You have many answers to this question and many different opinions. Some provide incorrect information in my opinion. Unless the scope of work is changed the appraiser is hired to provide an estimate of market value. This estimate will be the same regardless of if the client is a bank, mortgage broker, private owner, REO company, etc. Appraisers use three approaches to value- Sales comparison (also known as market approach), cost approach, and income approach. In general, for single family homes the income approach is not utilized. This leaves the cost and sales comparison approaches. The cost approach works up a value estimate based on national cost guides that use local adjusters to determine an estimated cost to build the home. The appraiser then depreciates the structure and adds in the value of the land. For newer homes the cost approach is a reliable indicator of value. For older homes the cost approach is not a reliable indicator due to the inaccuracies involved in estimating accrued depreciation. Generally you will see the cost approach used on newer homes or if the client request it be used.
Keep in mind there is the common misconception that cost equals value. This is not the case and I think this is the basis of your question. I have appraised new homes that have spent over $100,000 on site work for a variety of reasons (Soil condition, etc). Well this is clearly a cost to the owner however it didn't add anywhere near $100,000 in value to the home. I have a home right now that the owner claims cost $400,000 to build. However, he built the home on the corner of a busy road. Due to the external obsolescence created by the traffic noise the market value of the home is significantly less then the reported cost.
To answer your question, most of the time cost and market value are the same. However, sometimes they aren't. The cost approach serves a good check of the estimated market value. If a home buyer can build a new home cheaper they will choose building over buying an existing home.
Hope this helps!