1.2.1. The limits of traditional approaches

The comparables approach must allow us to define pertinent standards. This is a complicated task, however. In order for the sample to be reliable, it must indeed be representative of the business sector and account for a certain level of risk and development related to financial performance and a similar model. Moreover, significant deviations can be seen in the fact that the chosen standards might include international companies that apply different accounting norms. To limit large disparities, it is possible to apply regressive statistical tools. This reveals a linear relationship between a valuation multiple and the principal performance criteria that affects them. In the case of transactional comparables, we must recall that a control premium was applied by the buyer.

It is therefore necessary to subtract value in order to correct this effect. Traditionally, practitioners begin with a large standard that becomes smaller over time to maintain companies or “satisfying” transactions, with respect to the different points raised here. Otherwise, the major inconvenience of the patrimonial approach is that it does not consider the growth potential of a company. In the DCF approach¹, the company value (or enterprise value, EV) is the discounted value of future free cash flows FCF, the discount rate being the weighted mean cost of capital or WACC K:

[1.1]

where E is the value of equity and D is the net debt. The WACC contained in the calculation of the company value is based on the equity value, which is found using the DCF method. It is the reason why practitioners include an iterative life cycle in their approach. By supposing an infinite rate of growth of FCF g starting at year 1 and a WACC equal to K:

[1.2]

By referring to the cost of capital adjusted by Modigliani and Miller (1963), we can eliminate the life cycle. Indeed, , where ρ is the cost of capital for a debtless company with the same sector-specific rate risk. In other words, thanks to the CAPM, ρ = r + β*[E(R_M) − r], where r is the rate without risk. Thus:

[1.3]

where Dτ is the tax rate that results from fiscal deductibility of interest to the extent that we suppose an infinite net debt. Indeed, in the Modigliani–Miller theory, Dτ comes from the simplification of , where iDτ is the interest tax economy and i is the corresponding tax rate. In this case, D is obviously the remaining debt owed, found in the latest available financial statements. When practitioners deduct D from EV to obtain the value of equity, the following formula E is obtained:

[1.4]

The Modigliani–Miller theory shows that the strike price on risky debt has no impact on the WACC, and, as a result of this, it has no impact on the value of equity: the cost of debt does not appear in the two previous formulas, and a rise in the strike price of the debt corresponds to a rise in the risk that can be tolerated by the investors and banks. It is therefore logical that a drop in risk is tolerated by shareholders. For a simple example, Table 1.1 shows that the transfer of risk between shareholders and investors does not change the value of the WACC.

With an FCF equal to 100, a risk-free rate of 2%, a market risk premium of 7% and a debtless beta of 0.9, two hypotheses about the cost of debt before taxes arise: 3.40%, based on a debt beta of 0.20, and 5.50%, based on a debt beta of 0.50. The corresponding indebted betas, based on the Hamada formula, are, respectively, 1.18 and 1.06, and the deducted equity costs are 10.27% and 9.43%, respectively. Thus, the two WACC and adjusted capital costs are 7.06%. Finally, the company value is the same in both cases: 2,538.

The calculation of the WACC is “subjective” given the numerous hypotheses to take into account:

• – the market risk premium depends on a hypothesis concerning the infinite growth rate of dividends for listed companies;
• – when the company is listed, the cost of capital can include either a beta (different depending on who provides the data) or an indebted beta based on a debtless industrial beta, which relies on the creation of a sample pair for the company that is to be valuated;
• – the weighted coefficients can correspond to the target financial structure, or be based on an iterative calculation. Thus, the equity value is the result of a valuation obtained via DCF.

In other words, each broker can justify their own discount rate.

The value of equity, moreover, is the difference between the value of the company EV and the net debt D. The net debt is the difference between the financial debt, on the one hand, and the cash flow and equivalents of cash flow, on the other. The maturity of the debt is not taken into account. So, if the EV is 100 and the financial debt is 60, supposing there is no cash flow nor any equivalents of cash flow, the value of equity will be 40, whether the debt reaches maturity tomorrow or in 2023.

