
The Equity Equation - rams
http://paulgraham.com/equity.html
======
cperciva
Nice article, but drastically oversimplified. Paul ignores two critical
issues: Risk, and non-linear utility-of-money functions. These two factors
become critical when there is a tradeoff between probability of success and
the payoff of success.

Suppose, as a simple example, that I have a startup which I think has a 50%
chance of succeeding and being sold for $1M, and a 50% chance of failing and
being worthless. Now suppose that Paul selects me to participate in YC, but
wants 10% of the company, and I think his help will leave the potential
valuation unchanged but increase the chance of success from 50% to 55%. If I
accept his offer, my EXPECTED return drops from $500k (50% of $1M) to $495k
(55% of $900k) -- but I'd still accept the offer, because increasing my chance
of getting that first $900k is worth far more than getting an additional $100k
on top of that.

On the other hand, suppose a venture capital company comes along and offers to
help me expand into a much larger market, where I'd have a 10% chance of the
company being worth $100M (and a 90% chance of the company being worthless),
in exchange for taking 50% of the company stock. If I accept the offer, my
EXPECTED return jumps from $500k to $5M (10% of $50M) -- but there's no way
that I'd accept the offer, because I really don't want to spend years of my
life on something which has a 90% chance of being worthless.

It's important to understand the numbers, but in the end the numbers, at best,
have to guide you rather than making decisions for you.

~~~
pg
Actually not. That's why I was careful to speak of the effect of trading
equity on the "average outcome" rather than e.g. "average valuation at
liquidity." What I'm literally saying is, does the trade improve your odds of
getting what you want? That subsumes both your risk aversion and your utility
function for money.

~~~
cperciva
Your math is still wrong, because of the non-linear utility of money. If I
give up 6% of my company, it costs me 6% of any MONEY I might end up getting,
but it doesn't cost me 6% of the UTILITY. If I have a utility-of-money
function of sqrt($), you don't have to increase my chance of success by 6.4%;
it's enough if you increase my chance of success by 3.2%.

~~~
pg
"Outcome" means the output of the utility function, not the input.

~~~
cperciva
Then you're still wrong. I quote from the article: "For example, suppose Y
Combinator offers to fund you in return for 6% of your company. In this case,
n is .06 and 1/(1 - n) is 1.064. So you should take the deal if you believe we
can improve your average outcome by more than 6.4%."

If by "average outcome" you mean "expected value of the utility function", and
assuming that my utility-of-money function is sqrt($), I don't need to improve
my "average outcome" by more than 6.4% for the deal to be worth accepting;
it's enough if I can increase my "average outcome" by 3.2%, since that's how
much UTILITY giving up 6% of the MONEY costs me.

~~~
palish
If a man is wrong, you don't need to tell him so. Just give it a rest and let
others form their own opinions.

Seriously, these issues, and a lot of other issues, are covered in "How to Win
Friends and Influence People". Read it. If I could figure out a way to get you
to feel like you came up with the idea to read it, I would, but I can't, so
just read it.

~~~
pg
Actually, if someone is wrong about math you probably should tell him so.

~~~
palish
I agree. In private.

------
sethlevine
Paul - This is Seth Levine (quoted in the USA Today article referenced and
appropriately called out in your post). Let me set the record straight. While
I've seen plenty of articles come to press that has somewhat inaccurate
quotes, this was the first time I've been completely misrepresented in an
article. I've written a full post on my views here -
[http://sethlevine.typepad.com/vc_adventure/2007/07/setting-t...](http://sethlevine.typepad.com/vc_adventure/2007/07/setting-
the-rec.html). It's particularly frustrating in this case, as I've spent
literally hundreds of hours working with TechStars and TechStars companies in
Boulder this summer (and am the lead mentor to one very promising project). I
actually believe strongly in the model.

I hope you'll consider posting this response up to your main site with a
reference to my post clarifying my views.

seth levine

~~~
pg
Ok, if you were misquoted, I'll take that paragraph out.

------
Anonymous314
The article ignores how market prices work - the formula presented lets you
know the maximum equity you can give up and still get a positive return by
doing so, but incorrectly explains why VCs accept much less - the minimum
equity a VC can accept and still expect a positive return on their investment
can be far lower than the maximum the startup can afford to give profitably.
The VCs are subject to competition with other VCs, so in such cases they
cannot force the startup to accept a just-better-than-breakeven deal.

~~~
pg
Why can VCs afford to give up stock and founders not? Are you talking about
liquidation preferences?

Startups are just as subject to competition. There's a profit margin on taking
investment just as there is on hiring someone, and it expands and contracts
depending on how hot the startups is.

