Prokter and Gramble $($PKGR$)$ has historically maintained a debt$-$equity ratio of approximately $0\mathrm{.}21.$ Its current stock price is $$51$ per share, with $2\mathrm{.}2$ billion shares outstanding. The firm enjoys very stable demand for its products, and consequently it has a low equity beta of $0\mathrm{.}525$ and can borrow at $3\mathrm{.}7\%,$ just $20$ basis points over the risk$-$free rate of $3\mathrm{.}5\%.$ The expected return of the market is $9\mathrm{.}8\%,$ and PKGR$\text{'}$s tax rate is $28\%.$

a$.$ This year, PKGR is expected to have free cash flows of $$5\mathrm{.}9$ billion. What constant expected growth rate of free cash flow is consistent with its current stock price?

b$.$ PKGR believes it can increase debt without any serious risk of distress or other costs. With a higher debt$-$equity ratio of $0\mathrm{.}525,$ it believes its borrowing costs will rise only slightly to $4\mathrm{.}0\%.$ If PKGR announces that it will raise its debt$-$equity ratio to $0\mathrm{.}525$ through a leveraged recap, determine the increase or decrease in the stock price that would result from the anticipated tax savings.