# Venture Capital Deal Algebra

Fred Wilson wrote a useful post on valuation today. It reminded me of a document I had Dave Jilk write when he was doing some work for me. I decided to write this “bladon” (Blog Add-on) post – inspired by Fred. Please read Fred’s post first – it lays the groundwork for why VCs do things this way.

I’ve found that even sophisticated entrepreneurs didn’t necessary grasp how valuation math (or “deal algebra”) worked. VCs talk about pre-money, post-money, and share price as though these were universally defined terms that the average American voter would understand. To insure everyone is talking about the same thing, I started passing out this document. Recognize that this is about the math behind the calculations, not the philosophy of valuation (which Fred’s blog addresses).

In a 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 “worth.”
• Great post. One additional suggestion would be to discuss the differences between preferences and participation – a subtle point that had to be explained to me a few times until I really understood it – and why simple preferences are actually good for a deal, since they increase trust around the table…

Dave

• Great post. One additional suggestion would be to discuss the differences between preferences and participation – a subtle point that had to be explained to me a few times until I really understood it – and why simple preferences are actually good for a deal, since they increase trust around the table…

Dave

• May I suggest that you next talk about investment rounds and discounting, please.

I've always supposed this valuation game goes somewhat like this:

1. Assume "final, desired" valuation V, at exit-time, Y years into the future.

2. Discount V (40-70%?) back to the present, giving V', the current valuation. Discount factor is subjective and depends on the perceived risk, of course.

How this ties into multiple rounds (with possibly different investors at each round) is what I'm unclear about, e.g., wrt number of shares to be issued at each round, etc.

Thanks.

• May I suggest that you next talk about investment rounds and discounting, please.

I've always supposed this valuation game goes somewhat like this:

1. Assume “final, desired” valuation V, at exit-time, Y years into the future.

2. Discount V (40-70%?) back to the present, giving V', the current valuation. Discount factor is subjective and depends on the perceived risk, of course.

How this ties into multiple rounds (with possibly different investors at each round) is what I'm unclear about, e.g., wrt number of shares to be issued at each round, etc.

Thanks.

• Venture Capital Deal Algebra
http://www.feld.com/blog/archives/2004/07/venture….

• Venture Capital Deal Algebra

• Dave Jilk

I can comment on the two prior comments:

Regarding investment rounds and discounting, the author clearly is thinking in terms of traditional corporate finance where value is discounted from some expected future value based on risk/volatility. Nothing could be further from the reality of early stage venture capital valuations. A true mezzanine (immediately pre-IPO) round might have some discounted value features.

Instead, valuations in institutional venture capital are primarily driven by prevailing trends, typical stage-related capital needs, and cap table expectations of later stage investors. For example, most Series A investors will look to take 30%-45% of the company on a fully-diluted basis for a \$2-4m investment. In 2001-2002, valuations were so low that it was hard to get Series A money, because investors could get the same pre-money for a Series B round in a company that had customers and revenue. There is much more to say here, but I'll end by noting that I have not mentioned expected future value or risk — early stage investors assume these to be roughly constants for a given stage of deal, if they like the market and the management team.

Note that one may run into VCs who try to do financial analysis of the kind mentioned, using an adjusted version of the company's financial model. These VCs do you a great service by demonstrating that they know next to nothing about early stage investing and therefore will be difficult to deal with in board meetings.

Regarding preferences and participation:

These are both potential features of preferred stock, the typical form in which a venture capital investor will have its holdings in the company. Most preferred stock is convertible into common stock, so in a liquidity event (when the company is sold or liquidated — IPOs usually require a conversion to common), the investor has the option to convert the preferred shares into common and receive its pro-rata share of the proceeds, or retain the preferred shares and receive a preferential share of the proceeds.

In the latter case, a "preference" simply describes how much the preferred shareholders receive before the remainder of the proceeds are divvied up among the common shareholders. A typical situation is that the investors get back their original investment, a 1-X preference. In some cases the investor is more aggressive and requires a multiple of the investment, e.g., a 2-X preference. In this case, if they invested \$3m, they will receive \$6m in proceeds before the common shareholders receive anything. Clearly one can calculate the liquidated value where conversion to common is better for the preferred shareholder.

