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The Equity Equation (paulgraham.com)
72 points by rams on July 18, 2007 | hide | past | favorite | 156 comments



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.


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.


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%.


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


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.


Suppose your present hope of future utility from your startup varies linearly with the number of shares. (This is not a radical assumption; essentially all startup shareholders feel this, at least for numbers near that of shares they own.) Suppose you trade 6% of your stock in a deal that will increase your average future utility by 6.4%. You've made a straight trade of hope of future utility for future utility. We don't even have to introduce money.


IF the expected utility varies linearly with the number of shares (and thus the expected amount of money received in the end), you're absolutely right. But does it?

For large investment or VC funds, the utility-of-money function associated with any particular investment is almost linear. There's a very good reason for this: As far as Sequoia is concerned, a dollar earned from their Google stock is pretty much equivalent to a dollar earned from their Loopt stock. Not quite equivalent, since there are non-tangible advantages for a VC fund to have many smaller success stories instead of one Google; but close.

As you point out in http://www.paulgraham.com/vcsqueeze.html, founders aren't "rational" in the sense of having the same approximately linear utility-of-money function as VCs: "... letting the founders sell a little stock early would generally be better for the company, because it would cause the founders' attitudes toward risk to be aligned with the VCs'. As things currently work, their attitudes toward risk tend to be diametrically opposed: the founders, who have nothing, would prefer a 100% chance of $1 million to a 20% chance of $10 million, while the VCs can afford to be "rational" and prefer the latter."

There's another reason to think that most people have concave utility-of-money curves: The insurance industry. If you buy house insurance, you are lowering your expected number of dollars (because even ignoring market friction, the insurance companies have to make a profit), but raising your expected utility.


Yes, for most founders hope of future happiness varies linearly with the number of shares-- at least, in the region of the number of shares they have. If someone gave them 10% more stock, they'd feel 10% richer-on-paper. (There are anomalies at the extremes. E.g. if you got 100% of the stock, your cofounders wouldn't be motivated, and that would decrease the value of your shares.)


You seem more suited to the VC side of the table, rather than the entrepreneur side.


"Know thy enemy". :-)


Not to split hairs, but at different points you said

- that for essentially all startup shareholders, the present hope of future utility varies linearly with the number of shares, and

- that the utility function for most founders is a step function.

Both sound right to me separately, but don't they contradict each other? Maybe most founders just live with this paradox without realising?


No, I don't think they contradict one another. The reason is that the most likely outcome is just to the right of the step.

Most startup founders (initially at least) hope to get a few million, and wouldn't risk that to get a few billion. That's the step. And the most common form of liquidity event is a small-scale acquisition that gives the founders just that level of wealth, since otherwise they won't sell. So in the most common (and most commonly hoped for) good outcome, happiness varies linearly with the number of shares.


Since you're talking about step functions and expectation, the final equation should be framed with a binary parameter in mind: x=0 (no liquidity event occurs), x=1 (liquidity occurs).


"The reason is that the most likely outcome is just to the right of the step."

"So in the most common (and most commonly hoped for) good outcome [...]"

Isn't the omission of good in the first paragraph a lapsus, i.e., do you mean most founders think success is the most likely outcome? Or do you mean founders should ignore the possibility of failure for the purposes of making these decisions about stock?


Yes, sorry, I meant good outcome.


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.


I know you are well intentioned, but if I'm full of it I'd rather someone told me, preferrably in a respectful but blunt way. I'll form my own opinion anyway.

I know I took criticism personally and reacted very badly once or twice in the past, so I see your point. But I realised I was being a baby and grew from the experience. No speech on humility can make you humble. At best, it will convince you you should be humble, and maybe by acting humble some of it will sink in and stick. Real humility comes from realising your mistakes. [Edit:] That's painful at first, but necessary to get over your ego.

[PS: Sorry, I drifted into replying to other comments of yours, and the end result may be confusing.]


You're right, of course.


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


I agree. In private.


You should tell him he's wrong, but you shouldn't be a jerk or gloat about it, which cperciva wasn't.


