Best Practices and Issues that Arise in DCF Models

Introduction

As is discussed in other chapters of this book, the discounted cash flow (DCF) model has become an established tool in calculating damages claims in inter­national arbitrations. This is because it can be used to calculate a claim for damages in many situations for any company that has reliable projections of future income. It also enables tribunals to base any damages amount on what is most likely to have happened to a claimant. Whether or not sufficient evidence exists for the tribunal to put its confidence in the output of the DCF model is hotly debated, but that is beyond the scope of this chapter.

Given this extensive use of DCF models and their importance to damages, it is important that arbitrators, lawyers and experts have a good understanding of model construction, the assumptions that underlie such models and the circumstances under which it is appropriate to use them. There are many badly constructed and badly explained models, but often it is left to the other side’s expert to try to understand the model and to explain its problems to the tribunal. In our view, reliance entirely on the experts is inadequate and it is necessary for a tribunal to understand the model if it is going to rely on it for an award of damages.

This chapter seeks to provide a guide for arbitrators to the key questions they should be asking when considering damages based on a DCF model. We look at the basics of DCF models, their construction and key issues that often arise in damages models.

Basics of DCF models

The DCF approach involves estimating the future cash flows of a company (or project), and then discounting these back to the net present value as at the valuation date (typically the date of the alleged breach) by applying a suitable discount rate. The big challenges in applying the DCF approach are calculating both a company’s future cash flows and the appropriate discount rate.

Components of future cash flows

Within a DCF model, a company’s future cash flows will typically comprise the following components:

• sales revenue earned from operations;
• less operating costs – direct and indirect costs of making the product or providing the service;
• less taxes – the corporation tax due on the operating profits (sales revenue less the operating costs) of the company;
• less investments in assets – for example, the cost of buying buildings, land, machinery, equipment and vehicles;
• plus non-cash items – including amortisation and depreciation, which are costs to reflect the decrease in value of intangible and tangible assets over their expected useful life. As these costs are charged to the profit and loss account, they will have been included within the ‘operating costs’ figure, above, which is deducted from ‘sales revenue earned from operations’. By adding these non-cash items here, they are removed from the cash flows; and
• less change in working capital – working capital is the cash a company needs for day-to-day operations and is calculated as current assets^[2] less current liabilities.^[3] If the change in working capital between periods is positive (i.e., working capital has increased), this is treated as a cost in the cash flow as it shows that more cash is tied up in working capital than in the previous period.

The first three components of the cash flow (sales revenue, operating costs and taxes) are essentially the net profit of a company, and will be based on figures included in the company’s profit and loss account.

Discount rate

The discount rate is applied to reduce the value of the future cash flows to the present value as at the valuation date.

Future cash flows need to be reduced because of the concept that a dollar today is worth more in economic terms than a dollar in a year’s time, which is because of two factors:

• the time value of money – if you receive $1 today and place it in an interest-bearing bank account, in a year’s time you will have the $1 plus interest, which is therefore worth more than receiving the $1 in a year’s time; and
• the risk and uncertainty attached to future cash flows – this means you would be prepared to accept a guaranteed lower lump sum today (e.g., $0.90) rather than being subjected to the future risk and uncertainty of possibly receiving $1 in a year’s time.

The discount rate is often one of the biggest factors affecting a damages claim. In international arbitrations, the methodology underlying the calculation of the discount rate has become reasonably settled and generally agreed among arbitrators; however, there are many major arguments about the parameters and assumptions applied to calculate it. For the purposes of this chapter, we do not go into the details of how a discount rate is calculated.

Arbitrators should understand how sensitive the present value of the forecast cash flows are to changes in the discount rate for each particular case. To this end, the key concepts to be aware of include:

• a higher discount rate will result in a lower present value for the forecast future cash flows and vice versa; and
• the further into the future a cash flow is, the more it will be discounted. For example, say the discount rate is 10 per cent, a forecast cash flow that was to occur two years into the future would be multiplied by 83 per cent^[4] to calculate its net present value, whereas a forecast cash flow that was to occur five years into the future would be multiplied by 62 per cent.^[5]

This means that the greater the proportion of cash flows that are forecast to occur far into the future, the greater the effect on the damages figure resulting from a change in the discount rate.

