Suppose$$ that, holding yield$$ constant, investors are indifferent as to whether they hold bonds issued by the federal government or bonds issued by state and local governments$($that is$,$ they consider the bonds the same with respect to default$$ risk, information$$ costs, and$$ liquidity$).$ Suppose that state governments have issued perpetuities$($or consoles$)$ with $$$$72$ coupons and that the federal government has also issued perpetuities with $$$$72$ coupons. If the state and federal perpetuities both have$$ after$-$tax yields of $9\%,$ what are their$$ pre$-$tax yields?$($Assume that the relevant federal income tax rate is $31\mathrm{.}53\%.)$

The$$ pre$-$tax yield on the state perpetuity will be

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