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$)17\mathrm{.}90$

b$)$The Prospective P$/$E ratio uses next year$$s $($forecasted$)$ earnings, E$1$:

P$0/$ E$1=[$d$1/$E$1]/($k $-$g$)$

For $2024$ assume the payout ratio is the same as $2023$ and that k is as given in part $($a$)(6\mathrm{.}5\%).$ If the analyst expects earnings per share to grow by $6\%$ in $2024,$ calculate the prospective P$/$E ratio for BAE.