In the 2003 film Lost in Translation, Bill Murray’s character experienced an acute culture shock when confronted with the differences between American and Japanese culture. This feeling must be shared by financial managers when forced to navigate the jargon surrounding the valuation of Black Economic Empowerment (BEE) transactions. Yet, it is critically important for the financial manager to understand the implications of what is being said.

**For the past few years, the**

South African business landscape has been dominated by BEE transactions, with most South African companies either initiating a BEE transaction, or being the beneficiary of one. One of the questions being asked by all stakeholders (investors, stock exchanges, the government, employees, auditors, the financial press and an interested public) is: “how much company value has been exchanged for BEE credentials?” Often the market capitalisation is used as a yardstick, but this misrepresents the economic value of the exchange.

Alternatively, option pricing models are used and these offer a better starting point for estimating economic value. Unfortunately though, the subjectivity involved in these calculations is often used as an excuse for poor implementation of the option pricing models. We will explore some general principles around the valuation of BEE transactions and how fair values differ depending on the correct implementation of the option pricing model.

The accounting angle

Since accounting is often the driver of BEE valuations, it makes sense to start here. IFRS generally requires initiators to apply IFRS 2 – Share-based Payment (IFRS 2) and beneficiaries to apply IAS 39 – Financial Instruments: Recognition and Measurement (IAS 39) – both standards requiring some form of fair value measurement. While there are some subtle differences in the fair value guidance, both standards have the same theme: fair value is the “amount for which an asset could be exchanged, or a liability settled, between knowledgeable, willing parties in an arm’s length transaction”.

This is where the subjectivity starts – until a secondary market develops, BEE transactions do not really have an observable price. So we need a model to estimate the fair value. While the accounting standards point to the need for fair value models to reflect the economic and contractual terms of the transaction accurately, we will see how significantly this can affect the fair value.

Before we continue our discussion on determining the fair value of a BEE transaction, let us look at the structure of a typical BEE transaction.

The typical BEE structure

A typical BEE transaction structure can be presented as follows: – see diagram 1 below.

Initially, the sequence of events is as follows:

- The SPV purchases a number of shares in Company X.
- The purchase of the shares is financed by Company X (vendor funding) and/or External Financiers (external funding).
- Company Y (the shareholder/beneficiary of the SPV) usually contributes a nominal amount to the SPV.

During the life of the transaction, the following occur:

- Interest accrues on the funding at either a fixed rate or a floating rate.
- Dividends received by the SPV on the Company X shares are typically used to service and repay the funding.

Although a myriad of contractual terms are used to transfer unconditional ownership of Company X shares to Company Y at maturity of the transaction, all result in one of the following scenarios:

- Scenario 1: the SPV/Company Y is unconditionally liable to repay the funding.
- Scenario 2: repayment of the funding is contingent on the value of the shares exceeding the value of the outstanding debt. If the value of the shares exceeds the value of the debt, the SPV will surrender a sufficient number of shares to redeem the debt, and have an unconditional claim on the remainder of the shares. If, however, the value of the debt exceeds the value of the shares, the SPV will surrender all the shares to settle the debt and the beneficiary will walk away.

If the maturity date is contractually specified, the BEE transaction is known, in finance parlance, as a “European” transaction. However, in some instances, Company Y can elect when the transaction is to be terminated. If this election can be made at any time during a pre-specified period, the transaction is known as an “American” transaction. An American feature is more valuable to the beneficiary as it brings him/her greater flexibility.

How to approach the valuation of the share-based payment made by Company X and conversely the investment held by Company Y, would depend on whether Scenario 1 or Scenario 2 is applicable at maturity of the transaction.

How to Approach the Valuation

**Scenario 1:**

Assuming that the funding is at a market-related rate, the value of the IFRS 2 charge is equal to the difference between the fair value of the shares and the purchase price paid by the beneficiary on grant date. The initiator then treats the shares as issued share capital. For the beneficiary, the shares held in the initiator company are measured at their fair value. The debt is accounted for by the beneficiary in terms of IAS 39 and the entity’s accounting policy for financial liabilities.

