The Pricing of BEE Share Purchase Schemes

Published: December 01, 2009

The Pricing of BEE Share Purchase Schemes

 by Graeme West and Lydia West, Financial Modelling Agency

Black Economic Empowerment (BEE) transactions are very topical, with companies that have to date failed to put in place meaningful BEE schemes under serious pressure from various interested parties. What is involved is the sale of a stake in the business to suitably qualified partners.

The Broad-Based Black Economic Empowerment Act (2003) was introduced in order to assist in ensuring a more equitable distribution of wealth amongst the people of South Africa. This act defines ‘black people’ and introduces legal mechanisms for their economic upliftment.

The core feature of these transactions is that the seller (vendor company) exchanges company value for BEE credentials. The buyer (BEE partner) provides

  • the legal requirement
  • avenues to new business, in particular statal and parastatal businesses
  • promotion of the vendor company, in particular as a BEE compliant company
  • assistance for the vendor company in staffing, affirmative action and its social responsibility programs.

Under most circumstances the designated partner does not have the resources to pay cash for their stake. Thus, structures need to be put in place to facilitate the purchase of the designated stake.

In the earliest stages of BEE these transfers were achieved somewhat cynically, by means of fronting. More or less any transfer of equity would be as a gift, in return for the privilege that the vendor would then enjoy of having a black name on letterheads.

In preparation for the Nedbank and Mutual and Federal BEE transactions, those companies introduced the option for all shareholders to receive dividends in cash or as stock.

The next stage is the vendor financing stage. Typically the structure consists of the following scheme: shares are transferred to the BEE partners by the vendor company at or at about market value. To pay for this, typically a small cash payment (usually 1% to 5%) is made, but the great majority of the payment is set up as debt issued by the BEE partners. The vendor company is the party that buys this debt.

During the debt period the transfer of shares is a legal transfer of ownership; in particular the BEE partner has voting rights.

Over time, the debt rolls up with interest, and rolls down with dividend flows that are received from the shares. At termination, if the share value is higher than the outstanding debt, the BEE partners keep their shares and pay off the outstanding debt, or surrender sufficient shares to pay off the debt. If lower, the BEE partners also surrender their shares, but walk away from the debt.

Thus, what the BEE partner owns is a European call option on the shares with the strike being the level of debt. This option is somewhat exotic because the strike of the otherwise vanilla call option is not known in advance.

Statements made by participants in these schemes can make mildly amusing reading given this understanding. When the vendor company wishes to trumpet the successful creation of a BEE structure, it announces that such-and-such a percentage of the company is now held by black partners. On the other hand, if it is being pressured about a grant which some parties – such as the financial press, for example - are viewing as too generous, then it will brazenly retort that the partner owns precisely nothing until such time as the debt has been paid down. As we now see, neither statement is correct: the truth lies somewhere in between.

In the next stage, institutional financing comes into play. In these cases, real money is needed to facilitate the transaction - for example, minorities may need to be bought out. In this case equity is purchased using financing from banks and other financial institutions. The financial institution structures their asset into a cascade, with senior, mezzanine and equity components. The senior and/or mezzanine tranches receive a spread above typical interest rates in the market, and will enjoy covenants on the equity. The financial institution might buy the senior tranche in its entirety, and will participate in equity upside.

Currently most common is a mix of the vendor and institutional financing models. We are now starting to see a few straight purchases: BEE companies will have enjoyed income from previous transactions that they can use to enter into new trades. This cuts out the institutions who are acting as quite pricey middle men here. We believe that this type of transaction will become more and more common. 

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The BEE transaction is a call option

The vendor company transfers shares to the BEE partner. The BEE partner pays a small deposit, but is unable to pay the full amount. The BEE partner then issues a bond and uses the proceeds to pay the remainder. The vendor company (vendor financing) or a financial institution(s) (institutional financing) or some combination subscribes to this bond.

To fix ideas let us focus for starters on the vendor financing model.

Over time (a period of about 10 years, say) this debt

  • rolls up at a fixed rate or is linked to some floating rate such as Prime or JIBAR or the inflation rate
  • is paid down by dividends.

The trade sits in an SPV, ring-fenced from any other transactions the BEE company makes. At maturity of the transaction, if the SPV’s value of equity holding is

  • greater than the debt level, the BEE partner uses the equity to pay down the debt and keep the remainder
  • less than the debt level, the BEE partner (technically, the SPV) walks away from the deal.

The only asset of the SPV is these shares, and the only liability this debt. Some vendor companies operate under the erroneous impression that at termination they will have legal recourse to ensure that the BEE party will honor the full debt amount that has accrued. Even in the case where a BEE company owns several assets, one will find that each asset is held by a separate SPV.

