In an option A contract, how can the Employer know that he can afford the cost of any additional works to be undertaken by the Contractor?
The clause that covers this is clause 61.2 for proposed instructions (which is now 65.1 under NEC4). If as the Employer you might want them to do something additional but you want to know what the cost/time impact would be first, you can instruct them to provide a quotation for a proposed instruction under 61.2. They then submit the quote, and you can then decide whether to go ahead with it or not. In the meantime they do NOT proceed with that work until they are instructed to proceed.
Other compensation events you simply will not always know the impact before they do the work. If for example the Contractor hits rock which is an unforeseen ground condition, this will be a compensation event to them and they will provide a quotation whilst still proceeding with getting through the rock (which they can do but just at a slower pace). You will not know the cost of that one before they start the work (unless you have instructed them to stop) and the affordability or not does not really come into it as the rock HAS to be moved to carry out the works. If the Employer can not afford the resultant cost, they would either have to apply for extra internal funding themselves or somehow look to de-scope the works to be able to pay for the additional unplanned work. To stop work whilst we agree the cost would probably cost more as that may lead to additional prelim type costs whilst they will still have to remove the rock.