The application of the option pricing model for the valuation of complex capital structures

The option pricing model (OPM) is a method for allocating the equity value to different classes of securities in a company's capital structure. It is (generally) not a method for estimating the total value of equity for the entire company, but an instrument for allocating an equity value that has already been determined. The OPM is particularly important in the valuation of start-up companies, as very often different rights, such as liquidation preferences, are granted to new investors or instruments such as convertible bonds are issued in successive financing rounds. Anti-dillution can also be taken into account in the OPM. In principle, the OPM treats each class of security as a call option on the total value of the company's equity and uses the Black-Scholes model to value the call options. The share price in the Black-Scholes model becomes the total value of the company's equity, while the strike price represents the so-called breakpoints of the equity at which the distribution of any exit proceeds among the different classes of securities changes. In case of a recent financing round, the OPM can be used to determine the value of equity using the backsolve method.

As already mentioned, under the OPM each equity tranche (assuming different rights) is treated as a call option on the entire equity value of the company.  This results from the different participation rules that would arise in case of an exit or an IPO. This so-called waterfall can be illustrated graphically as follows:​

The procedure for carrying out the OPM can then be summarized in the following steps:

Step 1: Analysis of the capital structure. Identification of all share classes and their respective rights (such as liquidation preferences). Any already agreed upon clauses that affect the capital structure in the period up to and including an exit, or that disproportionally change the payout of proceeds, must be identified. As an example these include liquidation preferences, but also kicker or bonus shares or options. It is essential to carry out this step conscientiously in order to gain a detailed understanding of the waterfall (or the distribution of proceeds) at the time of exit.

Step 2: Calculation of the breakpoints. A breakpoint is the equity value or exit proceeds at which the participation rules change among the various share classes. A new breakpoint must be defined for each such change. The equity value that exceeds a certain breakpoint corresponds to a call option on the company's equity with the breakpoint as the strike price. The equity value that can be allocated to the individual breakpoints can then be calculated as the difference between these call options.

Step 3: Determine the Black-Scholes parameters. The OPM generally uses the Black-Scholes option pricing model to determine the value of the various breakpoints as call options on the company's share value. In order to apply Black-Scholes, the following parameters are required:

Step 4: Calculation of each breakpoint value. The Black-Scholes model is used to calculate the values of the call options in each breakpoint and the values assigned to the respective breakpoints are derived from the differences between them. 

Step 5: Allocation to the share classes. As the breakpoints sometimes involve the participation of several unit classes, the last step is to allocate the values of the individual breakpoints to the respective participating unit classes. 

In summary, the following steps are necessary for implementation:

Consider a hypothetical company, XYZ AG, with a capital structure consisting of 1 million ordinary shares, 1 million preference shares with liquidation preference and options issued on 200,000 ordinary shares. The estimated enterprise value of the company is € 100 million and the company is debt-free. The estimated time to liquidity is 5 years and the volatility is 40 percent. The risk-free interest rate is 2 percent.

The preference shares have a liquidation preference of € 50 million (i.e. they would receive € 50 million in an exit event before holders of ordinary shares would be paid out) and are convertible 1:1 into ordinary shares. The options issued have a strike price of € 30.

First, the breakpoints (depending on the equity value) must be defined. The first breakpoint is € 50 million, until then only the preference shares participate, from this point onwards the ordinary shares participate. For the option holders, a conversion is profitable from a price per share of € 30, i.e., at an equity value of € 50 million + 1,000,000 * € 30 = € 80 million (second breakpoint). From this point, option holders and holders of ordinary shares initially participate up to an equity value of € 104 million (€ 50 (liquidation preference per preference share) * 2.2 million shares less payment of the strike prices of € 6 million) where a conversion would be advantageous for holders of preference shares (3rd breakpoint). For values above the 3rd breakpoint, all shareholders participate in proportion to their shares.

The value of the first breakpoint calculated using Black-Scholes is € 39.4 million and is only attributable to the preference shares. It is calculated as the value of equity less the call option at a strike price of € 50 million. The value of the second breakpoint of € 15.2 million is only attributable to ordinary shares. This in turn is calculated as the value of equity less the call option at a strike price of € 80 million and less the value of the first breakpoint. The value of the third breakpoint of € 8.8 million is allocated to the ordinary shares and option holders according to their respective shares and the residual amount of € 36.5 million is allocated proportionally to all shareholders after conversion. This results in the following overall distribution:

It can easily be observed that the liquidation preference assigns a significantly higher value to preference shares, as they are paid out preferentially if the company value falls.

With the help of the five steps described above, the OPM allows the value of equity to be allocated to a complex share structure with liquidation preferences or other more complex clauses. The stochastic distribution of future exit proceeds is taken into account, thus achieving a qualitatively better result than other methods such as the current value method. In particular, the OPM is able to quantitatively demonstrate the advantage of a liquidation preference and similar rights.