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There are 100 firms with risky payoffs, all identical ex ante. Half of the firms will turn out to be good, the other half

There are 100 firms with risky payoffs, all identical ex ante. Half of the firms will turn out to be good, the other half will turn out bad. On Monday at noon, the manager of each firm knows the true state of their own firm, but outside investors do not have that knowledge, they only know the 50/50 distribution. At that point in time, the manager needs to decide whether to expand or not, at a cost of 300 (million pounds). The only source of funding is by issuing new shares. Currently, each firm has 1 million shares. Good firms have an unexpanded present value of 400 million pounds, and their expan- sion has a net present value of 60 million pounds. Bad firms have an unexpanded present value of 180 million and their expansion has a net present value of 20 million pounds. Suppose that on Monday at noon all firms announce expansion, financed via an equity issue. Determine the share prices before and after the annnouncement, assuming that investors are unable to identify the true state of any of the individual firms. Hence determine the number of new shares issued by each firm, and hence determine the dilution factor. Suppose that one week later, investors become aware of the true state of each individual firm. What will they do? On this basis, draw conclusions for the theory of capital structure.

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