Final answer:
Without knowing the market price per share, it is not possible to calculate the firm's value based on the information provided.
Step-by-step explanation:
To determine the value of the firm after the stock repurchase, we can use the Modigliani-Miller theorem, which states that in an all-equity firm without taxes, the value of the firm is unaffected by its capital structure. As the firm is borrowing $1.8 million to repurchase 50,000 shares, there is no introduction of taxes, and the interest is only a shift from equity to debt. Accordingly, the valuation of the firm should remain the same pre and post borrowing. Therefore, to obtain the firm's initial value, we would multiply the total number of shares by the current stock price before the repurchase transaction.
However, with the provided information, we do not have the price per share to multiply with the number of shares in order to find the firm's initial value. Hence, using this approach is not feasible without additional data. Instead, to make use of the information provided in the vignettes, we observe that the firm will act on a 4.5% cost of financial capital. The provided references involve sums of $102 million and $183 million under different interest rate scenarios, which are not directly relevant to the transaction described in the student's question.
Given this, the problem seems incomplete or lacks sufficient data to provide a calculated response, leading to an inability to determine the exact value of the firm. Any possible value stated in the options would be speculative without knowing the market price per share.