Problem $1.$ Modigliani & Miller Propositions $($similar to P$13-15)(24$ points$)$

A certain firm with no debt that operates in perfect capital markets currently generates a $5\mathrm{.}5\%$ return for its shareholders and can issue a debt cost of $3\%.$

Determine the firm$$s ROE at the following debt$-$to$-$equity ratios: $\mathrm{.}5,1\mathrm{.}0,1\mathrm{.}5$