(a) If any taxable resident shall fail to file a return, or fail to include in any return all of his property made taxable by this act, or shall file a return which is false, incomplete, incorrect or inaccurate, the board shall make an assessment of tax against such resident of the amount of the tax for which such resident is liable, or for which he is believed by the board to be liable, to which estimated return the board shall add twelve per cent (12%), and the aggregate amount so obtained shall be the basis for taxation.

(b) The board shall notify, by mail, such resident of the estimated assessment. If such resident is dissatisfied with the assessment so made, he may, on or before the day fixed for appeals from assessments, present reasons, supported by oath or affirmation, for his failure to file a return, to include all of his taxable property therein, or for having made a return which was incomplete, incorrect or inaccurate, and the board may, if satisfied with the excuse so presented, permit the taxpayer to file his own return and substitute said return for the estimated return made by the board. In all cases where a false return has been filed by the taxpayer, the board may not relieve the taxpayer from the payment of the twelve per cent (12%) penalty, but the estimated return shall be final, except in those cases in which a true and correct return shall reveal a higher assessed value than that contained in the estimated return, in which case the tax and penalty shall be based upon the true valuation.