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Problem Set 3
1. There are two firms in a market – firm A and firm B. Insiders of firm A know that the
present value of future Free Cash Flows (FCFs) is $200 million. Insiders of firm B know
that the present value of future FCFs is $100 million. The outside investors perceive the
present value of future FCFs for both firms to be $100 million. If firm A does nothing to
signal its true value then there is nothing that changes the perception of the investors.
Both firms can invest in a project that requires an investment of $10 million that will
generate a present value of cash flows of $20 million, which is common knowledge. The
$10 million investment has to be funded by new equity from outside investors. One
action firm A could take to signal that its value is higher than what outside investors think
(and lower its cost of equity) is to pay an unexpected special dividend financed by a debt
issue such that firm B finds it sub-optimal to mimic this action. The cost associated with
the special dividend in terms of the opportunity cost, cost of making dividend payments,
and cost of the debt issue can be represented by C, where C is a function of the amount of
special dividend paid. Let C = 0.2*amount of special dividend. What is the lowest
amount of special dividend that can correctly signal that a firm that takes this action was
worth $200 million (before this action) and not $100 million as initially estimated by the
outside investors?
