(a) If in the construction of the fence of a fencing district any owner of land in the district shall be found to have built a fence which may be profitably made a part of the general fence for the district, being as good as that required by the system determined upon by the fencing board, the board shall appraise the value of the fence made by the owner and shall allow its value as a set-off against the assessment against his land.
(b)
(1) In case the fence made by the owner shall be found to fail to meet the required standard, the board may allow the owner the value of the materials of it, insofar as they may be profitably used in perfecting the fence of the district, as a set-off against the assessment against his land.
(2) In such a case, the board shall issue to the owner a certificate showing the amount of the set-off allowed, which certificate shall be received by the collector for the amount named in it in lieu of money charged against the holder's land.