Complex DCF Models and Financial Awards

04 July 2016


The discounted cash flow, or DCF, has become an established tool in calculating damages claims in international arbitrations. This is because it enables the Tribunal to turn its decisions on what would most likely have happened to a claimant in any one-off scenario into a quantum amount that can be awarded to the claimant.  One can see this from the published awards in investor state disputes.

Given this extensive use and their importance to damages one would expect arbitrators to have an in depth knowledge of their construction, the assumptions that generally underlie such models and the circumstances when it is appropriate to use them.  Sadly, this is not always the case.

At a recent international arbitration conference a panellist said publicly: 
“WACC, what is WACC?  I don’t understand EBITDA.”

Hopefully this was lightening the debate. But comments and findings in a number of awards suggest that the mixed reaction to this comment – nervous laughter and intakes of breath – point to a more general unease amongst many arbitrators about the extent to which they truly appreciate what is going on when they receive a 200 page expert’s evaluation of a claim for many billions of dollars.

This article attempts to explain these matters and provides a guide for arbitrators to the big questions they should be asking when considering damages based on a DCF.  It looks first at the construction of DCFs and second at the component of the DCF which drives substantial value – growth. It makes the overall point that, without a well-constructed DCF model, identifying issues affecting growth may go undetected.

The Basics

If they haven’t been exposed to the concept at school, or university, budding chartered accountants and CPAs get trained in the basic concept – the time value of money – in their studies leading up to qualification.

This is not so we can become forensic accountants evaluating commercial damages claims. Rather, it is because: firstly, the assessment of income-producing assets is a critical part of financial statements auditing; and secondly, the related concept of the internal rate of return – the discount rate at which future cash flows have a net present value of zero – is so important in budgeting and project assessment.

So, two factors – a future cash flow and a discount rate – are the basic building blocks of the DCF. To this has to be added a development over the last three decades, the absence of which would mean damages claims would be far less complex – the spreadsheet.

It is easy to overlook this basic tool and indeed panels probably rarely see the mechanics of a DCF model.  And for this reason we are going to dive into the principles of good spreadsheet design first.


Spreadsheets are ubiquitous in finance.  They are easy to use and represent a common language among finance people – although some speak that language better than others.

The flexible nature of Excel means that a user can develop a highly complicated model very quickly. However, such models vary in format and design.  Although it is common for time to be horizontal and, say, the components of a cash flow to be vertical there is no rule that says this has to be the case. Further, many users will write a spreadsheet as a narrative with little prior thought of an overall plan. Also, many spreadsheets are recycled, which means that any problems in the original spreadsheet will get recycled as well.

Badly designed spreadsheets are difficult to review –that is, if any review by someone other than the designer takes place at all.  Intuitively, such spreadsheets are more likely to contain errors, and spreadsheets are prone to errors – a great many errors.  Ray Panko of the University of Hawaii’s Shidler Business School presented a paper in London in 2005, based on extensive research into spreadsheet error. 

There were three overall conclusions:

  • spreadsheet errors are rare on a per-cell basis, but in large programs at least one incorrect bottom line value is likely to be present;
  • errors are extremely difficult to detect and correct; and
  • spreadsheet developers are over-confident in the accuracy of their spreadsheets. 

Other research cited by Panko indicates that over 90% of spreadsheets contain errors, 5% of cells reviewed have errors and while most are just typos the most insidious are not including something and logic errors.

The spreadsheet model is the basic tool used in complex financing transactions such as public-private infrastructure projects running to many billions. Banks and accounting firms that specialise in this type of work have whole teams devoted to modelling and checking models. Our own firm in its London office alone has 45 project finance specialists of whom 25 undertake model assurance. This is not surprising given the size of the projects and the implications of errors. Ten years ago we recall working on a damages claim arising from an error in a securitisation case involving consumer leases where it had been assumed – in error – that the leases would renew after four years. The obsolescent nature of the products leased made it highly unlikely that anyone would ever renew. The claim ran into hundreds of millions. The poorly designed model meant that the key assumption driving the claim was not immediately apparent. Such is the level of skill around design and review that claims like that are now far less likely.

