Estimating repairs & deductions from a tenancy deposit

A tenant has caused damage in excess of fair wear and tear and items need to be replaced. Damage in excess of fair wear and tear is the responsibility of the tenant. However, the tenant has indicated they me to arrange the work and deduct the costs from the deposit (the tenant is moving out).

Do I need to consider 'betterment' in terms of the costs of replacing the damaged item i.e. the damaged item that needs replacing was several years old and I would be replacing it with a new item (i.e. not like for like). Is it ok to charge the tenant the full price for the new item or do I have to reduce and charge for the price of the item, for example:

Cost to replace with new item = £800
Cost to replace with 2nd hand item (2 years old - same type and age of damaged item) = £400

Amount charged to tenant:

1. £800 for new item

or,

2. £800-£400 = £400 (if an adjustment is made for 'betterment')

Please reply if this is not clear.

Kind regards,

Kerry