$($Related to Checkpoint $20\mathrm{.}1)($Hedging with forward contracts$)$ The Specialty Chemical Company operates a crude oil refinery located in New Iberia, Louisiana. The company refines crude oil and sells the by$-$products to companies that make plastic bottles and jugs. The firm is currently planning for its refining needs for one year hence. Specifically, the firm's analysts estimate that Specialty will need to purchase $1$ million barrels of crude oil at the end of the current year to provide the feed stock for its refining needs for the coming year. The $1$ million barrels of crude will be converted into by$-$products at an average cost of $$40$ per barrel that Specialty expects to sell for $$170$ million, or $$170$ per barrel of crude used. The current spot price of oil is $$125$ per barrel and Specialty has been offered a forward contract by its investment banker to purchase the needed oil for a delivery price in one year of $$130$ per barrel.

a$.$ Ignoring taxes, what will Specialty's profits be if oil prices in one year are as low as $$110$ or as high as $$150,$ assuming that the firm does not enter into the forward contract?

b$.$ If the firm were to enter into the forward contract, demonstrate how this would effectively lock in the firm's cost of fuel today, thus hedging the risk of fluctuating crude oil prices on the firm's profits for the next year.

a$.$ Ignoring taxes, what will Specialty's profits be if oil prices in one year are low as $$110$ or as high as $$150,$ assuming that the firm does not enter into the forward contract? $($Round to the nearest dollar.$)$

$\backslash$table$[[\backslash$table$[[$Price of$],[$Oil$/$bbl$]],\backslash$table$[[$Unhedged$],[$Annual$],[$Profits$]]],[$$$110,$$