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Well, yes, that's the nub of the scheme.
You're not buying the bike. The company is buying a bike and then letting you borrow it for free. At some point you should want to buy the bike off the company, and so the fair price for this is based on asset depreciation (according to rules set out by HMRC).
But to begin with, since companies don't just buy bikes for people to use like this they need to have the money to buy the bike upfront and so they get the employee to agree to being paid less for a year to cover the cost of the bike that they will be borrowing. This works out cheaper for the employee than waiting to get the money (after tax) and buying the bike themselves. The company does end up paying for the whole bike up front and only slowly recouping that money over the space of a year, but it's a small price to pay for healthier and happier employees. The company also saves employer NIC contributions that would have been due on this extra pay, so it (the company) does save something extra too.
Leaving the scheme before the end of the first year could be bad, I'll have a go at working out the numbers in a sec.
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Companies can, may and do buy bicycles for employees to use - Much in the same way that they buy cars for employees to use.
As you say, though, many companies don't see the benefit of buying bikes for employees (and actively avoid it, banging on erroneously about Healthy & Safety and inferred liability) and choose to take advantage of the changes to PAYE and NI that the scheme permits - namely financing through salary sacrifice.
Leaving the scheme in the fist year would be a contractual issue on a hire purchase agreement - You could walk away with nothing, and pay nothing.
In theory, the company can rent the bike to you at any rate it sees fit - not just after the first year of ownership, but from the initial purchase point too.
In practice, this probably doesn't happen - definitely not if one of the scheme administrators is involved, and unlikely if the sachem is administered directly, unless the company is very generous.