The reason is because practitioners generally take the face value of the debt into account (without a reimbursement premium) instead of taking the economic value of the debt into account, even though the financial theory depends on the economic values of stocks, which are supplied by the shareholders of companies. If the debt reaches maturity tomorrow, its economic value corresponds to its face value, but if it reaches maturity in 2023, its economic value corresponds to the present value of cash flows expected by investors, with the discount rate reflecting the company’s risk of bankruptcy. In other words, the company’s risk of bankruptcy is not tied to the debt that is deducted from the company value and it is included in the weighted coefficients of the WACC.

Finally, the DCF method is based on FCF, which are implicitly considered determinants. They are discounted, which allows us to reduce their weight in the company value. Since the cost of equity, accounted for in the WACC, is based on the CAPM, the reference to the indebted beta of companies allows us to incorporate systemic risk. Moreover, an analysis of sensibility is generally accomplished by practitioners, in order to underscore the lack of certainty in creating business plans. Nevertheless, the risk, that is, the total volatility (σ) of FCF, is not taken into account.

The innovative approach of real options notably provides solutions by considering the economic value of a net debt, and by combining the strategic flexibility of an investment with its irreversible character³ and the risks that are associated with it. For any given level of irreversibility in an investment, the value of real options tied to a project will depend on the risk and managerial flexibility. Managers can then proceed to alternative choices in their management of the investment or when competing advantages allow them to wait before investing.

1.2.2. The alternative of real options

Financial options are meant to be used in speculative strategies, hedging and/or arbitration concerning an underlying asset. We have the right to call or put a financial asset on a given date (option in the European sense) or during a given period (option in the American sense) at a known price called the strike price. To become the owner of a financial option, we must pay a premium. The latter depends on the value of the underlying asset S, the strike price E, the remaining maturity before the due date τ, the volatility of the underlying asset σ and the risk-free rate r.

As for the premium, it includes an intrinsic value and a time value. The time value is the value complement beyond the intrinsic value, which indicates the expectation of a favorable evolution in the price of the asset between now and the deadline for the option. Insofar as the expectation is zero at maturity, the time value is also zero. The intrinsic value corresponds to the value of the option at a particular moment. For a call, the intrinsic value is equal to the max (S-E; 0). For a put, the intrinsic value is equal to the max (S-E; 0).

In the case of speculative strategies, the call must reflect the buyer’s (seller’s) expectations of an increase (decrease) in the underlying cost. Inversely, the put must reflect the buyer’s (seller’s) expectations of a decrease (increase) in the underlying cost. Supposing a premium of 10 € and a strike price of 100, we have the following graphs for each scenario.

The values of the underlying asset are on the horizontal axis; the gains and losses figure is on the vertical axis. The figures can be analyzed as such:

• – in the case of the purchase of a call, the perspective for losses is limited to the premium paid (10 €), while the perspective for gains becomes greater as the price of the asset rises;
• – in the case of the purchase of a put, the perspective for losses is limited to the premium paid (10 €), while the perspective for gains becomes greater as the price of the asset falls. It is a speculation strategy on the fall in price of the asset;
• – in the case of the sale of a call, the perspective for gains is limited to the premium received (10 €), while the perspective for losses becomes greater as the price of the asset rises. This is a speculation strategy on the fall in price of the asset and is riskier, with lower perspectives for gains than in the case of the purchase of a put. This strategy is recommended by a speculator of losses without liquidity;
• – in the case of the sale of a put, the perspective for gains is limited to the premium received (10 €), while the perspective for losses becomes greater as the price of the asset falls. This is a riskier speculation strategy on the rise of the price of the asset, with lower perspectives for gains than in the case of the purchase of a call. This strategy is recommended by a speculator of gains without liquidity.

The essential legal principle of an anonymous company is the limitation on shareholder responsibility with respect to creditors. Indeed, when a company goes bankrupt, shareholders can abandon the company to its creditors. In this context, shareholders can lose the entirety of their contributions while their gains are illimited, as long as the company generates value. Here, we see the foundation of an analogy with financial options: shareholders have a purchase option (call) over the company.

