Valuing a business $($S$4\mathrm{.}6)$ Mexican Motors' market cap is $200$ billion pesos. Next year's free cash flow is $8\mathrm{.}5$ billion pesos. Security analysts are forecasting that free cash flow will grow by $7\mathrm{.}5\%$ per year for the next five years. Assume that the $7\mathrm{.}5\%$ growth rate is expected to continue forever.

Hint: at the aggregate level, market cap is similar to price per share $($P$0),$ and free cash flow is similar to dividend per share $($DIV$1).$

For simplicity you can enter the values in billion pesos, where applicable.

a$.$ What rate of return are investors expecting?

$12\mathrm{.}07$

$\%($enter the value in xx$.$xx format in percent$)$

Mexican Motors has generally earned about $12\%$ on book equity $($ROE $=12\%)$ and reinvested $50\%$ of earnings. The remaining $50\%$ of earnings has gone to free cash flow. Suppose the company maintains the same ROE and investment rate for the long run.

b$.$ What is the growth rate of earnings and free cash flow?

$6\mathrm{.}00$

$\%($enter the value in x$.$xx format in percent$)$

c$.$ If the growth rate of earning is part b was g$=5\%,$ what is the new rate of return$)?$

$5\mathrm{.}03$

$\%($enter the value in x$.$xx format as percentage$)$