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No, dealers generally can't change the GFV. It gets spat out of their system and is calculated at 'group level'.
The calculations are usually a mix of market depreciation rates and historical used sales from their own database.
The only real change you can usually make is to pay more than the minimum amount (to get you to the GFV) so that you have a higher level of equity in the car at the end of the term.
PCP agreements will give a 'guaranteed future value' at the start of the term (in the contract) which is the minimum value the dealer will 'buy back' the car from you.
That number is usually 80-90% of the actual used value after three years (so the dealer isn't in negative equity).
Example sums:
Car value: £50,000
Deposit: £5,000
GFV: £25,000
36 payments of: £555.55
Acutal value after three years: £29,000
Money left for new deposit: £4,000
Of course, if the actual value at the end of the term is £24,000 as the arse fell out of the market, then the dealer would just buy it back at £25,000 and you'd walk away.