Final answer:
The total market value of the firm without leverage is calculated by dividing the $4 million investment by the 45% equity stake the investors receive, which equals approximately $8.89 million. This valuation assumes the firm's research is successful. Venture capital is known for being high-risk but potentially high reward.
Step-by-step explanation:
To determine the total market value of the unlevered firm, we work with the information that investors are ready to pay $4 million for a 45% equity stake in the firm. This implies that their investment reflects their valuation of that portion of the firm's equity. Therefore, to calculate the total market value of the firm without leverage, we divide the investor's $4 million investment by their 45% equity stake.
The calculation would be $4 million divided by 0.45, yielding approximately $8.89 million as the total market value of the firm. This is under the assumption that the firm's research is successful and the technology can be sold for $25 million. However, this valuation is speculative because success is not guaranteed, and in the case of failure, the technology would be worth nothing—as per the scenario described in the question.
It is important to note that venture capital is a high-risk, high-reward industry, and investors take calculated risks knowing that while many startups may fail, a successful investment in a firm like a biotech company could yield substantial returns.