Business Valuation Case Study

Introduction

Valuing performance-based stock options is a critical process that requires careful analysis and consideration. The objective is to determine the fair value of these options based on various factors and market conditions. This valuation procedure plays a crucial role in providing insights into the potential value and impact of these options on the overall financial position of the company.This knowledge is instrumental in making informed decisions regarding compensation packages, financial planning, and strategic initiatives.Now, let’s delve into a case study to examine the valuation of performance-based stock options.  

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Company Overview

The Company whose stock options we are analyzing is a trading member of various stock exchanges in India including, BSE, NSE, MSE etc. The Company is a SEBI registered Investment Adviser and Research Analyst.The Company acts as a holding company to several entities engaged primarily in Wealth Management, Investment Management etc. 

 

Overview of the Performance Based Stock Options

The options had the following terms: 

  1. The grant date was May 1, 2012 
  2. The exercise price was INR 1000 
  3. The options were to vest on the achievement of Target market capitalization of INR 10000 Crores of the company. The target market capitalization of the company was to be determined on the basis of daily Volume Weighted Average Price for six months.  
  4. On vesting, the holder had 5 years to exercise the option 

Valuation Methodology

We used a Monte Carlo simulation model which is implemented in a risk-neutral framework where the underlying (common stock in this case) price is assumed to follow a Geometric Brownian motion with a shift equal to the risk-free rate. 

𝑆t = 𝑆0 𝑒𝑥𝑝 ((𝑅f –𝜎2/2) 𝑇 + 𝜎√𝑇𝑍)

Where: 𝑆t = Stock price at the end of the period
𝑆0 = Stock price at the beginning of the period
𝑅f = Risk-free rate
𝜎 = Annualized standard deviation based on the logarithmic return of daily stock prices
𝑇 = Time until expiration
𝑍 = Standard normal random variable

Monte Carlo simulation is most commonly used when there’s a path dependency property required to determine the final payoff as in the case of many types of exotic options and market condition-based stock awards. 

The greatest advantage of using Monte Carlo simulation, as opposed to closed-form solutions and other numerical and analytical approaches, is its tremendous flexibility. It is possible to adjust Monte Carlo simulation models to price almost any kind of exotic options and market-based stock awards. 

A future value is calculated for each iteration of the Monte Carlo simulation model based on a payoff. Future values are discounted to the Valuation Date with the risk-free rate. Ultimately, the estimated fair value of the instrument is the average of all iterations of the Monte Carlo simulation model. 

In the case of the Options, since there are uncertainties around the payoff as well as the timing of the payoff based on certain market vesting conditions as described previously, we deemed the Monte Carlo simulation as the most appropriate approach. In each iteration, we estimated the time to vest based on the simulated stock prices and the Market Condition described previously as well as the stock price at the time of vesting (if it vests) to calculate the payoff which was then discounted back to the present using the risk-free rate. The Payoff on each Vesting date is calculated using the Black-Scholes Model. The final value was calculated by averaging the present value of the payoffs across 50,000 iterations. 

Findings

The average present value per share was determined to be around INR 10. Several factors contributed to an increase in this value, including a higher risk-free rate, lower volatility, and a longer vesting period term. However, it was the ratio of the strike price to the current price that had the most significant impact, driving the value down. The strike price of the options was exceptionally high, exceeding the valuation date price by more than four times. 

While volatility was relatively low and risk-free rates were high, their influence on the value was not substantial enough to cause significant changes. Additionally, although the vesting period was moderately long, it was unable to counterbalance the effect of the high strike price. 

It is worth noting that the options had vested in less than 1% of the simulations conducted, further indicating the limited value they held in the overall valuation. 

 Overall, the analysis reveals that the per-share average present value was primarily influenced by the ratio of the strike price to the current price, which was exceptionally high. This factor overshadowed the impact of other variables, resulting in a decrease in the value. 

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