No, really.. It is wise to never publically tell someone they are wrong, unless you're defending someone. You should wait until his friends and colleagues have left his side, then whisper your opinion into his ear. In the Internet world, that means sending him an email. To not do so is bad karma in every sense of the word.. My post above was modded down because I publically pointed out that he was wrong to point out Paul's percieved flaws in public; maybe I should have sent him an email instead. This wisdom is proven true over and over. My #lisp fiasco convinced me of that (long story).


You're wrong to tell people they're wrong to publicly tell people they're wrong.

Most mature and intelligent people love it when someone is able to offer useful critiques of their work, as long as they're civil about it. For example: http://en.wikipedia.org/wiki/Socratic_method


I don't see in there where you should prefix everything with "What an oversimplification! You're wrong, wrong, wrong!"

Seriously, would you want this guy making a few million? Not only would he be a douche, but he'd be a rich douche. Imagine how he'd treat his waitresses and waiters then. Or his local cops. Or anyone not as smart as he is, which is, apparently, EVERYONE. I'd even call him a detriment to our society, because the child just seems to act like a Paris Hilton with brains. Smart people can be civil, and it's just silly to watch everyone go "Cperciva you're so awesome! You should do X with your life!" and him go "Oh ho ho, didn't you think I already considered that? I turned down a headhunter yesterday, in fact. Now go make me a sandwich."

The dude's a genius, but he could learn a little humility. But he's obviously not going to learn until some event wakes him up to it, so I'm done caring that maybe one more nice person could exist in the world.


If cperciva is Paris Hilton with brains, I sure hope someone doesn't email me the video...


I would want this guy making a few million, if he doesn't steal them. His waitressers and waiters can quit anytime if their alternatives are overall better.

(Kudos for being able to imagine a Paris Hilton with brains.)


That's exactly the problem, a reward in the face of repugnant behavior. I wasn't going to respond, but I found this comment pretty depressing so I have to ask you: You seriously believe being rich is a license to be a douche? Or that everyone's allowed to act however they want to food service workers, or the people that guard you while you sleep? Or anyone at all? What if, for example, someone had to be a waitress to save up money for college? Sure, she could start a business, but what if she has literally zero money and no contacts, and she was just born like that?

What's depressing is how often people don't think of other people.


Being rich in this case wouldn't be a reward for his attitude, but for solving the problem of people who want secure, usable backup systems.

I'm not saying being rich would entitle him to any particular behaviour; they're orthogonal things.

About the hypothetical waitress, either she could find another job to pay for college, or otherwise her ability to go to college depends on cperciva getting rich.

There are other examples where you could argue that raw capitalism may not be in the general interest. Think, for example, of real state; that's more of a zero sum game. In my area, rich foreign people are buying most of the real estate for summer houses they'll visit once every other year or so, while locals have a hard time to find a first accomodation due to pumped prices. Many people have to migrate to save up for a house here. Since the utility of that real estate is way lower for the foreign rich than for the local poor, I claim that in this case raw capitalism is reducing overall value.


(PS: I misread 'waitress' as home servant.)


Since you're good at math and know something about finance, why not just get a job at a hedge fund?

You'll get rich, and you won't get heckled by a bunch of startup founders.


I know something about economics, but far less about finance. :-)

In any case, finance really doesn't interest me. I routinely tell Wall Street headhunters to stop bothering me because I would rather create something impressive than own something impressive. I'm not in this for the money.


Well, your demeanor is very ingrained into your personality. I doubt you can change it without a lot of effort. Even saying little things like "I routinely tell Wall Street headhunters to stop bothering me..." comes off as arrogant. Do you really not see that? Or do you just not care?

Let's put it this way: How arrogant you are perceived as can be measured by how many times you say "I".


And how condescending you are perceived as can be measured by how many times you say "you"


And how condescending you are perceived as can be measured by how many times you say "you"


In this case, oversimplifying is warranted, mostly because the things glossed over are either sufficiently complicated that it's hard to make simple, or are things are already generally known.

Take, for example, the 50% point. Once you hand over so much stock that the amount you and the people you implicitly trust hold dips below 51%, you've lost control. Clearly an issue outside of the 1/(1-n) equation, and yet not really relevant. Everyone knows this already.

