Today's post is written by Andrew Strickland of Scrutton Bland, Chartered Accountants. Andrew holds the positions of Head of the BVIUK Board and Head Tutor for the BVIUK Credentialing Programme. Additionally, he serves as Chair of iiBV's Educational Committee. With a specialisation in corporate finance and business valuation, Andrew brings extensive expertise to his roles. He is a member of the Valuation Committee of the ICAEW and is recognised as a subject matter expert. Andrew has completed numerous business valuation assignments, particularly in shareholder disputes and divorce cases. He also conducts fiscal valuations for various tax purposes.

### Introduction

Many clients are alive to the idea of providing equity incentives to managers. The problem is that even small percentage shareholdings in private companies can make the tax liability under section 62 ITEPA forbidding.

Very few managers want to receive shares if the immediate impact is a large tax bill with no immediate cash flow to settle it.

This is the situation in which growth shares can be relevant – they have the potential to do two things:

Make the upfront tax charge affordable;

Provide a genuine incentive to employees to grow the business.

### A Client with a Plan

We will imagine a very successful businesswoman with the Midas touch, Lydia. She has recently bought a well-established but old-fashioned freight forwarding business for an equity value of £10 million. We have a meeting with her. She wants to provide incentives to the operations director, the sales director and the finance director. She anticipates improving the business with better technology, and a better sales focus.

Her proposals which she wants to discuss are that individual managers may receive one of the following in a successful exit:

10% of the value above £11 million

10% of the value above £15 million

10% of the value above £20 million

How do we respond to her proposals? An excellent starting point is

### International Valuation Standards (“IVS”)

IVS state that valuers may use any reasonable method to determine the value of equity or a particular class of equity.

Having said that, IVS dissect three possible means of dealing with complex share classes.

These are:

The Current Value Method (“CVM”)

Option Pricing Method (“OPM”)

Probability Weighted Expected Return Method (“PWERM”)

### Current Value Method (CVM)

CVM is intuitively pleasing. It is likely to be the instinctive reaction of those unschooled in business valuation. If a company has a total equity value of £10 million, shares which only participate in value above £15 million might be thought of as worthless.

CVM assumes a sale of the entire equity at the valuation date. This is known as the liquidation preference. In a sale of the entire equity, shares that are “under water” receive no portion of the proceeds. It is this underlying assumption of CVM that betrays its weakness.

IVS describes this frailty:

“A limitation of the CVM is that it is not forward looking and fails to consider the option-like payoffs of many share classes.”[1]

We can ask ourselves if a business owner would give away shares which might participate in value in the future. We know that the answer to that question will almost certainly be in the negative. We also know that business owners will often reward members of the management team with such shares. Their intention in so doing is to provide incentives for making the business successful. If the shares are indeed worthless, there is no incentive.

The phrase “option-like payoffs” refers to an absence of symmetry between gain and loss with some securities. With so-called penny shares, the amount paid, and therefore the potential loss, is very modest. If there is some exceptional event in such companies they may either become insolvent or dramatically increase in value.

A more direct and obvious means of considering such a lack of symmetry is with the pricing of call options in the markets. We will look at an example:

Share price of £5

Call Option to Purchase at £6

Value of the two-year call option is 58p (Volatility of 30%, no dividends)

In the above example, the investor can pay 58p in order to have an interest in the upside of the movements in the share price. The investor looks at the share price in two years’ time. If it is £6.01 or more, the call option is exercised. If the share price is less than £6.01 the investor has no interest in how far that price has fallen. He does not exercise the call option.

He writes off 58p to experience. In this example the investor makes a return if the share price is more than £6.58 in two years’ time. He loses money, but only up to 58p, if the price is less than that.

The guidance from IVS is that CVM should only be used in the following circumstances:

A liquidity event is imminent;

The company is at an early stage and there is no value above the liquidation preference;

The company has made no significant progress with its business plan

There is no reasonable basis exists for estimating the value

### Probability-Weighted Expected Return Method (PWERM)

PWERM in its broader sense is something that we should be doing all of the time, assuming that we are spoilt with a richness of data. If there is a range of projections for a business (and therefore a range of valuations) we should not use the projection which is considered to be the most likely.

According to best practice we should assign a probability to each of the outcomes and then produce a blended valuation, with each of the projections having an influence on the final value.

We can all recognise the challenges of this theoretical position when faced with real life. For a great many companies, especially smaller ones, there will not be a range of projections to review. If there was more than one set of projections, the probabilities would be difficult to assign and would be intensely subjective.