This option is not financial but “real” because the underlying asset is not financial security, such as a share or bond, but the value of the company, that is, its investment portfolio; the strike price being the amount of borrowed debt; the maturity corresponding to the duration of debt and the volatility to that of the economic asset. Since at the maturity of the debt, shareholders decide whether or not to use their purchasing option and pay off the creditors, the value (premium) of the option therefore corresponds to the economic value of equity.

Inversely, it is possible to consider that creditors may have sold a “real” European sale option (put) over the value of the company; the strike price being the amount of loaned debt; the maturity corresponding to the duration of the loan and the volatility to that of the underlying economic asset. Indeed, their loan comes down to the fact that they invested in the riskless asset and sold a put over the economic asset to the shareholders; the strike price is the amount of borrowed debt. From this, if the company does not manage to repay its loan, the creditors recover the economic asset “purchased in spite of them” for the amount of the unreimbursed debt. Consequently, it seems legitimate for the creditor to add an interest rate superior to the risk-free rate in order to pay themselves. Indeed, by following the logic of options, the creditor runs the risk of the put being opted for by the shareholders, that is, the company would not reimburse the borrowed amount.

There is therefore a fundamental asymmetry between the status of the shareholder described previously and that of the creditor. The latter recovers the contractually expected fluctuations, at best. In other words, even if the required rate of return is identical for a shareholder and a creditor, their respective notions are fundamentally different: for the shareholder, this rate is closer to the expectation of gains, while from the creditor’s point of view, the rate has a very high probability of being reached and can, by no means, be surpassed.

Having established an analogy between the structure of liabilities and options, it would be interesting to develop the optional valuation models.

1.2.3. Black–Scholes optional modeling

Optional modeling began with Black and Scholes (1973)⁴. Their model in continuous time follows the principle of log-normalization of the underlying asset price. The latter defines a Brownian geometric motion:

[1.5]

where:

• – μ: expected return of the share (obtained using the CAPM);
• – σ: volatility of the share;
• – dz = ε dt with ε following a normal distribution.

The Ito lemma allows us to calculate the premium of the call:

[1.6]

The Black–Scholes formula starts with the creation of a risk-free arbitration portfolio. Supposing that the values of dz are identical for the option and for the underlying asset, insofar as only the term has a random variable, the portfolio will not have risk if the terms in dz compensate for each other. The portfolio P is thus made of a sold option and purchased shares:

[1.7]

and:

[1.8]

[1.9]

By simplifying with and , we have:

[1.10]

This risk-free portfolio gives the return r, homogeneous with dt. Thus:

[1.11]

By simplifying with dt:

[1.12]

Thus

[1.13]

By extending the reasoning, convergence points between the different fundamental models can be found. In this context, the equity, as well as the debt can be economically valuated.

1.3.1. Convergence between the Cox–Ross–Rubinstein (1979) and the Black–Scholes (1973) models and the Merton formula (1973)

The Cox–Ross–Rubenstein model (1979) supposes that the value of the underlying asset follows a binomial multiplication principle for discrete time. At the end of the first period, the underlying asset can indeed grow (uS) with the probability q or decrease (dS)⁷ with l-q. If the value of the asset grows (or decreases), the premium of the call also grows (or decreases) with the probability q (or with the probability l-q).

After creating a hedge portfolio P made up of the purchase of a call with the premium C and the sale of H shares, we have:

[1.14]

After taking a discount rate in continuous time:

[1.15]

where S_t is the value of the underlying asset at maturity.