Then there's the general notion of not handing out too much stock to too many factions, but this too is more or less established knowledge amongst the target audience.

Having said that, the nuance of factoring in odds of success is a worthwhile consideration. Hat off for explaining it!


I agree that simplifying is warranted! I can't understand complex things anyway. Plus if you can't explain it, you don't understand it.. here I feel like I got some modicum of insight.


"I really don't want to spend years of my life on something which has a 90% chance of being worthless."

How does that mesh with the fact that a failed startup is probably worthless (in the literal sense that you can't make money from it), and most startups probably have >90% failure rate?

I know there is a learning experience in startups and that working hard on something fun is valuable, so worthless is really just talking about immediate money here.


I don't think my probability of failure is 90%. :-)

This isn't as naive as it sounds: If you take VC with standard liquidation preference terms, the company needs to do really well before you get anything back -- so the amount of money you need to avoid "failing" is dramatically increased.

In my case, since I don't intend to take any VC, there's a wide range between "failure" (making less money than I would have earned risk-free by working at the university for the same duration) and "success" (making enough money that I never need to work again).

Also, on a more self-serving note: I'm a heck of a lot more competent than 90% of startup founders. Or even 90% of YC-funded-startup founders for that matter -- and YC-funded startups have distinctly less than a 90% failure rate.


Well, if you want to impress people with your startup prowess, you're better off succeeding in that context before bragging about it.

I have no opinion of you or your entrepreneurial abilities in the same way a physicist has no opinion of gravity.

If I can measure what you've done (e.g. in terms of customers, revenues, successful exit sale, etc.) then I'll respect you (or not).


"Or even 90% of YC-funded-startup founders for that matter"

Not to deny this, as I don't know anything about you, but... that is a very bold statement.


Of course it's a bold statement. But if I wasn't bold, I wouldn't have started university at age 13, set three world records for calculating pi (a stunt, I admit), ranked in the top six mathematics undergraduates in North America, received a $100k+ scholarship to Oxford University (not the Rhodes, unfortunately -- their mistake), received a doctorate in computer science from said university, and become the security officer for the FreeBSD operating system.


So you've shown that you have some (impressive) academic achievements, but have you had any business success? Just because you're book smart doesn't mean you will have a successful start up.

Many times people think that they can transfer great success from one domain into other domain. Michael Jordan and his short baseball stint is the first thing that comes to mind.


You're quite right, and if I do fail I entirely expect it to be due to a lack of business experience. But on this topic I'm working entirely based on what Paul says -- that being able to build something which people want is far more important than being able to sell it.


One personal tip, you come off as an arrogant prick because of your "I am holier than thou" statements. These kind of behaviors will drastically reduce the amount of people that will want to work with you or help you.

I work with MDs and PhDs on a daily basis, analyzing their technologies for their start up companies. By far, I am much more willing to put in extra hours for friendly people than those that cram down my throat how much better they are than me.


Again you're right, and I'm sorry about the attitude. Over the past year I've started to get rather defensive when people have suggested that I'm wasting my time on this project...


I get a whole lot of that (even from my family: my sister told me "So, mom and I were talking in the car, and it's great that you're doing this startup, but honestly I don't think you'll succeed.") When I gave notice today, I had to listen to my boss go on about how I was too young to start a startup (I'm 26), how he spent about 15 years after getting his Ph.D learning about business and working in the industry, how my technical skills were too weak (nevermind that I wrote two of his products, and he's never seen me program in a language other than Java), and how if my idea was any good at all, I'd have been able to secure funding for it (nevermind that we're not interested in outside funding until we have some traction).

I've found that the best response is to sit there, listen carefully, take note of any valid points, and ask followup questions if you need more information on one. You may learn something: despite the overall negativity of the conversation, my boss had many points that I'm going to want to keep in mind as we move forwards.

Understand, there is a lot of self-justification going around when it comes to entrepreneurship. As long as rich people are the distant Bill Gateses and Warren Buffets, people can put them up on a pedestal or say "Oh, they got lucky." But if someone you've grown up with or someone who used to work for you gets rich, you have to ask yourself "Why them and not me? Are they just smarter than me?"

