One glance around the gift shop at Edinburgh zoo is proof enough of the economic weight of panda power; recently expanded to near double its shelf space, the open area cum ticket hall is dominated by panda memorabilia.

There are shelves and baskets crammed to bursting with plush panda cuddly bears, some in kilts, others without; panda sweeties; panda caps and hats; “panda tartan” bags and silk voile scarves. There are even fate-tempting panda bears with cubs attached. You can spend £2.50 on a wooden panda keyring or £175 on a “Jura” panda tartan shoulder bag.

The hefty merchandising push by the Royal Zoological Society of Scotland to maximise the charisma and appeal of Tian Tian and her erstwhile mate Yang Guang – backed up by the hard-nosed decision to seek a wide-ranging copyright to ban anyone else using their Anglicized names of Sunshine and Sweetie – appeared fully justified by its far healthier finances last year.

But will the expected cub (or two) likely to be born to Tian Tian in the next week lead to another great surge in income and profits for the RZSS? An expert report on the economic value of Edinburgh’s pandas again being cited in the media (thanks to the new surge in panda cub hype) suggests not.

In fact, the Scottish Enterprise-funded study believes a new cub might not be as valuable as one might suppose or as valuable as the zoo itself believes.

In May, the zoo confirmed that its receipts and profits had been sharply boosted last year when visitor numbers rose by 51% to 810,000, thanks largely to Sunshine and Sweetie, with the RZSS’s income jumping by more than £5m to nearly £15m.

That extra income was crucial to the RZSS, which had in the previous year suffered a £1.2m deficit and been forced to seek hefty bank loans to bolster its books, amid other senior management disputes during 2010 and 2011.

Its chief executive, Chris West, predicted then that a cub would again boost its income and ticket sales by the same amount, therefore pushing its visitor numbers to about 1.2m for the first time – doubling its pre-panda figures.

That would briefly bring Edinburgh zoo within touching distance of matching Edinburgh castle’s record-topping annual visits of 1.2m last year (the castle had 1.3m visitor in 2011).

But that prediction is challenged by the report by the Bellshill-based Frontline consultancy for Scottish Enterprise. It did produce a startling headline figure about the potential, best-case scenario for the city’s economy.

It suggests that, assuming there was really intense worldwide promotion of the new panda family by all Edinburgh’s tourism bodies, public agencies and conference companies, including heavily-marketed “panda days” and commercial sponsorship deals, the city could earn an extra £27.6m from a single panda cub.

But Frontline also analysed the impact of panda cubs arriving in other Western zoos on the zoos themselves, and discovered that visitor figures to the zoo itself actually fell from their first year peak, when the adult pandas first arrived. And that was a consistent picture.

Melbourne zoo, the only one in the southern hemisphere with a panda cub, suffered a financial crisis after its birth. So the RZSS would not itself grow any richer. It seems counter-intuitive.

Frontline analysed three scenarios about how heavily the pandas and a theoretical cub might be promoted: “minimum impact”, “limited impact” and “panda premium”, for both pandas with and without a cub. Surprisingly, it predicts that even where a cub arrives, in the top two scenarios visitor numbers fall by at least 130,000 from the record-breaking heights a zoo enjoys in the first year of the adult pandas being on show.

In the “premium” scenario, the one which could earn Edinburgh an extra £27.6 in income and assumes a cub was born and went on show in 2013, visitor figures would fall from their 963,000 peak in 2012 (the first year that cub-less Tian Tian and Yang Guang went on show) to 825,000 in 2013 and again to 756,000 in 2014.

Only in the most pessimistic “minimum impact” scenario, one where the zoo and the city authorities do the very least to promote the pandas, does a cub boost visitor numbers – but only just over the first year record level. Under that set-up, they go from a 784,300 peak down to 620,600 but then briefly jump up again the next year (when the pandas are on show for a full year) to 794,600.

Fielding questions on behalf of Frontline, a spokeswoman for Scottish Enterprise told the Guardian:

In all cases the initial arrival of the pandas led to a massive surge in interest, effectively shifting the zoos from being ones of regional or national importance to ones of global significance (note that pandas can only be found in 16 places in the world outside of China, and Edinburgh Zoo is one of them).

Following this initial surge in interest the number of visitors has, in all cases, started to dip down again, while staying above the levels they were at prior to the arrival of the pandas. While the arrival of a cub undoubtedly has a very big impact on the zoos in terms of extra visitor numbers, it is generally not large enough to bring them back up to the big year one visitor figure.

Frontline added:

In every scenario we modelled, we have assumed a massive jump in visitor numbers in the year following the arrival of the first panda, followed by a gradual decline back to the original pre-panda numbers over the following ten years (this is the experience of all of the other panda zoos that we looked at).

In all cases, the arrival of the panda cub helps to keep the visitor number up close to the year one peak, but is never quite enough to take them above that peak.

Yet a cub will have longer-lasting economic value: even after it two year stint at Edinburgh ends (cubs are sent “home” to China aged two, to mirror their behaviour in the wild when they leave their mothers), the cub-effect lasts.

And there is always the chance Tian Tian will have more during her 10 years in Scotland, so Frontline estimates visitor numbers will remain healthily high at as much as 733,000 a year:

There are two reasons for this.

The first is that, in many of the cases we looked at, the panda couple went on to successfully produce further cubs over the course of the ten year period, leading to other regular bursts in visitor numbers over the course of the ten year period (we have smoothed out some of these impacts, rather than trying to second guess when every birth would be).

The second is that, even after the cubs leave, the marketing impact that it will have given the zoos will to an extent still be there. For example the famous ‘cub sneezing’ clip on YouTube is still receiving large numbers of hits, and generating publicity for National Zoo Washington, even though the cub is no longer physically there.

So the numbers suggest panda power is still significant, and would be enough to justify Edinburgh’s hefty institutional and reputational investment.

But there is a sting. Intriguingly, the report, finished in early 2012 but released in June last year, over-estimated Edinburgh zoo’s first year visitor figures by about 130,000, another hint that the public appetite for pandas is lower than might be expected.

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