You're probably familiar with the old expression, "there's more than one way to skin a cat". Like you, I'm pretty sure I don't want to know about any one of them. But it does illustrate a good point when it comes to estimating a painting project or any other trade estimates for that matter.
Regardless of the aspect of rebuilding you are planning, whether it be painting, carpentry, drywall, or whatever, there are as many options as there are ways to get the job done. You can also look for residential painting services online.
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However, the appraiser's bid usually takes into account only the scope of work, the method of execution, and the grade of material quality. Then, of course, if you simply choose the lower bidder, you'll know you'll likely miss out on the higher quality offerings and better materials and an overall better experience!
My experience is in painting so I'll be using artists and painters as guides here. However, you can apply this to most of the other transactions of potential users and contractors. And no matter what your trade is, if you're good at what you do and take your customers very seriously, you might not get the all-time lowest price.
But if you are like my painting company, strive to provide the best value for money to home owners and commercial clients. Unfortunately, artists are often only selected for a price based on the number of jobs assigned by the client (generally a "list") because people don't want to hire artists every day and rarely get to know each other.