Do we have anything similar in the DCF models underlying claims in international arbitration? Do arbitrators ever ask the question, has this model been thoroughly audited by the expert on the other side?; or should they get an independent model audit as part of their role as arbitrators?; and what impact would this have on model construction and ease of use? One occasionally sees awards making reference to errors in spreadsheet models – Yukos is a good example. But when some experts refrain from providing models – on the spurious grounds of a proprietary right – it can be very difficult to assess a model.

DCFs for damages claims can often be highly complex. A basic cash flow will run into many interlinked worksheets. If the underlying claim has a commodity element to it, then there may be an even more complex pricing model that links into the cash flow. Printing the whole thing out will often run into hundreds of pages, many of which will be of little use as printed documents because of the sizes of individual worksheets. If there is any element of bad design, the task of using one of these models or reviewing one will be made almost impossible given the exigencies of arbitration. And, given that a critical part of any review of a DCF will be analysing the impact of changing assumptions, the use and review by the preparer and the expert on the other side is vital.

The point this paper makes on DCF models in commercial arbitration is as follows – they have to be well designed and properly reviewed if they are to be used by a tribunal. If they are not, then there is always going to be a doubt as to any figure they produce. The reliability of the model should not be the focus of any argument if it is well designed, easy to use and shared with plenty of time for a model review to be undertaken.

The Preparer of the Model

The first responsibility for this is that of the preparer of the DCF model.  We suggest that preparers follow a number of basic principles around design.  There are a number of guides.  For example, the Institute of Chartered accountants in England & Wales publishes a list of twenty principles for good spreadsheet practice.  The list our own firm uses contains the following:

Explicit Layout

Inputs, calculations and outputs need to be clearly separated in the design.  This means that the following guide can be more easily followed:

  • the inputs area should only include data and assumptions.  Input areas should not include calculations;
  • the calculations area should only include individual calculations.  It should not have any hardcoding; and
  • the outputs area should not include any hardcoding or calculations except for clearly identified check formulae.

Finally, the spreadsheet should contain clear labelling.


Spreadsheets should have consistent design features, for example:

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

Well planned spreadsheets will have this as a matter of course.  Poorly designed spreadsheets, written as a narrative, will be beset with inconsistencies.

Further, there should be a consistent and linear flow of logic in the spreadsheet, that is left to right across worksheets and top to bottom down spreadsheets.

Further, where there are many worksheets, data should flow through a model in one direction.


We all recognise that spreadsheets can be complex; this does not mean they should lack clarity. Therefore, the use of short formula is recommended, as is breaking down a calculation into a series of steps on separate rows.  Many designers seem to think that there are prizes for writing complex formulae in as small a part of the worksheet as possible.

Other functions can be used indiscriminately, like range names.


On any complex model, documentation is key.  This includes a book on the data inputs and a user guide to the model with instructions on how to use and how to make changes to inputs.

A developer guide is also essential if the model is to be manipulated.  This will document the logic, the dataflow.  It will also include instructions on the use in the model of any complex formulae and macros.

Finally, add-ins to the basic Excel package – for example a Monte Carlo – need to be fully explained.

Quality Control – Preparer

Finally, the model should show evidence of quality control by the preparer.  This includes adequate and explicit checks and cross casts, ideally summarised in one place.

The preparer should also note his own sense checks on the outputs by reference to the inputs.

Quality Control – Reviewer

Similarly, someone separate from the preparer should undertake a quality control of the model.

Thinking back to our consumer products leasing case, would adherence to the above have guaranteed that error would not have occurred?  No – there is no such guarantee. That error arose from a commercial assumption in the model that was inconsistent with commercial reality.  But such an error is more likely to be spotted either by the preparer or the reviewer when they undertake their sense checks if the model is well laid out and accurate.

