The U$.$S$.$ company Colorado Co$.$ operates with a funding structure in dollars, comprising $60\%$ debt and $40\%$ equity. Its subsidiary in Qatar is financed in Qatari riyals, with a capital structure consisting of $50\%$ debt and $50\%$ equity. Both U$.$S$.$ and Qatar earnings are subject to a $30\%$ corporate tax rate $($federal and state combined$).$ The $10-$year risk$-$free interest rate stands at $6\%$ in the U$.$S$.$ and $10\%$ in Qatar, accompanied by an annual real interest rate of around $2\%$ in both countries. Adhering to interest rate parity, Colorado borrows at a rate $3$ percentage points above the risk$-$free rates, resulting in a before$-$tax cost of debt of $9\%$ in the U$.$S$.$ and $13\%$ in Qatar.

Colorado anticipates a $10\%$ annual stock market return in the U$.$S$.$ and a $15\%$ return in Qatar. The U$.$S$.$ business holds a beta of $0\mathrm{.}8$ relative to the U$.$S$.$ market, while the Qatari business has a beta of $1\mathrm{.}2$ relative to the Qatari market. Equity supporting Colorado$$s Qatari operations has originated from retained earnings by the Qatar subsidiary in preceding years.

Now, Colorado Co$.$ is contemplating a dual approach with a stock offering in Qatar denominated in Qatari riyals, targeting Qatari investors, and a separate stock offering in the U$.$S$.$ denominated in U$.$S$.$ dollars, targeting U$.$S$.$ investors. Evaluate the estimated cost of equity for Colorado in the United States and Qatar resulting from these respective stock offerings.

Group of answer choices

Cost of equity $($US$)=8\%$; Cost of equity $($Qatar$)=12\%$

Cost of equity $($US$)=9\mathrm{.}2\%$; Cost of equity $($Qatar$)=16\%$

Cost of equity $($US$)=16\%$; Cost of equity $($Qatar$)=9\mathrm{.}2\%$

Cost of equity $($US$)=12\%$; Cost of equity $($Qatar$)=21\%$