Final answer:
To determine the valuation of a firm, divide the investment amount by the percentage stake the investor receives. For a $100,000 investment at an 11.111% stake, the valuation of the firm is $900,000, which is the post-money valuation including the investment.
Step-by-step explanation:
The valuation of a firm can be determined if a venture capitalist offers to invest a certain amount of money for a percentage stake in the firm. In the given scenario, a venture capitalist offered $100,000 for an 11.111% stake in a new venture. To find the full valuation, we can use the formula:
Valuation = Investment Amount / Percentage Stake
Hence, the valuation of the firm is:
Valuation = $100,000 / 0.11111 (which is the decimal form of 11.111%)
Valuation = $900,000
This valuation represents the post-money valuation, which accounts for the money to be invested. Therefore, the pre-money valuation, which refers to the company's valuation before the investment, would be $800,000 ($900,000 - $100,000).