The Auditor's Cross Subsidy (Statistical Modelling Of Audit Prices)

By Professor Michael Mainelli, Ian Harris, and Alan Helmore-Simpson
Published by Strategic Planning Society E-Newsletter, Article 1 (June 2003, also published as Anti-dumping Measures & Inflation Accounting: Calculating the Non-Audit Subsidy,

Subsidy, What Subsidy?

For at least two decades, maybe longer, big accountancy firms have been loudly protesting that cross-subsidy of audit by non-audit services never occurs, and that low-balling of audit proposal fees in order to win a client’s other business is a vile slur on the integrity of the audit profession. Audit was a separate business, they said, uninfluenced by the add-on, sell-on businesses of consulting and tax. Consulting and tax favoured the incumbent audit provider because of the client and industry knowledge gained, not because audit was a loss-leading product.

Then one of the Big Four broke ranks. PricewaterhouseCoopers (PwC) was reported as acknowledging that “a company could secure a discount if it provided an accounting firm with non-audit work as well as the audit” [Financial Times, 30 June 2002]. To most of us, this sounds obvious; quantity discounts and loss leaders are a feature of most markets, and it isn’t really very shocking to learn that audit firms behave like other commercial organisations. Nonetheless, the same article reported that “three of the big four accounting firms denied any involvement in ‘low balling’…”

Then PwC went further. PwC’s global chief executive, Samuel DiPiazza, sought “a way that we can at least return enough to make our profession worthwhile” [12 December 2002]. A couple of months later, the firm reported that its ratio of audit to non-audit fees from FTSE-100 clients rose from 28% to 71% [Accountancy Age, 6 February 2003]. Making a virtue of necessity, the firm also announced that audit objectivity was no longer under threat as it raised fees markedly. We are not trying to pick on PwC, particularly as it seems to be starting to come clean about cross-subsidy. At least it’s facing public criticism as it puts its house in order. The other three of the Big Four, in the best traditions of the profession, have kept mum.

Increased audit risk is reflected in costs both within firms, i.e. what partners demand in risk-adjusted terms, as well as outside firms, e.g. insurance costs, supplier terms, cost of staff. As the perception of audit risk has risen, audit prices should rise. Financial Director [January 2003] has already recorded a steep 10% year-on-year increase in audit fees, but expects much more as its sixth annual survey of FTSE-100 audit fees was only starting to pick up post-Enron concerns about loss of consultancy income. Risk, and the perception of risk, is rising at the same time as firms are having more problems cross-selling services, due to a combination of regulatory disapproval and client unwillingness to be seen to be buying advisory services combined with audit. Without cross-sales and the implicit subsidy, audit fees need to rise even more.

You Saw the Whole of the Moon

We wondered how much audit fees might need to rise in order to cover the loss of subsidy. We were particularly curious because we realise that many of the recent price rises are being made in an unstable market. The market is unsure how much the “Enron” effect may adjust risk. The market is unsure how much non-audit business audit firms may be allowed to retain for larger listed companies. It might be interesting for finance directors to have an idea of how much further prices might rise. The answer, as shall be seen later, is significant.

In order to answer the question of “how high prices might rise”, we needed to build a statistical model of audit and non-audit fees among all UK firms. Our data came from BvD’s FAME database of 1.4 million UK companies. The data includes hundreds of data points for each firm, e.g. turnover, audit fees, balance sheet, employees, SIC codes, etc. We loaded the FAME data for the last three years into Z/Yen’s PropheZy risk/reward engine, a software tool developed by our Auguri research team. PropheZy takes databases and builds predictive models. PropheZy uses advanced statistical techniques, including a support vector machine, an optimiser and a set of decision tree tools to produce an easily interrogated “what-if?” program. We tested PropheZy’s models by asking it to provide a “Price-Your-Audit!” service. PropheZy scored very well in predicting audit prices, meeting or exceeding most tests of statistical accuracy across 200,000 companies.

We also built a “Recommend-an-Auditor?” model that seemed to identify the correct auditor for industries which concentrate on a few audit firms, e.g. specialist insurance. Likewise, Recommend-an-Auditor? seemed to “know” which industries preferred to “spread” audits around, presumably to avoid conflicts of interest, sensibly indicating that several would be adequate. Both Predict-Your-Audit! and Recommend-an-Auditor? ought to be useful tools for any audit committee. PropheZy has a number of other applications in finance, ranging from predicting restatements to replacing Z-scores, forensic assignments, finding new clients or identifying anomalous audit conclusions.

