Final answer:
The value of a firm is calculated by the Present Discounted Value of its dividends, discounted at the required return on equity. Before the debt issuance and special dividend, the firm's equity value is determined using the dividend valuation model, based on a 10% required return on equity and $70 dividend payment.
Step-by-step explanation:
The value of a firm can be determined using the concept of Present Discounted Value (PDV). If the required return on equity (rE) is 10% and the firm pays out a fixed dividend of $70, the present value of these dividends represents the equity value of the company before any new debt is issued or the special dividend is paid. When the firm announces the issuance of $400 in debt at an interest rate of 5% to fund a $400 special dividend, the core valuation of the firm before this transaction involves discounting the dividends it pays to shareholders at the required return on equity. Assuming all else remains constant, the equity value before the issuance of debt and special dividend payout can be found using the dividend valuation model (DVM).
However, the specific formula for calculating the equity value prior to the debt issuance and special dividend was not provided in the question.