Suppose that the free cash flow per share for the S&P $500$ companies as a whole was $$180$ last year. Currently, investors expect the free cash flow to grow by $2\%$ every year in real terms in future years. Assuming that investors demand a $5\mathrm{.}75\%$ real annualized rate of return, what would be the price per share? Use these numbers as the baseline scenario. Now assume that all of a sudden, investors expect a big but temporary recession to hit the U$.$S$.$ economy such that the free cash flow is expected to be $50\%$ smaller than the baseline projection in $2024,30\%$ smaller in $2025,$ and $20\%$ smaller in $2026,$ and the same as the baseline projection starting in $2027$ and all future years. What will be the new price per share when investors' expectation suddenly changes?