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Do you have a source?

> It is expected that Capita will earn £1.10bn – £1.55bn from its contract with the BBC if it runs its maximum 15 years from July 2012

The BBC gets over £4b per year.

> Thus, the licence fee made up the bulk (77.5%) of the BBC's total income of £4.827 billion in 2015–2016.[2][3]

I make that as Capita taking 2.5% gross revenue. Who know how much that costs them to administer over 15 years either.

The licensing website puts it at 5.5%. Either way, 40% is a silly number to throw around.

Doesn't that mean they'll earn 1.10 - 1.55bn over the 15 years? Not every year?

Yes, which is why I was asking for a source. I can't find anything which puts the figure any where near 40%.