Final answer:
The value of a firm with an equity return rate (rE) of 10% and a constant dividend of $70 can be calculated using present value methods. Issuing $400 in debt to fund a special dividend, theoretically, should not change the value of the firm after the payout due to capital structure irrelevance. However, such financial actions may affect investor expectations regarding dividends and capital gains, influencing the stock price.
Step-by-step explanation:
The value of a firm can be calculated using different methods, but a common approach is to use the present value of expected dividends. In this case, with an expected equity return rate, rE of 10%, and a constant dividend of $70, you might use the Gordon Growth Model to find the initial value of the firm. This model assumes that the dividends will grow at a constant rate in perpetuity.
However, when a company announces the issuance of $400 in debt at a 5% interest rate to fund a $400 special dividend, the value of the firm right after the payout, theoretically, should not change due to the principle of Modigliani-Miller theorem on capital structure irrelevance. This principle states that in a perfect market, the value of the firm is unaffected by how it is financed, whether through equity (stocks) or debt (bonds). So the firm's value just after the payout remains the same as before the debt issuance and special dividend, assuming no taxes, transaction costs, or financial distress costs, and that the markets are efficient.
It is also important to consider that investors receive a rate of return via dividends and capital gains. The expected rate of return will affect the price investors are willing to pay for stock, either reflecting their desire for dividend income or capital appreciation.