It is worth bearing in mind that, from the respondent’s expert’s perspective and that of the tribunal, it is the commercial assumptions that underlie the model that are – or should be – the subject of enquiry, challenge and debate. There is little merit in wasting time arguing about and correcting inconsistent formulae.

The Respondent’s Expert

The respondent’s expert clearly needs to be able to respond to the DCF model in every important sense, that is:

  • Do the assumptions make sense?
  • Are the inputs properly sourced?
  • Is the arithmetic correct?

It is difficult and may be virtually impossible to perform this work without a native copy of the model. In the absence of the model, the respondent’s expert is left trying to reconstruct the model to work out what the claimant’s expert has done, something that is less than optimal.

Why, therefore, does one still meet the situation where the claimant or the claimant’s expert refuses to supply the model either in native copy, or at all?  A model supplied as a set of PDF files is of little use and results in the respondent’s expert trying to build his own native copy.

On the basis that a native copy is supplied, the respondent’s expert is in the position of being able to understand the matters noted above, and where necessary flex and sensitise the model to allow for different commercial assumptions. He is also able to confirm, or otherwise, the arithmetic and trace the inputs to source documentation. There should be little need for the respondent’s expert to produce his own model, other than amending elements of the claimant’s expert’s model that represent his view regarding the assumptions.

But all of that of course depends on the claimant’s expert’s model being fit for purpose.  In cases where a model has large numbers of errors and suffers from major design faults, it may be virtually impossible to use it. The respondent’s expert may have little choice but to construct his own model or say that the model, as presented, is just not supportive of any claim.

The Experts Together

As noted above, the model really should not be the subject of dispute in the arbitration.  One method to get agreement on a model is by the experts meeting and coming up with areas of agreement and disagreement.

Areas of disagreement between financial experts are usually the result of the following:

  • different instructions;
  • legal issues; and,
  • commercial assumptions.

In valuation work, one can add to this list disputes between experts around the components of the discount rate.

The financial effects of these areas of disagreement can quite properly be represented in an agreed model, resulting in the presentation of a variety of outputs.

It is particularly important that by the time the hearing is reached, at the latest, both experts are working to a common model because it will be this product that the tribunal should use when making an award.

The Tribunal

Working on the assumption that the claimant is entitled to an award of damages, the tribunal could approach quantum in the following way.

Having a common model, as between the experts, the tribunal makes determinations of the issues in dispute between the experts. The determinations are fed into the common model and the result is the award. Or, the tribunal can request a number of variations to be completed to understand the impact of different assumptions that underpin the dispute and then consider this in the overall context before deciding on the outcome.

Experts can then be given the determined factors, asked to feed these new inputs in to the models and reach an agreed amount.

Practically, does this happen very often?  No. The reason it does not arise is primarily caused by two overriding factors. The first is that the financial models are often incapable of being agreed because of the design faults noted above. The second is the lack of agreement – or even a forum for discussion – between experts.

The result is that one sees tribunals wrestling with their own models, or their own methodologies, which suffer from three overall issues. Damages may be based on a methodology which is itself flawed. Second, in coming up with something novel or hybrid, the tribunal may be adopting something which the parties will argue they have not been able to make adequate submissions on. Finally, it amplifies the risk that the award itself contains arithmetic errors.

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. The answer to the problem of being presented with competing quantum calculations on completely different bases lies in getting DCF models prepared on a proper footing in the first place.

Growth in cash flows

The better the design of the DCF model, the better able a preparer or reviewer will be to concentrate on the things that matter in the DCF: the cash flows themselves.  In this part of our paper we look at the big commercial issue in forecasting cash flows – growth.  First, we look at the basics of the cash flow.

The Basics of the Cash Flows

The basic cash flow is composed of the following elements:

  • the cash flows from operations, that is revenues less costs with an adjustment for non-cash items like depreciation;
  • working capital consideration;
  • investments in assets; and
  • other cash flows, such as taxation, interest and dividends which may or may not be relevant to valuation depending on what is being valued.