~~~
Anonymous314
I think I was unnecessarily unclear - let's say we're talking about buying
eggs. Suppose I'm willing to pay up to $3 for a dozen. That doesn't mean that
I should buy them if I find eggs for $2.99 - I should keep shopping around,
because grocers can profitably sell eggs for $2 a dozen, so I'm bound to find
eggs closer to the $2 mark. I need to take into account what would be
reasonable for the other party when deciding if a deal is reasonable, not just
the limits of what would be reasonable for me. If I'm stuck, and _everyone_ is
selling eggs for $3 a dozen, then it matters whether that's beyond my personal
threshold or not. If I _only_ note how close a deal is to my personal
threshold, without noting whether the other party would be likely to agree to
a more favorable deal, I'm liable to get ripped off, unless I have no leverage
for negotiating anyway, and I can only take it or leave it.

------
ivankirigin
Even in a simple model, time should be incorporated, right? The total cost for
the life of the company of an employee is included, assuming a particular
growth rate. What about for investment? "the total cost of this round of
funding" doesn't make sense so much. And surely the rate of increased value of
your company matters.

Also, it seems, like you note in the end, that there is still a gut feeling,
and here it is stated simply: how can you predict how much your company will
grow because of an investment?

This is easier if you have sales numbers that show some trend, where investing
$N in business development yields X more users leading to Y more profit. If
you're reddit, and you haven't even monetized your users before being
purchased, this can be harder. Also organic growth implies less direct
business development.

One simple question that I think has a standard/GAAP answer: how much is your
company worth if you are making $X yearly and growing at a rate of Y%? I
vaguely recall terms like "good-will estimates" and "present value of future
money" in the single management class I've taken years ago. But is there
something standard for a company going through valuation for acquisition or
taking a next round of funding. [Ignore for the moment that a company making a
nice profit and growing ideally wouldn't need a next round of funding.]

~~~
nostrademons
"how much is your company worth if you are making $X yearly and growing at a
rate of Y%"

In finance, the standard answer is "the net present value of all future cash
flows". Basically, all cash that the company throws off beyond expenses
technically belongs to the owners. However, owners could've parked their money
in T-bills instead of investing it, and they'd receive interest for it. So you
discount these future cash flows by a factor that depends on the rate of
interest and the time between investment and cash flow, and then sum up all
these discounted cash flows over the life of the company. If earnings are
growing, you just figure the increased earnings into your calculations.
<http://en.wikipedia.org/wiki/Net_present_value>

I dunno if VCs and acquirers use this method: they face a problem in that it's
notoriously difficult to estimate the future cash flows of an unprofitable
technology company. They might be building a stellar product and growing
market share for years, then suddenly start raising their prices when they
become a monopoly. Or they might be building a mediocre product and growing
market share for years, and then lose them all when they start raising their
prices and a competitor comes along.

~~~
ivankirigin
Thanks!

Then my earlier points are even more important. How much will your company be
worth? How much _more_ is it worth after taking more funding? Who knows? All
hard questions.

------
eposts
Was this article written in response to Seth Levines comment? What Seth Levine
doesn't know or doesn't want to tell is that a lot of YC alums could raise the
5K/founder on their own, so money is NOT the primary reason they are there.

~~~
pg
No, I'd been working on it for a while.

I'd been thinking of taking that footnote out, since it seemed like everyone
now finally understood us. But when I saw that old dumb argument again in the
USA Today article, I decided to leave it in.

~~~
ordersup
I can't help but laugh at the audacity of another tech-related investment firm
commenting like that. He _is_ trying to persuade people that YC is just
writing cheques.

~~~
pg
I'm never sure whether such people are clueless or deliberately misleading.
I'm inclined to give most the benefit of the doubt and say clueless. When you
change the model for something, it takes people a long time to get what you're
doing. I remember from web-based software.

