Where did the number came from?
The £240.7 million figures most likely came from financial data of Blackbeard Productions LTD, a UK based production company which has been setup for the.
As mentioned on the Forbes article. "The expenses ... are consolidated in a single company .... It makes it easier to work out a movie’s entitlement under the tax credit scheme and it gives great insight into its finances".
Below is the breakdown of those cost, based on multiple reports from 2009 up to 2013. Note that those report doesn't provide detailed breakdown:
Oct 2009 - Sept 2010 111.554.389
Sept 2010 - Nov 2010 61.058.570
Nov 2010 - June 2011 39.695.862
June 2011 - April 2012 22.110.207
April 2012 - April 2013 6.202.109
Numbers are taken from Cost of Sales.
All unit in GBP (£) and unadjusted for inflation.
On Stranger Tides was released May 2011. Calculating nearest periods (Oct 2009 - June 2011) give us total of
212.308.821 GBP spent up to/ near release date and
28.312.316 GBP spent post-release.
I didn't bother to look up and verify the amount of tax rebate. But assuming Blackbeard claim maximum rebate (20%, as mentioned in the same article), we can easily calculate their total production costs that eligible for rebate:
94 million GBP/ 170.5 million USD. Given the big difference between those approximation and reported budget, I assume some major spending (actor's contract, for example) was not considered tax-rebatable.
From those figures, we can start to see budget report discrepancy between Blackbeard's reports and the press. Citing two articles referenced by Wikipedia page:
LA Times article dated May 03, 2010 reported:
Although it's still large — north of $200 million — it is at least a third less than the last "Pirates" movie
While Variety article dated May. 19, 2011 reported:
Budgeted at a reported $150 million, considerably less than its previous installments
Presumably the difference was due to different data source available at the time.
Where did the number goes to?
- Johnny Depp received around 33 million GBP.
- Production staff received around 10.4 million GBP (from the Forbes article).
There's no number provided for the remaining cast. Some factors to consider: Dead Man's Chest and At World's End was offered as single contract. And by the time they want to start the 4th, Pirates was already an established franchise.
Filming and Post-production
On Stranger Tides was filmed in 3D rather than using post-production conversion (except for one sequence). This increase filming cost considerably, while also complicate the shooting process. Especially in outdoor or underwater scene.
"We really felt like pioneers," he says. "We were taking 3D equipment into these remote locations where you have the possibility of one of two cameras breaking" -- which they did, several times.
- The Making of 'Pirates of the Caribbean'
Preparing and moving logistics across multiple premise also increase spending. While primary production was done in England, some had to be done in US (Hawaii, California, and Puerto Rico). This includes transforming The Black Pearl into Queen Anne's Revenge, and shooting Whitecap Bay scenes in Universal Studios. Compare this to the cost of Dead Men Tell No Tales, where filming was done in relatively close proximity, or it's two predecessor, where filming was done back-to-back.
Additionally, shortening schedule does not always translate to cheaper cost, especially in VFX and post-production phase.
Marketing and distribution
Compared to the original trilogy, On Stranger Tides was promoted more extensively. This including multiple tie-ins (lego, clothing, jewelry, etc) and Superbowl ad.
Looking up at IMDb specification page, On Stranger Tides was the most diverse movie in the series in terms of distribution media. It provide 35 mm, 70 mm, and D-Cinema format. Available both in 2-D and 3-D. This was arguably worthwhile investment, compared to another film in the Pirate franchise, On Stranger Tides is the highest-grossing outside US and second highest worldwide. Despite being the worst performer domestically (until the release of 5th movie).
As mentioned in John Smith's answer, it's rather unclear how Forbes (or Hollywood) categorise production budget. Given the limited data availability, we might never know for sure how much money Blackbeard spent.