Going back to the till: Series B

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Kind: captions
Language: en

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Where I left off in the last
video, my buddies and I, we

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had a business plan.

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We had a great idea to
sell socks online.

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We went to an angel investor.

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He had originally given
us $5 million.

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He valued what we already had
at $5 million dollars.

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So, since he was giving us $5
million and we had $5 million,

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he got 50% of the company.

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And we have the other 50%.

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We have two million
total shares.

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And we took four of that
million, let's say six months

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have passed.

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We hired 50 people, and we
finally built a working

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version of our website.

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But we now are about
to run out of cash.

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We still haven't started selling
things, and we'll

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actually have to start selling a
lot of things before we have

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enough money to support
ourselves.

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So we need to go start
raising money again.

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And we also want to spend money
marketing and all the

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rest. So we go to some
professional investors.

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We'll go to seed venture
capitalists, and we're going

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to do our Series A
round of funding.

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Which just means our first kind
of professional venture

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capital round of funding.

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We finally-- some guy finds
a team that, they like us.

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And we start getting
to the negotiation.

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They say, you know what?

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You guys say you need
$10 million.

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We believe you.

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We know that that's what it
takes and we think you have a

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good business.

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So, let's see, let me say that
we need to raise $10 million.

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Just so I make that clear.

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We need it for ongoing
expenses.

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And of course we'll have a big
business plan and everything

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that further fleshes this out.

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And we also have need-- we're
going to do some marketing, et

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cetera, et cetera.

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So they say, you know, we have
$10 million and we think this

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is a hot space, because we know
those other VC's across

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the street also invested in an
online undergarment play.

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And we know that that's the
hot thing right now.

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So we're also going to do it.

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So the question now is,
what do they get

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for their $10 million.

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So once again we get into
this what is the

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company worth right now?

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So once again, they're going to
do a pre-money valuation.

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So what is this whole thing
worth right now?

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So they'll say, the
idea's good.

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They won't break down.

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They won't say oh, the idea
is worth $5 million.

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But the general idea is,
hopefully, from that stage

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where the post-money valuation
was $10 million, right?

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Back here it was $10 million.

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Then we did a bunch of work.

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We used some of this
$5 million.

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We did a bunch of work.

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Hopefully we added value.

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If we added value, our value of
this stuff now, this-- we

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turned this cash into other
types of assets like a website

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and other things, and knowledge
in our firm, and

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expertise, and all that stuff.

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Hopefully now, what we have here
is worth more than $10

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million, right?

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Otherwise we kind of
destroyed wealth.

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And all of this is
very intangible.

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It's very hard for someone to
really place a value on things

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at this point.

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A lot of VC's, they kind of
swing for the fences.

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They're like, you know what,
these guys have a 10% chance

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of being worth a billion
dollars, and a 90%

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of being worth 0.

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If I make 10 of these bets, at
least one of them is going to

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pay off and make
my whole fund.

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And so that's how they
kind of think.

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So at this level, they'll do
some hard negotiating.

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But it often times is going to--
not at this level, this

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is where we are right now-- it's
kind of what other people

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got for this stage
of a company.

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They say oh, you know,
you have a pretty

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good built-up website.

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Those other guys who had a
pretty good built-up website

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at this point, those guys across
the street, they had to

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pay-- they had to give a $20
million pre-money valuation.

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But you know, you guys are a
little bit-- your market isn't

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quite as big as the broader
undergarments market.

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You're just socks.

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So the opportunity
isn't as big.

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So we'll give you a $15 million
pre-money valuation.

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So they're saying that what
we have right now

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is worth $15 million.

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And that's pretty good.

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If that were reality, if it
really is worth $15 million,

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then what are our shares
worth right now?

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Notice, they haven't
given us any money.

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This is the pre-money
valuation.

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So $15 million divided by two
million shares, right?

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That's how many we
have right now.

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So what is the value
per share?

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15 million divided by 2
is $7.50 per share.

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That's pretty good.

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Because back here-- remember,
this is kind of a scenario

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that didn't happen, that was
kind of a negative scenario--

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but back here when the pre-money
was $5 million for a

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million shares, it
was $5 per share.

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Then it became $10 million
for two million shares,

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still $5 per share.

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But before and after this round,
that angel said oh,

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your shares are worth
about $5 per share.

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Now this VC, who is a
professional investor and has

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teams of MBA's making
spreadsheets for him, says

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that actually, what we
have right here is

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worth $7.50 a share.

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So just over those six months
we actually got a 50% return

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on our shares, if you
believe that.

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And the angel investor's
happy.

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He feels good about it.

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This was vindication
for his bet on us.

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So we feel good.

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We feel like we've given
him, at least in the

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short term, a return.

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So anyway, we get a $15 million
pre-money valuation.

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And I'll let you think
about this one.

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What's the post-money
valuation?

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What happens when you layer on
the $10 million from this

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venture firm?

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Actually, just to make the math
simple, let's say that

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we're raising 7.5 million.

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Let's say that we wanted 10
million, but we were hoping

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for 20 million pre-money
valuation, because that's what

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the other guys got.

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And since they're only giving us
a $15 million pre-money, we

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just don't want to take as many
shares from them, because

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we don't want to give as much
of the company away.

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So we're just going to take $7.5
million, because we think

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that's just enough that
we need to keep going.

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So we do that.

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We take $7.5 million from this
seed venture capitalist. And

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he essentially valued our old
shares at $7.50 per share.

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So, for $7.5 million at $7.50
per share, he should get

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another million shares.

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So what we're going to do--
this angel investor is

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probably sitting on our board
now because he owns so many of

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the shares.

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The board of directors of a firm
is essentially elected by

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the shareholders.

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So if you have 50% of the
shares, you can put yourself

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on the board.

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You could probably put some
other people on the board of

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directors as well.

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So, we had two million.

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These guys get a million.

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How many shares do
we have now?

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We now will have three
million shares.

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So we had to issue another
million shares.

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And what is our post-money
valuation?

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Pre-money was 15.

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We have $7.5 million now.

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Our post-money valuation
is $22.5 million.

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And now, what percentage
do each of us own?

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So the angel investor owns one
million, not out of two

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million shares like
he used to.

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He now owns one million out
of three million shares.

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So now he owns 30%.

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The seed VC, he has a million
out of three million, so he

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owns-- well this is 33
and 1/3%-- the seed

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VC owns 33 and 1/3%.

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And then me and my buddies, we
collectively own 33 and 1/3%,

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and I have 1/5 of that, so
I have a little over 5%.

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So the founders, that's us, we
still have about a third of

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the company.

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And now we have the $7.5 million
we just raised, plus

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we have the million dollars
in cash we had before.

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We have $8.5 million to keep
on going with our business.

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Fair enough.

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So let's say another
six months go by.

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So our old balance sheet-- let
me draw all of the shares-- I

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want to do a couple of more
rounds of financing before I

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take the company public.

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So this is my slice down
here, $200,000.

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This is the angel investor.

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This is the seed VC.

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And then, of course, let's say
after, I don't know, another

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six months we burn
through the cash.

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We've marketed the website, we
have only $1 million left.

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And that's usually our trigger
point for when we want to

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raise more money.

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In fact we probably would have
to do it at $2 million because

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we've raised more employees, and
we're burning more cash.

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Your cash burn is essentially
how much cash is going out of

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the door every month, because
your business still isn't

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making money.

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And of course you have all of
the assets of the firm, which

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essentially, it's a website,
and offices, and the

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knowledge, some of
it intangible.

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So, website, and everything
that comes with it.

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Your brand now, you probably
have, because you've marketed.

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So people recognize
socksonline.com.

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I don't know if that already
exists so forgive me if I'm

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actually somehow insulting a
real business out there.

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But you have a brand now.

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And so you're almost ready.

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You're actually generating
revenue.

00:09:06.650 --> 00:09:08.990
But you're still kind of
cash flow negative.

00:09:08.990 --> 00:09:11.600
You're burning less money
because people are actually

00:09:11.600 --> 00:09:12.750
going to your site.

00:09:12.750 --> 00:09:13.830
They're buying stuff.

00:09:13.830 --> 00:09:16.740
But you just need a little bit
more money, you think, to get

00:09:16.740 --> 00:09:18.180
profitable, right?

00:09:18.180 --> 00:09:20.340
Once you get this amount of
money, you're ready to go.

00:09:20.340 --> 00:09:21.810
So you go to another VC.

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Once again, a lot of
them turn you away.

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But one guy finally says OK,
I'll give you some money.

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And you say, you know
I need $5 million.

00:09:27.500 --> 00:09:28.400
He says, fair enough.

00:09:28.400 --> 00:09:34.310
I'm going to value your business
at-- let's say we're

00:09:34.310 --> 00:09:36.290
in an optimistic world, so
we're doing up rounds.

00:09:36.290 --> 00:09:39.670
Up rounds are when your
pre-money valuation of this

00:09:39.670 --> 00:09:43.100
round is more than the
post-money valuation of the

00:09:43.100 --> 00:09:44.430
last round.

00:09:44.430 --> 00:09:45.780
So the value is going up.

00:09:45.780 --> 00:09:47.260
You are creating value.

00:09:47.260 --> 00:09:50.700
It would be a down round-- like
here, they valued us at

00:09:50.700 --> 00:09:53.970
$15 million.

00:09:53.970 --> 00:09:57.360
While the post-money of our last
round was $10 million.

00:09:57.360 --> 00:09:58.870
So that was an up round.

00:09:58.870 --> 00:10:01.460
If these guys said no way,
the world has changed.

00:10:01.460 --> 00:10:03.445
We're only going to value all
of this stuff at $8 million,

00:10:03.445 --> 00:10:05.720
then that would be a down round,
and no one's happy

00:10:05.720 --> 00:10:06.220
about that.

00:10:06.220 --> 00:10:08.660
We'll talk about the
repercussions of that in the

00:10:08.660 --> 00:10:10.830
future, why down rounds
aren't good.

00:10:10.830 --> 00:10:12.770
So often times, you actually
don't want to get too good of

00:10:12.770 --> 00:10:13.530
a valuation.

00:10:13.530 --> 00:10:16.310
Because if you get too good of a
valuation, in the next round

00:10:16.310 --> 00:10:18.900
it might be hard to get people
who are going to give you a

00:10:18.900 --> 00:10:19.910
better valuation.

00:10:19.910 --> 00:10:22.650
You might be forced to take
a down round, which

00:10:22.650 --> 00:10:24.260
has negative aspects.

00:10:24.260 --> 00:10:27.520
But just quick and dirty, you're
a prominent brand now.

00:10:27.520 --> 00:10:29.390
It's a little easier for
you to raise money.

00:10:29.390 --> 00:10:31.970
You go to some VC who
specializes in kind of helping

00:10:31.970 --> 00:10:34.260
people get to that profitability
stage.

00:10:34.260 --> 00:10:37.620
And what you do is you
raise your Series B.

00:10:37.620 --> 00:10:40.690
And just to put it simply,
it's an up round.

00:10:40.690 --> 00:10:43.830
Your post-money from your last
round was $22.5 million,

00:10:43.830 --> 00:10:45.930
right? $22.5 million.

00:10:45.930 --> 00:10:47.540
You've generated some value.

00:10:47.540 --> 00:10:49.140
So now they say,
you know what?

00:10:49.140 --> 00:10:51.310
Your business is worth
$30 million.

00:10:51.310 --> 00:10:53.860
And you need another
$10 million to

00:10:53.860 --> 00:10:55.110
really pump up the marketing.

00:11:05.130 --> 00:11:06.000
How many shares do they get?

