1) An oil and gas exploration and production company has a yearly net cash flow from operations that is distributed normally with a mean of $110 million and a standard deviation of $20 million. The firm pays an annual dividend of $40 million to its shareholders.
a) What is the firm's Cash Flow at Risk (CFaR) if the confidence level is 97.5%, i.e., the cash flow loss relative to the mean, such that there is only a 2.5% chance of losing more than the mean cash flow minus the CFaR? Show your work.
b) How much cash and/or liquid assets should the firm keep on hand if it wants to be 97.5% confident of being able to pay its dividend, assuming the company cannot raise external funding that would then be paid out as a dividend? Show your work.