Valuing Securities Using the Option Pricing Method by Frank Kiepura
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DEPARTMENTS | Business Valuation Valuing Securities Using the Option Pricing Method By Frank Kiepura he option pricing model (OPM) is a popular and results are analyzed with respect to the Black-Scholes option commonly used model to allocate equity value pricing model and how changes to its parameters can affect to securities in the complex capital structures of allocations of value. privately held companies. Given the absence of active markets for privately issued securities, one The OPM Tof the challenges that valuation specialists face is deter- Many venture capital and private equity backed compa- mining how to allocate value to each specific security in nies are financed through a combination of different equity the capital structure. Although the OPM is one of the more securities, each of which provides its holders with unique common methods, choosing it as the optimal allocation tech- rights. Because of the high risks associated with investments nique is dependent on certain characteristics of the company. in privately held companies, investors often require different The OPM is most appropriate for companies with longer classes of equity that convey various rights to their holders. liquidity event timelines and access to a variety of exit In many capital structures of privately held companies, options; the model also works well in valuing option-like these classes of equity consist of preferred shares, common payoffs (e.g., common stock options and warrants). Using shares, options, and other securities, all of which provide an example of a complex privately held company, the author different sets of preferences and privileges. The purpose of constructed a hypothetical capital structure that incorporates granting different rights to different groups of investors is the characteristics associated with choosing the OPM. The to facilitate financing through capital investments at various 50 JULY/AUGUST 2020 / THE CPA JOURNAL 07-2020-BusinessVal-Kiepura.indd 50 8/10/20 1:00 PM stages of enterprise development. By or control rights. Economic rights are ■ Risk-free rate. The risk-free rate is issuing different classes of securities designed to provide preferred share- derived from the yield on U.S. Treasury with different rights, companies create holders with superior economic returns instruments with a term equal to the time a situation where some securities have as compared to common shareholders. to liquidity utilized in the OPM. more economic privileges than others, These rights include preferred dividends, Step 4: Calculate each breakpoint and thus more value. redemption rights, conversion rights, value. The call option value for each The OPM is a method for allocating and participation rights; these are key breakpoint can be determined using the equity value to multiple classes of secu- to understanding liquidation preferences. Black-Scholes model. The call option rities in a company’s capital structure— Step 2: Calculate each breakpoint. value of the range between adjacent break- it is not a method for estimating the A breakpoint is the point at which each points is allocated to each security class. enterprise value for the entire company. class of equity reaches in-the-money Step 5: Allocate incremental option An overall equity value must first be status. The value in excess of any given values. Allocate the incremental option estimated using the valuation methods breakpoint is equal to a call option on values ownership interests to arrive at the under the asset, income, and market the total equity value of the company. per-share value of the equity securities. approaches before the OPM can be Step 3: Determine Black-Scholes applied. The OPM is a tool to allocate parameters. The OPM typically employs Comprehensive Illustration equity value; therefore, the value of the Black-Scholes option pricing model The following illustration is an exam- any debt should be removed from the to treat the different classes of securities ple of how to utilize the OPM to value enterprise value. as call options on the company's equity the equity securities of a privately held The OPM works by treating each value. The following are the inputs and company with a complex capital struc- class of security as a call option on the assumptions, some of which require a ture. To provide an example of a com- total equity value of the company. To significant degree of judgment: pany that a valuation specialist would accomplish this, OPM typically employs ■ Stock price. The stock price in the encounter in practice, securities with the Black-Scholes model to value the OPM is the total equity value of the sub- different issue dates and their own par- call options. The Black-Scholes model ject. The total equity value is estimated ticular set of economic rights are exam- incorporates the parameters of stock from the application of traditional valu- ined. The selection of a specific method price, exercise price, time, volatility, ation