00:11:06.000 --> 00:11:09.490
Well the pre-money was $30
million, we had three million

00:11:09.490 --> 00:11:13.610
shares, so they're assigning us
a value of essentially $10

00:11:13.610 --> 00:11:14.540
a share, which is great.

00:11:14.540 --> 00:11:17.950
Remember the first round, the
angel gave us $5 per share?

00:11:17.950 --> 00:11:19.950
Second round we got
$7.50 per share.

00:11:19.950 --> 00:11:22.020
And now we're getting
$10 per share.

00:11:22.020 --> 00:11:24.300
So if we're selling him shares
at $10 per share, we just have

00:11:24.300 --> 00:11:27.800
to issue another million shares
to get $10 million.

00:11:27.800 --> 00:11:29.820
It's another million shares,
and this goes to

00:11:29.820 --> 00:11:31.530
VC2, the second VC.

00:11:31.530 --> 00:11:33.300
And that's our Series B.

00:11:33.300 --> 00:11:36.170
We raised $10 million.

00:11:36.170 --> 00:11:36.870
Fair enough.

00:11:36.870 --> 00:11:39.500
So we've done one round
of angel investing.

00:11:39.500 --> 00:11:41.880
And then we've got
our Series A that

00:11:41.880 --> 00:11:43.760
gave us the $7.5 million.

00:11:43.760 --> 00:11:45.960
Then we did our Series B that
gave us $10 million.

00:11:45.960 --> 00:11:49.610
And we could keep doing this,
Series C, Series D, and so on

00:11:49.610 --> 00:11:50.410
and so forth.

00:11:50.410 --> 00:11:53.610
And I'll continue this
in the next video.


Getting a seed round from a VC

WEBVTT
Kind: captions
Language: en

00:00:00.915 --> 00:00:02.800
- [Voiceover] Where I had
left off in the last video,

00:00:02.800 --> 00:00:05.200
we had talked about the scenario

00:00:05.200 --> 00:00:07.900
where my buddies and I
we came up with this idea

00:00:07.900 --> 00:00:09.100
to sell socks online.

00:00:09.100 --> 00:00:10.400
We went to a rich investor

00:00:10.400 --> 00:00:12.800
we call an Angel investor
who's usually kind of

00:00:12.800 --> 00:00:15.800
a rich uncle type of
figure who gets excited

00:00:15.800 --> 00:00:18.000
by young guys innovating in the world.

00:00:18.000 --> 00:00:20.700
We say "Hey, we need $5 million."

00:00:20.700 --> 00:00:23.300
He says sure enough, I
think the idea you have

00:00:23.300 --> 00:00:25.300
by itself or maybe some kind of prototype

00:00:25.300 --> 00:00:26.600
you might have made or something.

00:00:26.600 --> 00:00:28.500
That's worth $5 million.

00:00:28.500 --> 00:00:31.200
I'll give you another $5 million of cash

00:00:31.200 --> 00:00:34.100
to get started, rent some
space, hire some people

00:00:34.100 --> 00:00:36.800
and for that since what
you had was $5 million,

00:00:36.800 --> 00:00:38.200
that's what you're bringing to the table.

00:00:38.200 --> 00:00:40.500
I'm bringing $5 million cash to the table,

00:00:40.500 --> 00:00:42.200
I essentially get half the company

00:00:42.200 --> 00:00:43.800
and the way that works is it's not like

00:00:43.800 --> 00:00:46.500
we each gave him half of our shares

00:00:46.500 --> 00:00:49.200
instead since we are the
board of the company,

00:00:49.200 --> 00:00:51.500
we issue another million shares.

00:00:51.500 --> 00:00:53.900
We doubled the share count
and we give it to him.

00:00:53.900 --> 00:00:57.200
This pre-money valuation's
really, really important

00:00:57.953 --> 00:01:01.300
because if we had agreed,

00:01:01.300 --> 00:01:02.892
if we said this wasn't five million,

00:01:02.892 --> 00:01:04.900
if we said that this is, I don't know.

00:01:04.900 --> 00:01:08.500
Let's say if he is a hard negotiator,

00:01:08.500 --> 00:01:10.523
he says "No, that's only
worth a $1 million,"

00:01:11.599 --> 00:01:14.100
and I'm going to give $5 million.

00:01:14.946 --> 00:01:16.200
Let me ask you,

00:01:16.200 --> 00:01:18.600
how many shares would we have to issue?

00:01:19.507 --> 00:01:20.400
Think about it.

00:01:20.400 --> 00:01:22.569
If he was a hard negotiator,

00:01:22.569 --> 00:01:23.600
let me draw it down here

00:01:23.600 --> 00:01:25.200
so I don't want to mess up the issue.

00:01:25.200 --> 00:01:27.200
Because our idea I mean really is

00:01:27.200 --> 00:01:29.930
a hard thing to estimate
what an idea is worth.

00:01:30.914 --> 00:01:33.800
He negotiates hard, at the end
of the day we're desperate,

00:01:33.800 --> 00:01:35.900
financial markets have collapsed

00:01:35.900 --> 00:01:37.500
so we'll take money from whoever's willing

00:01:37.500 --> 00:01:38.338
to give it to us

00:01:38.338 --> 00:01:39.738
and we really want to quit our jobs.

00:01:41.399 --> 00:01:44.700
He says that what we have right now,

00:01:44.700 --> 00:01:47.000
our idea is only worth a $1 million.

00:01:48.984 --> 00:01:51.100
He's going to give us $5 million.

00:01:51.100 --> 00:01:52.800
How many shares do we have to give him?

00:01:52.800 --> 00:01:55.100
This right here, this is a million shares.

00:01:55.100 --> 00:01:57.300
That's what we started off with

00:01:57.300 --> 00:01:59.400
so when he says that
what we have right now

00:01:59.400 --> 00:02:00.700
is worth a $1 million,

00:02:00.700 --> 00:02:02.400
he's essentially saying that's it's worth

00:02:02.400 --> 00:02:05.100
a dollar per share, a dollar per share

00:02:05.100 --> 00:02:08.930
so my 200,000 shares are worth $200,000

00:02:08.930 --> 00:02:10.400
according to his valuation.

00:02:10.400 --> 00:02:12.900
Up here we said that what we had before

00:02:12.900 --> 00:02:15.500
is worth $5 million in the previous video.

00:02:16.423 --> 00:02:18.700
If what we had before is worth $5 million

00:02:18.700 --> 00:02:20.600
and there were a million shares initially.

00:02:21.246 --> 00:02:23.100
This was the million shares

00:02:24.115 --> 00:02:25.800
then the pre-money valuation

00:02:25.800 --> 00:02:27.300
or actually it's the valuation

00:02:27.300 --> 00:02:30.500
either pre or post money
would be $5 per share.

00:02:33.530 --> 00:02:36.400
In the $5 per share world,

00:02:36.400 --> 00:02:39.100
what we did was we issued
another million shares

00:02:39.100 --> 00:02:40.800
and sold them for $5 million

00:02:40.800 --> 00:02:43.284
or we sell them for $5 per share

00:02:43.315 --> 00:02:45.400
to get the $5 million

00:02:45.400 --> 00:02:48.700
and so we ended up with a
50, 50 split of the company.

00:02:48.700 --> 00:02:50.407
This is the Angel investor

00:02:51.837 --> 00:02:53.800
and this is all of us down here.

00:02:53.800 --> 00:02:55.600
All of this is equity.

00:02:56.553 --> 00:02:59.400
No debt, no liabilities just yet.

00:03:00.553 --> 00:03:04.300
Now in this reality if he's
valuing what we have right now

00:03:04.300 --> 00:03:05.900
at essentially $1 per share.

00:03:05.900 --> 00:03:07.907
His is worth a $1 million,
you have a million shares.

00:03:07.907 --> 00:03:09.900
It's $1 per share.

00:03:09.900 --> 00:03:14.600
In order for him to give $5 million,

00:03:14.600 --> 00:03:18.000
he's essentially going to buy $5 million

00:03:18.000 --> 00:03:20.600
worth of stock at $1 per share.

00:03:20.600 --> 00:03:23.400
He's essentially going to
need five million shares,

00:03:24.523 --> 00:03:27.800
five million shares.

00:03:27.800 --> 00:03:30.100
Notice in this situation up here

00:03:30.100 --> 00:03:33.500
before when I have

00:03:33.500 --> 00:03:35.600
200,000 shares,

00:03:35.600 --> 00:03:39.200
well when I had 1/5 of $5 million,

00:03:39.200 --> 00:03:40.400
that was five million.

00:03:40.400 --> 00:03:42.400
When I had 1/5 of $5 million,

00:03:42.400 --> 00:03:45.100
the value of my shares was $1 million.

00:03:45.915 --> 00:03:50.600
Then when I have 1/10
of two million shares,

00:03:50.600 --> 00:03:55.000
I still have 1/10 of $10
million of total asset

00:03:55.000 --> 00:03:57.700
because now he threw in his $5 million.

00:03:57.700 --> 00:04:00.700
My share is still worth $1 million of it.

00:04:00.700 --> 00:04:02.400
I have a tenth of 10 million

00:04:02.400 --> 00:04:04.099
as oppose to a fifth of five million.

00:04:05.099 --> 00:04:07.700
In this situation, I used to have

00:04:07.700 --> 00:04:12.700
a fifth of one million
which would be $200,000.

00:04:15.646 --> 00:04:18.000
Now I have 200,000 over,

00:04:18.000 --> 00:04:19.601
how many total shares are there now?

00:04:19.601 --> 00:04:21.700
There are now six million shares.

00:04:22.869 --> 00:04:27.423
Now I have 1/60, is that right?

00:04:27.423 --> 00:04:30.500
I have 200,000 and I have 200,000

00:04:31.592 --> 00:04:35.500
over six million,

00:04:36.700 --> 00:04:39.400
that's 6,000,000 so that cancels out.

00:04:39.984 --> 00:04:42.700
I now own 1/30 of the company,

00:04:42.700 --> 00:04:46.200
before I had 1/5 and were
valuing it at six million

00:04:46.200 --> 00:04:48.899
because I have a million
here and five million here

00:04:48.899 --> 00:04:50.300
times six million.

00:04:51.469 --> 00:04:53.800
What's 1/30 of six million?

00:04:53.800 --> 00:04:56.900
1/6 over 30

00:04:57.223 --> 00:05:02.207
is equal to 1/5 of a million,

00:05:02.207 --> 00:05:04.722
so this is still $200,000.

00:05:04.722 --> 00:05:05.800
No matter what I do,

00:05:07.184 --> 00:05:10.400
between the pre-money and
the post-money valuation,

00:05:10.400 --> 00:05:13.300
my per share value doesn't change any

00:05:13.300 --> 00:05:14.300
and I want to show you that

00:05:14.300 --> 00:05:15.400
but this matters a lot

00:05:15.400 --> 00:05:18.400
because based on what this
pre-money valuation is,

00:05:18.400 --> 00:05:22.000
it tells us how many shares

00:05:22.000 --> 00:05:23.400
or what percentage of the company

00:05:23.400 --> 00:05:26.700
our Angel investor gets for
investing his $5 million.

00:05:26.700 --> 00:05:30.500
In this case he gets 5/6 of the company.

00:05:30.500 --> 00:05:31.900
What is that?

00:05:31.900 --> 00:05:34.701
Five times, that's like
80% of the company.

00:05:35.654 --> 00:05:37.938
I think roughly and we
are left with the other

00:05:37.938 --> 00:05:40.400
no 1/6 is, right.