DCF approach

The DCF approach can be used in a variety of circumstances, including the valuation of an entire company (for example, in quantifying damages in investment treaty expropriation cases), as well as the valuation of the loss of profits for a specific contract (for example, in quantifying damages because of an early termination of a contract).

The calculation of damages will entail comparing the net present cash flows with and without the alleged breach; that is, comparing the ‘but for’ scenario (the hypothetical situation the company would have been in if the alleged breach had not occurred) and the ‘actual’ scenario (the ‘actual’ situation of the company following the alleged breach).

The valuation period is from the date of the alleged breach until the point at which the alleged breach no longer has a financial impact on the company and, therefore, can be either:

• a definite period, whereby it is assumed that, in the future, the company will return to its pre-breach levels of performance (i.e., its previous levels of sales or profits); for example, a temporary factory closure or the early termination of a contract; or
• an indefinite period, whereby it is assumed that the value of the company is lost forever and will never return to the pre-breach levels; for example, the expropriation of a company.

With an indefinite period, it is necessary to calculate a terminal value for the company, as forecasting cash flows beyond a certain period is impractical.

The terminal value represents the sum of all future cash flows beyond the explicit forecast period. The explicit forecast period is typically until the forecast cash flows are in a steady state whereby no major changes to the company are expected that could have any impact on the future cash flows.

The terminal value is important as it can often represent the majority of the value or loss calculated in the DCF model.

Construction of DCF models and spreadsheets

DCF models are typically constructed using a spreadsheet. It is easy to overlook this basic tool and, indeed, tribunals probably rarely see the underlying native copy of the DCF spreadsheet model. For this reason, the next subsection discusses the principles of good spreadsheet design.

Spreadsheets

Spreadsheets are ubiquitous in calculating damages in international arbitrations. They are easy to use and represent a common language among finance people.

The flexible nature of Microsoft Excel – by far the most popular spreadsheet software program – means that a user can develop a highly complicated model very quickly, which is not necessarily well designed.

Importantly, badly designed spreadsheets are very difficult to review. They are also more likely to contain errors, which is a cause for concern given that all spreadsheets are inherently prone to errors – a great many errors. Raymond Panko, of the University of Hawaii’s Shidler Business School, carried out extensive research into spreadsheet error and presented his findings in a paper entitled ‘What we know about spreadsheet errors’. There were three important conclusions:

• spreadsheet errors are rare on a per cell basis, but in large spreadsheets at least one incorrect bottom line value is likely to be present;
• errors are extremely difficult to detect and correct; and
• spreadsheet developers are overconfident about the accuracy of their spreadsheets.^[6]

Other research cited by Panko indicates that more than 90 per cent of spreadsheets contain errors and that 5 per cent of cells reviewed have errors, including ‘mechanical errors’ (e.g., typos), logic errors (e.g., incorrect formulas) and omission errors (e.g., leaving something out of the spreadsheet that should be there).^[7] One occasionally sees damages awards making reference to errors in spreadsheet models – the Yukos award is a good example.^[8]

DCF spreadsheet models for damages claims can range significantly in their complexity, from basic models (e.g., with only a few worksheets, simple formulas and relatively few inputs) to highly complex models (e.g., with numerous worksheets, complicated formulas and lots of inputs).

Although it is difficult to guarantee that a complex DCF model is entirely free of errors, if best practice is followed in terms of the model design and quality control and testing of the model, this minimises the risk of material errors and inconsistencies being included in the model. We set out below the best practice in relation to the design and review of DCF models, with the key principles applicable to both basic and complex models.

Design of the model

If a DCF model is well formatted and labelled (e.g., notes are included that explain how figures have been calculated, it is clear which figures are inputs and which are calculations, and the sources of any inputs are clear), the model should be fully understandable, even from PDF prints of each worksheet, and even for complex spreadsheets that could run to hundreds of pages in a printed copy.

