Four companies belong to a group and are listed on a stock exchange. The cross-holdings of these companies are as follows:
• Company A owns 20 percent of Company B and 10 percent of Company C.
• Company B owns 15 percent of Company C.
• Company C owns 10 percent of Company A, 10 percent of Company B, and 5 percent of Company D.
• Company D has no ownership in any of the other three companies.
Each company has a market capitalization of $50 million. You wish to adjust for cross-holding in determining the weights of these companies in a free-float market capitalization-weighted index.
a. What are the market capitalizations of each company after adjustment to reflect free float?
b. What would be the total adjusted market cap of the four companies?