00:05:40.400 --> 00:05:41.561
1/6 no, it's more than 80.

00:05:41.561 --> 00:05:43.000
It's like 84%

00:05:43.000 --> 00:05:45.700
and we're left with
like 16% of the company.

00:05:45.700 --> 00:05:47.400
It's a very different scenario

00:05:47.400 --> 00:05:50.200
depending on what our
pre-money valuation is

00:05:50.200 --> 00:05:51.700
and of course the pre-money valuation

00:05:51.700 --> 00:05:54.700
is just you just take
the pre-money valuation

00:05:54.700 --> 00:05:56.200
plus the amount of cash they're given

00:05:56.200 --> 00:05:57.753
and that's the post-money valuation.

00:05:57.753 --> 00:05:59.400
The amount of money you get,

00:05:59.400 --> 00:06:03.200
pre-money and then post-money,
you have the money in

00:06:03.200 --> 00:06:05.300
and that's you get the
$6 million valuation.

00:06:05.300 --> 00:06:09.300
Fair enough, I think I've
beaten this horse dead now.

00:06:09.300 --> 00:06:10.315
I think you have a good sense of it

00:06:10.315 --> 00:06:12.700
and let's say that we end up lucky.

00:06:12.700 --> 00:06:14.106
The guy wasn't a hard negotiator

00:06:14.106 --> 00:06:16.900
and we ended up with that first situation.

00:06:16.900 --> 00:06:18.400
Let me redraw it.

00:06:18.969 --> 00:06:22.400
Now, if I were to draw the assets

00:06:22.400 --> 00:06:24.800
of this corporation,

00:06:26.200 --> 00:06:28.700
the assets of this corporation
at least at the time

00:06:28.700 --> 00:06:30.400
of that guy's investment

00:06:31.292 --> 00:06:33.600
where it's a very intangible asset.

00:06:33.600 --> 00:06:36.700
We call it the idea, it
now has a value $5 million

00:06:37.300 --> 00:06:39.100
and we have some cash,

00:06:39.100 --> 00:06:41.299
we have five million in cash

00:06:43.852 --> 00:06:46.300
and then if we do the shares,

00:06:46.300 --> 00:06:48.100
so we do that in another box.

00:06:52.237 --> 00:06:53.900
There you go, there are the shares

00:06:53.900 --> 00:06:54.930
and of that share

00:06:54.930 --> 00:06:56.700
we'll have two million shares outstanding,

00:06:56.700 --> 00:06:58.700
two million shares.

00:06:59.407 --> 00:07:02.237
I have one million to the Angel investor,

00:07:03.790 --> 00:07:06.700
he has 50% of the shares

00:07:06.700 --> 00:07:10.100
and just because I like
to keep track of my slice.

00:07:10.100 --> 00:07:12.700
There's 200,000 shares that go to Sal.

00:07:12.700 --> 00:07:14.300
Fair enough.

00:07:14.869 --> 00:07:16.646
Now I mean obviously
the whole point of this

00:07:16.646 --> 00:07:18.600
wasn't just a negotiate and raise money

00:07:18.600 --> 00:07:19.800
and quit our jobs.

00:07:19.800 --> 00:07:21.700
The whole point of this
was to start a business.

00:07:21.700 --> 00:07:24.000
Let's say we take this $5 million,

00:07:24.000 --> 00:07:26.300
we start hiring people
and really our first step

00:07:26.300 --> 00:07:28.138
is to build out our website

00:07:28.138 --> 00:07:30.700
and just have a working site going.

00:07:30.700 --> 00:07:34.500
Let's say we burn through
$4 million of that

00:07:34.500 --> 00:07:35.800
and we build a site.

00:07:35.800 --> 00:07:36.700
Let's say,

00:07:37.914 --> 00:07:39.300
we only have a $1 million left.

00:07:39.300 --> 00:07:41.300
This is maybe six months in the future

00:07:41.300 --> 00:07:43.800
we all quit our jobs, we
got some fancy loft like

00:07:43.800 --> 00:07:44.800
office space.

00:07:46.323 --> 00:07:50.000
We got a foosball table and
we also built a website,

00:07:50.000 --> 00:07:51.900
we hired some graphic
designers and things.

00:07:53.392 --> 00:07:55.400
We've burned through most of our cash

00:07:55.400 --> 00:07:56.700
and were starting to
get a little bit worried

00:07:56.700 --> 00:07:58.100
because we haven't made a profit yet

00:07:58.100 --> 00:08:00.200
but we have a neat website,

00:08:00.200 --> 00:08:02.384
we have a neat website.

00:08:04.200 --> 00:08:06.200
When we went to the Angel investors,

00:08:06.200 --> 00:08:08.823
we just had an idea, a business plan

00:08:08.823 --> 00:08:12.200
and we just have, hopefully
we had our charisma

00:08:12.200 --> 00:08:14.100
and we were able to sell
the guy on the idea,

00:08:14.100 --> 00:08:15.753
he thought we're going to be the next

00:08:16.692 --> 00:08:19.000
dominant sock player in the world

00:08:19.000 --> 00:08:20.700
but now we actually built something.

00:08:20.700 --> 00:08:22.200
We took his money and as promised,

00:08:22.200 --> 00:08:25.500
we built a nice website
and now we need to raise

00:08:25.500 --> 00:08:29.200
more money one, because
we've hired 50 people

00:08:29.200 --> 00:08:31.700
and this $1 million isn't
going to last us too long

00:08:31.700 --> 00:08:34.000
and that would be a
shame to run out of cash

00:08:34.000 --> 00:08:35.700
just when we're getting off the ground.

00:08:35.700 --> 00:08:38.200
We now actually have a
real website and offices

00:08:38.200 --> 00:08:40.900
and all of that and we
want to raise some money

00:08:40.900 --> 00:08:43.900
because we want to put
up some AdWords on Google

00:08:43.900 --> 00:08:45.200
so people know about our site.

00:08:45.200 --> 00:08:47.200
We want to spend a couple million dollars

00:08:47.200 --> 00:08:48.923
for Super Bowl ads so people know

00:08:48.923 --> 00:08:50.500
that they can get socks online now.

00:08:50.500 --> 00:08:52.200
We have to raise more money

00:08:52.200 --> 00:08:55.500
and now at this stage, we would go back

00:08:55.500 --> 00:08:57.000
to the venture capital community

00:08:57.000 --> 00:08:58.300
but we wouldn't go to the Angels.

00:08:58.300 --> 00:09:00.200
The Angels are the guys
who like the big picture

00:09:00.200 --> 00:09:03.100
who want just to throw some
money into an early idea.

00:09:03.100 --> 00:09:05.500
It's usually a relatively small amount,

00:09:05.500 --> 00:09:07.500
actually $5 million
would be a large amount

00:09:07.500 --> 00:09:08.400
for an Angel.

00:09:08.400 --> 00:09:12.500
We want to go to real professional VCs now

00:09:12.500 --> 00:09:16.300
and what we would do is
we would go to a seed VC.

00:09:16.300 --> 00:09:19.400
Seed VCs are kind of the first round

00:09:19.400 --> 00:09:21.500
and each round is every
time you have to go back

00:09:21.500 --> 00:09:22.900
to the till to raise money,

00:09:22.900 --> 00:09:24.400
that's kind of a round of financing

00:09:24.400 --> 00:09:28.700
but Seed Investors, so
there's a lot of words for it

00:09:28.700 --> 00:09:31.300
but seed investors are
usually VC investors

00:09:31.300 --> 00:09:33.600
who are actual professionals
at what they do.

00:09:33.600 --> 00:09:35.600
They're actually managing
other people's money

00:09:35.600 --> 00:09:37.400
and we'll do another
video on how they raise

00:09:37.400 --> 00:09:39.000
that money and it's very related

00:09:39.000 --> 00:09:40.500
to how private equity confirms

00:09:40.500 --> 00:09:42.600
and hedge funds also raise their money.

00:09:42.600 --> 00:09:45.000
They are usually managing
other people's money

00:09:45.000 --> 00:09:48.600
while an Angel investor is usually,

00:09:48.600 --> 00:09:51.192
he's just sitting on top
of a big pile of money

00:09:51.192 --> 00:09:52.353
and likes to play with it.

00:09:52.353 --> 00:09:54.100
They're managing other people's money

00:09:54.100 --> 00:09:56.400
and they intend to have some fancy NBAs

00:09:56.400 --> 00:09:58.000
that they just hired who'll make models

00:09:58.000 --> 00:10:01.200
and do projections and
negotiate a little bit harder

00:10:01.200 --> 00:10:03.300
with you when you're actually trying to

00:10:03.300 --> 00:10:04.700
get a value on your business

00:10:04.700 --> 00:10:05.700
but we have to go to these guys.

00:10:05.700 --> 00:10:07.500
They have some value, I
mean they all connect us

00:10:07.500 --> 00:10:08.500
with other dudes

00:10:08.500 --> 00:10:12.300
and they have experience
starting businesses.

00:10:12.300 --> 00:10:14.100
They can introduce us to other people

00:10:14.100 --> 00:10:15.500
who've done similar things

00:10:15.500 --> 00:10:16.900
and all the rest help us network

00:10:16.900 --> 00:10:18.400
and help us manage the business.

00:10:18.400 --> 00:10:20.100
We go to a venture capitalist

00:10:20.100 --> 00:10:22.000
and we get the door closed a lot of times

00:10:22.000 --> 00:10:23.200
but that's what one venture capitalist,

00:10:23.200 --> 00:10:26.200
one seed venture capitalist
finally comes to us.

00:10:26.200 --> 00:10:29.502
The terminology can be
a little ambiguous here

00:10:29.502 --> 00:10:32.000
but we'll call it our Series A financing,

00:10:32.000 --> 00:10:33.200
Series A.

00:10:33.200 --> 00:10:35.100
Sometimes it will be
called your seed financing

00:10:35.100 --> 00:10:36.200
but we'll call it Series A

00:10:36.200 --> 00:10:37.800
because we want to formalize it.

00:10:37.800 --> 00:10:39.946
Just so you know, the A is

00:10:39.946 --> 00:10:43.400
because it's our first real
formal round of financing.

00:10:43.400 --> 00:10:45.000
In our second round which I'll do

00:10:45.000 --> 00:10:46.823
probably in the next
video, it would be Series B

00:10:46.823 --> 00:10:49.200
and then Series C and then Series D.

00:10:49.200 --> 00:10:50.600
Every time we run out of cash,

00:10:50.600 --> 00:10:51.800
we want to go back to the till.

00:10:51.800 --> 00:10:53.100
We've already done the Series A,

00:10:53.100 --> 00:10:54.600
now we want to do a Series B

00:10:54.600 --> 00:10:56.500
and a Series C and so forth and so on

00:10:56.500 --> 00:10:57.900
and eventually we'll hopefully get to

00:10:57.900 --> 00:11:00.100
some type of an IPO which I'll talk about

00:11:00.100 --> 00:11:01.800
in the next video because I just realized

00:11:01.800 --> 00:11:03.100
I'm out of time again.


Raising money for a startup

WEBVTT
Kind: captions
Language: en

00:00:00.860 --> 00:00:04.480
Let's say I'm hanging out with
my buddies one night and we

00:00:04.480 --> 00:00:07.060
realize that there's a
huge opportunity in

00:00:07.060 --> 00:00:08.435
selling socks online.

00:00:11.780 --> 00:00:13.210
And so we decide to
start a company.

00:00:13.210 --> 00:00:14.710
So the first thing we
would do is we would

00:00:14.710 --> 00:00:16.160
write a business plan.