methods under the asset, income, to allocate value among different equity and risk-free rate to determine the price and market approaches. If the company's securities depends upon various factors of a European call option. In the OPM, enterprise value contains debt, the fair related to the specific facts and circum- the stock price becomes the company’s value of the debt should be subtracted stances of the company and its various total equity value, and the exercise price to derive the equity value. classes of equity securities. becomes the liquidation preference of ■ Exercise price. The exercise price Consider the hypothetical example of the security. When the OPM utilizes represents the equity value break point Cotopaxi Tech, a venture capital-backed the Black-Scholes model, it becomes determined in Step 2. startup, initially funded with the owners’ highly sensitive to estimates for time to ■ Time to liquidity. A single point is esti- capital in 2010. The company’s owners liquidity and volatility. The following mated for the liquidity event. Estimates currently hold 2 million common shares, is a detailed step-by-step process for for the time to liquidity can generally be which is the total amount of common applying the OPM. derived by reference to management’s shares issued and outstanding. Step 1: Analyze the capital structure. expected time to exit scenarios. From 2010 to 2016, Cotopaxi Tech Identify and understand the subject ■ Volatility. Volatility can be derived issued several financing rounds consist- company's equity interests outstanding from observed volatilities of guide- ing of Series A preferred stock. As of as of the valuation date. In addition to line public companies, benchmarks, the valuation date, there were 15 million common equity, a company's capital and other sources. For early stage Series A shares outstanding with a liq- structure can include preferred shares, companies, volatility will often uidation preference of $1.30 per share. restrictive shares, options, warrants, and approach the upper end of observed Series A shareholders are entitled to other dilutive securities. Estimating the volatilities for guideline public com- either participate in its liquidation pref- value of each of these different classes of panies. The range of guideline public erence or convert into common stock on equity requires an analysis of the rights company stock returns should equal a one-for-one basis. Series A preferred associated with each class. Generally, the same period as the estimated time shareholders earn a cumulative dividend preferred shareholders have economic to liquidity. of 10% per annum, payable upon the JULY/AUGUST 2020 / THE CPA JOURNAL 51 07-2020-BusinessVal-Kiepura.indd 51 8/10/20 1:01 PM DEPARTMENTS I Business Valuation EXHIBIT 1 - Capital Structure implementing the OPM. Information regarding the rights, privileges, and LiquidaonExercise Shares Conversion Fully DilutedPercentage of preferences of securities can be found Preference PriceOutstanding Rao Shares (FDS)FDS in the company’s purchase agreements, Series B $7,500,000 - 5,000,000 1.0 5,000,000 13.9% Series A Dividend $6,000,000 - - - - 0.0% shareholder agreements, and discussions Series A $19,500,000 - 15,000,000 1.0 15,000,000 41.7% with management. Common Shares - - 2,000,000 1.0 2,000,000 5.6% Series B holders have preference over Opons - 0.75 1,000,000 1.0 1,000,000 2.8% Warrants I- 2.00 10,000,000 1.0 10,000,000 27.8% all other securities and receive a return Warrants II - 3.00 3,000,000 1.0 3,000,000 8.3% on their original investment before distri- Total $33,000,000 36,000,000 36,000,000 100.0% butions can be made to any of the other equity securities. Upon the receipt of their initial investment, the shares con- EXHIBITEXHIBIT 2 - Breakpoint2 - Break-point Calc Calculationsulaons vert to common shares on a one-for-one Break-points #1 #2 #3 #4 #5 #6 #7 #8 basis. Series A cumulative dividends are Preferred Securies Series B$0 $7,500,000 $7,500,000$7,500,000$7,500,000 $7,500,000 $7,500,000 $7,500,000 due upon a qualifying liquidation event Series A Dividend - - 6,000,000 6,000,000 6,000,000 6,000,000 6,000,000 6,000,000 Series A- - - 19,500,000 19,500,000 - - - and are payable prior to the liquidation Liquidaon Preference A$0 $7,500,000 $13,500,000 $33,000,000 $33,000,000 $13,500,000 $13,500,000 $13,500,000 preference or conversion of series A to Equity Shares Series B- 5,000,000 5,000,000 5,000,000 5,000,000 5,000,000 5,000,000 5,000,000 common shares. Series A holders have Common Stock- - - 2,000,000 2,000,000 2,000,000 2,000,000 2,000,000 Opons - - - - 1,000,000 1,000,000 1,000,000 1,000,000 the option to either participate in the Series A- - - - - 15,000,000 15,000,000 15,000,000 Warrants I- - - - - - 10,000,000 10,000,000 proceeds of a liquidation event or convert Warrants II - - - - - - - 3,000,000 Total Outstanding Shares B- 5,000,000 5,000,000 7,000,000 8,000,000 23,000,000 33,000,000 36,000,000 into common shares on a one-for-one Price Per ShareC - - - - 0.75 1.30 2.00 3.00 basis upon the closing of such an event.