Assume no taxes or other frictions. Manufacturing Master Inc. $($MMI$)$ is an established manufacturing firm with a steadily growing free cash flow. In particular, the free cash flow next year $($year $1)$ is expected to be $$254\mathrm{.}86$ million, and subsequent growth is expected to be $3\mathrm{.}55\%$ a year perpetually. The free cash flow is all paid out. Currently $($year $0),$ MMI is all equity financed, with a cost of capital of $5\mathrm{.}24\%.$ The risk$-$free interest rate is $2\mathrm{.}95\%$ for all maturities.

MMI now decides to issue a new debt to buy back part of its equity. The new debt takes the form of a consol bond, paying $$53\mathrm{.}87$ million per year forever. The new debt is risk$-$free, given MMI$$s future cash flows.

Question : Next year $($year $1),$ after the payout to its equity and debt holders, what is MMI$$s debt to equity ratio?

i got the answer as $13\mathrm{.}7774\%$ but the ANSWER solution is $13\mathrm{.}242478\%,$ and it ONLY SHOULD BE $13\mathrm{.}242478\%,$ DO NOT ATTEMPT TO ANSWER MY QUESTION IF YOU CAN NOT FIND EXACT OR VERY CLOSE ANSWER "DIFFERENCE ONLY FROM $[13\mathrm{.}2425,13\mathrm{.}2424]$

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