Current square footage construction costs for 1 & 2 Family Dwelling (R-3) of wood frame construction (VB) as $94.06 per square foot heated space. 

For example:
New Residential dwelling of 2000 sq ft
$94.06 X 2000 sq ft = $188,120.00 calculated valuation
Using the Valuation of $188,120.00, got to the Building Permit Fees Chart

To calculate the estimated cost of the permit:
Round up to the next Thousand: $189,000.00
$460.00 for the fist $100,000
267.00 For the remaining $89,000 at $3.00 for each additional thousand.
$727.00 Permit Fee + 4.00 Permit box = 731.00 Total