The allocations of preferences among different series of preferred stock can get very complicated — sometimes it is pro-rata, sometimes it is tiered (Series C first, then B, etc.) However, the preferences can usually (not always) be summarized with a single number called "preference overhang," which is the amount of liquidation proceeds that go to the preferred shareholders before the common shareholders divide up what remains. This is the number that the founders and optionholders normally care about.

A "participate" is sometimes (by entrepreneurs) referred to as a "double-dip." What this means is that the preferred shareholders can retain their preferred stock in a liquidation event, receive their liquidation preference before the common shareholders receive anything, and then RECEIVE THEIR PRO-RATA SHARE OF THE REST. So for example, if the investors have a 1-X liquidation preference, invested \$2m for 30% of the company, and it is sold for \$5m, then they get a \$2m liquidation preference and 30% of the remaining \$3m, or \$900K, for a total of \$2.9m.

Thankfully, participates are usually capped at a multiple of the original investment, typically 2 to 5 times the investment.

Some venture firms avoid participates because it only encourages later stage investors to be aggressive in asking for them, and this causes the early stage investors to do worse in the long run. Entrepreneurs, especially less-seasoned ones, often see participates as somehow "unfair." It's not really unfair if you have no other financing options, but it does tell you something about how the VC will treat you going forward.

• Dave Jilk

I can comment on the two prior comments:

Regarding investment rounds and discounting, the author clearly is thinking in terms of traditional corporate finance where value is discounted from some expected future value based on risk/volatility. Nothing could be further from the reality of early stage venture capital valuations. A true mezzanine (immediately pre-IPO) round might have some discounted value features.

Instead, valuations in institutional venture capital are primarily driven by prevailing trends, typical stage-related capital needs, and cap table expectations of later stage investors. For example, most Series A investors will look to take 30%-45% of the company on a fully-diluted basis for a \$2-4m investment. In 2001-2002, valuations were so low that it was hard to get Series A money, because investors could get the same pre-money for a Series B round in a company that had customers and revenue. There is much more to say here, but I'll end by noting that I have not mentioned expected future value or risk — early stage investors assume these to be roughly constants for a given stage of deal, if they like the market and the management team.

Note that one may run into VCs who try to do financial analysis of the kind mentioned, using an adjusted version of the company's financial model. These VCs do you a great service by demonstrating that they know next to nothing about early stage investing and therefore will be difficult to deal with in board meetings.

Regarding preferences and participation:

These are both potential features of preferred stock, the typical form in which a venture capital investor will have its holdings in the company. Most preferred stock is convertible into common stock, so in a liquidity event (when the company is sold or liquidated — IPOs usually require a conversion to common), the investor has the option to convert the preferred shares into common and receive its pro-rata share of the proceeds, or retain the preferred shares and receive a preferential share of the proceeds.

In the latter case, a “preference” simply describes how much the preferred shareholders receive before the remainder of the proceeds are divvied up among the common shareholders. A typical situation is that the investors get back their original investment, a 1-X preference. In some cases the investor is more aggressive and requires a multiple of the investment, e.g., a 2-X preference. In this case, if they invested \$3m, they will receive \$6m in proceeds before the common shareholders receive anything. Clearly one can calculate the liquidated value where conversion to common is better for the preferred shareholder.

The allocations of preferences among different series of preferred stock can get very complicated — sometimes it is pro-rata, sometimes it is tiered (Series C first, then B, etc.) However, the preferences can usually (not always) be summarized with a single number called “preference overhang,” which is the amount of liquidation proceeds that go to the preferred shareholders before the common shareholders divide up what remains. This is the number that the founders and optionholders normally care about.

A “participate” is sometimes (by entrepreneurs) referred to as a “double-dip.” What this means is that the preferred shareholders can retain their preferred stock in a liquidation event, receive their liquidation preference before the common shareholders receive anything, and then RECEIVE THEIR PRO-RATA SHARE OF THE REST. So for example, if the investors have a 1-X liquidation preference, invested \$2m for 30% of the company, and it is sold for \$5m, then they get a \$2m liquidation preference and 30% of the remaining \$3m, or \$900K, for a total of \$2.9m.

Thankfully, participates are usually capped at a multiple of the original investment, typically 2 to 5 times the investment.

