YUMY restaurants reported dramatic growth in earnings and revenues between $2014$ and $2023.$ During this period, earnings grew from $$0\mathrm{.}08$ per share in $2014$ to $$0\mathrm{.}78$ per share in $2023.$ The dividends paid in $2023$ amounted to only $$0\mathrm{.}02$ per share. The earnings growth rate was expected to ease to $15\%$ a year from $2024$ to $2028,$ and to $6\%$ a year after that. The payout ratio was expected to increase to $10\%$ from $2024$ to $2028,$ and to $50\%$ after that. The beta of the stock was $1\mathrm{.}55,$ but it was expected to decline to $1\mathrm{.}25$ for the $20242028$ time period and to $1\mathrm{.}10$ after that. $($The Treasury bond rate was $6\mathrm{.}5\%,$ and the Equity risk premium is $5\%.)$

a$.$ Estimate the PE ratio.

b$.$ Estimate how much higher the PE ratio would have been if it had been able to maintain the growth rate in earnings that it had posted between $2014$ and $2023.$

c$.$ Now assume that disappointing earnings reports in the near future lower the expected growth rate between $2024$ and $2028$ to $10\%.$ Estimate the PE ratio.