From the Value Line report, KS corp.$$s beta is $0\mathrm{.}80.$ The risk$-$free rate on Treasury bonds at the end of $2021$ was about $3\%.$ Suppose that the expected market return was forecast at $10\%,$ roughly in line with its historical average. The KS corp.$$s earnings in $2021,2022$ and $2023$ were $$18,$ $$21,$ and $$24$ per share respectively, and pays out $30\%$ of its earnings in dividends at each year. The dividends were just paid and are expected to be paid annually. Value Line forecasts a steady$-$state growth from a dividend payout $40\%$ and an ROE of $12\%$ after $2023.$

$($a$)$ What is the forecast price at which we can sell the shares at the end of $2023,$ when dividends are assumed to enter their constant$-$growth phase?

$($b$)$ If the expected earnings in $2024$ is $$32$ per share. What is the PVGO $($present value of growth opportunity$)$ of the price in $2023?$ Verify whether this firm would be a takeover target for another firm or not.

$($c$)$ What is the intrinsic value of KS corp. at the end of $2020?$