M.co is a small consultancy firm fully owned by its founded and director, Mrs J. The value of the firm is given by the equation = 100 ! in million of pounds, where V is the firm value and F is the value of perks that the director of the firm enjoys. Mrs J utility function is given by = + 2, where M is the monetary value of her holding in the firm ( = ) and is the share of ownership that Mrs J has in M.co. a. Find Mrs J overall utility when she owns M.co fully (=100%) and she chooses to consume perks as a director equal to = 7 million pounds. (5 points) b. Suppose that Mrs J retains full ownership and control of her firm. What is the optimal amount of perks that she will choose to enjoy and what will be the firm's ultimate value? (10 points) c. Suppose now that Mrs J decides to sell 50% of the firm to an external partner in order to raise finance for future investment while retaining the position of the director. How much money will Mrs J decide to spend in perks after the sale of this equity stake? What is the firm's new value and how much money will Mrs J raise for investment? (15 points)