The issue of further shares has nothing to do with the valuation of the Company. It may be at par, at premium or at discount, as per the descretion of the Board. Hence, its a foolproof "no fraud" allotment.
Secondly, Section 81 is not applicable to pvt. company. You need to check the provisions of the Articles of the Company.
In case, it adhers to Section 81 (or any other such clause), then the shares must be offered to A too.
In case no, then, it is solely at the discretion of the Board whom to allot shares, as it is a private company.