00:00:16.160 --> 00:00:18.590
And say, you know what?

00:00:18.590 --> 00:00:21.530
In this business plan writing
process, this is all we've all

00:00:21.530 --> 00:00:23.400
contributed to it
individually.

00:00:23.400 --> 00:00:25.230
So we'll all be equal
shareholders.

00:00:25.230 --> 00:00:27.220
Let's say there's five
of us friends.

00:00:27.220 --> 00:00:30.570
So the first thing we want to
do is we want to start a--

00:00:30.570 --> 00:00:32.080
well you know, you could do in
different orders, you could

00:00:32.080 --> 00:00:33.920
just write up a business plan,
or you can start the

00:00:33.920 --> 00:00:34.620
corporation.

00:00:34.620 --> 00:00:37.800
But we'll just assume we
start a corporation.

00:00:37.800 --> 00:00:41.360
And I'm going to indicate the
corporation by creating a

00:00:41.360 --> 00:00:43.420
balance sheet right
from the get-go.

00:00:43.420 --> 00:00:46.370
So, what are the assets of the
corporation, and what are the

00:00:46.370 --> 00:00:48.720
debt-- and what are the
liabilities-- and we could

00:00:48.720 --> 00:00:50.900
talk a little bit about what
a corporation even is.

00:00:50.900 --> 00:00:53.860
So it's asset to begin with.

00:00:57.010 --> 00:00:58.350
It's essentially just an idea.

00:00:58.350 --> 00:01:03.050
I mean, you could say it takes
physical form to some degree

00:01:03.050 --> 00:01:07.040
in the business plan, but it's
just an idea first. And then,

00:01:07.040 --> 00:01:09.770
there are no immediate
liabilities, it doesn't owe

00:01:09.770 --> 00:01:10.890
anybody any money.

00:01:10.890 --> 00:01:13.480
And we learned in the balance
sheet videos-- and you might

00:01:13.480 --> 00:01:16.180
want to watch the balance sheet
videos as a prerequisite

00:01:16.180 --> 00:01:20.050
to this one-- but in general,
assets are equal to

00:01:20.050 --> 00:01:24.030
liabilities plus equity.

00:01:24.030 --> 00:01:26.450
So this is assets.

00:01:26.450 --> 00:01:29.300
The only asset we have right
now is our idea.

00:01:29.300 --> 00:01:33.040
Maybe you want to add the
potential talent that we have,

00:01:33.040 --> 00:01:35.780
maybe unique skills.

00:01:35.780 --> 00:01:39.370
They are very intangible
at this point.

00:01:39.370 --> 00:01:41.680
These are the assets that our
five buddies have together.

00:01:41.680 --> 00:01:42.670
And we have no liabilities.

00:01:42.670 --> 00:01:44.490
It doesn't sound like we
borrowed money or anything.

00:01:44.490 --> 00:01:46.860
So everything we have-- so the
assets are equal to our

00:01:46.860 --> 00:01:52.960
equity-- and I'll do that in a
brown color-- so there's no

00:01:52.960 --> 00:01:55.520
liabilities and we
just have equity.

00:01:55.520 --> 00:02:00.390
And equity is essentially what
the owners of the company have

00:02:00.390 --> 00:02:01.620
the rights to.

00:02:01.620 --> 00:02:04.250
For example, if-- I haven't
assigned any numbers here and

00:02:04.250 --> 00:02:09.360
I did that for a reason-- but if
the assets were $10 million

00:02:09.360 --> 00:02:12.760
and liability was $5 million,
if we had owed $5 million to

00:02:12.760 --> 00:02:14.860
someone else, then you
would have $5 million

00:02:14.860 --> 00:02:15.630
left for the equity.

00:02:15.630 --> 00:02:18.370
And that's what the owners of
the company would have.

00:02:18.370 --> 00:02:21.510
Me and my five buddies, or I
guess my four buddies, we

00:02:21.510 --> 00:02:24.220
decide we're the owners of the
company, so we'll be equal

00:02:24.220 --> 00:02:25.780
shareholders.

00:02:25.780 --> 00:02:30.130
So we would split the equity
between us five ways.

00:02:30.130 --> 00:02:32.300
So we just pick an
arbitrary number.

00:02:32.300 --> 00:02:35.220
Let's say to begin with we have
a million shares, so each

00:02:35.220 --> 00:02:40.870
of us have 200,000 shares
in the company.

00:02:40.870 --> 00:02:44.340
And that's a bit of an
arbitrary notion.

00:02:44.340 --> 00:02:47.300
And you normally do assign some
value to those shares

00:02:47.300 --> 00:02:49.450
initially, it's some pennies
per share, but I won't get

00:02:49.450 --> 00:02:53.200
into the technicalities
of that.

00:02:53.200 --> 00:02:56.980
Just fair enough to say that we
each have 200,000 shares in

00:02:56.980 --> 00:02:57.560
this company.

00:02:57.560 --> 00:03:01.000
And some of them go to me and
then the rest of them go to

00:03:01.000 --> 00:03:06.220
buddy one, buddy two, buddy
three, and buddy four.

00:03:06.220 --> 00:03:10.750
This is the equity right here.

00:03:10.750 --> 00:03:15.000
And there's a total of one
million shares outstanding.

00:03:15.000 --> 00:03:15.770
Good enough.

00:03:15.770 --> 00:03:18.740
Well, just an idea and some
paper and some well

00:03:18.740 --> 00:03:21.020
intentioned individuals
alone isn't

00:03:21.020 --> 00:03:22.300
enough to start a company.

00:03:22.300 --> 00:03:24.950
We're going to have to create
some type of an online

00:03:24.950 --> 00:03:28.340
presence, and do some
programming, and maybe have a

00:03:28.340 --> 00:03:29.940
warehouse, and do
some marketing.

00:03:29.940 --> 00:03:31.900
So we're going to have to-- and
really we're going to have

00:03:31.900 --> 00:03:34.250
to quit our jobs so that we can
work on this full time.

00:03:34.250 --> 00:03:35.500
So we're going to have
to raise some money.

00:03:35.500 --> 00:03:39.230
Money to hire some engineers, so
that we can quit our jobs.

00:03:39.230 --> 00:03:41.560
To hire some marketing people,
et cetera, et cetera.

00:03:41.560 --> 00:03:43.120
So where do we get
our money from?

00:03:43.120 --> 00:03:46.530
So this is where the whole
venture capital world comes

00:03:46.530 --> 00:03:48.140
into the picture.

00:03:48.140 --> 00:03:49.110
You've heard the word before.

00:03:49.110 --> 00:03:51.610
I think you have some
sense of what it is.

00:03:51.610 --> 00:03:57.230
And the venture capital world,
it's kind of separated into

00:03:57.230 --> 00:03:59.505
different people who invest
in different stages.

00:04:02.290 --> 00:04:05.150
So you'll have people, they're
called angel investors.

00:04:05.150 --> 00:04:07.720
And sometimes these people won't
even call themselves

00:04:07.720 --> 00:04:10.620
venture-- angel investors.

00:04:13.280 --> 00:04:16.540
And these are the guys that
are kind of these, I don't

00:04:16.540 --> 00:04:19.480
want to stereotype it, but
they'll be kind of like the

00:04:19.480 --> 00:04:22.250
old guys who made it big in
the `80s and now they're

00:04:22.250 --> 00:04:24.140
sitting on billions
of dollars.

00:04:24.140 --> 00:04:27.550
And they want to participate
in the neat, fun ideas that

00:04:27.550 --> 00:04:29.880
young guys like me and
my friends think of.

00:04:29.880 --> 00:04:31.760
And so they're kind of like your
rich uncle who says, oh

00:04:31.760 --> 00:04:33.560
that's a great idea, I'll throw
some money behind that.

00:04:33.560 --> 00:04:35.850
They usually invest at
a very early stage.

00:04:35.850 --> 00:04:37.090
So those are probably
the people

00:04:37.090 --> 00:04:38.290
we would go to initially.

00:04:38.290 --> 00:04:40.840
And then we'll talk to the
people after that, the other

00:04:40.840 --> 00:04:42.100
types of venture capitalists.

00:04:42.100 --> 00:04:45.080
But in general, venture
capital can

00:04:45.080 --> 00:04:45.650
meet a lot of things.

00:04:45.650 --> 00:04:47.940
But it means someone who's
going to give you money.

00:04:47.940 --> 00:04:50.090
They're going to take a stake in
your company and hope that

00:04:50.090 --> 00:04:52.380
your-- they give you enough
money to kind of get your

00:04:52.380 --> 00:04:53.170
venture going.

00:04:53.170 --> 00:04:55.240
To kind of start
your business.

00:04:55.240 --> 00:04:58.010
So let's say we go to an angel
investor, and we say hey,

00:04:58.010 --> 00:05:00.840
angel investor, don't you think
this is a great idea?

00:05:00.840 --> 00:05:03.040
We're going to sell
socks online.

00:05:03.040 --> 00:05:05.630
You know, socks are something
people run out of every week,

00:05:05.630 --> 00:05:08.170
we can even do subscriptions
for socks.

00:05:08.170 --> 00:05:11.640
You get 10 pairs of month,
et cetera, et cetera.

00:05:11.640 --> 00:05:12.550
You can give them as gifts.

00:05:12.550 --> 00:05:13.920
All of these lovely things.

00:05:13.920 --> 00:05:17.650
And the first nine guys slam
their doors on our face.

00:05:17.650 --> 00:05:18.570
They think our business
is stupid.

00:05:18.570 --> 00:05:21.960
But the tenth guy says, hey you
know, that's interesting.

00:05:21.960 --> 00:05:23.630
So we enter into negotiations.

00:05:23.630 --> 00:05:24.740
And he's like, you know what?

00:05:24.740 --> 00:05:27.850
I'm going to invest. But we have
to figure out what I'm

00:05:27.850 --> 00:05:30.330
going to get in exchange for
investing in your company.

00:05:30.330 --> 00:05:32.480
How much of your company
I'm going to get.

00:05:32.480 --> 00:05:36.300
And so this leads to a
process of valuation.

00:05:36.300 --> 00:05:40.050
So let's say we say need $5
million from the angel

00:05:40.050 --> 00:05:42.250
investor to get started.

00:05:42.250 --> 00:05:47.410
We need $5 million-- let me
write that down-- that's what

00:05:47.410 --> 00:05:48.410
we say we need.

00:05:48.410 --> 00:05:50.680
And that's what the angel
investor says that he's

00:05:50.680 --> 00:05:52.180
willing to give us,
because he agrees.

00:05:52.180 --> 00:05:55.960
$5 million, that's enough for us
to quit our jobs, and then

00:05:55.960 --> 00:05:59.300
we could all take salaries
for some time.

00:05:59.300 --> 00:06:00.880
We could hire a bunch
of people.

00:06:00.880 --> 00:06:03.060
We can rent office spaces.

00:06:03.060 --> 00:06:04.710
Do everything you need to
do to start a company.

00:06:04.710 --> 00:06:07.320
And $5 million will support
that for, I don't

00:06:07.320 --> 00:06:08.230
know, a year or two.

00:06:08.230 --> 00:06:10.760
I don't know, depending on how
many expenses we have.

00:06:10.760 --> 00:06:14.140
But the question is, what does
he get for that $5 million.

00:06:14.140 --> 00:06:15.830
So in order to come to that
conclusion, you have to

00:06:15.830 --> 00:06:18.860
determine what is what we had
before he came to the picture

00:06:18.860 --> 00:06:20.500
worth, right?

