Part 1You are an entrepreneur starting a biotechnology firm. If your research is successful, the technology can be sold for $ 25$25 million. If your research is unsuccessful, it will be worth nothing. To fund your research, you need to raise $ 3.1$3.1 million. Investors are willing to provide you with $ 3.1$3.1 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 $ 0.6$0.6 million. According to MM, what fraction of the firm's equity will you need to sell to raise the additional $ 2.5$2.5 million you need?c. What is the value of your share of the firm's equity in cases a and b? Part 1a. What is the total market value of the firm without leverage?The market value without leverage is $[input]6.96.9 million. (Round to one decimal place.)Part 2b. Suppose you borrow $ 0.6$0.6 million. According to MM, what fraction of the firm's equity will you need to sell to raise the additional $ 2.5$2.5 million you need?The fraction of the firm's equity will you need to sell is [input]enter your response here %. (Round to the nearest whole percentage.)

Question

Part 1You are an entrepreneur starting a biotechnology firm. If your research is​ successful, the technology can be sold for $ 25$25 million. If your research is​ unsuccessful, it will be worth nothing. To fund your​ research, you need to raise $ 3.1$3.1 million. Investors are willing to provide you with $ 3.1$3.1 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 $ 0.6$0.6 million. According to​ MM, what fraction of the​ firm's equity will you need to sell to raise the additional $ 2.5$2.5 million you​ need?c. What is the value of your share of the​ firm's equity in cases a and b​? Part 1a. What is the total market value of the firm without​ leverage?The market value without leverage is ​$[input]6.96.9 million. ​(Round to one decimal​ place.)Part 2b. Suppose you borrow $ 0.6$0.6 million. According to​ MM, what fraction of the​ firm's equity will you need to sell to raise the additional $ 2.5$2.5 million you​ need?The fraction of the​ firm's equity will you need to sell is [input]enter your response here ​%. ​(Round to the nearest whole​ percentage.)

BlackTom AI · Accepted Answer

Investors pay $3.1 million for 45% of the unlevered equity, so total firm value = 3.1 / 0.45 = 6.8889 → $6.9 million.

1) Relevant knowledge points and concepts
- Equity fraction = investment / total firm (post-money) value. Rearranging yields total value = investment ÷ fraction.
- Modigliani–Miller (MM) without taxes: capital structure (debt vs. equity) does not change total firm value; issuing debt reduces equity value by the amount of debt (V_E = V - D).
- To raise an amount by selling equity, fraction to sell = amount needed ÷ current equity value.

2) Step-by-step reasoning and intermediate calculations
a) Total market value unlevered:
- Given investors supply $3.1M for 45% → V = 3.1 / 0.45.
- Compute: 3.1 ÷ 0.45 = 6.888888... ≈ 6.9 million.

b) With $0.6M debt issued:
- By MM, total firm value stays V = $6.8889M.
- Equity value after borrowing: V_E = V - D = 6.8889 − 0.6 = 6.2889 million (≈ 6.3M).
- Need to raise additional $2.5M via equity sale. Fraction to sell = 2.5 ÷ 6.2889 = 0.3979 ≈ 39.8% → round to 40%.

3) Intermediate steps shown above (division and subtraction).

4) Why the correct answers are correct
- The $6.9M figure is the implied post-money valuation consistent with investors paying $3.1M for 45%. MM implies borrowing $0.6M does not change total firm value, so equity falls by the debt amount; selling $2.5M of that reduced equity requires selling about 40% of the equity (2.5/6.2889).

5) Why other answers would be incorrect
- Dividing 2.5 by the total firm value (2.5/6.8889 ≈ 36.3%) is a common mistake because it ignores that debt reduces equity value. Selling 45% again would ignore the new capital structure. Using the $25M sale amount directly is incorrect because the market valuation is set by the investors’ $3.1M for 45%.

Conclusion: The total unlevered firm value is $6.9 million, and you must sell about 40% of the firm's equity after borrowing $0.6M—matching the provided answers.

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