**Scenario 2:**

Where the beneficiary has the ability to walk away from the transaction, we evaluate the economic characteristics of the investment as follows:

- The beneficiary cannot realise a loss on the investment. If the value of the shares is less than the outstanding debt, the investor’s profit is zero. The maximum loss is the initial amount contributed to the SPV, which typically is not significant.
- Conversely, there are theoretically unlimited gains to be realised, to the extent that the fair value of the shares exceed the outstanding debt.

We can present this economic profile graphically as follows: –

The economic profile for the initiator of the BEE transaction is the inverse of the above:

Based on the economic profile, we can conclude that the economic characteristics of these BEE transactions mimic those of a call option. A call option is the right, but not the obligation, to buy an asset at a certain price at a future date. The beneficiary of the transaction holds this right (the long position) and the initiator of the transaction has granted this right (the short position). The holder of an option usually has to pay a premium to the writer of the option to acquire this right. The contribution to the SPV made by the beneficiary is analogous to the premium. What logically follows from this illustration is that, if these BEE transactions have the same economic characteristics as a call option, the fair value methodology should reflect this.

There are a number of option pricing models available in the market. We will discuss the three that are the most frequently encountered.

Option Valuation Models

**Black-Scholes**

The Black-Scholes model is probably the most widely known and commonly used option pricing model. It was developed to value “European” options on equity. A European option is an option that can only be exercised at maturity.

**Binomial model**

The Binomial model is the discrete-time version of the Black-Scholes model that can be adapted to price options that can be exercised prior to maturity, i.e. “American” options.

**Monte Carlo simulation**

Monte Carlo Simulation takes its name from the European gambling capital as it uses random trials to value options – much like the roulette gambler, who has but random odds of winning (http://www.investopedia.com, 2007). Monte Carlo Simulation offers a flexible, holistic approach to option pricing that can cater for the idiosyncratic features of BEE transactions. Although originally developed for European options, it can be adapted to price American options.

The interaction between option valuation models and inputs

Generally speaking, all option pricing models require the same basic inputs: the market share price on valuation date, the strike price (the amount at which the share can be bought at maturity), time to maturity, volatility (an indication of the expected fluctuation in the share price), the prevailing risk-free interest rate and the expected dividend yield. To determine the dividend yield, a forward expectation of dividends should be formulated with reference to existing budgets and management’s expectations. These dividends are then converted into a projected dividend yield.

There is a practice among some market participants to use a historical average dividend yield, but “using the historical dividend yield can lead to severe mispricing” (West, 2007, p.47). Naturally, the valuation model will only be as good as the inputs to the model – the adage “garbage in, garbage out” applies. But here’s the point: while inputs might be subjective, that does not excuse a model that fails to capture the terms of the transaction. Let us explore this in the context of the three models:

- The Black-Scholes model assumes a constant share price volatility, interest rate and dividend yield. The terminal strike price has to be determined “outside the model” and entered as a fixed input. This treatment ignores the fact that the final debt amount will depend on the share price performance and, specifically, the dividends it pays over the life of the transaction. If we consider a share worth R100, that is projected to pay a dividend of R5 in a year’s time, if the share price decreases to R15 due to financial difficulties experienced by the company, the projected dividend of R5 will not materialise. However, using the Black-Scholes model inherently assumes that it will. Another problem is one of consistency: if one is using Black-Scholes, one is forced to have projected dividends in the future share price that do not agree with those used to calculate the final debt.
- The Binomial model can incorporate changes in the interest rate and the dividend yield over the life of the option, as well as a varying strike price, but also cannot accurately reflect the interdependency between the dividend yield and the strike price.
- The Monte Carlo Simulation model uses a coherent approach that can incorporate changes in all inputs during the life of the option and accurately reflect interdependencies between all variables. The strike price is determined “inside the model” based on the opening debt balance, interest that accrues and dividends determined as a function of share price movements.