If a DCF model is well designed (and thus easy to use and understand) and shared with the other party in plenty of time for a model review to be undertaken, it should be possible for both experts to agree that the model is arithmetically accurate given the inputs and calculations included in the model. The experts and the tribunal can then be free to concentrate its enquiry, challenge and debate on the key issues with regard to the model, such as whether the commercial assumptions are reasonable, whether alternative inputs should be used (the common example is the discount rate or interest rate that should be applied) and the overall methodology used.

If a DCF model is poorly designed, the task of reviewing the model or trying to make changes to assumptions can be very difficult, as it becomes difficult even to understand how the model and the calculations within it are working, including what implicit assumptions are being made as part of the calculations and, thus, whether the model is accurate. For example, if the sources of the inputs are not clearly labelled within the model, it becomes difficult to agree the input figures contained in the model back to the source data.

The first responsibility for preparing a robust model lies with the preparer of the model. We suggest that preparers follow a number of basic principles around design. There are a number of guides that can be followed, for example, the Institute of Chartered Accountants in England and Wales publishes a list of 20 principles for good spreadsheet practice. The list that our own firm uses contains the following.

Structure

A well-designed model will have a clear and easy-to-follow structure, following best practice, including separate worksheets as follows:

• input worksheets: these should include only hard-coded input data and assumptions required for the calculation; for example, the assumed percentage change in sales revenue each year during the forecast period. They should not include calculations (other than potentially a sum or average calculation, e.g., summing monthly revenues to calculate the annual revenue). The inputs will then flow into the calculation worksheets;
• calculation worksheets: these should include only the detailed calculations required to assess loss, such as the calculation of the cash flow for the company in the but-for scenario during the relevant period. They should not include any hard-coded input data; any input data required in the calculation worksheet should be linked by a formula to the relevant input cell within the input worksheets. The calculations will then flow into the output worksheet; and
• output worksheet: this will generally be only a single worksheet and can be thought of as the ‘summary’ worksheet that provides the final output of the model based on the figures contained in the calculation worksheets (i.e., the overall loss incurred by the company as a result of the alleged breach). This should not include any hard-coded input data or calculations but rather should link to the relevant cells within the calculation worksheets.

Depending on the case, the output worksheet may take the form of a ‘dashboard’, which collects the key inputs of the model that can be varied and presents the headline outputs. Dashboards are useful to show the quantum result in a range of scenarios with different combinations of inputs and assumptions.

A well-constructed dashboard should be intuitive and capable of being used without any prior knowledge of Microsoft Excel; this is achieved with the inclusion of drop-down lists, automatic error messages that highlight errors, ‘reset’ buttons, and so on. This allows the tribunal to amend the inputs and assumptions within the model to understand the loss for a range of scenarios.

An illustrative example of a dashboard is shown below.

The more complex models will usually contain numerous input and calculation worksheets. If this is the case, all the worksheets for each category should be grouped together within the spreadsheet. Typically, input worksheets will be grouped together on the right of the tabbed worksheets, which then flow into the calculation worksheets in the middle, with the output worksheet on the left. In a well-designed spreadsheet with many worksheets, data will then flow through a model in one direction, from right to left across the tabbed worksheets.

Finally, each worksheet should be labelled clearly to explain its purpose. If a model has numerous worksheets, it can be helpful also to have a contents page as the first worksheet that sets out the title and purpose for each worksheet and the structure of the calculation.

Consistency

Spreadsheets should have consistent design features, for example:

• left–right consistency: each row should contain one formula copied across each row; and
• column consistency: the same period should be in the same column on each worksheet.

Clarity

We all recognise that spreadsheets can be complex, but this does not mean they should lack clarity. In particular, calculations should not be more complex than necessary, as the more complex a calculation becomes, the more difficult and time-consuming it is to understand the calculation and to verify that it is correct.

Best practice, therefore, is to use the shortest and simplest formula possible for each calculation, with complex multi-step formulas broken down into a series of steps on separate rows or columns.

