Chipotle Mexican Grill, Inc. $($CMG$)$ operates in the U$.$S$,$ Canada, and several European countries, including Germany, France, and the UK$.$ The CEO is considering two different expansion projects. Project $($a$)$: expand into Belgium, where the demand, costs, and risks, are similar to the hereto established markets. Project $($b$)$: create a high$-$end line of restaurants in existing markets where the demand, costs, risks, etc., are likely quite different from the existing business.

a$)$ For which project is the WACC more appropriate and why?

CMG is financed by $75\%$ equity and $25\%$ debt. The equity beta is $1\mathrm{.}2,$ the market risk premium is $10\%,$ the cost of debt is $5\%,$ the risk free rate is $2\mathrm{.}5\%$ and the tax rate is $30\%.$

b$)$ For project $($a$),$ what is the numerically correct discount rate?

c$)$ Using your answer from part $($b$)$ as the discount rate, calculate the NPV of the project. Should you take the project? Here$$s what you know: remember your tax rate is $30\%.$ You estimate the cost of construction, due immediately, to be $$2$ billion, which can be depreciated over the life of the project, which is $25$ years. You estimate operating profits will be $$0\mathrm{.}5$ billion and will begin in year t$=5($in other words, construction will take $4$ years and the first profits will be realized at the end of year five$).$ These profits will grow $7\%$ per year and will continue for an estimate $20$ years $($so year $25$ is the final year where profits will be realized$).$