The Broad-Based Black Economic Empowerment Act (2003) was introduced in order to assist in ensuring a more equitable distribution of wealth amongst the people of South Africa.

Thus, what the BEE partners own (technically, what the SPV owns) is a European call option on the shares with the strike being the level of debt. (Sometimes this debt is paid down to zero before the termination date of the deal, in which case there is early termination.) However, as we have already noted, we cannot apply a classic option pricing formula because the strike is not known in advance.

As the vendor company has given the BEE partners the option, it needs to be expensed at inception in accordance with IFRS2 IASCF [2006]. Even in the case where, for example, majority shareholders of the vendor company facilitate the BEE deal on behalf of the company, the company itself will have to recognize the expense so as to be compliant with ‘push down’ accounting regulations. The expense will be the fair mark-to-market value of the option. The only income it enjoys is the small physical cash payment that was made by the BEE partners. The bond issued by the BEE partners can obviously not be recognized as income.

As we will argue here, to provide appropriate valuation of this option we need to use a Monte Carlo valuation technique. Monte Carlo will pose no implementation problems as the option itself is European.

Roughly speaking, in each Monte Carlo sample, at maturity we test the value of the proportion of the company granted to the BEE partners versus that of the accrued loan; the terminal value of the deal to the BEE partners is the difference if positive. See Figure 1 and Figure 2. [[[PAGE]]]

Naïve use of Black-Scholes

Many participants in this market price this option using the Black-Scholes approach, with the strike of the option being set as the forward level of the debt. However, as we shall see, this approach is invalid, due to the path dependency of that level of debt, and can lead to severe mispricing of the option.

Currently most common is a mix of the vendor and institutional financing models.

When using the Black-Scholes formula for valuation of these options, the strike is calculated as the forward level of the debt. Here the terminal strike price has to be determined ‘outside the model’ (this terminology appears in van der Merwe [2008]) and entered as a fixed input. This treatment ignores the fact that the true final debt amount will depend on the dividends the share pays over the life of the transaction, thus, on the share price evolution: the option is path dependent. The final level of the debt may not be equal to the forward level of the debt.

Suppose as an example a tenor of 10 years, a spot price of 1, the initial debt of 0.95 (thus, the deposit was 5%), a volatility of 30%, a flat risk free rate of 10% (applying both to equity growth and to the debt), and dividends as in Table 1.


We find the forward level of debt to be 2.08.

The incorrect Black-Scholes approach using the ‘out of model’ strike of 2.08 gives the value of the option of 0.277. With a finite difference approach with the ‘out of model’ strike we get a valuation of 0.266.

The correct approach using Monte Carlo gives a value of 0.331.

A common variation is to declare a large first dividend, to give the debt paydown ‘a helping hand’. Of course, this reduces the valuation of the option being granted (which from the vendor point of view will be a good thing). For example, if in this example the first dividend is instead 0.07 cash, with all other dividends unchanged, then the ‘out of model’ strike is 1.97, the Black-Scholes valuation is 0.267, the finite difference valuation is 0.254, and the Monte Carlo valuation is 0.317.

If we suppose the same details except that all dividends are yield dividends, with those dividends being broadly proportional to the cash dividends where provided, the results are similar.

Nevertheless, there are two instances where using the Black-Scholes formula is valid.

Suppose all the dividends are known, or can confidently be forecast as cash amounts. (This is quite unrealistic except when a deal nears maturity.) Then the ‘out-of-model’ calculation of the strike is valid, and so Black-Scholes can be used - although a different argument will say that it shouldn’t, as conversion of cash dividends to a dividend yield for use in the formula is problematic for almost the same reason - see Frishling [2002], Bos and Vandermark [2002].

It has become more common for institutions to be invovled in the financing of BEE transactions.

The only practical occasion in which the Black-Scholes approach is valid is when dividends are paid using the stock, and that stock is paid into the basket of assets, with the debt never being paid down. In this case we use the Black-Scholes with a zero dividend yield.

In preparation for the Nedbank and Mutual and Federal BEE transactions, those companies introduced the option for all shareholders to receive dividends in cash or as stock. (A shareholder’s broker will contact them each dividend LDR to determine their election.) However, the BEE partner contractually elected to receive dividends as stock.

The Nedbank deal was restructured in May 2008, as it was felt that too much dilution of the stock was occurring. The modification is that the SPV will receive cash dividends, and will be obligated to buy shares in the open market with that cash, for inclusion in the basket of assets. Thus the valuation approach is unchanged, but the dilution problem is avoided. [[[PAGE]]]

Naïve use of binomial trees

Let us now consider pricing such an option in a two step binomial tree. We will explicitly see a numerical example of what can go wrong. Because of the path dependency, the debt tree will not recombine, even if we can ensure the stock price tree recombines.

