Valuation Models $(25$ marks$)$ At year$-$end $2023,$ the City of London expected BAE$$s plc$$s dividends would grow at $6\%$ for $3$ years, after which growth would fall to a long$-$term rate of $3\%.$ Analysts also projected a required rate of return of $7\%$ for the UK equity market, a UK T$-$Bill rate of $2\mathrm{.}0\%,$ and that BAE$$s beta was $0\mathrm{.}90.$ The following financial data for BAE and the FTSE$100$ index are given: BAE plc Selected Financial Data Year Ending December $31,2023$ Earnings per share $0\mathrm{.}80$ Dividends per share $0\mathrm{.}24$ Other Data on BP Common shares outstanding $($M$)9000$ Closing share price $15\mathrm{.}00$ FTSE $100$ Index Closing value $($price$)7500$ P$/$E ratio $($average$)17\mathrm{.}90($a$)$ As an equity analyst, suppose that you decide to use the following two$-$stage dividend growth model: Explain the logic behind the above equation to calculate BAE$$s share price. Using the data in the table and the above formula calculate the implied fair price of BAE shares using the dividend growth model. $(10$ marks$)($b$)$ Explain the advantages of using a two$-$stage dividend discount model $($DDM$)$ to value a share rather than a constant$-$growth dividend model. Using a simple numerical example, describe one weakness in all DDMs$.(5$ marks$)($c$)$ Define the price$-$earnings $($P$/$E$)$ ratio. Using the data in the table above, calculate BAE$$s historic price$-$earnings ratio and the price$-$earnings ratio relative to the FTSE $100$ index as of December $31,2023.$