Final answer:
To determine whether the all-equity firm should use cash for expansion or share repurchase, we applied the perpetuity formula. Expansion would raise future free cash flows to $100 million yearly, creating a present value of $1 billion, whereas repurchase keeps it at $500 million. Consequently, expansion is the better choice for increasing firm value and stock price.
Step-by-step explanation:
The question involves deciding between using cash for expansion or share repurchase by an all-equity firm and analyzing the impact on the stock price per share. The perpetuity formula will help to determine the present value of future free cash flows, which is key to this decision. Given a cost of equity of 10%, we will compare the value of investments into the firm's operations against the immediate increase in share value from a buyback.
Option 1: Utilizing cash for business expansion will increase future free cash flows to $100 million per year. Using the perpetuity formula (PV = C / r), where 'C' is the annual free cash flow and 'r' is the required rate of return or cost of equity, the firm's value can be estimated. When future cash flows become $100 million perpetually with a cost of equity of 10%, the present value is $100 million / 0.10 = $1 billion.
Option 2: If the firm repurchases shares with the $100 million cash, it reduces the number of outstanding shares, thereby potentially increasing the value of the remaining shares. However, the ongoing value of future cash flows remains at the initial $50 million per year (as no expansion occurs), equating to a present value of $50 million / 0.10 = $500 million.
Comparing the two values, it is clear that expansion would create a higher firm value. Thus, from a value-maximization standpoint, expansion is the superior option. Moreover, the stock price per share should react positively to the expansion news, as the company's overall value is expected to rise, barring any investor concerns about the risks of expansion.