Maleic Chemical Company has an annual revenue of $$2$ billion$/$year$,$ half of which $($$$1$ Billion$/$y$)$ comes from a single

product, Maleic Anhydride $($MA$,$ C $4$H $2$O $3).$ The company currently sells MA for $$2\mathrm{.}50/$kg $($$$2500/$ton$).$

Your boss asks you to reveiew several

issues., starting with risks to the current business.

MA is now produced from the oxidation of benzene $($C$6$H$6)$ using a vanadium pentoxide catalyst at $65\%$ yield:

The feed stock material, benzene, now purchased at $$1/$kg$,$ appears to have several associated risks. You meet with

the purchasing team, some suppliers and officials of the EPA and come up with $3$ possible outcomes:

$1.$ Benzene will continue to be avalable as needed, but with a $5\%$ year over year price increase over the next $6$ years

$($years $1-6).$ This was considered to the most likely scenario with a $50\%$ likelihood.

$2$ The use of benzene is restricted by the EPA to $100-$t$/$y$,$ years $4$ and beyond $(20\%$ likelihood$).$

$3.$ A biomass supplier will provide a renewable version of benzene for years $4$ and beyond, but with the new

technology, at a $7\%$ year over increase over the then previous year price of benzene $(10\%$ chance$).$

You may also assume that the MA selling price increases $3\%$ year over year $($years $1$ thrrough $6).$ Operating costs are

$$1/$y $($Year $0),$ increasing $2\%$ year over year $($years $1$ through $6).$ No change to sales volume or yield.

For each of the $3$ cases above:

a$.$ Caclculate the total profit from sale of MA$,$ for each of years $1$ through $6.$

b$.$ What is the Present Value of the profit for each year, based on a rate of return of $25\%?$

c$.$ What is the Present Value of Total Profit for Year $6,$ as a percentage of current $($Year $0)$ revenue from MA$?$