Voldemort Partners negotiated a deal with Malfoy Industries to purchase securities $($A Round$)$ whose terms included Full Ratchet Anti$-$Dilution. When the time came for the B round, Malfoy Ind. was not doing particularly well, and the value of the firm was clearly not keeping up with the projected growth.

While the A Round, at a time of optimism, was done by selling $400$k shares for $40\%$ of the company at a Pre$-$money valuation of $$6$ million, the B round was done at a Pre$-$money valuation of only $$2$ million, taking in $$2$ million in invested capital.

What is the New Conversion Ratio for the A Round investors?

$($Please put it in the format of $1$:x where $1$ is one Preferred Share, and x is the number of shares into which it converts; x is to be a single digit, so round if needed$)$

The correct answer is $1$:$5.$ provide step$-$by$-$step solution to arrive to the answer $1$:$5.$