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# Valuation of ordinary shares and preferred shares by using OPM method (Option Pricing Method)

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Niv Savion
December 4, 2017
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In order to evaluate the value of holdings in the Company's share capital, for purposes of sale, taxation, revaluation in the financial statements and other needs, we often find companies with a capital structure consisting of various types of shares with different rights on their holders. In order to assess the value of the holdings, we must first assess the value of each type of share and then assess the value of the holdings according to the number of shares of each type and the value of each type of share found. The common distribution is between ordinary shares and preferred shares, where preferred shares confer surplus rights over the ordinary shares. The excess rights usually include interest on the investment up to the time of the liquidation, payment of investment and interest before the ordinary shareholders, antidilution rights, and other.
The calculation of the value of each type of share can be performed:
• According to the price of one of the type of shares in which a transaction was executed close to the valuation date
• Based on the calculation of the total equity value by models of valuation (DCF, multiples, etc.)
In general, it is more recommended to the use of a share price according to an actual transaction between a willing seller and a willing buyer, on the assumption that this price reflects the market price of that type of share.
The accepted method for calculating the value of each type of share is by using Option Pricing Method (OPM). The common methods are:
1. Monte Carlo simulation
The Monte Carlo Method is a method for solving computational problems using random numbers (as opposed to the deterministic algorithms commonly used). Monte Carlo algorithms are computational algorithms that run random numbers a large number of times and perform calculations on the numbers that have been subtracted. Monte Carlo algorithms are often used to perform simulations on complex physical or mathematical systems.
The model assumes that the value of the Company's equity is distributed in a normal distribution around the average value and according to the variance typical of companies in the same industry in which the Company is engaged.
The value of the shares is calculated according to the following stages:
• Evaluate the time required to liquidation.
• Calculation of the rights of the shareholders of each type, at the time of the liquidation.
• Evaluation of the volatility of the Company's value based on a sample of companies operating in the sector in which the Company is engaged.
• Draw lots of scenarios (usually 10,000 scenarios) assuming a "random walk". For each value distribution scenario between the preferred shareholders and the ordinary shareholders according to the following mechanism:
o Distribution of the proceeds to the preferred shareholders up to the maximum of their rights.
o Distribution of the proceeds to the ordinary shareholders up to the maximum of their rights.
o Distribution of the balance according to the holdings of the ordinary shareholders and preference shareholders.
• Calculate the cash flow of each type of share for each scenario.
• Finding the value of the company by using 'goal seek' so that the value of the preferred shares will equal the value according to which the investment in the preferred shares was made or alternatively finding the total value of the shares will equal the value of the shareholders' equity that was valuated.
• Calculation of the value of an ordinary and a preferred share.

2. Black and Scholes
The calculation of the value of each type of share by the value of options is based on the distribution of the value of each option among the various shareholders according to the value of the future company. In other words, by calculating the value of the option to the price of the company in the future, it is possible to estimate the cash flow that the shareholders of the different types will receive. The cash flow summary for each type of stock will give an estimate of the share value at the valuation date.
Calculation of the value of the options is calculated according to the liquefaction period, the standard deviation selected and the value in each step.
The following is an example of the distribution of the value among the shareholders:

Both methods should reach the same result, but the use of the binomial model is sometimes required in cases where there is a complexity in the distribution of the cash flow between the types of shares.
The author is economic consultant specializes in valuations, economic opinions, business plans, PPA, impairment tests, projects feasibility studies and more.