Allocating value: An option-based approach

You might assume that a change in enterprise value completely accrues to equity investors; however, this is often not the case. Other claims, such as debt or equity warrants, also change in value as enterprise value changes. Understanding this effect can be important when analysing many companies, especially those in financial distress.

Option-like characteristics of debt and equity claims drive the allocation of changes in enterprise value between debt and equity investors. We apply an interactive model to analyse recent changes in the enterprise value of Air France–KLM.

There are two key stages to using an enterprise value based approach to equity valuation.  First, the valuation of the enterprise itself and, second, determining how much of that value is attributable to common shareholders after considering the other claims on the business, such as those of debtholders.

All claims on enterprise value are dynamic

As the value of that business changes, so does the value of all claims. It is a mistake to regard all other claims except for that of the common shareholders as fixed and, as a result, to attribute the whole increase or decrease in enterprise value to just the shareholders. In reality part would accrue to other claimholders. This also applies if your ‘target’ EV differs from the current market EV; you should not assume that this total difference in enterprise value leads to a similar increase or decrease in value for shareholders.

Although the value of all claims are dynamic, they vary in different ways, and to different degrees, depending on their nature and contractual terms. Straight debt, convertible debt, puttable non-controlling interests, pension liabilities, equity derivatives (such as employee stock options) are all components of EV, and all vary differently. Furthermore, these variations also depend on the value of the enterprise and particularly the degree of financial leverage. In this article we focus on (and provide an interactive model to illustrate) how shareholders are affected by two other claims – debt and written call options on common equity.

The dynamic nature of debt claims partly arises from the option-like characteristics of both debt and equity and the changes in the value of this option component. In debt valuation this manifests as a change in credit risk, and the resulting credit spread. In equity valuation it is less obvious, but no less relevant.

The current economic environment makes the option-like characteristics of debt and equity claims more relevant

These option characteristics are particularly apparent in times of financial distress, which is why, considering today’s economic environment, this is an opportune time to think about these issues. Lower equity prices, higher business risk and volatility, and increased debt, resulting from falling profitability and the associated cash flow pressures, all contribute to a higher value of the ‘shareholder put option’ and increase the amount of changes in EV that are shared with debt holders.

For other claims, such as equity derivatives, the impact on EV sharing may be very different and more significant at higher valuations. We shall return to equity derivatives and our example of share warrants later. First, we consider ‘straight’ debt and equity and why, in reality, these are themselves derivatives and why this is important.

The option characteristics of debt and equity claims

Otherwise ‘straight’ debt and equity claims on enterprise value exhibit option-like characteristics due to their different payoffs. As prior claimholders, debtholders have limited upside (the best they can hope for is the receipt of all principal and interest due) but on the downside can lose the full value of their investment. As residual claimholders, equity holders have unlimited upside if things go well, and they can ‘put’ the business onto the debtholders and walk away (albeit with nothing) if the business value falls below the claim of debtholders.

Payoffs for holders of equity and debt claims

Note: The binary outcome shown in this table is the basis for valuing debt and equity claims as options. However, in practice, the payoffs and value effects are more complex. Real-world complexities, such as debt restructurings, affect the outcomes and valuation; however, the principle of debt and equity having option characteristics remains.

The option characteristics of debt and equity claims can be explained and calculated in two ways – either as put or call options. Put-call parity means that, while initially looking rather different, they are, in effect, the same. 

  • Equity as a long call: Equity instruments can be thought of as a call option, with the underlying being the value of the business (the enterprise value) and the exercise price equal to the outstanding debt. The option has intrinsic value if the enterprise value exceeds the debt claim. Equity holders would only exercise the call option if it is ‘in the money’ i.e. the enterprise value exceeds the debt. The option has time value because enterprise value volatility, combined with the option effect, produces a more valuable upside compared with downside. With equity viewed as a long call, debt instruments represent an interest in the underlying enterprise less a written call option on that enterprise.
  • Equity as ‘intrinsic value’ plus a put: An alternative (and equivalent) way to think about the option effect is to regard equity holders as owning a put option, while debtholders are ‘short’ that same put. Equity value becomes the value of the underlying enterprise less debt (measured on a credit risk free basis), plus the value of the put option. The put option value reflects the fact that if the value of the enterprise falls below the debt, equity investors can walk away and hand the remaining assets over to the debt holders. In this approach the value of debt equals the value of debt cash flows excluding the option effect (i.e. excluding credit risk), less the value of the written put option. The put option is reflected in debtholders’ required return and the credit spread. A more valuable shareholder put option reflects higher credit risk, increases the credit spread and reduces debt value.

