$1.$ Zegala Inc. is an all$-$equity funded company that operates in two businesses and derives all of its revenues in the United States.

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Estimated Value $($in $ millions$)$

Unlevered Beta

$$

Hotels

$$500\mathrm{.}00$

$$

$0\mathrm{.}90$

Travel Services

$$1,000\mathrm{.}00$

$$

$1\mathrm{.}20$

Company

$$1,500\mathrm{.}00$

$$

$1\mathrm{.}10$

The firm is considering borrowing $$1\mathrm{.}5$ billion and expanding its hotel business into Mexico. The US $10-$year T$.$bond rate is $3\%,$ the Mexican government $10-$year peso rate is $8\%,$ the equity risk premium for the US is $5\%$ and the total equity risk premium for Mexico is $7\mathrm{.}5\%.$

a$.$ Estimate the cost of equity in US $ terms for the company, after the expansion. $($The marginal tax rate is $25\%)(3$ points$)$

b$.$ Starting from unlevered beta estimated in point a$.,$ estimate the levered beta of the company assuming the company raised new equity to maintain a cash position of $400$ million dollars $($firm value $=$ operating assets $+$ cash $=3,400)(1$ point$)$