~~~
pg
Maybe this is not so innocent as I thought. Apparently Seth Levine is the
partner of Brad Feld, the founder of Techstars:

<http://www.foundrygroup.com/team.php>

What a slimy move. It won't make any difference in the long run though.

~~~
garbowza
Definitely self-serving move, and certainly won't make any difference in the
end... articles like the USAToday one always need to find that contrarian view
in order to seem unbiased. I'm sure Seth Levine was all to happy to provide
them the material. But how would you feel if you were a Techstars startup
group and you see him making comments like that - blasting the model of his
partner's program!?

------
donna
From my perspective it's partically an emotional path, not merely an
analytical path. A company that's a startup has an intention, and it's one of
these:

1\. You use resources to incrementally grow a user base and get market share,
then sell it off to a bigger company

2\. You develop technology that enhances a company's market share and pulls
users from a competitive company's market

3\. You lose, and the investor loses a small amount of money

The bottom line for me is that the value of your start-up is based on the
number of users you can get. It's about your intention X with the assistence
of your investor will find the users and people you need. Whether it's a good
deal or not is irrelevant if those are not true - take the journey.

Whether it's a Mobius or another VC, for me as an entrepreneur, they have not
established a community tool to have access to a community that will help grow
the start-up quickly. You're not just buying equity in the equation X you're
buying into the community's collaboration.

The equity value is not just based on "here's some money for X cents on the
dollar" X it has to go beyond that.

~~~
byrneseyeview
"The equity value is not just based on "here's some money for X cents on the
dollar" X it has to go beyond that."

Uh, no it doesn't. Equity has value, and so does what you get when you give up
value. When you're like for like, emotional attachment doesn't make sense.

------
sanj
It's not an equation, but for employee options my gut has always been that you
get options as a function of how much your improve the odds of the company's
ultimate success.

Founders get a lot because they take it from zero to something.

Senior folks get a lot because the influence it significantly.

Early grants > Later grants because the ability to change the trajectory is
typically smaller.

------
togilvie
This is a nice analysis and good thinking, though it's worth noting that
liquidation preference makes the VC equation less favorable. I'm not sure how
Y Combinator works, but preference plays a shockingly large role when you run
these types of calculations against your hypothetical VC deal.

~~~
zach
Given PG's formulation, liquidation preference plays no part in the value-of-
equity equation, since it can be factored out into the average outcome.

But sure, it does tend to depress average outcome. Then again, if your outcome
is dominated by the presence of very-high-value possibilities, a reasonable
liquidation preference may be no big deal.

------
johnrob
A smart company would give 6% equity to YC just for the advice and publicity.
The cash is the least valuable part of the equation. 5k per person can be
saved up in a number of months, even for relatively low salaries if you are
stingy.

~~~
abstractbill
I'd honestly be surprised at this point if nobody has offered to _pay_ YC to
take equity in a startup.

~~~
nostrademons
Am trying to remember if I did that after I was rejected from SFP2005...I know
that I offered them free equity in exchange for advice and the ability to come
to the YC dinners, but I can't remember if I offered cash. Probably not, as I
was poor at the time.

My offer was ignored, BTW.

~~~
create_account
Not surprising... the benefit of getting accepted is getting face time for
advice and networking with potential investors at their dinners, etc., not the
funding.

If they said yes to that, there'd be no need to apply, we'll all just show up
at Graham's house every day.

~~~
nostrademons
Well, if they said yes to that, they'd have equity in a huge number of
companies too. ;-)

But yeah, I can understand why they didn't go for it. It's turned out that
yCombinator partner time is the scarcest resource in the Founders Programs. It
makes sense to concentrate that where it's most likely to have the most
effect, in the accepted founders. Which unfortunately doesn't include me.

This was for the first funding cycle though: at the time, nearly everyone
harped on the money and not on the fringe benefits. Maybe Graham et al knew
that partner bandwidth would be scarce, but I thought I was being clever by
going for the part I really needed and offering to give up the part that
didn't matter so much to me.

~~~
euccastro
It's not only time but respect too. The ability of YC to connect startups with
investors and acquirers depends on its ability and commitment to select only
the most promising teams. Anything that may look like a deviation from that
would harm the YC brand.

Waiving the cash suggests that you have your priorities right, but if YC
believes in you, that money serves you both better in your pocket than in
YC's, don't you think?