Augur, Augur on the Wall

Satisfied with PropheZy’s ability to predict, we then examined the largest 100 companies in the UK by turnover. Seven of the 100 do not currently purchase non-audit services from their auditors. We then asked PropheZy to predict what audit fees would be in two years if non-audit fees were reduced to nil for the other 93. PropheZy referenced its statistical model, taking into account the correlations it had built using 200,000 UK companies. The results are shown in the table below:

Top 100 UK Firms Current Audits Predicted Audits
Total turnover £801,000,000,000 £801,000,000,000
Total audit fees £197,000,000 £311,800,000
Audit fees/turnover 0.025% 0.039%
Total profits £19,727,000,000 £19,614,000,000
Audit fees/profit 1.00% 1.58%
Total non-audit fees £474,000,000 -
Non-audit fees/turnover 0.06% -
Employees 4,467,000 4,467,000
Audit fees/employee £45 £70
Audit fee range £40,000 to £17,000,000 £300,000 to £17,500,000
Audit fee median £1,394,000 £2,900,000
Audit fee mean £1,973,000 £3,118,000
Non-audit fee range £0 to £47,000,000 -

So, the Top 100 UK companies are looking at an estimated rise of £115,000,000 in audit fees. Profits will be hit by 0.58%, a not insignificant amount. Even at current P/E ratios, this would knock well over £1 billion off the market capitalisation of the Top 100. PropheZy can only predict when the data supports prediction, but recent rises in risk perception will be only weakly indicated in the data. If, as many pundits do, one believes these risk costs are rising, then PropheZy’s predictions are low.

It is clear that smaller companies are going to be hit harder, as evidenced in both the sharp rise from the lowest audit fee of £40,000 today to £300,000 in two years, as well as the sharp rise in the median audit fee from £1,394,000 to £2,900,000, a total of 108%. This is probably explained by the fact that the very largest audits, e.g. BP, Unilever, Tesco, are substantial projects priced in their own right, while for smaller companies auditors count on sell-on business. As one senior partner of a large firm remarked on seeing this data, “we’re still trying to break even on small audits”. As the smallest of the Top 100 companies has a turnover exceeding £3 billion, this bodes ill for mainstream companies whose turnover is measured in millions of pounds.

After decades of relative price reduction, perhaps as a subsidy to win other services, prices are rising. Audit committees are under huge pressure to play safe and be seen to be allowing their auditors to do a good job. Audit firms may think they have audit committees over a barrel. It would look as if finance directors and audit committees would benefit from a Price-Your-Audit! predictor as they prepare to negotiate for bigger stakes than they know. Surely, audit firms are already working on theirs.

[A version of this article originally appeared "The Auditor's Cross Subsidy" (statistical modelling of audit prices), Strategic Planning Society Newsletter (June 2003). Also published as "Anti-dumping Measures & Inflation Accounting: Calculating the Non-Audit Subsidy" (19 June 2003)]

More information:

Press release - Non-audit susbsidy

Results - “As Predicted By PropheZy” in Now & Z/Yen May 2004 issue.

Michael Mainelli, FCCA, originally did aerospace and computing research, before stooping to finance. Michael was a partner in a large international accountancy practice for seven years before a spell as Corporate Development Director of Europe’s largest R&D organisation, the UK’s Defence Evaluation and Research Agency, and becoming a director of Z/Yen (

Ian Harris, ACA, made an absurd decision in his youth, thus landing in accountancy rather than law. He spent a number of years writing humorous songs bemoaning his choice while advising his management consulting firm’s clients about mid-range and large-scale financial systems before co-founding Z/Yen with Michael (

Alan Helmore-Simpson leads Z/Yen’s Auguri Project and the development of PropheZy. Alan has a deep mathematical and information technology background ranging from investment banking through interactive television, defence and cryptography.

Z/Yen Limited is a risk/reward management firm working to improve business performance through better decisions. Z/Yen undertakes strategy, finance, systems, marketing and organisational projects in a wide variety of fields (, such as recent projects managing development of a client profitability system or the benchmarking of transaction costs across 25 European investment banks. Michael and Ian’s humorous risk/reward management novel, “Clean Business Cuisine: Now and Z/Yen”, was published in 2000; it was a Sunday Times Book of the Week and even Accountancy Age described it as “surprisingly funny considering it is written by a couple of accountants”.