In the context of complex share classes, PWERM is being used in a rather narrower sense: it refers to a range of different outcomes when close to an exit such as:

Go for an initial public offer; or

A trade sale; or

Retain and continue to grow the business.

IVS 2022 state: “Typically, the PWERM is used when the company is close to exit and does not plan on raising additional capital.”[2]

So far we have learnt that CVM should be used only in constrained circumstances. PWERM is normally applied when a company is close to an exit. We are then left with the third alternative, OPM, which comes in several different forms.

### Option Pricing Method (OPM)

The most commonly used of the option pricing methods is the Black Scholes method. This provides the most solid of intellectual foundations as it has the status of a mathematical proof.

To explain this method, we are going to approach it using another method, the binomial expansion model.

We will start with a very simple illustration. One thousand people are each asked to toss an unbiased coin 100 times and record the results. A large number of those people will have tossed between 45 and 55 heads. There will be some who have tossed 30 or 60 heads. There will be very few who have tossed more than 80 or less than 20 heads - but there may be some.

If the number of people doing the test is not one thousand, but one million, the results will get ever closer to the smooth bell shape of a normal distribution.

A binomial model seeks to approximate a normal distribution. It is visible to the eye and that may help in the conversion of some people to the Black Scholes method, despite the complexity of the maths. It gives us a window to conceptualise what is happening.

OPM takes the current value of the company of £10 million. It then slices that value over different value layers: there is a value to the slice above £20 million; there is even a small value to the slice above £50 million. There are also values to the slices below that.

We therefore recognise the simple truth: the company has a current value of £10 million regardless of how many share classes are created. However, each class of shares has some contingent equity interest.

The inputs into both the binomial model and Black Scholes are the same:

The risk-free rate for length of period

Period to a Liquidity Event

Current value of equity

Hurdle Value for each class of Shares

Volatility of the shares if they were publicly traded

Now this may seem rather other-worldly with mathematical theory taking over pragmatic realism, We can see that this does, in fact, reflect a commercial reality: if Lydia entered into a transaction in which she gave up the value above £20 million for a six year period, would she give that value away? Alternatively, as a willing seller, would she agree to give up that right for a reasonable payment of say £1.2 million?

If she sold that right, she would know that in a sale, in the next six years, she would receive the first £20 million of proceeds; she would have reduced her risk by lowering her investment by the amount of £1.2 million that she had received. The person buying the right would be doing so in the belief that the eventual realisation would be above £21.2 million in order to deliver a profit.

The closeness of growth shares and call options in the markets is illustrated below:

Call options | Growth shares |

Based on values above a stated value | Based on values above a stated value |

Relatively modest cost to buy | Relatively modest cost to buy |

Modest downside, significant potential upside | Modest downside, significant potential upside |

Strike price paid for full participation | No strike price, participation above hurdle only |

We can now provide a summary of the outputs from Black Scholes, which can be used for our discussions with Lydia:

Value above £20 million | 1,172,000 |

Value: £15 million to £20 million | 753,000 |

Value above £15 million | 1,925,000 |

Value £11 million to £15 million | 1,030,000 |

Value above £11 million | 2,955,000 |

Value £10 million to £11 million | 350,000 |

Value above £10 million | 3,305,000 |

Value up to £10 million | 6,695,000 |

Total value | 10,000,000 |

We can see that of the total value of £10 million, Black Scholes has allocated just over £3.3 million to all of the value layers over £10 million.

That £3.3 million is then allocated over the various strata above £10 million.

We therefore have three values for the entire layers above £11 million, above £15 million and above £20 million, as we promised Lydia. We also have them presented as part of a coherent structure. If Lydia wanted another break point at say £12 million or £30 million, we could rapidly produce it using Black Scholes.

We can then consider the minority discounts that we think are applicable to holdings of 10% in each of those layers.

The value up to £10 million is worth less than £10 million which might be considered a surprising outcome. This is because the array of possibilities within Black Scholes inevitably include some circumstances in which the future value will be below that figure. If Lydia sold the value above £10 million for six years, she could receive consideration of some £3 million. She has reduced her investment to £7 million and knows that she will receive the first £10 million of any proceeds.

The simple practical application of OPM using the power of a spreadsheet means that this is the method that is favoured by many valuation practitioners, unless the share rights and hurdles are especially complex.

[1] IVS 2022 200.130.10

[2] IVS 2022, 200.130.22

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