Running a sensitivity analysis on event ROI before you present one number

A show director tells the board the event ran at 51 per cent margin. Three weeks later group finance publishes a portfolio pack with the same show at 37 per cent. Nobody changed the ledger, nobody made an error, and both numbers came out of the same trial balance.

That gap is the reason to run a sensitivity analysis on event ROI before anyone sees a single figure. The ledger is not in dispute. What is in dispute is the handful of decisions sitting on top of it, each of which has two defensible answers, and each of which moves the result by several points.

The three inputs that carry the judgement

Most of an event P and L is arithmetic on invoices. Space sold, venue hire, build, freight, catering, the sales commission actually paid. Nobody argues about those and a sensitivity analysis over them is wasted effort.

Three inputs are different, because no invoice settles them.

Overhead allocation. Somebody picks a rate at which central cost is charged to a show, and the rate is a policy. In portfolios I have seen it argued at anything from the high single digits to the mid teens as a share of show revenue, and the argument is genuine on both sides.

Sponsorship valuation. Group sells a package across four shows and pushes a share down to each. At rate card, or at the realised rate after the portfolio discount? The two answers differ by a fifth or more on the sponsorship line.

Barter treatment. You gave a trade publisher exhibition space and took advertising back. The transaction never touched cash and it has to be valued.

What is wrong with moving one assumption at a time?

The instinct is to hold everything at base, move the overhead rate, write down the answer, put it back, move sponsorship, write that down. It feels thorough and it systematically understates how much the answer can move.

Saltelli and Annoni set out the reason in Environmental Modelling and Software in 2010, in a section headed with the claim that one-factor-at-a-time analysis cannot work. Their argument is geometric. Every point a one-at-a-time design visits lies inside the hypersphere inscribed in the cube of possible input combinations, and that sphere shrinks fast as inputs are added. With two uncertain inputs it covers about 0.78 of the space, with three about 0.52, and by twelve inputs the fraction reaches 0.000326, less than a thousandth. The corners, where several inputs are at their extremes at once, are never sampled.

Event ROI has a specific reason to care. Overhead is usually charged as a percentage of revenue, so any input that changes recognised revenue also changes the overhead charge. That is an interaction, and one-at-a-time is blind to it by construction.

Working all eight corners on one show

Take a show with 6.1 million of exhibit space revenue, 0.6 million of delegate income, sponsorship of either 1.70 million at rate card or 1.57 million at realised rate, and a media barter deal worth 0.31 million that is either recognised at fair value on both sides or netted out to nothing. Direct show cost is 4.1 million, plus the 0.31 million of advertising received if the barter is recognised. Overhead is charged at somewhere between 8 and 14 per cent of revenue.

Three inputs, two settings each, eight combinations.

Follow one row so the rest are checkable. Sponsorship at rate card and barter recognised gives revenue of 6.1 plus 1.70 plus 0.6 plus 0.31, which is 8.71 million. Direct cost is 4.1 plus 0.31, or 4.41 million, so contribution is 4.30 million. Overhead at 8 per cent of 8.71 is 0.6968 million. Net is 3.6032 million, and 3.6032 over 8.71 is 41.4 per cent.

The band runs from 34.6 to 43.2 per cent, a width of 8.6 points. Every row is defensible and none involves a mistake.

Now run the one-at-a-time version from a midpoint of 11 per cent overhead, sponsorship at rate card and barter recognised, which gives 38.4 per cent. Moving the overhead rate alone reaches 35.4 and 41.4. Moving sponsorship alone reaches 37.6. Moving barter alone reaches 40.2. The widest span any single move produces is 6.0 points, against a true width of 8.6. One-at-a-time hides 30 per cent of the range, and it hides it at the bottom, which is the end the board cares about.

How wide should each band be?

The bands do the real work here and they invite two failures. Set them too narrow and the analysis tells you the answer is precise when it is not. Set them at plus or minus fifty per cent because it looks rigorous and the output is a range so wide nobody uses it.

The rule I would apply is that a bound has to have a name attached. For overhead allocation, the low bound is the lowest rate actually charged to any show in the portfolio this year and the high bound is the highest, both pulled from the group's own allocations. For sponsorship, the two bounds are the two valuation methods that group commercial and show finance each already use. For barter, full recognition and full netting, because both are in live use across the industry.

If nobody can name the source of a bound, drop the input from the analysis and hold it at base. An input in the grid with an invented band contributes an invented range.

Barter is the input with a rule attached

Of the three, barter is the one where an outside standard narrows the argument. A staff paper prepared for the IASB in March 2015 on non-cash consideration states that paragraph 66 of IFRS 15 requires non-cash consideration to be measured at fair value. It records in a footnote that where an entity cannot reasonably estimate that fair value, paragraph 67 directs it to measure the consideration indirectly by reference to the stand-alone selling price of what it promised the customer in exchange.

Read against a media contra deal, that says the space you gave the publisher is revenue at fair value and the advertising you received is a marketing cost. Netting both to zero is the treatment that needs defending.

The effect on the arithmetic above is worth noticing, because it is counterintuitive. Recognising the barter adds 0.31 million to revenue and 0.31 million to cost, so contribution in currency does not move at all. The margin percentage falls, because the denominator grew, and the overhead charge rises, because overhead is a share of revenue. A decision with no cash consequence moves the reported margin by about 1.8 points at the 8 per cent overhead rate.

What goes on the slide

One number and one band. The point estimate from the assumption set your finance function has signed off, then the range, then a single line naming which input contributed most of the width.

In the example that line is easy to write. Overhead allocation moves the answer by 6.0 points on its own, sponsorship valuation by 0.8 and barter by 1.8. Two thirds of the uncertainty sits in one policy choice that the show team does not control, which is a more useful thing for a board to hear than a fourth decimal place on the point estimate. The full construction of the point estimate itself, contribution over direct show cost with the boundary written on the front, is the event ROI calculation in D17 and this analysis takes it as given.

How to word the range so a board reads it as discipline is a separate problem, and it belongs with stating uncertainty in show reporting in D40. The short version is that the band goes next to the number, in the same sentence, in the same size type.

Where this stops

A sensitivity analysis measures how much your answer depends on your assumptions. It says nothing about whether the assumptions are right.

If your overhead allocation rule is wrong in the same direction for every show in the portfolio, varying the rate from 8 to 14 per cent produces a confident band around a wrong centre. The same applies to any input where both bounds share a defect, and shared defects are common, because the two candidate treatments usually come from the same finance team reading the same policy.

There is a second limit that catches teams out. The grid holds inputs where you can name two positions. It does not hold the inputs where the disagreement is about what belongs in the show at all, such as whether a hosted buyer programme is a cost of the show or a cost of audience acquisition, which the same attendee analytics reporting has to answer before the P and L is drawn. Those are boundary questions and the grid will silently exclude them. So will the analysis for a feature area inside the show, where the harder problem is double counted revenue rather than assumption width, and that sits with the ROI of a show feature area in D20.

Start with two rows, not eight. Take last edition's closed P and L, recalculate the margin at the highest overhead rate charged to any show in your portfolio and at the lowest, and put those two percentages side by side in an email to whoever owns the allocation policy. If the gap is under a point, you can stop. If it is six, you have found the number your reporting has been treating as settled.