Piedmont Instruments Corporation has estimated the following costs of debt and equity capital for various fractions of debt in its capital structure.

a$.$ Based on these data, determine the company's optimal capital structure $($i$)$ with financial distress costs and without agency costs and $($ii$)$ with financial

distress and agency costs.

i$.$ The optimal capital structure is: $45\%$ debt $+55\%$ equity $vv.$

ii$.$ The optimal capital structure is: $50\%$ debt $+50\%$ equity $.$

b$.$ Suppose the company's actual capital structure is $30$ percent debt and $70$ percent equity. How much higher is $k_a$ at this capital structure than at the

optimal value of $k_a$ with financial distress and agency costs? Round your answer to two decimal places.