Many smart people will do just about anything to avoid admitting that others are smarter than them, so they instinctively say "Oh, he's just going to fail." And when you succeed, they'll say "Oh, he just got lucky." If you succeed again they'll start saying "The game is rigged!".

But if you stoop to their level and say "Oh, look how smart I am, of course I'm going to succeed," you're just engaging in self-justification yourself. And that's a dangerous mental attitude to get into, because it blinds you to details. The reason you're smart in the first place is because you pick up details that other people don't; you can easily become stupid by believing yourself smart. This comes from experience: I did precisely this in high school and college, and then found that when I actually tried to get something done, the results were much more disappointing than I would've liked.

(Therapy for myself: I think you're smarter than me, I think you will succeed, and I think that if you do succeed, it will be because of skill. But keep what I say in mind anyway. It may be useful.)


Great analysis.

I have a friend who (years ago) told me "Damn you're lucky! You have a horseshoe stuck up your [butt]. But you seem to work really hard for it..."

I never forgot that, and in the intervening years I've attributed the majority of my success to luck, rather than skill. Luck, however, that I work hard to create.

The reason is this: If you believe that your success is due to your own skill, you become lax. Complacent. Entitled. You've succeeded so far, so clearly you're da man and you should succeed going forward.

If, on the other hand, you ascribe it to luck, you acknowledge that there's little that you did to make it work. And so you have to keep working hard and scrambling to make the next project successful. Because your previous successes have little bearing on future performance.


But if you stoop to their level and say "Oh, look how smart I am, of course I'm going to succeed," you're just engaging in self-justification yourself. And that's a dangerous mental attitude to get into

Very well said.

Remember, whatever disappointments you have, don't come off sounding like this guy (someone who did well in school, but couldn't get hired at the firm he wanted): http://www.autoadmit.com/thread.php?thread_id=445136&mc=...


The letter in the link is probably the most pathetic letter I've ever read.


Clearly, you've never seen this letter before: http://www.snopes.com/embarrass/email/tripplehorn.asp


Good god, the amount of useful and practical advice in this comment is astounding. I hope you get 20 karma points. If you follow that advice you're 90% to success, because it says a lot about your personality. No wonder YC wants people to participate in YC News.. If I had any money I'd invest it in you.


I was going to vote him up, but then his post has exactly 20 points at the moment, so I guess I'll leave it at that ;-)


Were these people questioning your ability to pull off the technical challenges? If they were questioning the business potential of the idea, your impressive credentials in math and programming are besides the point.


Whoever downmodded: I'm interested in your counterpoint. Please reply here or privately at the address in my profile. TIA!


That is entirely the wrong way to respond: you will get a lot of that (from VCs, prospective clients, etc.) and dealing with it like that is guaranteed to lead you to failure, simply because everyone will come to see you (rightly or wrongly) as a complete prick.


A crucial part of making something people want is finding out what people want. Intelligence is an advantage, of course, but is no guarantee. For one thing, it may make it harder for you to understand the needs of the less gifted and educated.


Friend, if you don't mind taking more of Paul's advice, read "How to Win Friends and Influence People" by Dale Carnegie. That, combined with your impressive record, will make you an unstoppable force at whatever you pursue.

http://www.abebooks.com/servlet/SearchResults?bx=on&sts=...


Did you win the Putnam?

If not, please don't be "bolder" than this guy: http://en.wikipedia.org/wiki/Ravi_Vakil


"Did you win the Putnam?"

Yes, I did.


That has to be the comeback of all time.


News.YC does flame wars a whole lot better than the rest of the internet...


Sometimes with the flames on here however, it feels like Craigslist forums, in all of their 2.0 glory... ;)


HAHAHA! Awesome.


This whole thread is hilarious.


Damn. I'm totally busted.

Just the once, though, huh?


Yes, only once. But I actually consider my first score on the Putnam (53, ranked 53.5th in North America) to be my most impressive performance on the Putnam, considering that I was only 14 years old at the time.


Test Pilots are bold by definition. Entrepreneurs are not necessarily bold. People tell me all the time how "brave" and "bold" I am for starting a startup and it's complete BS. The only think we're risking is some money, reputation and ego. All of which grow back in time. If we were doused with gas, lit on fire and smashed with ewok log traps if our startups failed then we would be bold. As it is we're just different.


