Let's break down the problem step by step to answer the three parts.

a. What is the implied price per share?

The venture capitalist (VC) is offering $1.07 million for 780,000 new shares. To find the implied price per share, we simply divide the amount of money the VC is offering by the number of shares they are buying:

$\text{Implied Price Per Share} = \frac{\text{Amount Offered}}{\text{Number of Shares Bought}} = \frac{1,070,000}{780,000} = 1.3718$

So, the implied price per share is $1.3718.

b. What is the post-money valuation?

The post-money valuation is the total value of the company after the investment. This is calculated by multiplying the implied price per share by the total number of shares in the company after the investment.

Before the investment, you own 5.46 million shares. After the investment, there will be 5.46 million existing shares plus 780,000 new shares, which gives:

$\text{Total Shares After Investment} = 5,460,000 + 780,000 = 6,240,000$

Now, multiply the total number of shares by the implied price per share:

$\text{Post-Money Valuation} = \text{Total Shares After Investment} \times \text{Implied Price Per Share} = 6,240,000 \times 1.3718 = 8,561,664$

So, the post-money valuation is $8.5617 million.

c. What fraction of the firm will you own after the investment?

Before the investment, you owned 100% of the company. After the investment, you will still own your 5.46 million shares, but the total number of shares has increased due to the VC's investment. The fraction of the firm you will own is the ratio of your shares to the total number of shares after the investment:

$\text{Fraction Owned} = \frac{\text{Your Shares}}{\text{Total Shares After Investment}} = \frac{5,460,000}{6,240,000} = 0.8740$

So, you will own approximately 87.4% of the firm after the investment.

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Summary:

• Implied Price Per Share: $1.3718
• Post-Money Valuation: $8.5617 million
• Fraction of the Firm You Will Own After Investment: 87.4%

Would you like further details on any of these steps?

5 Related Questions:

1. How does the post-money valuation differ from the pre-money valuation?
2. What happens to your ownership percentage if the VC invests in more shares?
3. How does the price per share change if the VC's offer increases?
4. What if the VC's offer was for fewer shares? How would it affect ownership?
5. How does this investment affect future fundraising rounds?

Tip:

When calculating valuations and ownership percentages, always be mindful of both the pre-money and post-money valuations to fully understand your dilution and the company's worth.