From the Value Line report, FR corp.$$s beta is $0\mathrm{.}90.$ The risk$-$free rate on Treasury bonds at the end of $2020$ was about $5\%.$ Suppose that the expected market risk premium was forecast at $7\%,$ roughly in line with its historical average. The FR corp.$$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 plowback ratio of $60\%$ and an ROE of $10\%$ 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 $2025$ is $$20$ per share. What is the PVGO $($present value of growth opportunity$)$ of the price in $2024?$ Verify whether this firm would be a takeover target for another firm or not.

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