✏️ Ownership Fractions and Post Money Valuation

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One equation that is familiar but helpful is

$$\% ownership = \frac{\# SharesYouOwn}{\# SharesTotal}$$

If new shares are issued:
$\%\ ownershipfor\ new\ owner = \frac{\# SharesIssued}{\# SharesIssued + \# SharesOriginal}$

✏️ If a firm has $5M$ shares outstanding and issues $1M$ more shares to a small VC for $\$67M$, what percentage of the firm does the VC own?

✔ Click here to view answer

We could use either formula for this:

$\%\ ownershipfor\ VC = \frac{\# SharesYouOwn}{\# SharesTotal} = \frac{1M}{6M} = 16.67\%$

$\%\ ownershipfor\ original\ investors = \frac{\# SharesYouOwn}{\# SharesTotal} = \frac{5M}{6M} = 83.33\%$

$\%\ ownershipfor\ new\ owner = \frac{1M}{1M + 5M} = 16.67\%$

Post money valuation

Post-money valuation is just calculating the market cap using the share price from the most recent financing transaction. We return to the previous example:

✏️ If a firm has $5M$ shares outstanding and issues $1M$ more shares to a small VC for $\$67M$, what is the post-money valuation?

✔ Click here to view answer

These shares were purchased for $\$67$ each:

$$\frac{TotalPrice}{Total \;\# \;Shares} = \frac{\$67M}{1M} = \$67$$

Currently, there are $6M$ shares outstanding. Therefore, the new market cap, using the new share price, is:

$$6M \ × \$67 = \$402M$$

↑ Note that when doing a “post-money valuation,” you use all numbers from after the investment. Specifically, you use the new number of shares outstanding: $6M$, not $5M$.

Bruce’s example:

✏️ You founded your own firm two years ago. You initially contributed $\$100,000$ of your money and, in return received $1,500,000 shares of stock$. Since then, you have sold an additional $500,000$ shares to angel investors. You are now considering raising even more capital from a venture capitalist (VC).

This VC would invest $\$6 million$ and would receive $3 million$ newly issued shares. What is the post-money valuation? Assuming that this is the VC’s first investment in your company, what percentage of the firm will she end up owning? What percentage will you own?

✔ Click here to view answer

The key #s are: Shares before transaction = $2M$
New Shares = $3M$
New Share Price = $6M/3M ← = TotalVCPrice/Total#VCShare

Post money valuation = $5M × \$2 = \$10M$ ← using the market cap formula using the new numbers

$\% \;owned \;by \;VC = 3M/5M = 60\%$
% owned by original investors $= 2M/5M = 40\%$
% owned by you $= 1.5M/5M = 30\%$

↑↑ Note that you originally paid $\$100K/1.5M = \$0.0667$ per share, but that price is out of date now. Now the best estimate of the share value is $\$2$.

To calculate the value of any ownership position in the firm, just multiply the %ownership times the market cap. For example, if you own 15% of a company that has a post-money valuation of $20M, then the value of your stake is $3M

Formula #1:

$$\begin{aligned} \text{\% ownership} × \text{valuation of firm} &= \text{valuation of your stake in firm} \\ 15\% × \$20M &= \$3M \end{aligned}$$

A second way to solve this is just to multiply the # of shares you have times the new (post money) price:

Formula #2: valuation of your stake in firm = #SharesYouOwn × $PricePerShare

✏️ Returning to the original example, what is the value of your stake in the firm?

✔ Click here to view answer

Let’s calculate this using both formulas:

Formula #1: Value of My Shares = %ownership × valuation of firm = 30% * $10M = $3M

Formula #2: Value of My Shares = #SharesYouOwn × $PricePerShare = 1.5M × $2 = $3M

Databricks Example

https://techcrunch.com/2021/08/31/databricks-raises-1-6b-at-38b-valuation-as-it-blasts-past-600m-arr/?guccounter=1>

Featured Article

Databricks raises $1.6B at $38B valuation as it blasts past $600M ARR

Rapid growth helps Databricks scale its private-market valuation

Databricks this morning confirmed earlier reports that it was raising new capital at a higher valuation. The data- and AI-focused company has secured a $1.6 billion round at a $38 billion valuation, it said. Bloomberg first reported last week that Databricks was pursuing new capital at that price.

The Series H was led by Counterpoint Global, a Morgan Stanley fund. Other new investors included Baillie Gifford, UC Investments and ClearBridge. A grip of prior investors also kicked in cash to the round.

The new funding brings Databricks’ total private funding raised to $3.5 billion. Notably, its latest raise comes just seven months after the late-stage startup raised $1 billion on a $28 billion valuation. Its new valuation represents paper value creation in excess of $1 billion per month.

The valuation typically used in articles like this is the post-money valuation. Therefore, in this question, we are given the post-money valuation and the investment amount.

✏️ What percentage of the firm did the most recent investors and the previous investors receive?

✔ Click here to view answer

We will be using the following formula from above:

%ownership × valuation of firm = valuation of your stake in firm

At this point, we just Plug and chug: (help)

1. Equation → %ownership × valuation of firm = valuation of your stake in firm

2. Plug 🔌 → Starting with the previous round: %ownership × $28B = $1B

3. Solve 🚂 → %ownership = $1B / $28B = 1/28= 3.57%

4. 🧠 → If you own 3.57% of a $28B firm, your stake should be worth 3.57%*28=$0.9996B ✔

We can do the current round more quickly: $1.6B/$38B = 1/6/38 = 0.0044

	Previous Round (7 months ago)	Current Round (now)
Valuation	$28B	$38B
Investment	$1B	$1.6B
% Ownership	3.57%	4.4%

Let’s add additional numbers to make this more interesting. We don’t know the true numbers, but let’s make assumptions to make this a better example.

Eight months ago, there had been approximately $3.5B - $1B - $1.6B = $900M of funding. Let’s assume that there are currently 900 million shares outstanding.

✏️ What was the price per share in the previous round of financing. How many shares were created in that round?

✔ Click here to view answer

✔When in doubt, use plug and chug. We will start by calculating how many shares created in the firm.

Plug and chug: (help)

1. Equation → We know the new % ownership in the firm: 3.57%. We also assumed above that previous to that investment, there were 900 million shares outstanding. We want to know how many shares were created.

$\%\ ownershipfor\ new\ owner = \frac{\# SharesIssued}{\# SharesIssued + \# SharesOriginal}$

2. Plug 🔌 →

$$3.57\% = \frac{\# SharesIssued}{\# SharesIssued + 900M}$$

3. Solve 🚂 →

3.57% = y /(y+900M)
3.57% × (y+900M)= y
3.57% y + 3.57*900M = y ← next, subtract 3.57% from both sides
3.57% y + 3.57*900M = y - 3.57%y = 96.43% y
$32.13M = 96.43% y
y = 32.13/96.43% = 33.32M shares issued

4. 🧠 → Let’s confirm that this new investor ends up with 3.57% of the firm.

$$\begin{aligned} \text{\% ownership} &= \frac{\# SharesYouOwn}{\# SharesTotal} \\ &= \frac{33.32}{933.32} \\ &= 3.57 \% \end{aligned}$$

Next, let’s calculate the share price. Based on the new share price the firm is now worth $28B and there are 933.32M shares. This implies a share price of 28/.93332=$30