You have been asked to estimate the peso cost of equity for Bandanas Holdings, a firm that has all of its operations in Mexico. You decide that you will compute a dollar cost of equity first and then convert into a peso cost of equity.

The Mexican government has dollar denominated bonds yielding $8\%$ and peso denominated bonds yielding $12\%.$ The treasury bond rate in the United States is $5\%$ and you believe that a mature market equity risk premium is $4\%.$

Your company is in two businesses $$ chemicals and real estate and derives roughly $50\%$ of its value from the first one. The unlevered beta of chemical companies globally is $1\mathrm{.}15$ and the unlevered beta of real estate is $0\mathrm{.}6.$

You have $100$ million shares trading at $20$ pesos per share and debt outstanding of $1$ billion pesos $($in market value terms$).$ Your firm faces a $30\%$ marginal tax rate.

Estimate the peso cost of equity if inflation rate in Mexico is expected to be $7\%$ and the inflation rate in the U$.$S$.$ is expected to be $2\%.$