Mauna Loa Greenhouses, Inc. has determined that its optimal capital structure consists of $40\%$ equity and $60\%$ debt. The company must raise additional $($new$)$ capital to fund its upcoming expansion costing $$5$ million, and its tax rate is $25\%.$ The firm has $$0\mathrm{.}4$ million coming from retained earnings that has a cost of $11\mathrm{.}5\%.$ Its investment bankers have informed the company that it could issue up to an additional $$2\mathrm{.}8$ million of new common equity at a cost of $13\%.$

Furthermore, the firm can raise up to $$1\mathrm{.}4$ million of debt at an interest rate of $8\%$ and an additional $$1\mathrm{.}8$ million at $9\mathrm{.}6\%$ interest rate. What is the average after$-$tax cost of capital for the entire $$5$ million that the company will be raising if the firm maintains its optimal capital structure?

a$.10\mathrm{.}40$ percent

b$.10\mathrm{.}16$ percent

c $9\mathrm{.}35$ percent

d$.9\mathrm{.}06$ percent

e$.9\mathrm{.}54$ percent