. We demonstrate this for a recent convertible note issue by Twitter.

On March 2, 2021 Twitter announced the issue of a $1.44Billion zero coupon convertible note. The conversion price was set at$130.03, a 67.5% premium above the then stock price of $77.63. #### Twitter$1.44Billion 0% convertible notes

We estimate that the pre-tax cost of capital for this security at the time of issue is about 5.1%, which is a combination of our assumed straight debt cost of 3.25%2Our estimated straight debt yield is derived from data provided by Twitter regarding their convertible note hedge (see below). We assumed that the cost of the hedge equalled the value of the conversion option and from that determined the value of the bond component of the convertible and hence the implicit debt yield. and our calculated cost of the conversion option of 15.4%.

In practice, you will also need to consider the tax consequences and include a post-tax cost of the convertible in a WACC calculation. Generally, the bond component would be tax deductible, however, exactly how this works (including the tax consequences of related hedging transactions we describe below) may vary by jurisdiction.

The full calculation is shown below. The model is interactive so if you disagree with some of our input assumptions, such as the equity risk premium or equity beta, you can make changes to calculate your own estimate of the cost of this convertible. Changes to the inputs of equity volatility and straight debt yield affect the prices of the conversion option and debt components respectively. If you change one of these you will also need to change the other to ensure that the convertible value is the same as the issue price in order to present a cost of capital at the time of issue.

Input data relates to the Twitter $1.44bn convertible note issue in March 2021 Note: This model is based on a simplified Black-Scholes option valuation and may not reflect the full complexities of a convertible bond and its pricing. You will find more explanations about the model and the simplifying assumptions we have used in the downloadable version. Please enter your email address to receive an excel version of this model I agree to your privacy policy and to receive email notification of future articles. You can unsubscribe any time. It is often claimed that the benefit of using convertibles is that they represent both cheap debt and cheap equity. For the convertible issued by Twitter certainly the debt looks inexpensive considering the zero coupon. In addition, if the bond is converted, equity is issued at a much higher price ($130.03) than it would have been in a straight equity issue ($77.63). This reduces the dilutive effect and (it is asserted) the cost to existing shareholders – full conversion increases the share count by 11.1m shares, whereas a straight equity issue to raise the same amount of capital would have resulted in the issue of 18.5m shares. We think that these claims are flawed. Only if the market is inefficient in pricing these securities would such statements be valid. • Convertibles are not cheap debt: The low coupon does not result in cheap debt when the conversion option is taken into account. Only part of the issue price is payment for the debt component, the rest is for the conversion option. If the value of the conversion option is stripped out then the debt becomes a discounted bond and the accretion of that discount produces a cost of debt comparable to equivalent straight debt. • Convertibles are not cheap equity: The conversion premium does not result in cheap equity when the optionality is taken into account. The cheap equity only applies if conversion takes place, if the stock price falls then there is no such benefit. The conversion option component of a convertible is very similar to issuing a stand-alone warrant. The cost of capital for a warrant is always higher than that of the underlying equity due to the higher price volatility and higher beta factor. Combining the cost of the debt component with the cost of the conversion option results in an overall cost of a convertible being somewhere between the cost of straight debt and straight equity, as we illustrate above. This is not surprising given the hybrid nature of this financing. The fact that the cost of convertibles is above the cost of straight debt, or that the cost of the conversion option is higher than the cost of equity, does not indicate a detrimental effect on the overall cost of capital (WACC). The risk absorbing nature of a written call option means that the cost of equity is itself lower as a consequence. For a practical illustration of how risk is shared between providers of capital, see our article Allocating value: An option based approach. ## Convertible ‘hedging’ transactions One concern of companies and equity investors regarding convertible financing is the potential for additional equity shares to be issued and therefore the dilution of existing shareholders. This dilution could be offset by simple share repurchases, but many companies seek to manage the dilutive effect by the use of a derivative structure. The most common strategy involves purchasing a call option with the same terms as the written conversion option, thereby, in effect, negating the conversion option from the issuer’s perspective. The issuer at the same time writes another similar call option (often labelled a warrant), again on the same terms, except at a higher exercise price. The cash received from selling the warrant with the higher exercise price would be lower than the cost of purchasing the call option, which means that the strategy involves a net cash outlay. This reduces the net proceeds of the convertible note offer and hence increases the effective debt cost, but the benefit is that the effective conversion price is increased and, hence, the potential for dilution reduced. Twitter has done exactly this transaction in respect of the convertible note offer we describe. The conversion option embedded in the convertible involves the potential issue of 11.1 million shares at a conversion price of$130.03. Twitter purchased a call option with the same exercise price to economically offset the conversion option and issued a warrant at the same time with an exercise price of $163.02. Twitter paid a net$52.4m for both transactions, comprising $213.5m for the purchased call less$161.1m received from the sale of the warrants.

#### Twitter convertible note hedge and sale of warrant transactions

Twitter states that the “convertible note hedges and the sale of such warrants are intended to offset any actual dilution from the conversion of the 2026 Notes and to effectively increase the overall conversion price from $130.03 to$163.02 per share”. It is correct to say that the purchased call offsets the dilution that arises from the convertible. In fact, these two transactions taken together, in effect, produce a straight bond issue, where no dilution can arise. The combined position is a zero-coupon bond issued at a discount to the par value, with the accretion of that discount resulting in a cost of 3.25%.

However, the issued warrants will still have a dilutive effect, except there is a lower probability of actual dilution compared with the original convertible issue, considering the higher exercise price of the warrants. Indeed, the stock price at the time of these transactions would have to rise by more than 110% for any dilution to occur.

In our view, convertible note hedges do not directly create value; all they achieve is to modify the effective terms of the convertible. Twitter issued a convertible with a conversion premium of 67% and raised that conversion premium to 110% through the derivative overlay. But the result is the same as issuing the convertible with a higher conversion premium in the first place, while offering a higher coupon to compensate for the lower value of the conversion option. In the derivative overlay approach, there is an implicit increase in the debt cost because the net proceeds received are reduced, but this issue discount is economically no different from a higher coupon.

Of course, a convertible that is more debt-like would have a lower cost of capital (as demonstrated by the chart in our model), but this merely reflects a different risk profile and is not in itself something that adds value.

Only if there is an indirect benefit of the derivative strategy can it create value, such as if this creates greater investor demand for the offer, and hence a better pricing outcome for the convertible itself, or if there is a separate taxation or accounting advantage.

## Insights for investors

• The cost of capital for convertible bonds reflects their hybrid nature – it is higher than the cost of debt and generally lower than the cost of equity
• Convertibles do not represent cheap debt or cheap equity. Unless market pricing is inefficient, the cost of capital reflects the risk characteristics and, assuming no externalities, such as the tax shield, issuing convertibles will not affect WACC.
• The high cost of capital for equity call options, such as a convertible conversion option, arises because of the higher risk absorption by the equity option investors. This in turn reduces the beta for straight equity.
• A convertible note hedge merely changes the economic characteristics of the financing. If the result is financing that is more debt-like, the cost of capital for the convertible is reduced; however, this does not directly add value.
• A derivative strategy that results in a higher effective conversion price reduces the (net) value of the conversion option and reduces the likelihood (and potentially the magnitude) of future dilution.

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