Do you charge if the customer rejects the repair cost?

Hi all

If you run a repair business do you charge anything if the customer rejects the cost of a repair?

Lets say something comes in with a fault. You diagnose the fault and find you need a part. However the customer does not want to carry out the repair due to the cost of the part.

For me I have still done work to find the fault, find the part and come back with options.

How would you feel if you put your laptop into a shop and they charged you a small amount to discover a motherboard needed replaced and they suggested that you do not go ahead as the cost of the motherboard and labour is the same as buying a new laptop.