The Pedroia Corporation has two business units that compete in different product markets. The current market value of Pedroia Corporation is $$235$ million. One hedge fund investor is clamoring for the firm to be broken up into two independent companies. Business Unit A has revenue of $$75$ million per year and a profit margin of $12\mathrm{.}5\%.$ Business Unit B has revenue of $$180$ million per year and a profit margin of $3\mathrm{.}5\%.$ The investor has conducted a break$-$up value analysis using price$-$earnings ratios to value the units as independent entities. That investor calculated that Business Unit A has focused rivals who have an average price$-$earnings ratio of $25x.$ He has estimated that Business Unit B has focused rivals who have an average price$-$earnings ratio of $10x.$

a$.$ Based on the numbers above, is the hedge fund investor correct to be arguing for the break$-$up of the Pedroia corporation?

b$.$ Another investor from a mutual fund company has analyzed the company using a discounted cash flow methodology to value the units as independent entities. She has calculated that the NPV of free cash flows for Business Unit A equals $$165$ million $($if the unit is spun off on its own$).$ Moreover, she has estimated that the NPV of free cash flows for Business Unit B equalis $45$ million $($if spun ofi$).$ Do you think she agrees or disagrees with the conclusions of the hedge fund investor?