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Valuation Algebra
Ever wonder why many smart investors are able to calculate valuations and other investment related numbers in their heads? During deal negotiations, this used to both amaze and confound me until a good friend explained the process in terms that almost anyone can understand. It took me a while but I think I can safely say that even sophisticated entrepreneurs don’t grasp how valuation math works. VCs talk about pre-money, post-money, and share price as though these were universally defined terms that the average citizen is expected to understand. To ensure that everyone is talking about the same thing, I started forwarding the following explanation. Folks, this is about the math behind the calculations, not the philosophy of valuation.
In a private equity or venture capital investment, the terminology and mathematics can seem confusing at first, particularly given that the investors are able to calculate the relevant numbers in their heads. The concepts are actually not complicated, and with a few simple algebraic tips you will be able to do the math in your head as well, leading to more effective negotiation.
The essence of a venture capital transaction is that the investor puts cash in the company in return for newly-issued shares in the company. The state of affairs immediately prior to the transaction is referred to as ‘pre-money,’ and immediately after the transaction ‘post-money’.
The value of the whole company before the transaction, called the ‘pre-money valuation’ (and similar to a market capitalization) is just the share price times the number of shares outstanding before the transaction:
Pre-money Valuation = Share Price * Pre-money Shares
The total amount invested is just the share price times the number of shares purchased:
Investment = Share Price * Shares Issued
Unlike when you buy publicly traded shares, however, the shares purchased in a venture capital investment are new shares, leading to a change in the number of shares outstanding:
Post-money Shares = Pre-money Shares + Shares Issued
And because the only immediate effect of the transaction on the value of the company is to increase the amount of cash it has, the valuation after the transaction is just increased by the amount of that cash:
Post-money Valuation = Pre-money Valuation + Investment
The portion of the company owned by the investors after the deal will just be the number of shares they purchased divided by the total shares outstanding:
Fraction Owned = Shares Issued /Post-money Shares
Using some simple algebra (substitute from the earlier equations), we find out that there is another way to view this:
Fraction Owned = Investment / Post-money Valuation = Investment / (Pre-money Valuation + Investment)
So when an investor proposes an investment of $2 million at $3 million ‘pre’ (short for premoney valuation), this means that the investors will own 40% of the company after the transaction:
$2m / ($3m + $2m) = 2/5 = 40%
And if you have 1.5 million shares outstanding prior to the investment, you can calculate the price per share:
Share Price = Pre-money Valuation / Pre-money Shares = $3m / 1.5m = $2.00
As well as the number of shares issued:
Shares Issued = Investment /Share Price = $2m / $2.00 = 1m
The key trick to remember is that share price is easier to calculate with pre-money numbers, and fraction of ownership is easier to calculate with post-money numbers; you switch back and forth by adding or subtracting the amount of the investment. It is also important to note that the share price is the same before and after the deal, which can also be shown with some simple algebraic manipulations.
A few other points to note:
- Investors will almost always require that the company set aside additional shares for a stock option plan for employees. Investors will assume and require that these shares are set aside prior to the investment, thus diluting the founders.
- If there are multiple investors, they must be treated as one in the calculations above.
- To determine an individual ownership fraction, divide the individual investment by the post-money valuation for the entire deal.
- For a subsequent financing, to keep the share price flat the pre-money valuation of the new investment must be the same as the post-money valuation of the prior investment.
- For early-stage companies, venture investors are normally interested in owning a particular fraction of the company for an appropriate investment. The valuation is actually a derived number and does not really mean anything about what the business is actually ‘worth.’
OK… how about a shortcut if there are existing investors and you know both how much they invested and also the percentage ownership they have. Let’s say that investor Z paid $4m for 12% of company Y. This translates to 100%/12% = 8.3 and $4m x 8.3= $33.3m. So from the perspective of investor Z, the company was worth $33.3m at the time s/he purchased the shares.