In these calculations the outstanding debt excluding the put option reflects a risk-free valuation (discounting debt cash flows at a rate that does not include a spread for credit risk) and not the balance sheet value. This is because the impact of credit risk is separately captured in the put option value. The balance sheet historical cost amount of debt is not relevant as it includes the value of the put option at the time the debt was originally issued. What matters in valuation is the value of this put option today.

Put and call approaches to equity and debt values

We have created a simple interactive model to illustrate this option-based approach to valuing debt and equity. The model is easy to use, just enter your input values in the blue cells. The model calculates the resulting shareholder put option adjustment, together with the values of each claim and their implied volatility. We also show how changes in enterprise value are shared between the claimholders. The charts illustrate how these outputs vary for different inputs of enterprise value.

There are further inputs for an additional share warrant claim – a written call option on the ordinary shares. The amount of these warrants is set to zero when the model is first loaded. We will come back to the warrants later and see how adding this claim affects the outcome.

The model also enables you to input your own target enterprise value (in the form of a difference compared with the current market EV) and observe how any upside or downside would be shared between claimholders.

For more explanation about the methodology select the links immediately below the model.


Interactive model: Option adjusted values of debt and equity claims

— iphone and ipad users: This model formats best if viewed in Google Chrome —


Note: This model is simplified and is based on a number of underlying assumptions. Click on the headings below to find out more about the underlying methodology, inputs, outputs and charts, and assumptions.

The model uses a simple underlying Black-Scholes option pricing calculation. The equity claim is valued as a call option with the underlying asset being the value of the enterprise, the strike price being the amount of debt, and the option term equal to the maturity of that debt. The amount of debt is the approximate value if it had zero credit risk, in other words the value excluding any option effect. This is calculated from the balance sheet amount of debt (which we assume to be measured on a historical cost basis), the debt interest rate and the risk-free interest rate.

Total equity value is split into common equity and share warrant components by pricing the warrants relative to the common equity using a similar Black-Scholes model. The underlying this time is the common equity. The volatility input for this is derived from the assumed asset volatility using the following formula.

Equity volatility = Asset volatility x Option delta x (1 + Value of debt / Value of equity)

The ‘option delta’ in this calculation is the delta in the valuation of the equity call option.

Our methodology is certainly not perfect given the complexities of valuing options, particularly in the context of debt and equity claims, and the simplifying assumptions we have made; however, we think it is sufficient to illustrate the concepts.

Enterprise value: This is the value of the business on which the debtholders, common shareholders and stock option holders each have a claim. The model has two enterprise value inputs, the second of which can be used to investigate how the difference between a current market enterprise value and an investor’s target EV would be shared between different claimholders.

Asset volatility: The figure is the annualised volatility (standard deviation) of expected returns on the enterprise value. There is no market data for asset volatility, but it can be calculated from implied equity volatility measures derived from traded options or equity volatility observed from historical stock price changes. The relationship between asset and equity volatility is a function of leverage and the delta of the shareholder call option on the enterprise.

Equity volatility = Asset volatility x Option delta x (1 + Value of debt / Value of equity)

Debt inputs: The model uses the book value of debt and from this determines an approximate credit risk-free debt value and an approximate fair value based on the option pricing approach. The debt interest rate input is therefore the debt yield at the time of issue.

Share warrant inputs: The option exercise price is input as a percentage of the stock price. This means that if you change another input and the common stock price changes then so too does the warrant exercise price. The amount of options is expressed as a percentage of the common shares. For example, if you enter 20% then this means that if there are 100 common shares issued, then the warrants represent options over 20 shares.

Implied equity and debt values at current market EV: Although the model values equity as a call option, the result is presented as equity and debt values excluding the option feature, plus the value of the put option for equity and less the same put option value for debt. If you also include share warrants as a claim, then the total equity value is split between the common stock and warrant components.

