I strongly agree with najaB in the need for you to assess the Company's losses acurately, and to demonstrate your reasoning for calculating the losses in the way that you do.
But I'm not persuaded that by simply adding £100 as a contribution to their costs makes an adequate settlement. I would suggest at least twice that for costs (to include a reasonable proportion of the costs of providing Revenue Protection personnel across the network who detect, deter and report irregularities, and in the course of those duties may work for hours without detecting any irregularity [might!] at all). An offer based on all of the above would simply return both the Company, and you, to the correct position you'd both have been in if all your fares had been paid correctly at the time of travel.
I would suggest that you also add a modest contribution as a voluntary 'penalty' to reflect your recognition that you have acted fraudulently and that you wish to accept some disadvantage for your wrongdoing, and that you are appreciative of the Company's offer to make a settlement which avoids the inevitable Criminal fine, the inevitable Company's legal costs against you, the inevitable Victim Surcharge, and possibly legal costs of your own, and which avoids all your time, expense, inconvenience and anxiety of responding to a Criminal Prosecution in the Magistrates Court.
I will leave you to choose that figure, but there has to be an element in your calculation which takes you beyond simply repaying whatever you hadn't paid when you travelled. Three digits.
Decline the offer, and those 'savings' from an Out of Court Settlement are likely to cost you £400 - £1k. That's in addition to the fares avoided and costs of investigating.
Accept the offer, and save costs (and the Fine, which goes to the state), so maybe 25% of that range.
