The main idea behind the Backsolve method is to use recent transaction price for one of the classes of shares, Black-Scholes option pricing model and other additional information that can be derived from company’s capital structure to determine estimated fair value (FV) of equity.

Application of the Backsolve method is performed using the following steps:

Step 1 – Identify pricing terms of the recent equity transaction;

Step 2 – Identify relevant dividend/distribution rights and related “breakpoints”;

Step 3 – Prepare FV equity equation;

Step 4 – Estimate required inputs for option pricing model: risk-free rate, expected terms, volatility;

Step 5 – Calculate estimated FV of equity using “trial and error” approach;

FV equation in Step 3 represents a formula with two unknowns, being estimated FV of equity and estimated FV of a call option. Standard Black-Scholes equation also shows the above two variables and three other inputs, i.e., risk-free rate, expected volatility end option term. The three inputs can be determined using market information and management estimates.

The two equations, i.e., Black-Scholes formula and equity equation with two unknowns, being FV of stock and call option can be resolved to determine unknow values.

The practice approach used to determine the two unknowns is “trial and error” where a specialist considers multiple equity values (or option values) to make sure the two equations are appropriately resolved.

When company’s equity has two classes, i.e., Series A and common stock, equity formula is as follows:

Estimated Equity FV = Estimated FV of Series A + FV of Call Option on Common at break 1 Share of Series A in Distribution after break 2 x Call Option on Series A at break 2

Estimated FV of Series A is derived from recent equity transaction. Share of Series A in distribution after break 2 is a known number reflecting company’s distribution terms.

General equity formula for N classes of stock and N breakpoints is as follows:

Estimated Equity FV = Estimated FV of Series A + FV of Call Option on Series B Stock at break 1 Series A Share in Distributions After Break N x Call Option on Series A Stock at break N.

The above equity formula equity can be used as part of application of Backsolve method for any amount of equity classes. The application of the formula still depends on company’s specific equity structure and terms of distribution.

Verbal interpretation of the above formula is that estimated FV of company’s equity depends on the following specific inputs:

  1. known dollar value for Series A stock;
  2. FV of Call Option on Series B stock at break 1;
  3. share Series A in distribution after break N;
  4. FV of Call Option on Series A stock at break N;

Series A and Series B as used in the above formula and the list of inputs, simply refer to first and second classes of equity in the order of distribution priority. If a company only has two classes of equity, e.g., Series A preferred and common stock, Series B means common stock.

Other factors, including terms of company’s debt may impact application of the Backsolve method. Generally, debt holders may be entitled to distributions prior to any equity holders, thus impacting the order of distribution used in the application of the Backsolve method. Valuation specialists should carefully review and understand company’s capital structure and distribution terms. The above and other relevant factors will impact reasonableness and accuracy of valuation results.

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