At time t = 0, let S = 20, r = 9%, σ = 30%, simple dividend after one year of q = 6% of the stock price at that time, initial debt level D = 17, and initial deposit = 3.

We consider a two year option and build a two step tree (steps of one year each).

From Cox et al. [1979] we find the up factor u = 1.350, the down factor d = 0.741, and the risk neutral probability of an up move π = 0.580.

We calculate the expected dividend
qE[S(1)] = qSer.

The forward level of debt is calculated as
(Der – qSer)er = (D − qS)e2r = 18.916.

However, notice how in Figure 3 the debt is path dependent. If the stock goes up and then down, the debt is 18.58; if it goes down and then up, the debt is 19.38.

  • We can price incorrectly, using a call strike of 18.916 throughout, and discounting through the tree in the usual way. The value then is e-2r[π 215.34] = 4.313. All other paths end out of the money.
  • We can price incorrectly, using a call strike of 18.916 throughout, and applying the Black-Scholes formula. We first need to find the dividend yield continuous per annum: this is the value y in 1 ? 0.06 = e-2y, giving y = 3.094%. Then using the Black-Scholes formula we get an option value of 4.643.

Remember the Black-Scholes price is the limit, as we increase the number of time steps, of the price found using a binomial tree.

  • Pricing correctly (within this binomial world) we discount along every path one at a time, gives a value of e-2r[π 215.68 + π (1 − π )0.22] = 4.452.
  • Pricing correctly using a Monte Carlo approach gives a value of approximately 4.744.

It may be possible to use a many-stepped tree in the spirit of this example with a path dependent extra factor (being the level of debt) as in [Hull, 2005, §24.4]. However, this approach only works while the underlying tree of stock prices is a recombining tree. Usually this doesn’t occur: it only occurred even in our simple two step example, because there was a simple dividend yield.

The problem is if we want to model that the stock pays some discrete dividends, and not only percentage dividends. This will almost always be the case, as broker forecasts will be of cash amounts for the next two or three years, say. Furthermore there will often be other complicating features which make Monte Carlo pricing almost a forced approach.

Our preferred approach is as follows: use broker forecasts in the short and medium term, and then forecast percentage dividends in the long term using the model of [West, 2008, §6.6].

[[[PAGE]]]

The institutional financing style of BEE transactions

It has become more common for institutions to be involved in the financing of BEE transactions.  In this case, the institution buys the bond with real money which is passed to the vendor. In the simplest such cases, the vendor receives full and immediate value for their sale, so they are not required to pass an expense as in §2.

We believe BEE partners should be doing more hedging than they are.

Broadly speaking, the institution has bought a bond which will roll up with a contractually specified interest rate, and will roll down with dividends that they receive. At the termination date any residual value of the bond will be extinguished with equity, and the residual equity will accrue to the BEE partner.

Of course, reality will be far more complicated. The equity of the BEE partner is serving as the guarantee for the performance of the bond. Thus the bond will typically have covenants attached to it. If certain asset coverage ratios (ACRs) are not achieved then there might be contractual requirements to pay down the debt by liquidating part of the equity holding. In extreme cases, the deal might be unwound in its entirety.  We have seen this occurrence in the market turbulence of early 2008.

Furthermore, it is typical for the bond to be structured as a typical securitized vehicle, with senior and mezzanine debt. In this case the covenants of the senior tranche take precedence over those of the mezzanine tranche. The portion belonging to the BEE partner will be the equity of the vehicle.

Typically, the institution will share in this equity as well (the so called ‘kicker’).

Our approach

We have focused on the simplest issues that arise. There are much more complicated BEE transactions; some of the features that arise are

  • trickle dividends (dividends that are received and are spent, leaving the system)
  • the proportion of the dividends paid as trickle vs. those used to pay down debt is a function of some price or earnings target
  • American/Bermudan features
  • the need to have models of the forward prime curve or forward inflation curve. The debt rollup is often associated with one of these curves. We then have separate curves for the equity growth and for the debt growth.
  • the covenants in the institutional financing case can be quite complicated.
  • possibly the need to model the evolution of the asset rather than the equity.

These features can be handled by a careful use of Monte Carlo.

We take the usual approach in valuing equity derivatives: we assume that the various interest rates (risk free curve, prime curve, inflation curve) will evolve according to their forward levels. Only the stock price (and possibly its volatility) will evolve randomly. [[[PAGE]]]

We bootstrap our own yield curves using market rates and the methods in Hagan and West [2006], Hagan and West [2008].

For major stocks we use implied volatilities provided by a prominent market participant and dividend forecasts from a major broker. For smaller stocks we use historical volatility estimates and note the dividends that have occurred recently. In either case we then forecast percentage dividends further out in time using the simple ‘repeating-yield’ model of [West, 2007, §6.6].