00:06:20.500 --> 00:06:22.980
Notice, when I did this balance
sheet I didn't even

00:06:22.980 --> 00:06:24.250
write what these assets
are worth.

00:06:24.250 --> 00:06:27.050
What is this worth?

00:06:27.050 --> 00:06:30.560
And this value, this is called
a-- well in general, whenever

00:06:30.560 --> 00:06:32.345
you're valuing anything, it's
called a valuation.

00:06:37.200 --> 00:06:39.540
And since we want to know what
this is worth-- this is before

00:06:39.540 --> 00:06:41.830
we got any kind of money from
investors-- this would be

00:06:41.830 --> 00:06:43.260
called a pre-money valuation.

00:06:49.960 --> 00:06:52.120
And I'll show you why that
matters in a second.

00:06:52.120 --> 00:06:59.170
Because, if us and this angel
investor agree that this-- our

00:06:59.170 --> 00:07:02.410
assets before we go to them--
are worth $5 million.

00:07:02.410 --> 00:07:06.180
So if we agree that they're
worth $5 million-- let me draw

00:07:06.180 --> 00:07:09.020
that so, what color was
I doing that in?

00:07:09.020 --> 00:07:12.680
It was in yellow-- so if we
agree-- let me draw it a

00:07:12.680 --> 00:07:16.820
little bit smaller-- essentially
it's just an idea,

00:07:16.820 --> 00:07:20.150
and then we have the shares,
a million shares.

00:07:20.150 --> 00:07:23.090
Of that million,
I have 200,000.

00:07:23.090 --> 00:07:28.460
The other 800,000 are
with my friends.

00:07:28.460 --> 00:07:33.990
These are one million shares
total, or shares outstanding.

00:07:33.990 --> 00:07:38.440
So if this idea-- we agree with
the angel investor-- if

00:07:38.440 --> 00:07:40.470
we agree this is worth
$5 million.

00:07:44.680 --> 00:07:47.080
So everything we have today
is worth $5 million.

00:07:47.080 --> 00:07:49.720
Then when he gives us
another $5 million,

00:07:49.720 --> 00:07:50.600
that's an asset, right?

00:07:50.600 --> 00:07:53.890
We'll have $5 million in cash.

00:07:53.890 --> 00:07:55.850
So he'll give us another
$5 million.

00:07:58.950 --> 00:08:02.020
He'll essentially get
50% of the company.

00:08:02.020 --> 00:08:03.900
He'll get all of these
shares up here.

00:08:03.900 --> 00:08:05.850
Now how does that work out?

00:08:05.850 --> 00:08:10.340
Well if you think about it,
this is the post-money

00:08:10.340 --> 00:08:11.600
company, right?

00:08:11.600 --> 00:08:12.730
So let's think about
it a couple ways.

00:08:12.730 --> 00:08:14.060
This is $5 million.

00:08:14.060 --> 00:08:15.250
That's the idea.

00:08:15.250 --> 00:08:16.890
What is the $5 million worth?

00:08:16.890 --> 00:08:18.110
That's not a trick question.

00:08:18.110 --> 00:08:21.020
That's worth $5 million,
right?

00:08:21.020 --> 00:08:23.320
It's worth $5 million.

00:08:23.320 --> 00:08:26.365
So what is the post-money
valuation?

00:08:26.365 --> 00:08:29.760
When we talk about valuation
we're talking about the value

00:08:29.760 --> 00:08:32.250
of the assets, especially
because we're not dealing with

00:08:32.250 --> 00:08:33.530
any debt right now.

00:08:33.530 --> 00:08:35.260
Everything on the right-hand
side is equity,

00:08:35.260 --> 00:08:36.190
so this is all equity.

00:08:36.190 --> 00:08:39.510
Let me write that, no
liabilities yet.

00:08:39.510 --> 00:08:43.580
And in general, when you're
doing a startup company, if I

00:08:43.580 --> 00:08:48.310
want to start socksonline.com,
and I go into my local bank

00:08:48.310 --> 00:08:50.070
and say, hey give me a
loan, they're just

00:08:50.070 --> 00:08:50.910
going to turn me away.

00:08:50.910 --> 00:08:54.920
Because if you have a venture
that really doesn't exist yet

00:08:54.920 --> 00:08:57.500
and has no cash flow, they know
that you're not going to

00:08:57.500 --> 00:08:59.380
pay the interest on the debt, so
you're not going to even be

00:08:59.380 --> 00:09:02.250
able to raise debt until you
are a more mature company.

00:09:02.250 --> 00:09:04.980
Or until you-- maybe you could
post some collateral.

00:09:04.980 --> 00:09:06.070
And I'll talk more about that.

00:09:06.070 --> 00:09:08.710
Maybe you could say hey,
I'll use my house.

00:09:08.710 --> 00:09:10.790
If I don't pay the debt, you
can take my house, or

00:09:10.790 --> 00:09:11.280
something like that.

00:09:11.280 --> 00:09:13.580
But for the most part we
don't want to do that.

00:09:13.580 --> 00:09:18.430
So the only way to raise money
at this early stage is by

00:09:18.430 --> 00:09:19.560
issuing equity.

00:09:19.560 --> 00:09:21.670
So going back to what we were
talking about, what is the

00:09:21.670 --> 00:09:22.310
post-money valuation?

00:09:22.310 --> 00:09:25.210
We said before any of this stuff
on the top existed, the

00:09:25.210 --> 00:09:30.000
pre-money valuation of just
our idea was $5 million.

00:09:30.000 --> 00:09:33.680
Now, the angel investor, if we
value this at $5 million,

00:09:33.680 --> 00:09:35.350
he'll give us $5 million more.

00:09:35.350 --> 00:09:38.240
What is the total value of
all of the assets now?

00:09:38.240 --> 00:09:40.530
Well if we said this was $5
million, that's just something

00:09:40.530 --> 00:09:40.860
we agreed with.

00:09:40.860 --> 00:09:42.760
This is worth $5 million.

00:09:42.760 --> 00:09:46.210
So the combined assets, if you
believe that this is worth $5

00:09:46.210 --> 00:09:49.660
million, is now $10
million, right?

00:09:49.660 --> 00:09:52.410
And this would be the post-money
valuation.

00:09:57.870 --> 00:10:00.780
And if you think about it, if
you think about the company in

00:10:00.780 --> 00:10:03.820
this form right now, we-- me
and my buddies-- we've

00:10:03.820 --> 00:10:06.800
contributed half of the
value of the company.

00:10:06.800 --> 00:10:10.640
And this rich guy, he's
contributed the other half of

00:10:10.640 --> 00:10:11.050
the company.

00:10:11.050 --> 00:10:14.200
So it makes sense that he
has 50% of the company.

00:10:14.200 --> 00:10:15.760
So how is that going to work?

00:10:15.760 --> 00:10:19.100
Well, I don't give away any of
my shares, and neither are any

00:10:19.100 --> 00:10:20.070
of my friends.

00:10:20.070 --> 00:10:21.780
They're all going to
keep their shares.

00:10:21.780 --> 00:10:26.030
So we had five chunks of
$200,000 that went-- 200,000

00:10:26.030 --> 00:10:27.930
shares that went
to each of us.

00:10:27.930 --> 00:10:30.780
All right, that was buddy
one, two, three, four.

00:10:30.780 --> 00:10:34.250
So what we'll do is, we'll
actually issue another million

00:10:34.250 --> 00:10:36.920
shares and give it to
this rich dude.

00:10:36.920 --> 00:10:38.780
So this is another one
million shares.

00:10:41.710 --> 00:10:44.670
So as the company board, you
can actually authorize to

00:10:44.670 --> 00:10:46.050
create shares.

00:10:46.050 --> 00:10:49.260
And that's what we did, and we
essentially sold those shares

00:10:49.260 --> 00:10:50.500
for $5 million.

00:10:50.500 --> 00:10:53.730
So now instead of having one
million shares, you have two

00:10:53.730 --> 00:10:56.160
million shares.

00:10:56.160 --> 00:10:59.150
So something interesting here,
and some people often talk

00:10:59.150 --> 00:11:01.540
about the notion of
dilution, right?

00:11:01.540 --> 00:11:05.680
Because before, I had 200,000
out of a million shares.

00:11:05.680 --> 00:11:09.750
So before, I had 20%
of the company.

00:11:09.750 --> 00:11:11.330
And now what do I have?

00:11:11.330 --> 00:11:13.820
Well we've essentially doubled
the share count, so now I only

00:11:13.820 --> 00:11:16.190
have 10% of the company.

00:11:16.190 --> 00:11:18.390
So some people say, oh you know
what, my share of the

00:11:18.390 --> 00:11:19.950
company got diluted.

00:11:19.950 --> 00:11:24.000
But it really isn't the case,
because the company has gotten

00:11:24.000 --> 00:11:26.020
all this cash.

00:11:26.020 --> 00:11:29.810
I now own 10% of something
that's twice as valuable, as

00:11:29.810 --> 00:11:32.230
opposed to 20% of something
that's half as valuable.

00:11:32.230 --> 00:11:34.200
If you really believe
that, then this

00:11:34.200 --> 00:11:35.480
was no change, right?

00:11:35.480 --> 00:11:40.250
I now own 10% of ten million,
which in theory should be

00:11:40.250 --> 00:11:42.330
worth a million dollars.

00:11:42.330 --> 00:11:46.190
Before I owned 20% of five
million, which was also worth

00:11:46.190 --> 00:11:47.380
a million dollars.

00:11:47.380 --> 00:11:49.910
So if you believe these
valuations, I

00:11:49.910 --> 00:11:51.990
probably-- I'm neutral.

00:11:51.990 --> 00:11:54.890
And we're going to put this
$5 million to work.

00:11:54.890 --> 00:11:57.470
And actually let me take a
step-- actually no, I just

00:11:57.470 --> 00:11:58.530
realized I'm out of time.

00:11:58.530 --> 00:12:01.360
Let me continue this
in the next video.


Birthday probability problem

WEBVTT
Kind: captions
Language: en

00:00:00.990 --> 00:00:03.690
One of you all sent a fairly
interesting problem, so I

00:00:03.690 --> 00:00:05.360
thought I would work it out.

00:00:05.360 --> 00:00:08.430
The problem is I have a
group of 30 people, so

00:00:08.430 --> 00:00:09.580
30 people in a room.

00:00:09.580 --> 00:00:13.820
They're randomly
selected 30 people.

00:00:13.820 --> 00:00:22.490
And the question is what is the
probability that at least 2

00:00:22.490 --> 00:00:29.640
people have the same birthday?

00:00:29.640 --> 00:00:32.930
This is kind of a fun question
because that's the size

00:00:32.930 --> 00:00:33.680
of a lot of classrooms.

00:00:33.680 --> 00:00:36.260
What's the probability that at
least someone in the classroom

00:00:36.260 --> 00:00:40.200
shares a birthday with someone
else in the classroom?

00:00:40.200 --> 00:00:41.740
That's a good way
to phrase as well.

00:00:41.740 --> 00:00:45.720
This is the same thing as
saying, what is the probability

00:00:45.720 --> 00:00:53.820
that someone shares with
at least someone else.

00:00:53.820 --> 00:00:55.570
They could share it with 2
other people or 4 other

00:00:55.570 --> 00:00:56.420
people in the birthday.

00:01:03.860 --> 00:01:06.260
And at first this problem seems
really hard because there's

00:01:06.260 --> 00:01:08.810
a lot of circumstances
that makes this true.

00:01:08.810 --> 00:01:11.270
I could have exactly 2 people
have the same birthday.