Documentation

Documentation is key to understanding any model.

Within each worksheet, the basis of each figure should be labelled clearly. For example:

• inputs: references should be provided to the source document or an explanation setting out how the assumption was arrived at;
• links: cross-references should be provided between the different worksheets within the spreadsheet; and
• calculations: these should either be clear from the face of the spreadsheet (i.e., without looking at the formula, such as the total of the rows immediately above) or explained in a note within the spreadsheet.

For more complex models, a user guide to the model should be included that sets out:

• the structure of the model;
• the flow of information through the calculation (i.e., how the different worksheets within the model link to each other);
• whether any inputs are variable inputs and can be flexed (e.g., drop-down lists that allow different interest rates to be selected); and
• explanations of any complex formulas, macros^[9] or non-standard program add-ins^[10] contained within the model.

Quality control and testing

The model should contain elements of quality control such as adequate and explicit cross-checks; for example, a formula that checks that a balance sheet does balance, or a formula that flags where a calculated number that should always be positive is negative. In more complex models that contain a lot of error checks, it can be helpful to summarise all these checks in a single worksheet within the spreadsheet.

In addition, given that spreadsheets are inherently prone to errors, it is best practice for all DCF models used in international arbitration to be verified by a team independent of the team that prepared them. This independent team should verify the model by confirming that the inputs agree to the source documents and that the formulas within the model are correct (for example, all the relevant years are included within a formula calculating the total).

Although some experts have company rules that require the verification of a firm work-product (and some have specialist teams who focus only on verifying models), this is not the case for all experts.

Particular issues that arise in DCF models

A key commercial issue that arises in DCF models relates to the forecast cash flows, in particular the growth of those cash flows.

Forecast cash flows

The overall problem one faces with forecast cash flows is that they are, by their nature, forecasts and, therefore, composed of inherently uncertain items.

Revenues are traditionally the most difficult item within the cash flow to forecast. Costs of sales are generally easier to forecast than revenues and, in some cases, may even be based on revenues (e.g., where the cost of sales is calculated as a set percentage of sales volume). Overheads are normally the easiest to forecast, particularly fixed overheads that do not change as production changes (e.g., the rent paid on a factory is the same whether one unit or 500 units of product are made).

The overall commercial assumptions underpinning each element of the cash flow forecast (as set out above) need to be looked at sceptically with a view to answering the following two questions: (1) What supports them? (2) Do they make sense?

In particular, the growth of the cash flows can often be a big area of debate among the parties.

Growth of cash flows

One of the biggest areas of contention in a DCF valuation is likely to be the growth of the cash flows built into them, whereby the growth includes:

• the assumed year-on-year growth of the cash flows during the forecast period (which is driven by the growth in the individual components of the cash flow – i.e., revenues, costs, etc.); and
• the assumed stable growth rate applied in the terminal value (for those cases where a terminal value is required).

In simple terms, the main causes of the growth of a company’s cash flows include:

• an increase in the volume of goods or services produced and sold, through increasing its capacity by investment in assets or in labour (e.g., a cake manufacturer could increase its production by hiring more workers or by buying additional equipment);
• an increase in the volume of goods or services produced and sold, through increasing productivity (the cake manufacturer could increase its production by increasing the productivity of its existing machinery or workforce);
• an increase in the price charged for the good or service sold (the cake manufacturer could charge its customers more for each cake); or
• an increase in efficiency such that the same level of production and sales can be achieved for a decreased cost (the cake manufacturer could reduce wastage of flour and butter to cut the costs of raw materials).

When assessing the level of growth assumed within a DCF model, it is important to understand the causes of the growth and determine whether these are reasonable. For example, although a company can cut its costs (either as a one-off or over the course of a few years) to grow its cash flows, a company cannot continually cut costs year on year forever, otherwise eventually costs would reduce to zero.

In practice, generally, companies do not experience consistent growth rates year on year. Although a consistent growth rate across a forecast period makes modelling easier, it may be unrealistic to achieve for a sustained period.

