The management of Mitchell Labs decided to go private in $2002$ by buying all $2\mathrm{.}60$ million of its outstanding shares at $$23\mathrm{.}50$ per share. By $2006,$ management had restructured the company by selling off the petroleum research division for $$11\mathrm{.}50$ million, the fiber technology division for $$8\mathrm{.}75$ million, and the synthetic products division for $$22$ million. Because these divisions had been only marginally profitable, Mitchell Labs is a stronger company after the restructuring. Mitchell is now able to concentrate exclusively on contract research and will generate earnings per share of $$1\mathrm{.}60$ this year. Investment bankers have contacted the firm and indicated that if it reentered the public market, the $2\mathrm{.}60$ million shares it purchased to go private could now be reissued to the public at a P$/$E ratio of $12$ times earnings per share.

a$.$ What was the initial cost to Mitchell Labs to go private?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places. Enter your answer in millions, not dollars $($e$.$g$.,$ $$1,230,000$ should be entered as $"1\mathrm{.}23").$

Initial cost

million

b$.$ What is the total value to the company from $(1)$ the proceeds of the divisions that were sold, as well as $(2)$ the current value of the $2\mathrm{.}60$ million shares $($based on current earnings and an anticipated P$/$E of $12)?$

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places. Enter your answer in millions, not dollars $($e$.$g$.,$ $$1,230,000$ should be entered as $"1\mathrm{.}23").$

Total value to the company

million

c$.$ What is the percentage return to the management of Mitchell Labs from the restructuring? Use answers from parts a and $b$ to determine this value.