Based on an analyst report, technology company X has $35\%$ dividend payout ratio, $$3$ current earnings per share, which in recent years have been growing steadily at $5\%$ annually, while the risk$-$adjusted cost of capital is $12\%.$ Company X has discovered a new product, which is expected to increase the company's growth rate to $8\%$ for the foreseeable future.

Calculate the PE per share of company X before company X$\text{'}$s public announcement of the discovery of the new technological product.