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What is Black-Scholes and how does it fit AASB 2?

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When it comes to the term “option valuation”, you can’t read anything on this topic without seeing the name “Black-Scholes” mentioned.

Fischer Black and Myron Scholes published an article in 1973 entitled “The Pricing of Options and Corporate Liabilities”, in which they laid out their formula for risk neutral portfolio management that effectively separated the option from the risk of the underlying security. This formula was then coined the “Black-Scholes options pricing model” by Robert Merton, and together Merton and Scholes received the 1998 Nobel Memorial Price in Economic Sciences for their work (Black unfortunately died in 1995).

While the use of the formula has been expanded on and adapted for many different applications such as used by investment banks and hedge funds, the formula itself is still very useful in determining a value for an option given a set of inputs.

The Black-Scholes formula relies on one risky asset – usually the share over which the option has been issued – and one riskless asset, which is usually a zero-coupon government bond yield rate.

The variables that are needed to input into the Black-Scholes model are:

  • The share price on the grant date, or issue date
  • The exercise price of the option
  • The time to expiry (in years)
  • The risk free rate
  • The volatility of returns of the share price
  • The dividend yield of the share

These variables are all quite easily determined for any exchange listed company, as they are publicly available, or can be quite easily calculated based on publicly available information.

One limitation of the formula is that it assumes the option to be a European option, or one that can only be excercised at the end of the option life. This contrasts to American options, which usually can be exercised at any time during their life.

While Black-Scholes is formulaic and relatively easy to calculate, when is it an appropriate valuation technique for AASB 2?

AASB 2 and Black-Scholes

AASB 2 requires that for the valuation of share options, factors such as the typical long lives of options issued by companies, and the ability to exercise the options at any time during their life (American options), might preclude the use of the Black-Scholes formula which does not allow for the possible early exercise of options.

However, where the options have relatively short contractual lives, or they must be exercised within a short period of time after the vesting date, those factors may not apply and the Black-Scholes formula may produce a value that is substantially the same as a more flexible option pricing model.

We usually find that where the company does not pay dividends, then the value of the option will be very much the same regardless of which model is used. The reasoning behind this is that the option holder will want to hold their cash for longer and earn a rate of return on that cash, rather than invest it in the share and subject themselves to market risk.

Even where the option may be an American style option, in some instances a Monte Carlo simulation can be used to determine the expected exercise of the option, and this time period can then be used in a Black-Scholes formula to calculate the value of the option.

How does Black-Scholes work for performance rights?

Performance rights usually do not require the employee or recipient to pay anything in return for the issue of a share. In this most basic form, the performance right can be considered to be a zero exercise price option, and the value can then be calculated using an option valuation methodology.

If there are no market conditions e.g. share price hurdles, or Total Shareholder Return (TSR) hurdles then the Black-Scholes model may be an appropriate way to value those performance rights issued by the company.

If there are market conditions such as share price hurdles or TSR hurdles, then another valuation methodology may be more appropriate. Even in these circumstances, the valuation technique will start with the basis of treating the performance right as a zero exercise price option, and then incorporate the specific terms and conditions to derive the value.

As the performance right is a zero exercise price option, then the value of the performance right for a non-dividend paying share will be the same as the share price on the date of issue. As a consequence, the time to expiry and volatility will have no influence on the valuation of the performance right.

When is the best time to use Black-Scholes?

Black-Scholes is a good starting point for valuing options, as it is simple and doesn’t require too much complicated computing in order to get a result.

While this starting point can give you an indication of an option’s value, if there are any market conditions or any element of the conditions of the option that require more customisation of the valuation technique, then Black-Scholes can quickly become unsuitable as the primary valuation model.

Unsure whether Black-Scholes is an appropriate valuation model?

Contact us at Value Logic to help you out with your valuation, and give yourself peace of mind that your valuation will be correct.

Why does AASB 2 require option and performance right valuations?

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AASB 2 Share-Based Payment and its predecessors have now been in force for over 15 years, so the requirement to record any issue of shares, options and performance rights to employees and consultants as part of their remuneration is not new.

For equity settled share based payment transactions, the key is that the entity shall measure the goods or services received at the fair value of the goods and services received, unless that fair value cannot be estimated reliably. If the entity cannot estimate the fair value of the goods or services received, the entity shall measure their value by reference to the fair value of the equity instruments granted (para 10).

Typically, the services received will be employment services. As the valuation of employment services is variable and can be difficult to estimate due to that variability from company to company and person to person, the better source of valuation is the equity instrument issued in return for the services.

Option and performance right valuation

The value of the equity instrument is measured at the measurement date, or grant date of the option. This value is based on market prices if available, and if not available, the entity shall use a valuation technique to estimate what the price of those equity instruments would have been on the measurement date in an arm’s length transaction between knowledgeable parties. The valuation technique has to be consistent with generally accepted valuation methodologies for pricing financial instruments and must incorporate all factors and assumptions that participants would consider in setting the price (para 16-17).

What does this typically mean for a company that needs to value these equity instruments?

If the company issues shares, and that company is publicly listed, then the value is typically taken from the share price on the grant date – this is the day that the equity instruments are issued, or approved by shareholders if shareholder approval is required for their issue.

If the company has issued options or performance rights, then it is usually the case that similar options or rights are not listed on the stock exchange, and as such there is no reference to a market price for those instruments. This is where a valuation technique is required to determine a value for the equity instruments issued – typically options or performance rights.

Treatment of vesting conditions

Equity instruments issued in return for services will usually have a vesting or performance condition attached to them, although this is not always the case as they may vest immediately.

If there is a vesting condition, then the type of condition will determine whether that vesting condition is required to be taken into account when the option or right is valued.

Vesting conditions that aren’t market conditions, are not taken into account when estimating the fair value of the options or rights at the measurement date. Instead, the performance conditions are taken into account by adjusting the number of instruments included in the measurement of the instruments.

For example, the performance condition might be that the employee has to remain an employee for three years for the options to vest. The value of the options does not get adjusted for this requirement, but the total number of options expected to vest may be adjusted. Historically the company might have an employee turnover rate of 30% over three years. Applying that data, the company may include in their measurement of the share based payment 70% of the options issued, on the basis that 30% are not expected to vest within the three years.

When do vesting conditions affect the valuation?

Where the performance conditions are market conditions, then those performance conditions are taken into account when calculating the value of the equity instrument issued.

Market conditions are performance conditions that are related to the market price of the entity’s equity instruments, such as:

  • attaining a specified share price or a specified amount of intrinsic value of a share option; or
  • achieving a specified target that is based on the market price of the entity’s equity instruments relative to an index of market prices of equity instruments of other entities

Examples are that the share must exceed a certain price by a certain date, or the total shareholder return for the company’s shares has to exceed the total shareholder return of an index to which the company belongs, or a general index such as the ASX200.

These conditions will then be taken into account when valuing the options or performance rights issued, and will require a valuation technique that is able to take into account these performance or market conditions when calculating a value.

Which valuation technique should I use to meet the requirements of AASB 2?

The valuation technique that is used is dependent on the terms and conditions of the options or performance rights issued.

The valuation technique should fit the options, and you should not be trying to make the options fit a particular valuation technique.

The simplest way to work out which valuation technique should be used, is to first work through the terms and conditions of the options or performance rights, and the features of the company’s shares.

Once you have determined the terms and conditions, then you will know which valuation technique will be the most appropriate for your situation.

And if you need to value options or performance rights and you aren’t sure how you should go about valuing those instruments, then contact us at Value Logic to help you out meeting the requirements of AASB 2 and ensuring that your period end audit will be smooth sailing.

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