In all cases where a paving or any other street improvement is constructed under agreement with the property owners whereby the cost and expense of such street improvements is paid without special assessment against the property, there shall be added to the contractor's bid therefor five percent for the purpose of paying engineering, supervision, and other incidental expenses, which five percent shall be retained by the city instead of the ten percent as provided by Iowa Code, Sections 417.18, 417.19, and 391.44 as amended.