Lots of good advice!
Cheapest or most expensive is not always best. Ask yourself, if you did this job according to the Customers desire for cheapest but they are expecting to get the "most expensive" outcome and the results are to meet your expectations (for you), would it be wise and would you be happy using "your" product?
As others have said, agree on a price or rate and if it is not fair for you (or the Customer, but this is his choice), walk away. Remember, you also will be first contact point for when there is a problem or a failure to meet the expectations "expected or demanded" by the Customer. If what you did can't meet those expectations what are you going to do? It's your reputation after all and you have to supply some sort of warranty.
Don't sell yourself short or doubt your abilities by trying to do a good job at an unrealistic price or with inferior parts - you have to eat too and breaking even or running at a loss doesn't work for very long.
One of my Niece's partners does 4x4 add-ons and upgrades, he is in high demand because of his workmanship and reputation and is not inexpensive but he often spends much of his time fixing up 4x4 add-on botch jobs done by the lowest bidder because they stuffed it up. The moral here is that cheapest generally ends up costing more than what was "saved". A new bonnet or fender because the stuffed up one is impractical or too expensive to fix (labour costs) and needs replacing to start and do the job again but properly.
Someone always has to be your first Customer so get it right first time then they can be a happy and supportive reference.
Another Aussie $0.02 :-)