Symmetric Inc. has two profit centers (North and South) operating in different regions of the world. North and South divisions sell identical services to similar types of customers. However, because of their geographic separation, the two divisions do not share common customers. Most of the compensation of the senior management teams of North and South is tied to their division’s profits, and the remainder is base salary. Annual profits in the two divisions depend heavily on the effort and skill of the senior management teams. Nonetheless, random shocks to each division’s regional economy can cause its profits in any given year to add or subtract $ 100 million (each equally likely) from the profits the division would have earned absent the shock. For example, if the South Division would have earned $ 200 million absent the shock, after the shock, it would have earned either $ 100 million or $ 300 million. Random economic shocks to North’s profits are uncorrelated (independent) with random shocks to South’s regional economy. Both divisions have the same expected profits.
The CFO of Symmetric wants to allocate $ 80 million of fixed corporate- level overhead costs to the two divisions, and is considering one of two possible allocation schemes: (1) allocate the
$ 80 million based on the profits of the two profit centers, or (2) allocate the $ 80 million evenly, that is, $ 40 million to each division irrespective of the actual profits of the two profit centers.

Required:
Critically analyze the two alternative overhead allocation schemes and make a recommendation to senior management based on your analysis. Your recommendation should be supported by a rigorous quantitative analysis of the situation.