00:01:11.270 --> 00:01:14.170
I could have exactly 3 people
have the same birthday.

00:01:14.170 --> 00:01:17.060
I could have exactly 29 people
have the same birthday and all

00:01:17.060 --> 00:01:20.500
of these make this true, so do
I add the probability of each

00:01:20.500 --> 00:01:21.830
of those circumstances?

00:01:21.830 --> 00:01:24.990
And then add them up and then
that becomes really hard.

00:01:24.990 --> 00:01:26.510
And then I would have to
say, OK, whose birthdays

00:01:26.510 --> 00:01:27.280
and I comparing?

00:01:27.280 --> 00:01:28.020
And I would have to
do combinations.

00:01:28.020 --> 00:01:32.200
It becomes a really difficult
problem unless you make kind

00:01:32.200 --> 00:01:37.560
of one very simplifying
take on the problem.

00:01:37.560 --> 00:01:41.310
This is the opposite of--
well let me draw the

00:01:41.310 --> 00:01:43.810
probability space.

00:01:43.810 --> 00:01:46.250
Let's say that this is
all of the outcomes.

00:01:46.250 --> 00:01:47.630
Let me draw it with
a thicker line.

00:01:51.250 --> 00:01:53.770
So let's say that's all
of the outcomes of my

00:01:53.770 --> 00:01:54.630
probability space.

00:01:54.630 --> 00:01:56.590
So that's 100% of the outcomes.

00:02:01.730 --> 00:02:04.000
We want to know-- let me draw
it in a color that won't

00:02:04.000 --> 00:02:06.680
be offensive to you.

00:02:06.680 --> 00:02:09.030
That doesn't look that
great, but anyway.

00:02:09.030 --> 00:02:12.620
Let's say that this is the
probability, this area right

00:02:12.620 --> 00:02:14.250
here-- and I don't know
how big it really is,

00:02:14.250 --> 00:02:16.070
we'll figure it out.

00:02:16.070 --> 00:02:18.140
Let's say that this is the
probability that someone

00:02:18.140 --> 00:02:21.220
shares a birthday with
at least someone else.

00:02:21.220 --> 00:02:23.410
What's this area over here?

00:02:23.410 --> 00:02:25.080
What's this green area?

00:02:25.080 --> 00:02:27.970
Well, that means if these are
all the cases where someone

00:02:27.970 --> 00:02:31.170
shares a birthday with someone
else, these are all the area

00:02:31.170 --> 00:02:32.850
where no one shares a
birthday with anyone.

00:02:39.230 --> 00:02:45.735
Or you could say, all 30 people
have different birthdays.

00:02:51.430 --> 00:02:53.850
This is what we're
trying to figure out.

00:02:53.850 --> 00:02:56.500
I'll just call it the
probability that

00:02:56.500 --> 00:02:57.630
someone shares.

00:02:57.630 --> 00:03:00.170
I'll call it the probability
of sharing, probability of s.

00:03:02.760 --> 00:03:08.540
If this whole area is area 1 or
area 100%, this green area

00:03:08.540 --> 00:03:14.760
right here, this is going
to be 1 minus p of s.

00:03:14.760 --> 00:03:16.540
This is going to be
1 minus p of s.

00:03:16.540 --> 00:03:20.200
Or if we said that this is the
probability-- or another way we

00:03:20.200 --> 00:03:22.310
could say it, actually this is
the best way to think about it.

00:03:22.310 --> 00:03:24.780
If this is different, so
this is the probability

00:03:24.780 --> 00:03:26.610
of different birthdays.

00:03:26.610 --> 00:03:28.770
This is the probability
that all 30 people have

00:03:28.770 --> 00:03:30.410
30 different birthdays.

00:03:30.410 --> 00:03:32.300
No one shares with anyone.

00:03:32.300 --> 00:03:36.630
The probability that someone
shares with someone else plus

00:03:36.630 --> 00:03:39.460
the probability that no one
shares with anyone-- they all

00:03:39.460 --> 00:03:42.960
have distinct birthdays--
that's got to be equal to 1.

00:03:42.960 --> 00:03:44.950
Because we're either going to
be in this situation or we're

00:03:44.950 --> 00:03:45.990
going to be in that situation.

00:03:45.990 --> 00:03:47.670
Or you can say they're
equal to 100%.

00:03:47.670 --> 00:03:51.191
Either way, 100% and 1
are the same number.

00:03:51.191 --> 00:03:53.460
It's equal to 100%.

00:03:53.460 --> 00:03:56.990
So if we figure out the
probability that everyone has

00:03:56.990 --> 00:03:59.830
the same birthday we could
subtract it from 100.

00:03:59.830 --> 00:04:00.710
So let's see.

00:04:00.710 --> 00:04:02.090
We could we just rewrite this.

00:04:02.090 --> 00:04:04.710
The probability that someone
shares a birthday with someone

00:04:04.710 --> 00:04:11.390
else, that's equal to 100%
minus the probability that

00:04:11.390 --> 00:04:15.080
everyone has distinct,
separate birthdays.

00:04:15.080 --> 00:04:18.190
And the reason why I'm doing
that is because as I started

00:04:18.190 --> 00:04:20.190
off in the video, this is
kind of hard to figure out.

00:04:20.190 --> 00:04:23.140
You know, I can figure out the
probability that 2 people have

00:04:23.140 --> 00:04:26.520
the same birthday, 5 people,
and it becomes very confusing.

00:04:26.520 --> 00:04:28.560
But here, if I wanted to just
figure out the probability that

00:04:28.560 --> 00:04:31.860
everyone has a distinct
birthday, it's actually a much

00:04:31.860 --> 00:04:34.190
easier probability
to solve for.

00:04:34.190 --> 00:04:35.830
So what's the probability
that everyone has a

00:04:35.830 --> 00:04:37.440
distinct birthday?

00:04:37.440 --> 00:04:38.300
So let's think about it.

00:04:41.690 --> 00:04:43.880
Person one.

00:04:43.880 --> 00:04:46.370
Just for simplicity, let's
imagine the case that we only

00:04:46.370 --> 00:04:47.790
have 2 people in the room.

00:04:47.790 --> 00:04:51.770
What's the probably that they
have different birthdays?

00:04:51.770 --> 00:04:57.870
Let's see, person one, their
birthday could be 365 days

00:04:57.870 --> 00:05:00.520
out of 365 days of the year.

00:05:00.520 --> 00:05:02.390
You know, whenever
their birthday is.

00:05:02.390 --> 00:05:06.440
And then person two, if we
wanted to ensure that they

00:05:06.440 --> 00:05:09.340
don't have the same birthday,
how many days could

00:05:09.340 --> 00:05:10.720
person two be born on?

00:05:10.720 --> 00:05:13.130
Well, it could be born
on any day that person

00:05:13.130 --> 00:05:14.240
one was not born on.

00:05:14.240 --> 00:05:19.080
So there are 364
possibilities out 365.

00:05:19.080 --> 00:05:21.550
So if you had 2 people, the
probability that no one

00:05:21.550 --> 00:05:23.110
is born on the same
birthday-- this is just 1.

00:05:23.110 --> 00:05:30.330
It's just going to be
equal to 364/365.

00:05:30.330 --> 00:05:33.740
Now what happens if
we had 3 people?

00:05:33.740 --> 00:05:35.470
So first of all the
first person could

00:05:35.470 --> 00:05:38.280
be born on any day.

00:05:38.280 --> 00:05:42.990
Then the second person could
be born on 364 possible

00:05:42.990 --> 00:05:45.390
days out of 365.

00:05:45.390 --> 00:05:49.220
And then the third person,
what's the probability that

00:05:49.220 --> 00:05:51.810
the third person isn't
born on either of these

00:05:51.810 --> 00:05:52.620
people birthdays?

00:05:52.620 --> 00:06:03.110
So 2 days are taken up, so
the probability is 363/365.

00:06:03.110 --> 00:06:04.330
You multiply them out.

00:06:04.330 --> 00:06:11.480
You get 365 times 36-- actually
I should rewrite this one.

00:06:11.480 --> 00:06:14.420
Instead of saying this is 1,
let me write this as-- the

00:06:14.420 --> 00:06:21.370
numerator is 365 times
364 over 365 squared.

00:06:21.370 --> 00:06:23.140
Because I want you
to see the pattern.

00:06:23.140 --> 00:06:30.640
Here the probability is 365
times 364 times 363 over

00:06:30.640 --> 00:06:35.610
365 to the third power.

00:06:35.610 --> 00:06:41.100
And so, in general, if you just
kept doing this to 30, if I

00:06:41.100 --> 00:06:47.610
just kept this process for 30
people-- the probability that

00:06:47.610 --> 00:06:55.560
no one shares the same birthday
would be equal to 365 times 364

00:06:55.560 --> 00:06:59.280
times 363-- I'll have
30 terms up here.

00:06:59.280 --> 00:07:01.760
All the way down to what?

00:07:05.080 --> 00:07:07.120
All the way down to 336.

00:07:07.120 --> 00:07:15.810
That'll actually be 30
terms divided by 365

00:07:15.810 --> 00:07:17.380
to the 30th power.

00:07:17.380 --> 00:07:19.220
And you can just type this into
your calculator right now.

00:07:19.220 --> 00:07:21.910
It'll take you a little time to
type in 30 numbers, and you'll

00:07:21.910 --> 00:07:25.960
get the probability that no one
shares the same birthday

00:07:25.960 --> 00:07:27.700
with anyone else.

00:07:27.700 --> 00:07:29.900
But before we do that let
me just show you something

00:07:29.900 --> 00:07:31.250
that might make it a
little bit easier.

00:07:31.250 --> 00:07:33.970
Is there any way that I can
mathematically express

00:07:33.970 --> 00:07:35.130
this with factorials?

00:07:35.130 --> 00:07:38.730
Or that I could mathematically
express this with factorials?

00:07:38.730 --> 00:07:40.380
Let's think about it.

00:07:40.380 --> 00:07:44.120
365 factorial is what?

00:07:44.120 --> 00:07:55.320
365 factorial is equal to 365
times 364 times 363 times--

00:07:55.320 --> 00:07:56.710
all the way down to 1.

00:07:56.710 --> 00:07:57.870
You just keep multiplying.

00:07:57.870 --> 00:08:00.040
It's a huge number.

00:08:00.040 --> 00:08:03.830
Now, if I just want the 365
times the 364 in this case,

00:08:03.830 --> 00:08:07.610
I have to get rid of all of
these numbers back here.

00:08:07.610 --> 00:08:10.690
One thing I could do is I
could divide this thing

00:08:10.690 --> 00:08:12.140
by all of these numbers.

00:08:12.140 --> 00:08:17.630
So 363 times 362-- all
the way down to 1.

00:08:17.630 --> 00:08:23.820
So that's the same thing as
dividing by 363 factorial.

00:08:23.820 --> 00:08:27.370
365 factorial divided by 363
factorial is essentially this

00:08:27.370 --> 00:08:31.260
because all of these
terms cancel out.

00:08:31.260 --> 00:08:38.230
So this is equal to 365
factorial over 363 factorial

00:08:38.230 --> 00:08:40.725
over 365 squared.

00:08:40.725 --> 00:08:42.870
And of course, for this case,
it's almost silly to worry

00:08:42.870 --> 00:08:45.000
about the factorials, but it
becomes useful once we have

00:08:45.000 --> 00:08:47.230
something larger than
two terms up here.