------
kalid
Here's a quick calc to help play with the numbers:

<http://tinyurl.com/yorkoq>

Feel free to click and change change any of the assumptions as you guys fight
it out :)

------
davemc500hats
at a high-level i agree with the post, however practically speaking, you're
overlooking several significant issues: 1) diff between preferred vs common
shares 2) liquidation preferences in terms sheets 3) supply/demand for
investor capital in the market 4) competitive position of VC/company in the
market 5) exit targets / preferences / restrictions by investors /
entrepreneurs

these 5 factors (& many others) have _DRAMATIC_ impact on the 1/(1-n)
calculation you mention. while i don't disagree with you in theory,
practically applied the outcomes matter a fuckload.

see leo dirac's presentation on term sheet liquidation preferences for just
one perspective on this: <http://www.embracingchaos.com/2007/08/vc-term-
sheets-.html> \- dave mcclure <http://500hats.typepad.com/>

------
EBB
Very good article thanks -- why am I not surprised? :-) Few minor points.
Sometimes, not often, your initial valuation may affect the subsequent rounds
(they shouldn't but may). Crowded cap tables are also problematic. Initial
employees contributions, however small, will entitle them to more shares that
the later ones -- which may cause discontent. Finally think about how many
6.7% you can give up?

I am not even going to get into option analysis; talk about introducing non-
linearities. But even in a linear stream Paul's footnote that YC combinator
brings to table a lot more than 6.7% (?) is probably correct, but it should
also take into account the effects of the multiplier of the later rounds and
options on both side.

------
jmah
But it's not that simple. Startups are always measured against their
competitors. So even if the 1/(1-n) shows that it is a net gain for me, it may
be an overall loss if my competitors make deals that are worth significantly
more for them.

------
daveschappell
My apologies -- here's a version with a better formatted URL for the Equity
Formulas spreadsheet:

<http://www.nosnivelling.com/Paul-Graham-equity-formulas.xls>

------
edfrench
For me, the question that the startup should ask more critically is around the
total dilution-to-exit. If taking Paul's money for 6% now reduces the dilution
at some subsequent round from, say, 40% to 30%, then by my reckoning the
founders end up with 66% instead of 60% of the final position. Key here is
usually a combination of the value-add from the VC, and their ability to
underwrite/cornerstone a good part of that follow-on round. (Although
obviously this is only relevant if a larger follow-on round is going to be
needed!)

------
EBB
I read only some of these comments and I have to say: EASY !!!

This is static analysis of a single decision; and it has to be viewed with
those limitations in mind.

Option analysis and risk, nor is dilution after each round is talked about
here. Yes if the Google founders had given shares left an right they would be
in serious trouble making isolated decisions. Nonetheless, it is hard if not
impossible to bring mathematical rationality to something fairly dynamic, if
not irrational.

------
SK
These comments are very confusing. Paul -- a simple question: doesn't the
amount of capital offered/invested have a big impact on the calculation? Sure
I'd give up 6% of my pre-natal company for $1 million. But would I for $1
thousand? No. Doesn't your analysis suggest that in both cases the calculation
is 1/(1-n)? Yet the ability to add 6.4% value at exit given $1 million is
vastly different than if given $1 thousand...

------
jemroc
I guess I'm the only dumb one here. Can someone explain to me how he came up
with the 1.5 as a multiplier for the new hire's salary? Also the part where he
talks about making a 50% "profit" on the new hire and then proceeds to
subtract a third from 16.7%. Why 50% and why 1/3? How did he come up with
those numbers? Please enlighten me.

------
spineofgod
ok, so we're a new c-corporation out of north carolina, three new unc mba
graduates with a fourth ruby coder out in pasadena. we have a hotmail-sized
concept with a working prototype already built. it's addictive, the kids are
going to love it (parents too). all we want to do is hire ourselves and knock
the project into beta. we also know that if we launch and gain x users right
out of the gate, we will be able to get a better deal from investors.

questions = what is x? how many users does a hot new web 2.0 service need
before jaded vc's start paying attention? what are the other eye openers in
your opinion? until i read this article, i had been of the point of view that
you should turn down all investment until you launch if at all possible. is
that correct or am i wrong?

\- Srini

------
bootstrapper
I am thoroughly fed-up hearing this self-serving tripe from investors.

If all I am looking for is financial independence (say $3M), why would I trade
an 80% probability of success for a 5% probability of achieving 100 times that
by selling out to VCs?

Sure, my expected return is 6 times greater, but now I need approximately 31
(=log 0.2 / log 0.95) bites at the cherry to guarantee an 80% probability [1]
of success. That's 6 lifetimes of startups for a serious serial entrepreneur
(most of us have energy for one, maybe two, startups).

Unlike VCs, who invest in a portfolio of companies, I don't have a portfolio
of lives.