Implied volatilities: The volatility measures are annualised standard deviations of the returns for each claim. Debt and total equity volatilities are derived from the input asset volatility, the delta of the total equity call option and the degree of financial leverage. You should find that debt volatility is lower, and equity volatility higher, than the input enterprise asset volatility. Debt volatility will only be zero if the put option has no value and debt is risk-free (we assume that the risk-free rate is constant). Equity volatility is further split between the volatility of the price of the warrants and the volatility of common shares.

Share of incremental changes in enterprise value: These percentages represent in what proportion an incremental change in enterprise value is shared between the different claimholders. These are derived from the delta of the shareholders’ call option and are only applicable for a marginal effect. With share warrants added as a claim, the share applicable to total equity is further split between the common shares and warrants.

Debt and equity values at target EV: This reflect all of the same inputs as for the implied debt and equity values above, except for the enterprise value which is set equal to the market EV plus or minus the input upside or downside. The absolute and percentage upside or downside for each claim is the difference between the values in this section and those in the top output section.

Chart – Equity and debt claim components of enterprise value: This shows enterprise value split into the debt and equity components and how those components change for different inputs for enterprise value. The vertical line represents the selected EV input.

Chart – Sharing of incremental changes in EV: This shows the percentage split of incremental changes in EV between debt and equity holders based upon different inputs for enterprise value. The vertical line shows the split based on the selected enterprise value input.

The model is based on a number of simplifying assumptions. These simplifications do not invalidate the message of the option feature having an effect on debt and equity values, but they do affect the accuracy. The model is particularly unlikely to closely replicate real world values where extreme inputs are used, such as very high debt relative to EV. The key assumptions include:

Returns are normally distributed: The model uses a simple Black-Scholes option pricing mechanism to generate the values. This in turn assumes that returns are (log) normally distributed. The problem is that, in practice, distributions of returns can vary. Often there are higher probabilities of extreme changes in market value than would be predicted by a normal distribution (the so-called fat-tail problem or, in statistical terms, kurtosis). If returns exhibit this characteristic, then our model will likely understate the option value.

Average debt maturity is fixed: The period of time until debt repayment is a key determinant of the option value and the model assumes that input period does not change as EV changes. This is likely to be unrealistic at times of financial distress. If a company gets into trouble with EV falling to close to, or less than, the outstanding debt, then it is likely that debt covenants would be breached, which may in turn lead to an effective reduction in the maturity of debt. This is likely to result in a lower option value than if debt maturity were fixed.

Debt and equity payoffs are binary: The model is based on a binary outcome that depends on whether enterprise value is above or below the outstanding debt at the time of debt maturity. Either the debt is repaid, and equity investors receive the rest of EV, or there is a default, equity investors receive nothing, and the debtholders receive whatever is left. The reality is more complex; in particular, the model does not allow for other outcomes such as debt restructuring.

Distributions are ignored: Distributions that affect the value of the underlying asset have an impact on option values. For the warrant valuation we assume that dividend yield of the common shares is zero. This may overstate the value of the warrants for dividend paying companies. We also ignore how the enterprise free cash flow generated by the business is used. Whether this is reinvested, used to pay down debt or distributed to equity investors would impact how enterprise value is shared between claimholders.


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The scenario portrayed when the model is first loaded represents a relatively high risk and high financial leverage business, possibly one in financial distress. You will notice that the impact of the put option on the values of the debt and equity components of enterprise value is significant, with the fair value of debt below what it would be if there were no credit risk (and hence no value to the option). In this scenario the fair value of debt is also less then book value due to the debt interest rate not fully compensating investors for the credit risk. The negative effect of the put option on debtholders is mirrored by a positive effect for the equity investors.

To better understand how the option characteristics affects valuation try the following by changing the model inputs:

