You have been given the task of estimating the cost of capizal for $$ Valdez Inc., a Colombia$-$based company that operates in two businesses $-$ food processing and grocery retail$-$ and in two countries $-$ the United States and Colombia. The estimated values of the businesses is broken down in the table below $($with the values in millions of US dollars$)$:

$\backslash$table$[[,$Colombia,USA,$\backslash$table$[[$Unlevered Beta for$],[$business$]]],[$Food processing $($value of business$),1,000,0,0\mathrm{.}90],[$Groceries $($value of business$),500,1,000,0\mathrm{.}60],[$Government bond rate $($in US $$),7\mathrm{.}37\%,3\mathrm{.}52\%,],[$Government bond rate $($in Pesos$),12\mathrm{.}75\%,$NA$,],[$Marginal tax rate,$25\%,28\%,]]$

The company has $$500$ million in debt, all in its US operations, with a synthetic rating of BBB and a company default spread of $2\%.$

$($a$)$ What is the value of the firm?

$($b$)$ Estimate the unlevered beta.

$($c$)$ Estimate the $($levered$)$ beta that you would use for Valdez Inc.

$($d$)$ Calculate the Colombian default spread.

$($e$)$ Calculate the risk free in USA.

$($f$)$ Estimate the cost of equity in US dollars.

$($g$)$ Estimate the after$-$tax cost of debt in US dollars.