In any county in which there are situated any lands assessed for special drain taxes, or any townships, cities or villages assessed at large for the construction of county or inter-county drains, and where bonds have been issued on behalf of the drainage district in anticipation of the collection of such drain taxes, under Act No. 316 of the Public Acts of 1923, as amended, being section 4838 to 4979, inclusive, of the Compiled Laws of 1929, the board of supervisors may extend the time of payment of such drain taxes in the manner and on the conditions hereinafter set forth.