00:08:47.230 --> 00:08:50.940
So by the same logic, this
right here is going to be equal

00:08:50.940 --> 00:09:01.780
to 365 factorial over 362
factorial over 365 squared.

00:09:01.780 --> 00:09:03.390
And actually, just another
interesting point.

00:09:03.390 --> 00:09:05.580
How did we get this 365?

00:09:05.580 --> 00:09:08.620
Sorry, how did we get
this 363 factorial?

00:09:08.620 --> 00:09:12.250
Well, 365 minus 2
is 363, right?

00:09:12.250 --> 00:09:15.940
And that makes sense because we
only wanted two terms up here.

00:09:15.940 --> 00:09:17.670
We only wanted two
terms right here.

00:09:17.670 --> 00:09:21.760
So we wanted to divide by a
factorial that's two less.

00:09:21.760 --> 00:09:24.670
And so we'd only get the
highest two terms left.

00:09:24.670 --> 00:09:28.180
This is also equal to-- you
could write this as 365

00:09:28.180 --> 00:09:36.870
factorial divided by 365 minus
2 factorial 365 minus 2 is 363

00:09:36.870 --> 00:09:39.210
factorial and then you just end
up with those two terms

00:09:39.210 --> 00:09:40.630
and that's that there.

00:09:40.630 --> 00:09:45.580
And then likewise, this right
here, this numerator you could

00:09:45.580 --> 00:09:54.980
rewrite as 365 factorial
divided by 365 minus 3-- and

00:09:54.980 --> 00:09:58.190
we had 3 people-- factorial.

00:09:58.190 --> 00:09:59.380
And that should hopefully
make sense, right?

00:09:59.380 --> 00:10:04.780
This is the same thing as 365
factorial-- well 365 divided

00:10:04.780 --> 00:10:08.090
by 3 is 362 factorial.

00:10:08.090 --> 00:10:13.430
And so that's equal to
365 times 364 times

00:10:13.430 --> 00:10:16.380
363 all the way down.

00:10:16.380 --> 00:10:20.550
Divided by 362 times
all the way down.

00:10:20.550 --> 00:10:22.870
And that'll cancel out with
everything else and you'd

00:10:22.870 --> 00:10:24.860
be just left with that.

00:10:24.860 --> 00:10:26.600
And that's that right there.

00:10:26.600 --> 00:10:35.190
So by that same logic, this top
part here can be written as

00:10:35.190 --> 00:10:41.160
365 factorial over what?

00:10:41.160 --> 00:10:46.660
365 minus 30 factorial.

00:10:46.660 --> 00:10:49.360
And I did all of that just so
I could show you kind of the

00:10:49.360 --> 00:10:52.200
pattern and because this is
frankly easier to type into a

00:10:52.200 --> 00:10:54.700
calculator if you know where
the factorial button is.

00:10:54.700 --> 00:10:58.330
So let's figure out what
this entire probability is.

00:10:58.330 --> 00:11:01.710
So turning on the calculator,
we want-- so let's

00:11:01.710 --> 00:11:02.790
do the numerator.

00:11:02.790 --> 00:11:09.820
365 factorial divided by--
well, what's 365 minus 30?

00:11:09.820 --> 00:11:12.020
That's 335.

00:11:12.020 --> 00:11:19.560
Divided by 335 factorial and
that's the whole numerator.

00:11:19.560 --> 00:11:25.630
And now we want to divide
the numerator by 365

00:11:25.630 --> 00:11:29.610
to the 30th power.

00:11:29.610 --> 00:11:34.100
Let the calculator think
and we get 0.2936.

00:11:34.100 --> 00:11:37.990
Equals 0.2936.

00:11:37.990 --> 00:11:45.350
Actually 37 if you rounded,
which is equal to 29.37%.

00:11:45.350 --> 00:11:48.550
Now, just so you remember what
we were doing all along, this

00:11:48.550 --> 00:11:52.610
was the probability that no one
shares a birthday with anyone.

00:11:52.610 --> 00:11:56.180
This was the probability of
everyone having distinct,

00:11:56.180 --> 00:11:58.090
different birthdays
from everyone else.

00:11:58.090 --> 00:12:00.580
And we said, well, the
probability that someone shares

00:12:00.580 --> 00:12:03.930
a birthday with someone else,
or maybe more than one person,

00:12:03.930 --> 00:12:07.830
is equal to all of the
possibilities-- kind of the

00:12:07.830 --> 00:12:12.800
100%, the probability space,
minus the probability that no

00:12:12.800 --> 00:12:15.030
one shares a birthday
with anybody.

00:12:15.030 --> 00:12:20.990
So that's equal to
100% minus 29.37%.

00:12:20.990 --> 00:12:25.660
Or another way you could write
it as that's 1 minus 0.2937,

00:12:25.660 --> 00:12:29.860
which is equal to-- so if I
want to subtract that from 1.

00:12:29.860 --> 00:12:34.330
1 minus-- that just
means the answer.

00:12:34.330 --> 00:12:37.280
That means 1 minus 0.29.

00:12:37.280 --> 00:12:40.630
You get 0.7063.

00:12:40.630 --> 00:12:43.720
So the probability that someone
shares a birthday with someone

00:12:43.720 --> 00:12:47.420
else is 0.7063--
it keeps going.

00:12:47.420 --> 00:12:53.090
Which is approximately
equal to 70.6%.

00:12:53.090 --> 00:12:56.250
Which is kind of a neat result
because if you have 30 people

00:12:56.250 --> 00:12:58.030
in a room you might say,
oh wow, what are the odds

00:12:58.030 --> 00:12:59.580
that someone has the same
birthday as someone else?

00:12:59.580 --> 00:13:02.170
It's actually pretty high.

00:13:02.170 --> 00:13:04.870
70% of the time, if you have a
group of 30 people, at least 1

00:13:04.870 --> 00:13:07.500
person shares a birthday
with at least one other

00:13:07.500 --> 00:13:08.260
person in the room.

00:13:08.260 --> 00:13:10.990
So that's kind of
a neat problem.

00:13:10.990 --> 00:13:12.950
And kind of a neat result
at the same time.

00:13:12.950 --> 00:13:15.740
Anyway, see you in
the next video.


Statistics: Alternate variance formulas

WEBVTT
Kind: captions
Language: en

00:00:00.740 --> 00:00:03.960
I think now is as good a time as
any to play around a little bit

00:00:03.960 --> 00:00:07.100
with the formula for variance
and see where it goes.

00:00:07.100 --> 00:00:10.330
And I think just by doing this
we'll also get a little bit

00:00:10.330 --> 00:00:12.730
better intuition of just
manipulating sigma notation,

00:00:12.730 --> 00:00:13.670
or even what it means.

00:00:13.670 --> 00:00:18.989
So we learned several times
that the formula for variance--

00:00:18.989 --> 00:00:20.780
and let's just do
variance of a population.

00:00:20.780 --> 00:00:22.905
It's almost the same thing
as variance of a sample.

00:00:22.905 --> 00:00:25.220
You just divide by n
instead of n minus 1.

00:00:25.220 --> 00:00:27.910
Variance of a population
is equal to-- well,

00:00:27.910 --> 00:00:32.350
you take each of the
data points x sub i.

00:00:32.350 --> 00:00:35.000
You subtract from that the mean.

00:00:35.000 --> 00:00:36.150
You square it.

00:00:36.150 --> 00:00:38.220
And then you take the
average of all of these.

00:00:38.220 --> 00:00:43.940
So you add the squared distance
for each of these points from i

00:00:43.940 --> 00:00:46.480
equals 1 to i is equal to n.

00:00:46.480 --> 00:00:49.710
And you divide it by n.

00:00:49.710 --> 00:00:51.780
So let's see what
happens if we can-- maybe

00:00:51.780 --> 00:00:53.790
we want to multiply
out the squared term

00:00:53.790 --> 00:00:55.610
and see where it takes us.

00:00:55.610 --> 00:00:56.250
So let's see.

00:00:56.250 --> 00:00:58.630
And I think it'll take
us someplace interesting.

00:00:58.630 --> 00:01:08.590
So this is the same thing as the
sum from i is equal to 1 to n.

00:01:08.590 --> 00:01:09.850
This, we just multiply it out.

00:01:09.850 --> 00:01:16.690
This is the same thing as x
sub i squared minus-- this

00:01:16.690 --> 00:01:18.945
is your little
algebra going on here.

00:01:18.945 --> 00:01:21.320
So when you square it-- I
mean, we could multiply it out.

00:01:21.320 --> 00:01:22.600
We could write it.

00:01:22.600 --> 00:01:30.010
x sub i minus mu times
x sub i minus mu.

00:01:30.010 --> 00:01:33.720
So we have x sub i times x
sub i, that's x sub i squared.

00:01:33.720 --> 00:01:38.270
Then you have x sub
i times minus mu.

00:01:38.270 --> 00:01:40.702
And then you have
minus mu times x sub i.

00:01:40.702 --> 00:01:42.160
So when you add
those two together,

00:01:42.160 --> 00:01:48.560
you get minus 2x sub i mu,
because you have it twice. x

00:01:48.560 --> 00:01:51.890
sub i times mu, that's
1 minus x sub i mu.

00:01:51.890 --> 00:01:54.510
And then you have another
one, minus mu x sub i.

00:01:54.510 --> 00:01:57.400
When you add them together,
you get minus 2x sub i mu.

00:01:57.400 --> 00:01:59.930
I know it's confusing with me
saying sub i and all of that.

00:01:59.930 --> 00:02:01.513
But it's really no
different than when

00:02:01.513 --> 00:02:03.550
you did a minus b squared.

00:02:03.550 --> 00:02:05.800
Just the variables look a
little bit more complicated.

00:02:05.800 --> 00:02:09.060
And then the last term is
minus mu times minus mu,

00:02:09.060 --> 00:02:14.540
which is plus mu squared.

00:02:14.540 --> 00:02:15.700
Fair enough.

00:02:15.700 --> 00:02:18.070
Let me switch colors just
to keep it interesting.

00:02:20.620 --> 00:02:23.520
Let me cordon that off.

00:02:23.520 --> 00:02:25.270
The sum of this
is the same thing

00:02:25.270 --> 00:02:27.186
as the sum of-- because
if you think about it,

00:02:27.186 --> 00:02:28.920
we're going to
take each x sub i.

00:02:28.920 --> 00:02:30.894
For each of the numbers
in our population,

00:02:30.894 --> 00:02:32.310
we're going to
perform this thing.

00:02:32.310 --> 00:02:33.400
And we're going to sum it up.

00:02:33.400 --> 00:02:34.816
But if you think
about it, this is

00:02:34.816 --> 00:02:36.449
the same thing
as-- if you're not

00:02:36.449 --> 00:02:38.490
familiar with sigma notation
this is a good thing

00:02:38.490 --> 00:02:40.614
to know in general, just
a little bit of intuition.

00:02:40.614 --> 00:02:44.340
That this is the same thing as--
I'll do it here to have space.

00:02:44.340 --> 00:02:52.500
The sum from i is equal to
1 to n of the first term,

00:02:52.500 --> 00:02:59.900
x sub i squared minus--
and actually, we

00:02:59.900 --> 00:03:02.900
can bring out the
constant terms.

00:03:02.900 --> 00:03:05.140
When you're summing, the
only thing that matters

00:03:05.140 --> 00:03:07.200
is the thing that
has the i-th term.

00:03:07.200 --> 00:03:08.450
So in this case, it's x sub i.

00:03:08.450 --> 00:03:09.785
So x sub 1, x sub 2.