Whatever the level of growth that the expert assumes (whether that is no growth, negative growth, or small or large positive growth), the tribunal and the other party’s expert should question whether the assumed level of growth makes sense in the context of:

• the historical performance of the company;
• the growth of the market in which the company operates;
• the size of the company – the larger the company, the more difficult it becomes for it to generate the same percentage growth it realised when it was smaller;
• the level of investment that is assumed in the model; and
• the level of working capital that is assumed in the model.

Overall, growth assumptions should always be looked at thoughtfully and the reasons for the growth fully understood.

Growth of market

It is important to be aware that no company can grow at a rate above that of the market in which it operates for a sustained period. High-growth companies will always see growth fall off eventually, as the market is always looking for returns, and any industry or sector enjoying high or above average returns will see competitors entering the market, which in turn drives down growth.

Chasing more growth and more returns often means companies need to enter new markets. However, this can then expose a company to increased competition and make the company more complex; both of these can limit the growth that can be achieved by expanding into new markets.

Size of the company

In terms of size, the bigger the company, the more difficult it becomes for it to generate the same percentage growth it realised when it was smaller. For example, a small company that had been selling 100 units can grow by 10 per cent by selling an additional 10 units (10 per cent of 100 units), whereas a large company that had been selling 100,000 units will have to sell an additional 10,000 units to grow by 10 per cent. Selling an additional 10 units is clearly much easier than selling an additional 10,000 units.

A potential cross-check can be to compare the growth of companies of a similar size in the same market to the growth forecast in the DCF model.

Investment

As noted above, to support the growth of cash flows, a company can invest in assets (also known as capital), such as:

• purchasing machinery to add a new production line;
• investing in a new information technology system to improve efficiency and productivity; or
• purchasing new premises to sell in new regions.

It is important to assess whether the level of investment assumed in the DCF model is reasonable, based on the assumed level of growth of the cash flows.

A key consideration will be to understand the cause of the growth in the cash flows. It logically follows that the more the growth in the cash flows is driven by making investments in capital (rather than through making investments in labour, increasing productivity, increasing the sales price or increasing efficiency), the higher the level of investment in capital that should be included in the DCF model.

Another consideration is the industry in which the company operates. All other things being equal, to achieve the same level of growth, a company operating in a capital-intensive industry^[11] will need to invest in more capital than a company operating in a labour-intensive industry.^[12]

The other party’s expert and the tribunal should also consider what the implied return on investment is, given the assumed level of investment and growth within the DCF model.

Say a company is forecasting a growth rate in cash flows of 20 per cent per year over five years and that during this same period the company is investing 10 per cent of those cash flows per year. This implies massive returns on the new capital invested and could indicate that either the investment rate is understated or the growth rate is overstated, or a combination of both. Either an increase in the investment rate or a decrease in the growth rate would lead to a reduction in the forecast cash flows. Well-constructed models will include calculations of ratios, such as the return on investment, as part of the quality control and testing undertaken, which can be reviewed easily to identify any unexpected results arising from the combination of assumptions made.

It is worth bearing in mind that the level of investment used in a DCF model should allow not only for investment in new capital to improve growth but also investment to maintain the company’s existing capital base. The investment required to maintain a company’s existing capital base will depend in part on the industry in which the company operates (i.e., whether it is a capital-intensive industry).

Working capital requirements

Any assumptions about growth require the following question to be considered: What is the financial impact on working capital?

As noted above, working capital is the cash a company needs for its day-to-day operations and is calculated as current assets (such as stock and debtors) less current liabilities (such as creditors).

In most cases, the growth of a company requires greater amounts of working capital, which must then be factored into the forecast cash flows. It is therefore important to consider whether the level of working capital assumed in the forecast cash flows is consistent with the assumed level of growth of the cash flows.

As a general rule, if the value of sales is growing then the company’s working capital needs will also grow. This is because if the value of sales increases, this will usually lead to an increase in debtors (money due from customers) and this causes the working capital requirement to increase. For example, if sales increase by 5 per cent, a reasonable assumption is usually that debtors also increase by 5 per cent, which (assuming no other changes) then increases the working capital requirement by 5 per cent.