In these deals there are several important dates, namely:

  • the commencement date, the effective date, the maturity date
  • dividend declare, LDR and payment dates
  • debt rollup and paydown dates
  • trickle dividend dates.

There might be as many as 150 dates here, although 10-40 is most common. As already discussed, because of the path dependency, we are using the Monte Carlo method to price the transaction.

Thus we need low discrepancy sequences in high dimensions. Sobol’ sequences are most suitable here, see [Jäckel, 2002, Chapter 8].

Risk management of BEE transactions

Strategies for risk management of BEE transactions have never really gained any serious momentum. One can, to a greater or lesser extent, claim that these transactions typically are unhedged.

Let us be clear that by hedging we do not (necessarily) mean the (possibly) disastrous futures or forward programs that one often reads about. Rather we are talking about a suitable suite of protective options.
Different issues arise for the different participants in the market:

  • The BEE partner: we believe BEE partners should be doing more hedging than they are.  Very often, the BEE partner believes in the business they are participating in - as they should - and so are happy to take pure exposure in what more or less amounts to an outright position. Such a policy makes sense at inception, when they have nothing, or very little, to lose. However, as the deal matures, significant value may build up. It makes sense to now hedge this, particularly if this health in the balance sheet is being used to leverage other transactions.

The simplest solution in these situations is to buy protective puts from a financial institution.  In a very real sense, this is insurance, and the partner must simply swallow the pill of paying for this insurance. Whether they would be willing to or not is another matter. They might try to time the market in purchasing these options.

Of course, this argument applies to listed vendors. When the vendor is unlisted, hedging might be viewed as impossible. The BEE partner might be reluctant to choose a surrogate listed entity with which to hedge, or to take on the basis risk that will arise. [[[PAGE]]]

  • The vendor: in order to hedge a transaction, the vendor will have to trade in their own shares. Unquestionably this will introduce problems and headaches for management. Besides outright legal constraints that might arise, the company might give the wrong signals to the market and/or take on reputational risks, with significant amounts of trade in their own underlying stock.

The vendor could rather source derivative overlays from a financial institution, very much in the same way as for the BEE partner above.

  • The financing institution: in the typical scenario, where a financial institution has made a loan (we called it a bond earlier), they experience a capital charge for making that loan. There is no regulatory relief from that charge when hedging takes place, and so, typically, hedging does not take place! On the other hand, if there was no loan, there would be no capital charge. With the wisdom of hindsight, it makes more sense for financial institutions to participate by providing hedges as above (to either BEE partners or vendors) rather than in making loans.

Many financial institutions are now feeling a lot of pain, the gains in value experienced in the bull market having been wiped out in the last year or so. Historically, one sees the usual spurious reasons for not hedging: when the market is up, hedging is just a useless luxury, and when the market is down (and volatility up) hedging is too expensive. Nowadays, one sees a more sober attitude: incremental hedges are put in place as and when the relevant trade can be undertaken.

Of course, if hedging, one needs to be calculating hedge ratios from within the correct model. Even if pricing errors are fortuitously in your favour, such windfalls can be eliminated through incorrect hedging. In our simple example from the section on binomial trees, the delta of the call under the Black-Scholes model is 0.689, under the Monte Carlo model is 0.724.   


References
 

Michael Bos and Stephen Vandermark. Finessing fixed dividends. Risk, 15(9):157–158, 2002.
John Cox, Stephen Ross, and Mark Rubinstein. Option pricing: a simplified approach. Journal of Financial Economics, 7:229–263, 1979.
Volf Frishling. A discrete question. Risk, January(1), 2002.
Patrick S. Hagan and Graeme West. Interpolation methods for curve construction. Applied Mathematical Finance, 13(2):89–129, 2006.
Patrick S. Hagan and Graeme West. Methods for constructing a yield curve. WILMOTT Magazine, May:70–81, 2008. URL http://www.finmod.co.za/interpreview.pdf.
John Hull. Options, Futures, and Other Derivatives. Prentice Hall, sixth edition, 2005.
IASCF. International financial reporting standard 2: Share-based payment, 2006. This version includes amendments resulting from IFRSs issued up to 31 December 2005.
Peter Jäckel. Monte Carlo Methods in Finance. Wiley, 2002.
Claudette van der Merwe. Lost in BEE Valuation. ASA, 2008. URL http://www.accountancysa.org.za/resources/ShowItemArticle.asp?ArticleId=1348&Issue=935.
Graeme West. The Mathematics of South African Financial Markets and Instruments: Lecture notes, 2008. URL http://www.finmod.co.za/safm.pdf.

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Article Last Updated: May 07, 2024

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