Four companies belong to a group and are listed on a stock exchange. The cross-holdings of these companies are as follows.

? Company A owns30% of Company B and 10% of Company C.

? Company B owns 20% of Company C.

? Company C owns 10% of Company A, 20% of Company B, and 30% of Company D.

? Company D owns 20% of company B.

Each company has a market capitalization of $100 billion. You wish to adjust for cross-holding to reflect the weights of these companies in a market-capitalization weighted index.

a. What adjustments would you make in the market capitalization of each company to reflect the free float?

b. What would be the total adjusted market capitalization of the four companies?