$-$ Presently, the firm generates after$-$tax operating earnings of $300$ million from revenues of $10$ billion, with a capital turnover ratio of $2\mathrm{.}5.$

$-$ It is anticipated that $60\%$ of the after$-$tax operating income will be reinvested.

$-$ The company is entirely financed through equity and maintains a cost of capital of $10\%.$

To estimate the firm's value, assuming ongoing adherence to existing policies indefinitely, we calculate the present value based on constant returns on capital and reinvestment rates.

Assuming a potential increase in after$-$tax operating margins from $3\%$ to $5\%,$ while keeping the capital turnover ratio constant, and reducing the reinvestment rate to $40\%,$ alongside a shift to the optimal debt ratio which would lower the cost of capital to $9\%,$ we can assess the potential increase in the firm's value.

By implementing these changes, the firm's value would likely experience a significant boost.

Estimate the change in value.