Well, I hope your startup idea isn't this:

http://www.daemonology.net/blog/2006-09-13-encrypted-backup....

This post also shows a phenomenal misunderstanding of what it takes to create a successful software startup:

http://www.daemonology.net/blog/2007-06-21-think-before-codi...


That is my startup idea. I don't want to take this thread even more off-topic (if that's even possible), but please feel free to contact me at the address in that first post to explain why you think it is a bad idea.


we're in a similar space -- http://www.getdropbox.com (and part of the yc summer 07 program) basically, sync and backup done right (but for windows and os x). i had the same frustrations as you with existing solutions.

let me know if it's something you're interested in, or if you want to chat about it sometime.

drew (at getdropbox.com)


Will your service offer a full server backup, or just selected files?


It looks like a great idea - except - the sucking up of bandwidth to make the first backup. I'm definitely looking for a better remote backup service for my Architecture firm, for which I currently pay far too much, but my server unfortunately is Windows SBS 2003 - whose OS I truly dislike. I am forced to do this for compatibility with my Revit BIM software unfortunately, so I guess your product won't help me.


If that would be a problem, give that first upload for free. Or is your concern about something other than cost?


As a major bandwidth user, mainly bandwidth actually. But having the first upload for free would be a great incentive.

I think it took several days to move my data to the current system remotely which was not fun. I think its just an unavoidable problem. The severity was lessened by the service calibrating the upload to occur in the middle of the night, which really did help a lot. All of the incremental uploads also are scheduled at night, which is an obvious move.


Hm, what about FedEx-ing a HD with the encrypted data? It might be faster/cheaper/more practical?

Edit: That's assuming cperciva has physical access to his server, rather than working with e.g., EC2, or that he has more bandwith to spare.


I think it's a good idea, but already done, though. I use Carbonite to keep an online remote backup of my hard drive. They charge a fixed rate regardless of the capacity of the drive. Of course there is always space for competition, so if you think you can improve on their offering, then go for it.


If you use Carbonite, you're considerably braver than I am. Carbonite has no effective technological security, so you'd better hope that nobody breaks into their offices, none of their employees "go bad", and they're never confronted by a subpoena or have the PATRIOT act invoked against them; and they only keep the latest version of any file, so if you ever accidentally mangle a file you'd better hope that you can retrieve the unmangled version before Carbonite backs up the mangled version and throws away the older copy.


Right, but they're secure enough for most people. Think about it, the chances that someone gets access to my own computer (stealing it, breaking into my home, or hacking it over the Internet) are higher than the chances of that happening to a professional service provider. At least that's the case for most computer users. I heard recently that 25% of all computers in the world are zombified. So much for security on your own computer.

But anyway, that's why I said if you can improve on their offering then go for it. Given the current options, they're the best that I know of; and I say that knowing that they have a lot to improve. So, if you build a better service, I'd consider switching.


_none of their employees "go bad"_

This won't happen to you? Okay. I trust you.

_never confronted by a subpoena_

If you get a subpoena for a passphrase for a client, you will give it up. Yes you will. Now, if someone was holding terroristic bombcodes or whatever and REALLY didn't want people getting them, they ain't backing up anything online. The same people who need real security aren't going to be uploading their data anywhere .


"I trust you"

"If you get a subpoena for a passphrase for a client, you will give it up."

Not if I don't have it. This is the point of strong security -- you don't NEED to trust me, because I am not technically capable (nor, unless I'm quite mistaken, is the NSA) of decrypting data backed up using tarsnap.


This would be off-topic in this thread, but definitely not in this forum. If you make a new top level post requesting feedback, more people will be able to contribute and benefit from it.


My first reaction was: I see this more as donationware open source. But then again, if you feel your technology would be hard to replicate, and if the cost is on the S3 ballpark, I'm in.


I just read more about your security strategy - and that is definitely something people really want - reliable and secure data backup. Good luck.


