A new firm is developing its business plan. It will require $$665,000$ of assets $($which equals total invested capital$),$ and it projects $$450,000$ of sales and $$355,000$ of operating costs for the first year. Management is reasonably sure of these numbers because of contracts with its customers and suppliers. It can borrow at a rate of $7\mathrm{.}5\%,$ but the bank requires it to have a TIE of at least $4\mathrm{.}0,$ and if the TIE falls below this level the bank will call in the loan and the firm will go bankrupt. The firm will use only debt and common equity for financing. What is the maximum debt to capital ratio $($measured as debt$/$total invested capital$)$ the firm can use? $($Hint: Find the maximum dollars of interest, then the debt that produces that interest, and then the related debt to capital ratio.$)$Do not round your intermediate calculations.

Group of answer choices

$51\mathrm{.}90\%$

$51\mathrm{.}43\%$

$47\mathrm{.}62\%$

$35\mathrm{.}71\%$

$52\mathrm{.}86\%$