  • Increase enterprise value: You will notice that the values of both debt and equity rise and the amount of the put option effect is reduced. The increase in enterprise value is shared between equity and debtholders as long as the put option has value. If a company’s debt is trading below its credit risk-free value due to credit risk, the increase in enterprise value will also lead to an increase in the debt value as credit risk recedes. If the put option has no value, the incremental growth in enterprise value all goes to the equity holders.
  • Increase volatility: This increases the value of the put option effect and hence increases the value of equity but reduces debt value by an equal amount. In this model, a change in volatility does not automatically change the enterprise value because both are independent inputs. This is likely to be unrealistic; an increase in volatility would probably result in a higher discount rate applicable to the enterprise (WACC) and hence a lower EV. The wealth transfer due to the option effect is still present, but values are also impacted by other factors.
  • Increase debt maturity: The maturity of debt affects the time value of the option. A longer period before the debt must be repaid results in a higher put option value. Of course, short-term debt is likely to be replaced by other debt finance once it matures. However, because at that point the debt is repriced (a new coupon rate is set) the debtholders are able to avoid the option effect beyond the original debt maturity. In effect, the new option value is priced into the amount debtholders are willing to pay for that new debt (i.e. the new spread).

Not all of an increase in EV accrues to equity investors

In addition to explicitly allowing for the option effect in valuing debt and equity claims the model also illustrates how change in enterprise value is shared between different claim holders. In the high leverage scenario shown when you first load the model (refresh the page to go back to it) you will notice that the high value for the put option means that a significant part of any change in enterprise value accrues to the debt holders; 19% in this case. Try changing the inputs to see what increases or reduces this amount.

Applying the model: Air France-KLM

Air France–KLM (AF-KLM) is a good example of a highly leveraged company for which the shareholder put option value is likely to be a significant factor in determining the value of debt and equity claims, and in explaining how changes in enterprise value are shared between those claimholders. Like other airlines the business has been significantly impacted by Covid-19, with a share price decline of 57% in the month from 18th February, (when the economic effects of the pandemic started to be priced into European stocks) to 18th March 2020.  It is the changes between these dates we examine below. The price temporarily rallied in early April but as of mid-May, when we wrote this article, it is back at the level it was in March.

The value of AF-KLM debt is also down. At 31 December 2019, disclosures in the financial statements indicate that the fair value of gross debt was about 102% of book value. Based on available AF-KLM bond prices we estimate that this was little changed at 18th February but that one month later fair value had declined to approximately 80% of book value.1This is more difficult to determine than the change in equity value, given that only a portion of the AF-KLM debt is quoted and, even then, limited liquidity make price quotes potentially unreliable. Our estimated value change for AF-KLM debt is therefore approximate. Bond prices have increased a little since but they are still significantly down on their pre-Covid-19 level.

Air France-KLM enterprise value

We have not included the AF-KLM pension deficit as a claim when calculating enterprise value.2The pension is, in effect, treated as an operating liability and the value of the enterprise is the underlying business value less the effect of the pension liability. The reason is that, while pension deficits are similar to debt and, ordinarily, we would regard it as a component of EV, the underlying gross pension fund assets and liabilities, if not fully asset-liability matched, adds further complication to the analysis. This does not affect the validity of the analysis but does mean that our estimates of asset volatility may be too high (and not comparable with other companies that have a different pension position) considering the underlying operational business risk. We also assume that the balance sheet debt at these valuation dates is the same as at the previous balance sheet date on the basis that new debt issues are approximately offset by debt repayments during this period.

The sharing of changes in enterprise value between claimholders can be clearly seen in the above. The €4,791m reduction in enterprise value is shared almost equally in absolute terms between debt and equity investors, although the percentage reduction in equity value is much higher.

We entered the above data for EV and the book value of debt in the model, together with values for the debt yield, debt maturity and risk-free interest rate. The critical factor that determines how that enterprise value is split between debt and equity investors, considering the shareholder put option, is the asset volatility. As we wish to investigate market prices we back-solved for the volatility input that resulted in a model output that replicates the observed (and estimated in the case of debt) market prices on each date. The inputs and resulting model outputs are summarised below.

Air France-KLM equity as an option analysis

The increase in asset volatility from 23% to 30% that is implied by the change in market prices is perhaps not surprising considering the high degree of uncertainty regarding when, and to what extent, air travel will be resumed. Higher asset risk is likely to have contributed to the fall in enterprise value through a higher discount rate, considering the link between asset volatility and asset beta. However, higher asset volatility has increased the value of the shareholder put option which mitigates the fall in equity value and exaggerates the fall in debt prices. The result is that the debt claim has become more ‘equity-like’, as evidenced by the estimated implied debt volatility rising from 8% to 18%.