If a corresponds to the minimal number of upward movements of the asset over the next n periods, such that the call is “in the money” and will be exercised, and if F (a,n,p) is related to the binomial distribution function inherent to the probability that allows the call to be exercised at maturity, we have:

[1.16]

Cox and Rubenstein (1985)⁸ show that when the number of periods between the evaluation date and the maturity date of the option tend towards infinity, their formula converges towards that of Black–Scholes. Indeed, if n is very high, the binomial multiplication principle of the price of the asset follows a normal log distribution and:

[1.17]

with:

[1.18]

[1.19]

[1.20]

where:

• – S: spot of the underlying share;
• – E: strike (exercise price) of the option;
• – τ: time to maturity (in years);
• – r: discrete risk-free rate;
• – r’: continuous risk-free rate, with: r’ = ln(1+r);
• – σ: volatility of the underlying asset;
• – Φ(.): normal distribution function;
• – Φ(d₂) replaces F(a,n,p) and corresponds to the probability that the call will be exercised at maturity.

Merton (1973)⁹ allows for a payout of dividends in continuous time at the annualized rate q¹⁰. If a dividend distribution is made between the dates t = 0 and t = T, the price of the asset S is replaced by S T. e^qt. The effect of the distribution of dividends is then integrated in the Black–Scholes formula by replacing S by S. e-^qt:

[1.21]

The analogy between financial options and real options leads us to consider the parameters in Table 1.2.

From this, we arrive at the fundamental mechanisms listed in Table 1.3.

1.3.2. Convergence between the CAPM and the Modigliani–Miller theory

In the absence of taxation, two companies should be considered identical in terms of business sector, assets and earnings before interest and taxes, but not from the perspective of financial structure: one company has debt, the other does not. The notations used in the following formulas are:

• – V: the company value of an indebted company;
• – V*: the company value of a debtless company;
• – R_i: share performance for the indebted company;
• – R*_i: share performance for a debtless company;
• – R_M: market performance;
• – β_i: market volatility of the indebted company share;
• – β*_i: market volatility of the debtless company share;
• – REX: gross earnings of each of the two companies;
• – D: net debt of the indebted company;
• – E: equity of the indebted company;
• – E*: equity of the debtless company;
• – r: risk-free rate with which we suppose it is possible to enter debt.

According to the formula for the securities market line derived from CAPM on the one hand, and the notion of equity profitability that comes from financial analysis on the other, we have:

[1.22]

[1.23]

Now, it is assumed that the two companies have the same assets, V = V*. In this case, the second equation is written as:

[1.24]

By isolating E[R_M] − r in the expressions E(R_i) and E(R*_i), we get:

[1.25]

By returning to the definition of earnings expectations:

[1.26]

or still yet:

[1.27]

Finally:

[1.28]

In this way, we arrive at the formula for the beta in terms of the debt-free beta in the absence of taxation. By reintroducing this result in the formula for the security market line, we have:

[1.29]

[1.30]

[1.31]

The only thing left to do is to point out, like Modigliani and Miller, that E(R*_i) = ρ. In this case:

[1.32]

In the presence of taxation, that is, the tax rate t on companies:

[1.33]

[1.34]

Or

Then:

[1.35]

[1.36]

Using the first equivalence:

[1.37]

[1.38]

with REX and R_M being the only random variables in the covariance. From there, by multiplying each element in the equivalence by E:

[1.39]

And using the second equivalence:

[1.40]

[1.41]

From there, multiplying each element in the equivalence by V*:

[1.42]

And combining the equivalences [1.39] and [1.42], we get:

[1.43]

Or finally, by simplifying with λ(1 − t). cov[REX, R_M] and r:

[1.44]

[1.45]

which indeed corresponds to the Modigliani–Miller formula in the presence of taxation.

1.3.3. Convergence between the Black–Scholes model and the Modigliani–Miller theory outside of taxation

We consider the hypothesis at the base of the Black–Scholes model, that is, a share whose return defines a Brownian motion with a trend.

So:

• – S = value of a share, similar to a call on the company assets with a value V, and whose exercise price is the amount of net debt to repay;
• – μ = instant drift;
• – σ = instant volatility.

S is a function of V and the time left to maturity.