The overall problem one faces with a cash flow is that it is, by its nature, a forecast and therefore composed of inherently uncertain items. Traditionally, cash flows are produced from the top down that is from revenues through costs of sales and into overheads and then interest and tax.  The top down approach also reflects a level of increasing certainty because, generally, revenues are more difficult to forecast than costs of sales which are more difficult to forecast than overheads. However, to a great extent, revenues “drive” the other numbers in a cash flow.

It is, therefore, the revenues that come under most scrutiny for all the interested parties either looking at or reviewing a cash flow and that means that the overall commercial assumptions need to be looked at sceptically with a view to answering the following two questions:

  • What supports them?
  • Do they make sense?

One of the biggest areas of contention over the revenues in a DCF valuation is likely to be the growth for the simple reason it has a multiplicative effect on value.


Many cash flows make assumptions that are unrealistic about future growth. Such cash flows will make one of the following assumptions:

  • assume growth of any amount where none is likely;
  • assume growth rates which are inconsistent with macroeconomic factors;
  • assume rates of growth that are stable over time; and
  • assume growth for a period of time that is highly unrealistic.

Each of these will happen if there is insufficient investment – which we cover in the next section. But even with sufficient investment, growth is very difficult to achieve; and the bigger the company gets – the more it has grown – the more difficult future growth becomes.

Every valuation that makes an assumption about growth, which is all of them, is making implicit or explicit assumptions about: growth in the general economy; growth in the subject entity’s sector or market; and the development of products or services to sell into those markets.

Separating out these elements will make it clearer the extent to which a company is dependent on, for example, continued growth in Chinese GDP at rates of 10% per annum, or stability in commodity prices.

Not only is growth difficult, when it comes it never comes consistently. While a regular 5% growth rate looks neat in a spreadsheet and makes modelling easier, it is hugely unrealistic over any sustained period of time. In effect, using 5% in the terminal value means that you are growing the company cash flow at 5% per annum into perpetuity.

High growth companies will always see growth fall off, mature companies will not see any growth if they fail to innovate. The market is always looking for returns and any industry or sector enjoying high or above average returns will see competition.

No company can grow at a rate above that of the market or its sector for a sustained period of time. Size, a lack of effective innovation and competition all drive growth down.

Growth assumptions should always be looked at thoughtfully and with caution.

Growth in Sales or Growth in Cash Flows

It is vitally important to identify what growth we are talking about.  A company can grow its revenues at 5%. But that does not mean it will be growing its value by the same amount.  What drives growth in value is growth in net cash flows. So if a company grows its cash flows by 5%, to grow its value by the same amount its costs have to remain the same.

Therefore to grow by x%, companies need to grow their revenues at a rate above x%.

Investment and Re-investment

One of the “answers” to the growth question above is investment.  If a firm invests enough then it should be able to achieve that elusive growth. This is true, up to a point. However, this view, when converted into numbers in a cash flow, often makes two very big conceptual errors. The first is the wild expectation of incremental growth relative to incremental investment. The second is the need for re-investment to protect existing revenues.

In the first case, say a company is anticipating a growth rate in cash flows of 20% a year over a five year period. Say that company is investing 10% of those cash flows in the business – new products, new markets, etc. This implies massive returns on the new capital invested, and beyond that of existing investments. The reinvestment rate is clearly understated (or growth overstated) – the implication is over value because adjusting for either will reduce future cash flows. So what should the re-investment rate be? Looking at the relationship between growth rate and the cost of capital rate is more likely to come up with the required re-investment rate.

This last point raises another issue, often ignored – not all investments will add value for its investors. Where a company makes returns on its investments that are less than its cost of capital, it is effectively destroying shareholder value – even as it becomes bigger.

