Which of the following statements most accurately defines the trade$-$off theory of capital structure?

A$.$ A company, in selecting an optimal capital structure, will balance the benefits of debt financing in relation to interest tax shields with the increased costs of higher financial leverage relating to higher interest rates and a higher risk of financial distress and bankruptcy

B$.$ There is a trade$-$off between the increase in interest tax shields arising from debt and a company's taxable income

C$.$ There is a trade$-$off between the cost of equity and the cost of debt

D$.$ The value of debt will fall as the value of equity increases

E$.$ A higher debt component within a firm's capital structure will result in a lower equity value

$$a$.$ There is a trade$-$off between the increase in interest tax shields arising from debt and a company's taxable income

$$ b$.$ There is a trade$-$off between the cost of equity and the cost of debt

$$ c$.$ A company, in selecting an optimal capital structure, will balance the benefits of debt financing in relation to interest tax shields with the increased costs of higher financial leverage relating to higher interest rates and a higher risk of financial distress and bankruptcy

$$ d$.$ A higher debt component within a firm's capital structure will result in a lower equity value

$$ e$.$ The value of debt will fall as the value of equity increases