$2.$ There has been only one round of financing for KATATO $($a Series A investment of $$10$ million in convertible participating preferred at a $$15$ million pre$$money valuation$).$ If converted, the Series A investors would own $40\%$ of the company $($$$10$M$/($$$10$M $+$ $$15$M$))$ and the entrepreneur would own $60\%.$ The company has an offer to be acquired for $$70$M$.$ The Series A preferred shares have a liquidation preference of $1$X and participate with a $3$X cap. $(3$ points$)$

$(1)$ Under thecapped liquidation preference how much money would the Series A investor receive?

$(2)$ By converting to common stock, how much would the investor receive?

$(3)$ So$,$ is it better to convert or take the liquidation preference?