Groupe Ariel S$.$A$.$: Parity Conditions and Cross$-$Border Valuation:

$1.$ Check $($as far as possible$)$ to what extent relative purchasing power parity and interest rate parity is reflected in the historic data given in the case.

$2.$ Explore the relevance and influence of assumptions regarding parity conditions. What is your result in part $1$ if you assume parity conditions to hold? What if you apply alternative assumptions not consistent with parity? Try different assumptions regarding inflation rates.

$3.$ Should Groupe Ariel approve the equipment purchase? Include hedging and financing considerations into your discussion and recommendation. $-$The actual $1-$year and $2-$year forward rates at the date of the case were MXN $16\mathrm{.}4331/$EUR and MXN $16\mathrm{.}9998/$EUR$,$ respectively $($mid$-$points between bid and ask$).$ Longer rates were not available.$-$ Kindly include quantitative results in the answers.