PotashCorp announced a program to buy back up to 5% of its common shares between August 2013 and July 2014.

When a company has a strong balance sheet with surplus cash, it needs to find a use for that cash consistent with its strategic goals and the current business environment. When economic conditions aren’t favourable for spending the cash to pay off debt, acquire another company or expand operations, it can use its cash in two other ways: (1) announcing a special dividend, and (2) buying back shares, otherwise known as stock repurchase agreements. Both of these options return value to shareholders. The difference between them is that share buy-backs can be done gradually over several quarters and the amount of the buy-back can be adjusted to the surplus cash available in future quarters; special dividends, on the other hand, require the company to be pretty certain that a base level of surplus cash will continue to be available in future quarters.

Suppose you’re advising the board of directors of a major company that needs to decide between a share buy-back and a special dividend. Surplus cash during the past eight quarters is given in the table. (Quarter 8 is the most recent.)

The board will issue a special dividend if it can be both 95% certain that surplus cash will exceed $1.15 billion in quarter 9 and 95% certain that it will exceed $1.2 billion in quarter 10. It will announce a share buy-back program if it can be both 90% certain that the total surplus cash from quarter 9 will exceed $1.15 billion and that the surplus cash from quarter 10 will exceed $1.2 billion. Use linear regression to advise the board of directors about its options.