Clearly there are subtle distinctions between option pricing models that dictate the decision of which model to select to value a specific type of transaction. For ease of reference, we will establish an algorithm to facilitate the decision-making process.

Which model to select?

BEE transactions are complex and idiosyncratic instruments. In most cases valuation models have to be custom-built or tailored to price a BEE transaction correctly. No ready-made, off-the-shelf model exists that can be used to price a BEE transaction without some modification. If an inappropriate model is selected, no amount of tailoring will achieve correct pricing of the transaction.

To assist in the process of selecting an appropriate valuation model, let us consider the following decision tree: see diagram 4 below.

One might well ask: “What would the impact be if an inappropriate model is selected to value the BEE transaction?” Let us look at an example.

The impact of selecting an inappropriate model

Company X has entered into a BEE transaction with Company Y. The SPV purchased 15m shares in Company X at R60 per share. The purchase was funded through 50% vendor funding and 50% external funding. Interest is payable at 10% and dividends received by the SPV from Company X are to be used to redeem the debt. After four years, if the shares are worth more than the outstanding debt, Company Y will sell a sufficient number of shares to redeem the debt, and will take unconditional ownership of the remaining shares. Conversely, if the shares are worth less than the outstanding debt, Company Y will surrender the shares and walk away from the debt.

We will value this transaction using the Black-Scholes model and the Monte Carlo Simulation model and compare the results. see table below.

The example illustrates the importance of selecting the appropriate model and the severe mispricing that can result from an erroneous selection. This difference is not caused by subjective inputs, but rather the inability of the Black-Scholes model to capture the intricacies of most BEE transactions coherently.

This example, however, does not illustrate many of the complexities that additional contractual terms can introduce to the valuation.

The importance of incorporating the contractual terms

Many BEE transactions have unique contractual terms, e.g.

- Dividends payable to the beneficiary (often referred to as a “trickle” dividend).
- Covenants such as debt coverage ratios.
- A portion of share price growth payable to the financiers (profit share).
- Seniority distinctions between different sources of funding.
- Scrip lending arrangements with the external financiers.

These types of contractual terms can be incorporated with ease into a Monte Carlo Simulation model, but generally not into the other models.

Conclusion

The impact of BEE transactions is widespread, and accounting and valuation requirements affect both initiators and beneficiaries of transactions significantly, due to the materiality of the transactions. BEE valuations are unique, complex and computationally multifaceted. Although experts generally perform the valuations, it is important for management to exercise oversight to ensure selection of an appropriate model, accurate computation of inputs and inclusion of all relevant contractual terms in the valuation.

Bibliography

Hull, J. (2003), *Options, Futures, and Other Derivatives*, 5^{th} Edition, Prentice Hall

*IAS 39, Financial Instruments: Recognition and Measurement*, International Accounting Standards Board

*IFRIC 8, Scope of IFRS 2*, International Accounting Standards Board

*IFRS 2, Share-based payment*, International Accounting Standards Board

Investopedia^{® }(22 September 2007), Dictionary

*http://www.investopedia.com

West, G. (2007), ‘South African Financial Markets’.

*http://www.finmod.co.za/safm.pdf

Claudette van der Merwe CA(SA), FRM, is a Manager in the Actuarial & Insurance Solutions division of Deloitte & Touche.

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Black-Scholes | Monte Carlo Simulation | |

Model Inputs: | ||

Share price on valuation date | R64.00 | R64.00 |

Time to maturity (in years) | 4 | 4 |

Volatility | 30% | 30% |

Risk-free rate | 8.61% | 8.61% |

Dividend yield | 4.27% | 4.27% |

Strike price | Strike price at maturity date: R77.93 (determined “outside the model” as R60.00 plus interest minus projected dividends) | Modelled “inside the model” as initial value of R60.00, increased by interest and decreased by dividends (as a function of the share price) over the life of the transaction |

Valuation Results | R184m | R219m |

Difference | R35m (19%) |

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