[1] This assumes only two outcomes from a VC-backed company: zero return or
$300M exit. Obviously there are a range of returns, but this is a reasonable
approximation since VCs have no interest in seeing low returns - they'd rather
kill the company than waste their time.

~~~
pg
And I am thoroughly fed up with people who jump to conclusions after
misunderstanding something I've written, and post comments using language
they'd never use talking to someone in person. (At least, language I hope
they'd never use.)

This is covered in other essays, e.g.
<http://www.paulgraham.com/guidetoinvestors.html>

~~~
bootstrapper
I don't see how I have misunderstood you, eg:

"The reason Sequoia is such a good deal is that the percentage of the company
they take is artificially low. They don't even try to get market price for
their investment; they limit their holdings to leave the founders enough stock
to feel the company is still theirs."

If Sequoia took _ordinary_ stock for their money that argument would have some
legs. But otherwise, it is self-serving (for the VCs). Once you take their
money at valuation X, liquidation preferences and control clauses guarantee
that you're not getting anything until the company is worth at least 10X. It
doesn't matter whether the founders still have 95%, they've given up control
over the outcome that matters to them.

Angels are a different story. I have angel investors myself, carefully chosen,
and with a term sheet that is much fairer than anything you'll get from VCs
(they can't screw me; I can't screw them).

I used to have some deference for VCs, but after hearing their self-serving
arguments and witnessing their arrogance for years, I don't waste my time
(being profitable also helps).

Don't get me wrong, we could grow faster with VC money, and I'd do it on the
right terms. But these days, if a VC contacts me I always ask them within the
first 2 minutes whether they'd invest on similar terms to the existing angels.
The answer is always "no". They never have a good response to the obvious
question: "how do your terms make sense for a founder?".

As for language, I apologise. I have not used the expression "self-serving
tripe" in person with a VC, but I've been close. They need to hear it
sometimes.

~~~
pg
What you misunderstood was that this article was simply about the math of
trading equity, not higher level issues like one's personal goals, which I
talk about elsewhere.

Incidentally, your specific claim that if you take VC money "you're not
getting anything until the company is worth at least 10X" is false. Many VCs,
including Sequoia, will let founders sell some of their stock on the way up
for diversification. Such deals are usually kept quiet, but they're quite
common.

~~~
bootstrapper
Trading equity only makes sense in terms of my goals. The founders own 90% of
this company. We're not trading equity unless the math makes sense. If your
math says it makes sense when it doesn't, your math is wrong (specifically,
money has nonlinear utility for founders, but linear utility for VCs, or more
specifically, for limited VC partners).

"Many VCs, including Sequoia, will _let_ founders sell some of their stock on
the way up"

How very generous of them. They may deign to "let" you sell some of your
stock. Come hither dumb hacker, trade that unencumbered stock for paper you
don't even have the right to sell. And just to prove how generous we are,
we'll let you keep 70% of the paper no one is allowed to sell (of course, we
reserve the right to do whatever we please with our 30%).

Be in no doubt that they 0wn your ass, regardless of the percentage of your
company they have. Hence why discussion of equity percentages makes no sense
unless we're comparing the same class of stock.

~~~
ph0rque
hey bootstrapper, what is your company?

------
daveschappell
Just in case readers would like the formulas in a simple spreadsheet, I posted
it as a download from my server:

<http://www.nosnivelling.com/Paul> Graham equity formulas.xls

------
innonate
So very useful. These are issues we all have to parse through and while you
note it's not a magic formula, it's certainly a good one to understand as a
young entrepreneur. Thanks. Nate Westheimer BricaBox.com

------
dawie
Paul, I really liked your article and I have always wondered about working out
these financial details. Its cool how you did it for employees. I liked the
fact that you kept it simple.

~~~
adamdoupe
The famous KISS principle. In case you don't know: Keep It Simple, Stupid

------
mulcher
Great article! Very informative.. I think you just improved my prospects by
10% and that advice was free!

------
shahper
Sorry for my ignorance, how can one calculate his company value ?

~~~
mulcher
Most of the time it is made up..

The theory is that the market will grow and/or you will exhibit exponential
growth. Take for example Google which is valued by the outstanding shares
value (market cap) which is driven mostly by public perception of market
growth and Google's operation with respect to real and perceived growth..

So apply this to your startup.. get VCs to bid on it.. If you have revenues
then you can go to a bank and see what type of credit line your business
qualifies for. But since most startups don't have revenue then you really
don't know.

Essentially your initial idea is worth $0... this is why angel investors are
nice to have. They make the first real valuation.

------
superpepe
How can you determine the improved outcome? thanks!

