Let's address each part step by step:

Part A: Total Market Value Without Leverage

The total market value of the firm without leverage (unlevered value) can be calculated by considering the equity investment and the ownership stake investors receive.

Investors are providing $5.9 million in exchange for 45% of the unlevered equity. Therefore, the total unlevered equity value, $V_U$, can be calculated as follows:

$V_U = \frac{\text{Investment Amount}}{\text{Percentage of Equity}}$

$V_U = \frac{5.9 \, \text{million}}{0.45}$

Let me compute that.

The total market value of the firm without leverage is approximately $13.1 million.

Part B: Equity Sale with Leverage

If you borrow $0.4 million, you only need to raise an additional $5.5 million. According to Modigliani-Miller (MM) theory, the amount of equity sold would still be proportional to the total firm value.

First, we calculate how much equity $X$ you need to sell to raise $5.5 million, given the firm's unlevered value.

The new amount of capital you are raising ($5.5 million) will be for some fraction of the firm's equity. So, the equity percentage required is:

$X = \frac{5.5 \, \text{million}}{13.1 \, \text{million}}$

Let me calculate that.To raise the additional $5.5 million, you would need to sell approximately 41.95% of the firm's equity.

Part C: Value of Your Share in Both Cases

• Case (a): Without leverage
  Initially, you hold $100\% - 45\% = 55\%$ of the firm's equity. The value of your share is:

  $\text{Your Share Value} = 55\% \times 13.1 \, \text{million}$

• Case (b): With leverage
  After borrowing, you sold an additional 41.95% of the firm's equity. Your new ownership percentage is:

  $\text{New Ownership} = 100\% - 45\% - 41.95\%$

  Your share value now will be based on this new ownership percentage of the unlevered firm value.

Let me calculate your share value in both cases.- Case (a): Without leverage, the value of your share is approximately $7.21 million.

• Case (b): With leverage, after selling additional equity, the value of your share is approximately $1.71 million.

Summary:

• (a) The total market value of the firm without leverage is $13.1 million.
• (b) You would need to sell approximately 41.95% of the firm's equity to raise $5.5 million after borrowing $0.4 million.
• (c) Your equity value:
  • Without leverage: $7.21 million.
  • With leverage: $1.71 million.

Would you like further details or have any questions?

Here are some related questions to expand your understanding:

1. How does borrowing affect ownership dilution in equity financing?
2. What are the risks associated with leveraging a biotechnology firm?
3. How does Modigliani-Miller theory apply to corporate finance decisions?
4. What factors could influence the market valuation of a biotech firm?
5. How do investors calculate the expected return on their equity?

Tip: When issuing more equity to raise funds, always weigh the cost of dilution against the potential gains from the investment!