If the DCF model forecasts an increase in sales revenue but no increase in working capital, although there may be reasons that explain this, the other party’s expert and the tribunal should understand these reasons and challenge whether they are reasonable.

Terminal value

All companies mature (unless they truncate). In valuation terms, this is referred to as having a stable or constant growth rate and is reflected by the calculation of the terminal value – essentially the value of the future cash flows on the day the company reaches maturity.

Growth rates in the terminal value is another area where modelling mistakes can be made. If a terminal value calculation assumes a 5 per cent stable growth rate, the expert is assuming that the company’s cash flow will grow at 5 per cent per annum in perpetuity.

To assess at a high level whether the stable growth rate used in the terminal value calculation is reasonable, there are two key points that tribunals should consider.

First, stable growth rates for a company cannot be more than the long-term growth rate in the economy in which the company operates. The reason is simple – such an assumption would mean the company eventually grows larger than the economy in which it operates.

Second, a stable growth rate is in fact likely to be lower than the growth in the economy. An economy is made up of high-growth and stable-growth companies, with the growth rate of the economy an average of all these individual companies’ growth rates. This means that stable-growth companies will have growth rates lower than the growth rate of the economy, and high-growth companies will have growth rates higher than the growth rate of the economy.

Role of tribunal in relation to the model

On the basis that quantum has been calculated by both parties’ experts, the tribunal may receive one or two models, depending on whether a common model has been agreed by the experts.

If the experts do not agree on a common model, it is helpful for the tribunal to understand where the disagreements lie. Some common areas of disagreement include:

• different instructions;
• legal issues;
• commercial assumptions;
• sources for the data;
• design of the model; and
• complexity of the model.

We set out below a checklist of questions that a tribunal can consider when determining whether it can rely on a model, which focus on determining whether the model is fit for purpose based on the requirements of the tribunal.

Our recommended approach for the tribunal to approach quantum is as follows:

• the tribunal decides which model it can rely on (taking into account the questions set out above);
• the tribunal makes its determinations of the issues in dispute in relation to the model (e.g., which discount rate should be applied, which growth rate of revenue should be used). In some cases, to make its determinations, the tribunal may request that the experts run a number of variations through the model to understand the effects of different assumptions on the overall loss (if this functionality is not already built into the model to allow the tribunal to carry this out itself); and
• depending on the model, the tribunal or the experts (or the expert appointed by the tribunal, if there is one) can then input the determinations into the model, with the resulting output equalling the amount of the damages to be awarded.

In the absence of their own tribunal-appointed expert, unless the quantum calculations are very simple, tribunals should be wary of undertaking their own calculations of damages, as they will potentially suffer from three overall problems:

• the damages calculated may be based on a methodology that is flawed because of complexities in the models of which the tribunal has not taken full account;
• in coming up with something novel or hybrid, the tribunal may be adopting something on which the parties will argue they have not been able to make adequate submissions; and
• it amplifies the risk that the award itself may contain arithmetical errors, which can open up the opportunity of challenging or discontent with the whole arbitration process. For example, in one of our cases, the tribunal copied and pasted profit figures from one spreadsheet into another – but this did not take account of the effect of tax or inflation.

Conclusion

We believe that well-constructed DCF models that have undergone adequate review, and that are sufficiently explained and documented, are key to effective awards in arbitration in which damages are likely to be complex. They are also likely to lead to a more efficient arbitral process.

In addition, a properly constructed DCF is more likely to result in the key drivers of value and the commercial assumptions underlying them being properly analysed and challenged more effectively.

Conversely, poorly constructed models that have not been undergone quality control testing lead to inefficiencies in arbitration with resources devoted to arguments about model design and corrections of errors.

As a fundamental point, it is very important that DCF models in arbitrations are well designed and properly reviewed if they are to be used by a tribunal. If they are not, then any figure they produce may be subject to doubt.

Notes