On the need for re-investment to protect existing cash flows, all of those charges for depreciation that got backed out of the operating profits and increased the cash flows will usually get put back into the DCF to replace existing capex. That is not capex for investment in new products but maintaining the existing capital base, which if you link with a 5% growth in your terminal value means that you will either be able to increase prices, improve productivity or reduce costs every year in order to achieve your 5% growth rate into perpetuity, as you have not allowed for any Investment.

Working Capital Needs

Any assumptions about growth require this question to be asked and answered: what is the financial effect on working capital? It should go without saying that most growth requires greater amounts of working capital, which has to be financed out of cash flows. However, cash flows for valuation that we have seen often leave out increases in working capital, only to subsequently justify the omission on the grounds of increased efficiency by larger companies, financing out of trade creditors or immateriality.

Looked at this in the round, from the perspective of the non-accountant or economist, the idea that there is a “reduction” in value because a company is successful and a consequence of that success is the need to finance the debtor book seems counter-intuitive. But that is to ignore the drain on resources that growth has, be it investment in new products or increased working capital tied up in the business and therefore not available to investors.

Efficiency, Size and Maturity

There is one area of growth that does not depend on re-investment and that is becoming more efficient. Regardless of what management are doing to become more efficient, this either means cutting costs but generating the same revenues, or generating higher revenues out of the same cost base, or a combination. Both lead to growth cash flows and therefore growth and increased value.

Business common sense holds that one cannot cut costs for ever and one should be very dubious about sustained periods of efficiency savings.

As noted above the bigger the size the more difficult it becomes for a business to generate the growth it saw when it was smaller.  Bigger companies also tend to end up with more infrastructure. Chasing more growth and more returns often means new markets and at the same time more competition.  Businesses become more complex and that has a cost.

Finally, all businesses 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 business reaches maturity.

Growth rates in the terminal value are another area where mistakes can be made.
First, stable growth rates cannot be more than the growth rate in the economy in which the business operates. The reason is simple – such an assumption would mean the business eventually becoming bigger than the economy in which it operates.

Second, the stable growth rate is in fact likely to be lower than the growth in the economy.  On the basis that an economy is made up of high growth and stable growth firms, the latter will have growth rates lower than the economy and the former growth rates higher than the economy.

Discount rates and comparables

We have not mentioned discount rates in this article, but here too is an implication for growth.

The discount rate is usually checked against comparable company data.  If the comparable companies are forecasting average growth of 5% per annum and the company being valued is forecasting 20% growth per annum for 5 years, it doesn’t appear to be rocket science that a company forecasting 20% growth in cash flows per annum has a higher risk than one forecasting 5%.

And the often derided comparable companies approach is relevant here, as a cross check. A DCF that arrives at a valuation that equates to a very high or very low multiple of earnings could indicate issues with the DCF, over ambitious and unsupported growth or an understated discount rate are two issues that might warrant further consideration in these circumstances. 


The architecture of DCFs in international arbitration gets little notice until a public award refers to significant errors.

We believe that well-constructed DCFs that have the support of both sides’ experts and in which the tribunal have confidence are key to effective awards in arbitration where damages are likely to be complex, such as the expropriation of a business. They are also likely to lead to a more efficient arbitral process.

Conversely, poorly constructed DCFs lead to inefficiencies in the arbitration with resources devoted to arguments over models and corrections.

A properly constructed DCF is more likely to result in the key drivers of value and the commercial assumptions underlying them being analysed and challenged.

In many DCFs, the key driver of value is the growth in the subject entity, a product of the growth in revenues. However, growth is not free and successful growth needs a number of components. These components are more likely to be revealed by the well constructed DCF.

We appreciate that there are other areas of the DCF that attract interest, the key one being the composition of the discount rate. However, while the elements of a discount rate can be analysed and challenged, no matter how poorly constructed the DCF is, analysing the components of the growth of a business requires a well-constructed model.

Reproduced with permission of Global Legal Group Ltd. This article is due to be published in the thirteenth edition of The International Comparative Legal Guide to: International Arbitration; (

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