Some venture firms avoid participates because it only encourages later stage investors to be aggressive in asking for them, and this causes the early stage investors to do worse in the long run. Entrepreneurs, especially less-seasoned ones, often see participates as somehow “unfair.” It's not really unfair if you have no other financing options, but it does tell you something about how the VC will treat you going forward.

• Venture Capital Deal Algebra

• Well, what about antidilution? Nothing like reading it from seasoned pros

• Well, what about antidilution? Nothing like reading it from seasoned pros

• Heh heh. I've really seen/read presentations that use the corporate finance discounting method for VC valuations, by VCs or maybe people who coach other people on dealing with VCs. 😉

Thanks for the clarification on both counts.

• Heh heh. I've really seen/read presentations that use the corporate finance discounting method for VC valuations, by VCs or maybe people who coach other people on dealing with VCs. 😉

Thanks for the clarification on both counts.

• Valuation

I have been reading up lately on Venture Capitalist as part of my research. Being always fascinated with the work they do, most of the research I do has been kind of entertaining since I like reading about startups.

From what I have read, although t…

• Valuation

I have been reading up lately on Venture Capitalist as part of my research. Being always fascinated with the work they do, most of the research I do has been kind of entertaining since I like reading about startups.

From what I have read, although t…

• Five year cash flow predictions

Predicting your business is always tricky. Especially in cases where you have not yet started. A young industry with less…

• Valuaci

• Valuaci

• Valuaci

• Another way to look at this topic is "deals are negotiated on percents, but structured on shares." I walk through the implications of this and some examples at http://www.andrew.cmu.edu/user/fd0n/2%20Arithmeti… & http://www.andrew.cmu.edu/user/fd0n/3%20Arithmeti

• Another way to look at this topic is “deals are negotiated on percents, but structured on shares.” I walk through the implications of this and some examples at http://www.andrew.cmu.edu/user/fd0n/2%20Arithmeti… & http://www.andrew.cmu.edu/user/fd0n/3%20Arithmeti

• Alain Chetrit

How do VCs get compensated by their limited partners? What protective provisions and preferences do Limiteds have?

• Raj

regarding carving a certain percentage option pool before round 1, how do round 1 VCs feel about maintaining that percentage post round 2 ?

• anand

When a comapany has given that they hav raised series A,Series B and Second round of financing. i want a clarification that when u show their financings how do show them. means either show in a Series format or a Round format, if company is given both series and round how should i convert those rounds into Series.

• Anand – I’m not sure I understand your question. The terms “Series” and “Round” are often interchangable, although you might have multiple “rounds” that are the same “Series.” Series tends to link directly to the terms; Rounds are individual financing events. These are often – but not always – the same things.

• This was a helpful post and some of the links were also valuable. As a referrence, there is a burgenoning site that has captured rules of thumb for the finance and venture capital industry. It is a wiki page so that users can easily add their own rules of thumb.

http://www.rulesofthumbs.com

• Hi Everyone!,

I was wondering how to evaluate a dot com startup in the consumer internet space prior to approaching VC’s. Shall be just ask the VC’s on what they think is a fair valuation or go by industry experiences of investments made in similar space? Some suggestions will surely help.

Regards
Anil Tandon

• Rajiv Seth

I am surprised by one comment in Dave Jilk’s post – that those who do financial analysis for an early stage company know nothing about investing. It is strange for me to hear that every early stage company has the same valuation, as is implied by a \$2-4 m for a 35-40% stake. Would others agree to such a sweeping generalization?

• Rajiv Seth

Found some downround math here: http://www.financeoutlook.com/index.php?itemid=25

• “Venture Capital Deal Algebra” discusses the basic concepts of "pre-money" and "post-money" valuation and how to calculate the shares to be issued. Among the information it shares are some very simple formulas that could be extremely helpful for deal novices.
—————-
Stellathomas

• Curious

Might you be able to elaborate on the below? Thank you!

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 “worth.”

• This is a fancy way of saying “early stage valuations are arbitrary and negotiated, rather than based on a set of financial models.”

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• It's a difficult thing to listen to feedback from your initial users, the first 25,000, and do the opposite of what they recommend. You alienate your "support base" etc etc. Tough situation.

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