Cole & Co mines and sells coal to power plants. Cole & Co expects to sell $50,000$ metric tons of coal next year. However, there is uncertainty regarding the spot price of coal next year as follows.

Probability $$/$Metric ton

$10\%$ $$25$

$50\%$ $$90$

$40\%$ $$130$

If revenues of Cole & Co fall below $$1,500,000,$ the company$$s ability to repay its debt is impaired, and the ensuing financial distress will induce a firm value loss of $$1,000,000.$ Currently, the company is considering a $1$ year forward contract on coal with a forward price of $$99\mathrm{.}5$ per metric ton to hedge against fluctuations in the spot price of coal. Should Cole & Co hedge? If so$,$ what position should the company take on with the forward contract, and what would be the value gained next year by hedging? Ignore taxes.

a$.$ Cole & Co should not hedge since it does not add any shareholder value.

b$.$Cole & Co should enter a forward contract to long $50,000$ metric tons. Compared to not hedging, their expected profit next year will be greater by $$100,000.$

c$.$ Cole & Co should enter a forward contract to short $50,000$ metric tons. Compared to not hedging, their expected profit next year will be greater by $$100,000.$

d$.$ Cole & Co should enter a forward contract to short $50,000$ metric tons. Compared to not hedging, their expected profit next year will be greater by $$1,000,000.$