Interesting project, unfortunately I didn't found any way to enter in contact with you. You can contact me through my project web site http://www.disnetwork.info

I'll be glad to discuss this remote secure backup project with you. It was once on top of my list for a DIS application, but I dropped it for various reasons that I would be glad to share with you.


His address is at the end of the blog entry in which he introduces his idea (the first of the links above).


Remember that success comes from improving OTHER people's lives. All your achievements, while probably very gratifying to your mother, have not improved my life at all.


Do you use OS X or Mozilla? Have you ever used their software update mechanisms?

If yes, I've improved your life -- they use my delta compression work (bsdiff, originally written as part of FreeBSD Update) to reduce the size of updates which have to be downloaded. As of about a year ago, my work had saved users around the world well over a hundred years of waiting for updates to download.


"Remember also that every time you open your mouth in the presence of a person who has an abundance of knowledge, you display to that person your exact stock of knowledge or your lack of it! Genuine wisdom is usually conspicuous through modesty and silence."


That's a two-way street, dbosson. I wouldn't hasten to silence him, nor chasten him for opening his mouth "in the presence of a person who has an abundance of knowledge," as you put it.


That's a two-way street, dbosson.


If we assume 100 million internet users that you saved 100 years, that's roughly 30 seconds per user. Let's say just 10% of people use OS X or Mozilla - that's 5 minutes per user.

This is not to belittle, just to put your "100 years" in context. It's great work and you've saved me personally a lot more than 5 minutes.


Wow. You really need to read this:

http://paulgraham.com/bronze.html


A few tips:

1. Open up Microsoft word.

2. Type all that out.

3. Save it as "Resume.doc"

4. Don't open it again until your next job search.


Psssh... He wrote an OpenOffice clone in a programming language he himself designed with syntax like vector calculus.

Seriously, Word?!


yep, immediately thought of that too. PG writes VERY good stuff most of the time and is very smart about a lot of things, but when he strays into areas in which he is not well versed (the unions essay comes to mind), he ends up writing pieces with obvious holes.


Do you have any specific holes you could point to as examples?


I read the union essay a while ago, but your failure to sufficiently consider risk-aversion in this one was a major hole. I don't mean to really criticize that much, you write consistently great stuff.



That works, except then I guess the hole was not making it clear enough that you were talking about utility rather than expected value. The problem with your response, and the reason that I don't really see it as a good explanation, is that your basic principle is far less useful if it requires the user to calculate their expected utility.


In practice it's not hard, because nearly all founders' utility functions are practically step functions.


Entrepreneurs face some pretty tough questions at a very early stage. Should I take Angel or VC money? How much money should I raise? How much equity should I give up? How much equity should I grant to early employees?

The math equation is correct, but the likely outcomes are nearly impossible to estimate. I have been on the management team of 5 startups and advised many others. There are some "norms" and guidelines for how much to raise at each stage, how much equity to give up, and even how much stock to grant employees as you grow the company.

I wrote an in depth blog on these questions, too long to detail here, but Paul is on the right track. For more details see How much Equity for Investors and Employees?

http://dondodge.typepad.com/the_next_big_thing/2007/08/how-m...


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.... 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


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


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.


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.


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.


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.]


"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.


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.


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.


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.


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.


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.


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.


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!?


Good catch Paul! Surprise, surprise Seth Levine is a "mentor" at Techstars: http://www.techstars.org/site/page/pg5883.html

What a shame!


Possibly not the sole reason, but the first footnote leads on to this.


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.


"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.


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.


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.


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.


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.


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


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.


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.


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.


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?


I'd be more surprised if that ever worked. Sounds clueless and suplicating at best, insulting otherwise.


Yes, of course I don't think it would work - I'd just be surprised if nobody has tried it.


Are you asking if YC charges potential investors to attend their demo days?

Interesting if they did... part of YC's function is to introduce follow-on investors to their startups, but I've never thought about their charging investors for that privilege.

Who says there's no business model in the Web 2.0 world?


You're kidding, right? :)


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 :)


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/


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.


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.


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


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!)


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.


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...


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.


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


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.


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


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.


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.


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.


hey bootstrapper, what is your company?


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


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


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.


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


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


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


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.


How can you determine the improved outcome? thanks!




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