From there:

[1.46]

And according to the Ito lemma:

[1.47]

which tends towards when dt tends towards 0

We then have:

[1.48]

Now, ∂S/∂V represents the variation in the price of the share, that is, the premium of the option on the company assets with respect to the underlying assets. It is therefore a delta that, according to the Black–Scholes model, corresponds to Φ d1.

In this case:

[1.49]

where ρ corresponds to the profitability of the asset (return on indebted company equity) and dS/S corresponds to the return on indebted company shares, written from here on out as R_i.

This expression allows us to obtain β_i:

[1.50]

Finally:

[1.51]

By returning to the securities market line formula, it is possible to calculate the cost of equity for an indebted company:

[1.52]

Moreover, the securities market line formula applied to a debt-free company allows us to arrive at the expression for β*_i.

[1.53]

By replacing the value that was just obtained for β*_i in the expression of the cost of equity for the indebted company, we arrive at the conclusion that:

[1.54]

Finally:

[1.55]

It is possible to express the cost of the debt according to the same approach by starting with the beta of the debt, written β_D. It has been established that, when dt tends towards 0:

[1.56]

Then, by replacing S with D:

[1.57]

Now

[1.58]

As a result:

[1.59]

Then:

[1.60]

Since

[1.61]

We conclude that

[1.62]

and according to the formula for the securities market line applied to the cost of the risky debt, written i:

[1.63]

and since it has been established that:

[1.64]

we arrive at:

[1.65]

In order to get the desired convergence, we must apply the formula for the mean cost offset of capital:

[1.66]

or even

[1.67]

In this way, we have established that in the absence of taxation, the cost of capital corresponds to the cost of debt-free company equity (which presents the same industry risk), which is what the first proposition in Modigliani and Miller (1963) states.

The convergence between optional models and the theory of financial structure imagined by Modigliani and Miller lead us to examine the optional mechanisms that exist in the reduction of risky debt.

1.4.1. The economic value of equity and net debt

Insofar as the balance of statements requires equality between assets and liabilities, the company value must be equal to the sum of equity capital and financial debt. Let us consider a company via shares that has only produced one type of debt (zero-coupons), payable at maturity in one lump sum (capital and interest). Depending on the economic asset value at the time of maturity, two cases can occur:

• – if the economic asset value is greater than the amount of debt to be repaid, shareholders will allow the company to repay creditors and recover any residual value. In this case, the value of shareholders’ call is positive, the value of the put of creditors is zero and the value of equity has a positive value (corresponding to the value of the call over economic assets);
• – if the value of economic assets is less than the amount of debt to be repaid, shareholders will invoke the clause of limited risk to their contributions, lose only their contributions and abandon the economic assets to the creditors. The latter will in turn take on the difference between the value of the economic asset and the amount of their debt. In this case, the value of the shareholder call is zero, the value of the creditor put is positive and the equity no longer has value.

Present value of debt as a risk-free rate

[1.68]

Value of the call

[1.69]

Now:

Purchasing a call

[1.70]

Value of the economic assets

[1.71]

Equity can be considered a residual claim for shareholders, since they have a claim to any cash flow remaining in the company once it has honored its financial obligations with its investors (financial debt, priority shares, etc.). Thus, from the perspective of liquidity, shareholders receive the money left over in the company once all company debts are paid off.

Nevertheless, the principle of “limited responsibility” protects shareholders in companies listed in the stock market if the value of the company is less than the value of the outstanding debt. In this case, the investors take control of the company and the shareholders receive nothing. In other words, the value of equity from the perspective of liquidity, or in the presence of a maturity date for the debt is equal to: max (EV-D;0).

The value of debts is then repaid by equity that depends on the value of the company. The latter can be considered an underlying asset since its value changes over time in an unpredictable way. The value of equity is therefore the premium of a call with the following parameters:

• – S: the spot for the underlying asset, that is, the EV on the evaluation date;
• – E: the exercise price, that is, the debt to be repaid at maturity;
• – σ: volatility of the underlying asset, that is, the volatility of EV;
• – r: risk-free rate;
• – τ: maturity.

