In $2006$ and $2007,$ Kenneth Cole Productions $($KCP$)$ paid annual dividends of $$$$0\mathrm{.}76.$ In $2008,$ KCP paid an annual dividend of $$$$0\mathrm{.}35,$ and then paid no further dividends through $2012.$ Suppose KCP was acquired at the end of $2012$ for $ $15\mathrm{.}01$ per share.

a$.$ What would an investor with perfect foresight of the above been willing to pay for KCP at the start of $2006?($Note$$: Because an investor with perfect foresight bears no$$ risk, use a$$ risk$-$free equity cost of capital of $4\mathrm{.}7\%.)$

b$.$ Does your answer to $($a$)$ imply that the market for KCP stock was inefficient in $2006?$