You are an entrepreneur starting a biotechnology firm. If your research is​ successful, the technology can be sold for 

$ 28$28 

million. If your research is​ unsuccessful, it will be worth nothing. To fund your​ research, you need to raise 

$ 5.9$5.9 

million. Investors are willing to provide you with 

$ 5.9$5.9 

million in initial capital in exchange for 

45 %45% 

of the unlevered equity in the firm.

**a.** What is the total market value of the firm without​ leverage?

**b**. 

Suppose you borrow 

$ 0.4$0.4 

million. According to​ MM, what fraction of the​ firm's equity will you need to sell to raise the additional 

$ 5.5$5.5 

million you​ need?

**c.** What is the value of your share of the​ firm's equity in cases 

​(**a**​) 

and 

​(**b**​)?

Question content area bottom

Part 1

**a.** What is the total market value of the firm without​ leverage?

The market value without leverage is 

​$enter your response here 

million.  ​(Round to one decimal​ place.)

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!

You are an entrepreneur starting a biotechnology firm. If your research is successful, the technology can be sold for $28 million. If your research is unsuccessful, it will be worth nothing. To fund your research, you need to raise $5.9 million. Investors are willing to provide you with $5.9 million in initial capital in exchange for 45% of the unlevered equity in the firm.

a. What is the total market value of the firm without leverage?
b. Suppose you borrow $0.4 million. According to MM, what fraction of the firm's equity will you need to sell to raise the additional $5.5 million you need?
c. What is the value of your share of the firm's equity in cases (a) and (b)?

Learn how to calculate the total market value of a biotechnology firm without leverage, how much equity to sell to raise additional capital, and the impact on the entrepreneur's share. This problem explores key concepts in corporate finance, including the Modigliani-Miller theorem and ownership dilution.

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