The probability that the call will be exercised at maturity is Φ(d₂), which corresponds to the probability that the debt will be repaid at maturity. Φ(d₂) is therefore the probability that the company will be “in bonis” at maturity. Thus, the probability that the debt will not be repaid because the value of the company is less than D (which means the company will go bankrupt) is 1 - Φ(d₂) = Φ(-d₂).

Let us suppose that the EV of a company is 800 when it has to repay a zero-coupon for an amount of 1,000. If the debt reaches maturity tomorrow, the probability of finding 1,000 for tomorrow is zero and the company will go bankrupt. The value of its equity is zero since the shareholders abandon the company to the investors and banks. But if the debt can be restructured and its repayment postponed for 10 years, the value of equity corresponds to a call that is still “out of the money” but can provide a time premium: thanks to the volatility of EV, established by past performance, the EV is capable of increasing beyond the outstanding amount of debt over the 10 years.

Supposing a volatility of 40% of the EV, the value of equity is 373, in the sense that the probability of bankruptcy is reduced from 100% to 74%. If the payment date is postponed to 20 years instead of 10, the time premium goes up and gives 528.

Such an approach allows us to obtain the economic value of the debt, which is the difference between the company value and the value of equity. If the debt reaches maturity tomorrow, there is no equity value; therefore, the value of the debt is 800, which corresponds to the raised funds if all of the assets were sold. If the debt reaches maturity in 2025, the value of the debt is reduced to 427, and to 272 if it reaches maturity in 2035.

The principle of limited responsibility also allows shareholders to abandon a company to investors if the value of the company is less than the outstanding debt. In other words, shareholders have a put over the totality of company assets that is exercised when a company defaults. If it turns out that the debt is risk-free, its present value would be B = D.e^-rt. But since it is a risky debt, its economic value must be reduced by the expected discounted loss by taking the risk of bankruptcy into account. The expected discounted loss, which is absorbed by investors, corresponds to the premium of the put (P), which is granted by the investors to the shareholders. Thus:

[1.72]

Thanks to the call-put parity, using the usual Black–Scholes notations:

[1.73]

with S = EV and E = D:

[1.74]

[1.75]

is the amount of debt which will be recovered by the investors if the put is exercised. Then, is the recovery rate and . EV is the expected discounted loss that will be absorbed by the investors given the hypothesis of the company default. Since Φ(−d₂) is the probability of bankruptcy, is the expected discounted deficit. In the end:

where LGD¹¹ corresponds to the losses in case of a default.

The time value of an option increases with the volatility of the underlying asset. Indeed, the more the company conducts its business in a market where the industry risk is great, the more the volatility of the economic assets will be high, impacting the rise in the value of equity. Because of this, real options provide a particular utility in valuating risky, expensive projects financed via debt (start-ups, mining and petrol industries, etc.).

1.4.2. The impact of the risk debt on the time value of equity and the resolution of conflict between creditors and shareholders

The time value depends on the position of the exercise price with respect to the price of the underlying asset. In other words:

• – when a call is out the money, that is, the value of the economic asset is inferior to the amount of debt to be repaid, the value of equity is entirely made of time value. The investors then hope that the company’s situation will improve, keeping in mind that the intrinsic value is zero;
• – when a call is at the money, that is, the value of the economic asset is equal to the amount of debt to be repaid, the time value of capital can no longer grow. Since all scenarios are possible, the theory of real options finds its utility since it allows us to quantify the hope of investors;
• – when a call is in the money, that is, the value of the economic asset is superior to the amount of debt to be repaid, the intrinsic value of equity quickly appears greater than the time value. The debt is less and less risky, and theoretically, it is without risk if the value of the economic asset tends towards infinity. The explanation depends on the fact that, when the value of the economic asset rises, the risk of probably bankruptcy falls, as well as the cost of the debt, which approaches the risk-free rate.

Finally, the time value rises with the maturity. A company in difficulty therefore benefits from an advantage if they renegotiate an increase in the maturity of its loans. Take for example a company with a debt of 50 payable in one year at an interest rate of 5%; we can conclude that at maturity, the company will have to pay its creditors 52.5 (50 x 1.05).