Higher asset volatility increases the value of the shareholder put and creates a wealth transfer from debt to equity investors

In effect, higher volatility results in a wealth transfer from debt to equity investors. Had the asset volatility not changed (but EV had still fallen by the same amount) we estimate that the share price would have declined by 70% rather than the actual decline of 57% over this period.

Equity volatility implied by the model has risen even further – from 63% to 87%. This is consistent with implied volatility that can be derived from  AF-KLM traded options, although it appears the amount derived from our model is somewhat higher. This could indicate a disconnect in the pricing of the debt and equity claims compared with the traded options market or, perhaps, it is simply due to the assumptions we made in our analysis.

A further complicating factor in the analysis of AF-KLM is the potential for structural changes to the business, including the possible intervention by the French or Dutch states. Clearly the nature and probability of such changes must be a significant factor in current market prices, but it is not something that is contemplated by our model. We do not think this invalidates our analysis, but, as always, the results from models like this are more likely to be the starting point for further analysis rather than the full answer.

But do you really need to explicitly measure the shareholder put?

The type of analysis we have presented in our model, and that we have applied to AF-KLM, provides useful insights. However, it can be challenging and the results uncertain, particularly where capital structure is complex. But even if it cannot be directly calculated, we think it is important to be aware of the potential impact of the option effect and of the dynamic nature of different claims.

In any case, an explicit calculation of the shareholder put option may not actually be necessary. Enterprise value equals the sum of the market values of debt, equity and other claims. Therefore, it follows that an equity valuation simply requires that EV be estimated (for which the option value is not relevant) and the fair value of debt and other non-equity claims deducted. The result is an equity value that automatically includes the value of the shareholder put.

Fair value captures option characteristics, but use the right fair value

However, it is important is that the fair value of debt is correctly determined. Firstly, it must be fair value and not book value. Secondly, it must be the fair value of debt that is consistent with your estimate of the value of the enterprise (your target EV). If, based upon your analysis, you believe that the enterprise value should be higher than that currently implied by market prices, you need to determine whether this would materially impact the fair value of the outstanding debt (and any other claims). If the change in EV would indicate a stronger company, and result in better financial ratios, you should be able to estimate by how much the credit rating improves, the debt yield falls and consequently how the fair value of the debt rises.

What about other claims?

Perhaps the most common capital structure complication is written call options on the company’s equity, either in the form of share warrants, conversion options embedded in convertibles or employee stock options.

Share warrants and other written calls on a company’s equity represent a more highly leveraged and, therefore, a riskier form of equity. The price of these calls is more sensitive to changes in EV than equity itself. This is a further drag on stock price appreciation for investors in common stock. At lower enterprise values, an increase in EV may be shared with debtholders through a reduction in the value of the embedded put option. At higher EVs, an increase may affect debt much less, but share warrants and employee stock options may kick in and form a different barrier. Clearly, a rise in EV produces a rise in the common stock price but the sharing of this increase with other claimholders may be a significant investment consideration.

We have included an equity call option claim in our model, labelled as share warrants. If you change the input of the ‘amount’ of these options from 0% to, say, 20% of equity then you will see that part of the enterprise value (and part of the total equity value) is now shared with these new claimholders.

You should charts like that those below. Notice that as the enterprise value rises common shareholders share less of the change with the debt holders but increasingly more with the warrant holders.

Impact of share warrants on the allocation of enterprise value

Try changing the inputs to see how this affects the split of enterprise value between the claimholders and how changes in EV are shared. You will find that the majority of the change in EV accrues to the common shareholder but that this can easily be significantly less than the commonly assumed 100%

Insights for investors

  • An equity claim is, in reality, a call option on the underlying enterprise, with an exercise price equal to the amount of outstanding debt.
  • The option effect increases the value of equity and reduces (through a higher spread) the value of debt.
  • Higher business risk and asset volatility creates a wealth transfer from debt holders to shareholders (in addition to affecting the value of the enterprise itself).
  • A change in EV is shared between claimholders. The proportion of an increase in EV that accrues to equity investors may be significantly less than you might expect.
  • Remember that the current fair value of debt and other claims reflects the current enterprise value. If you believe EV should be higher or lower, then this will also impact the value of these other claims.
  • Fair value measures include the market’s assessment of embedded options. Deducting the fair value of debt and other claims from your estimate of EV automatically includes option value in your target stock price.

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