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.

For which project is the WACC more appropriate and why?

The WACC is most suitable for Project $($a$),$ the expansion into Belgium, as it aligns with the risk and operational characteristics of Chipotle's established markets. WACC accurately represents the average rate of return required by all investors and reflects the typical riskiness of the company$$s operations, making it an appropriate measure for this project$$s expected cost of capital.

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 $30\%.$

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

R$\_$e $=$ R$\_$f$+\backslash$beta $($R$\_$m$-$ R$\_$f $)$

$=0\mathrm{.}025+1\mathrm{.}2\backslash$times $0\mathrm{.}1$

$=0\mathrm{.}145$

$=14\mathrm{.}5\%$

WACC$=$ E$/$V $\backslash$times R$\_$Equity$+$D$/$V $(1-\backslash$tau $)\backslash$times R$\_$Debt

$=0\mathrm{.}75\backslash$times $14\mathrm{.}5\%+0\mathrm{.}25(1-0\mathrm{.}30)\backslash$times $5\%$

$=11\mathrm{.}75\%$

The numerically correct discount rate for Project $($a$)$ is $11\mathrm{.}75\%.$

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$).$

NPV Calculation for Project $($a$)$:

Given:

$-$ Initial Investment $=$ $$2$ billion $($t$=0)$

$-$ Annual Depreciation $=($$$2$ Billion$)/25=80$ million

$-$ Tax rate $=30\%$

$-$ Annual Tax Shield $=$ Depreciation x Tax Rate

$-$ Operating profits start at end of year $5($t$=5),$ growing at $7\%$ annually for $20$ years $($t$=5$ to $25)$

$-$ Discount rate : WACC $=11\mathrm{.}75\%$

$-$No salvage value