Supposing, moreover, that the economic value of the assets is 120, the value of capital that we can calculate using a classic approach is 70. By reasoning however using the logic of options, and taking the risk-free rate to be 3%, the present value of the debt including the payment of interest is 50.97 (52.5/1.03). The value of the debt can be considered as the difference between the value of the latter, discounted at the risk-free rate, and the value of a put.

In this case, the value of the put is 0.97 (50.97 – 50). The value of equity at 70 is split between an intrinsic value of 67.5 (120 – 52.5) and a time value of 2.5 (70 – 67.5).

Thus, in this example, we see that the time value (from the perspective of intrinsic value) and the premium of the put are limited. From that point, the interest rate of the debt is no longer considered to be 5%, but 10%:

• – the amount the company must repay in one year to its creditors is 55 (50 x 1.1);
• – the current amount of debt becomes 53.40 (55/1.03);
• – the value of the deducted put is 3.4 (53.4 – 50);
• – the value of equity at 70 is now split between an intrinsic value of 65 (120 – 55) and a time value of 5 (70 – 65).

As a result, since the probability of non-repayment of the debt increases, the premium of the put increases. Moreover, the equity risk is greater, which explains why its value incorporates more time value.

The appearance of hybrid financial products that combine equity and debts, such as convertible options or bonds with redeemable share warrants, is meant to fight against possible conflicts between shareholders and creditors. It is a way to give company creditors a call over equity. The conflicts between these different interested parties can be resolved as long as, if the shareholders have the power to make investment and financing decisions that can ruin the creditors, the latter have the option to exercise their share warrants or convert their investment into shares.

Jensen and Meckling (1976)¹² were determined to prove that the production of convertible investments reduced the risk to company asset substitutions with riskier assets by increasing the volatility of assets and, because of this, the value of equity.

In practice, when a debt arrives at maturity, a company repays a part of the amount using its available cash flow and refinances the remainder with a new loan. And even if, in theory, the cash flows are greater than the amount of debt to repay, they are generally generated over a longer lapse of time. In other words, the duration of cash flow is greater than the flows tied to the repayment of loans.

Consequently, the cash flows become insufficient from a liquidity perspective. The company is thus presented with the risk of rising interest rates and the risk of liquidity. The risk of liquidity cannot be covered because its cost can be considered excessive or, more simply, because the company can expect that it will never actually be exposed to such a situation. It therefore seems useless to prepare for it. Aït-Mokhtar (2008)¹³ suggests that the difference between the duration of available cash flows and the duration of debt maturities is similar to company liabilities, just like a swap for which it would pay a variable interest rate and benefit from a fixed interest rate. This is to consider that at the maturity of its debt, a company will only have the option to repay it if it finds lenders, keeping in mind that the available cash flows are considered inconsequential for repaying the loans in question in fine. Thus, a company accepts getting into further debt in the future at an unknown interest rate.

If, in a healthy financial situation, the value of this liability is negligible, in a time of cash flow crisis or in the scenario where the repayment maturities are very near, this gap in refinancing can take on an entirely different value. It can correspond to the degree of uncertainty with respect to the future interest rate or, in theory, the very ability to cover costs. In this context, the value of equity – initially equal to the economic value of assets from which we must subtract the value of net debt – must be retired from the value of this financing impasse.

Thus, if the worry over the ability of the company to find new financing grows, then the value of equity is negatively impacted. Otherwise, it is possible to imagine that if this situation continues, the company lenders may wish to complete forward sales (overdrawn) of company shares to cover the risk of depreciation in the value of their debt securities. Hence, an increase in the stock market after an increase in capital can be justified. Indeed, this phenomenon can be explained as the way companies have found to refinance their debt.

If the value of the share lessens because of a transfer of value to the creditors, the refinancing impasse disappears – such that it is worth more than the reduction of debt – therefore positively impacting the value of equity.