00:03:09.785 --> 00:03:11.160
So that's the
thing that you have

00:03:11.160 --> 00:03:14.160
to leave on the right hand
side of the sigma notation.

00:03:14.160 --> 00:03:17.720
And if you've done the
calculus playlists already,

00:03:17.720 --> 00:03:21.000
sigma notation is really
like a discrete integral

00:03:21.000 --> 00:03:22.250
on some level.

00:03:22.250 --> 00:03:25.350
Because in an integral, you're
summing up a bunch of things

00:03:25.350 --> 00:03:27.146
and you're multiplying
them times dx,

00:03:27.146 --> 00:03:28.520
which is a really
small interval.

00:03:28.520 --> 00:03:29.936
But here you're
just taking a sum.

00:03:29.936 --> 00:03:33.120
And we showed in the
calculus playlist

00:03:33.120 --> 00:03:35.440
that an integral actually
is this infinite sum

00:03:35.440 --> 00:03:36.870
of infinitely
small things, but I

00:03:36.870 --> 00:03:38.410
don't want to digress too much.

00:03:38.410 --> 00:03:41.700
But this was just a long way
of saying that the sum from i

00:03:41.700 --> 00:03:45.590
equals 1 to n of the second term
is the same thing as minus 2

00:03:45.590 --> 00:04:05.460
times mu of the sum from i is
equal to 1 to n of x sub i.

00:04:05.460 --> 00:04:10.590
And then finally,
you have plus-- well,

00:04:10.590 --> 00:04:12.142
this is just a constant term.

00:04:12.142 --> 00:04:13.350
This is just a constant term.

00:04:13.350 --> 00:04:14.380
So you can take it out.

00:04:14.380 --> 00:04:24.030
Times mu squared times the
sum from i equals 1 to n.

00:04:24.030 --> 00:04:26.460
And what's going to be here?

00:04:26.460 --> 00:04:28.340
It's going to be a 1.

00:04:28.340 --> 00:04:29.320
We just divided a 1.

00:04:29.320 --> 00:04:30.403
We just divided this by 1.

00:04:30.403 --> 00:04:32.610
And took it out of the
sigma sign, out of the sum.

00:04:32.610 --> 00:04:36.060
And you're just
left with a 1 there.

00:04:36.060 --> 00:04:38.870
And actually, we could have
just left the mu squared there.

00:04:38.870 --> 00:04:41.670
But either way, let's
just keep simplifying it.

00:04:41.670 --> 00:04:44.830
So this we can't really do--
well, actually we could.

00:04:44.830 --> 00:04:47.490
Well, no, we don't know
what the x sub i's are.

00:04:47.490 --> 00:04:49.120
So we just have to
leave that the same.

00:04:49.120 --> 00:04:50.720
So that's the sum.

00:04:50.720 --> 00:04:53.150
Oh sorry, and this is
just the numerator.

00:04:53.150 --> 00:04:55.900
This whole simplification, we're
just simplifying the numerator.

00:04:55.900 --> 00:04:57.830
And later, we're just
going to divide by n.

00:04:57.830 --> 00:05:00.760
So that is equal to
that divided by n,

00:05:00.760 --> 00:05:02.894
which is equal to this
thing divided by n.

00:05:02.894 --> 00:05:04.060
I'll divide by n at the end.

00:05:04.060 --> 00:05:06.340
Because it's the numerator
that's the confusing part.

00:05:06.340 --> 00:05:10.019
We just want to simplify
this term up here.

00:05:10.019 --> 00:05:11.060
So let's keep doing this.

00:05:11.060 --> 00:05:15.910
So this equals the sum
from i equals 1 to n

00:05:15.910 --> 00:05:19.695
of x sub i squared.

00:05:19.695 --> 00:05:25.860
And let's see, minus
2 times mu-- sorry,

00:05:25.860 --> 00:05:27.400
that mu doesn't look good.

00:05:27.400 --> 00:05:35.710
Edit, Undo, minus 2 times
mu times the sum from i

00:05:35.710 --> 00:05:42.210
is equal to 1 to n of xi.

00:05:42.210 --> 00:05:43.670
And then, what is this?

00:05:43.670 --> 00:05:45.390
What is another
way to write this?

00:05:45.390 --> 00:05:48.860
Essentially, we're going
to add 1 to itself n times.

00:05:48.860 --> 00:05:51.380
This is saying, just look,
whatever you have here,

00:05:51.380 --> 00:05:53.619
just iterate through it n times.

00:05:53.619 --> 00:05:55.160
If you had an x sub
i here, you would

00:05:55.160 --> 00:05:57.757
use the first x term,
then the second x term.

00:05:57.757 --> 00:06:00.090
When you have a 1 here, this
is just essentially saying,

00:06:00.090 --> 00:06:04.820
add one to itself n times,
which is the same thing as n.

00:06:04.820 --> 00:06:14.260
So this is going to be
plus mu squared times n.

00:06:16.810 --> 00:06:21.787
And then see if there's
anything else we can do here.

00:06:21.787 --> 00:06:23.370
Remember, this was
just the numerator.

00:06:23.370 --> 00:06:25.580
So this looks fine.

00:06:25.580 --> 00:06:27.090
We add up each of those terms.

00:06:27.090 --> 00:06:32.030
So we just have
minus 2 mu from i

00:06:32.030 --> 00:06:36.260
equals 1 to-- oh well,
think about this.

00:06:36.260 --> 00:06:37.470
What is this?

00:06:37.470 --> 00:06:40.330
What is this thing right here?

00:06:40.330 --> 00:06:44.250
Well actually, let's
bring back that n.

00:06:44.250 --> 00:06:46.480
So this simplified
to that divided

00:06:46.480 --> 00:06:50.800
by n, which simplifies to
that whole thing, which

00:06:50.800 --> 00:06:55.500
is simplified to this
whole thing, divided by n,

00:06:55.500 --> 00:07:00.464
which simplifies to this whole
thing divided by n, which

00:07:00.464 --> 00:07:02.880
is the same thing as each of
the terms divided by n, which

00:07:02.880 --> 00:07:07.230
is the same thing as that,
which is the same thing as that,

00:07:07.230 --> 00:07:10.290
which is the same thing as that.

00:07:10.290 --> 00:07:12.060
And now, well, how
does this simplify?

00:07:12.060 --> 00:07:13.770
This is the interesting part.

00:07:13.770 --> 00:07:15.800
Well, this, nothing
much I can do here.

00:07:15.800 --> 00:07:22.220
So that just becomes the
sum from i is equal to 1

00:07:22.220 --> 00:07:28.590
to n x sub i squared
divided by big N.

00:07:28.590 --> 00:07:31.080
Now this is interesting.

00:07:31.080 --> 00:07:35.230
If I take each of the terms in
my population and I add them up

00:07:35.230 --> 00:07:37.880
and then I divide it
by n, what is that?

00:07:37.880 --> 00:07:41.190
This thing right here?

00:07:41.190 --> 00:07:43.450
If I sum up all of the
terms in my population

00:07:43.450 --> 00:07:45.480
and divide by the number
of terms there are?

00:07:45.480 --> 00:07:46.626
That's the mean, right?

00:07:46.626 --> 00:07:48.000
That's the mean
of my population.

00:07:48.000 --> 00:07:50.950
So this thing right
here is also mu.

00:07:50.950 --> 00:07:55.700
So this thing
simplifies to what?

00:07:55.700 --> 00:07:58.040
Minus 2 times what?

00:07:58.040 --> 00:08:00.250
Mu times this whole
thing is mu too.

00:08:00.250 --> 00:08:02.760
So times mu squared.

00:08:02.760 --> 00:08:06.270
mu times mu, this is the
mean of the population.

00:08:06.270 --> 00:08:08.120
So that was a nice
simplification.

00:08:08.120 --> 00:08:11.565
And then plus-- what
do you have here?

00:08:11.565 --> 00:08:14.270
Well let's see,
you have n over n.

00:08:14.270 --> 00:08:15.060
Those cancel out.

00:08:15.060 --> 00:08:16.490
So we just have plus mu squared.

00:08:16.490 --> 00:08:18.670
So that was a very
nice simplification.

00:08:18.670 --> 00:08:21.910
And then this simplifies to--
can't do much on this side.

00:08:21.910 --> 00:08:36.669
So the sum from i is equal to 1
to n of x sub i squared over n.

00:08:36.669 --> 00:08:39.710
And then you see, we have minus
2 mu squared plus mu squared.

00:08:39.710 --> 00:08:47.380
Well, that's the same
thing as minus mu squared.

00:08:47.380 --> 00:08:49.860
Minus the mean squared.

00:08:49.860 --> 00:08:53.170
So this already we've
come up with a neat way

00:08:53.170 --> 00:08:58.090
of writing the variance.

00:08:58.090 --> 00:09:01.020
You can essentially take the
average of the squares of all

00:09:01.020 --> 00:09:03.740
of the numbers in this
case, a population,

00:09:03.740 --> 00:09:08.250
and then subtract from
that the mean squared

00:09:08.250 --> 00:09:09.070
of your population.

00:09:09.070 --> 00:09:11.444
So this could be, depending
on you're calculating things,

00:09:11.444 --> 00:09:15.009
maybe a slightly faster way
of calculating the variance.

00:09:15.009 --> 00:09:17.550
So just playing with a little
algebra, we got from this thing

00:09:17.550 --> 00:09:19.966
where you have to each time
take each of your data points,

00:09:19.966 --> 00:09:21.800
subtract the mean from
it, and then squared.

00:09:21.800 --> 00:09:23.674
And of course, before
you have to do anything

00:09:23.674 --> 00:09:25.260
you have to calculate the mean.

00:09:25.260 --> 00:09:26.260
And you take the square.

00:09:26.260 --> 00:09:27.010
And then you sum them all up.

00:09:27.010 --> 00:09:28.800
Then you take the
average, essentially,

00:09:28.800 --> 00:09:30.410
when you sum and divided by n.

00:09:30.410 --> 00:09:33.150
We've simplified it just
using a little bit of algebra

00:09:33.150 --> 00:09:34.650
to this formula.

00:09:34.650 --> 00:09:37.200
We're getting to something
called the raw score method.

00:09:37.200 --> 00:09:40.160
And what we want to do is write
this right here just in terms

00:09:40.160 --> 00:09:41.097
of xi's.

00:09:41.097 --> 00:09:43.180
And then we really are
what you call the raw score

00:09:43.180 --> 00:09:45.030
method, which is
oftentimes a faster

00:09:45.030 --> 00:09:47.470
way of calculating the variance.

00:09:47.470 --> 00:09:49.950
So let's see what
is mu equal to?

00:09:49.950 --> 00:09:51.370
What is the mean?

00:09:51.370 --> 00:09:58.060
The mean is just equal to the
sum from i is equal to 1 to n

00:09:58.060 --> 00:10:00.780
of each of the terms-- you
just take the sum of each

00:10:00.780 --> 00:10:04.320
of the terms-- and you divide by
the number of terms there are.

00:10:07.760 --> 00:10:09.890
So if we look at this
thing, this thing

00:10:09.890 --> 00:10:14.660
can be written as-- let
me draw a line here.

00:10:14.660 --> 00:10:22.330
This thing can be written as the
sum from i is equal to 1 to n

00:10:22.330 --> 00:10:30.360
of x sub 1 squared all of
that over n minus mu squared.

00:10:30.360 --> 00:10:31.930
Well, mu is this.

00:10:31.930 --> 00:10:35.640
So this thing squared is what?

00:10:35.640 --> 00:10:46.520
This is x sub i take
the sum up to n.

00:10:46.520 --> 00:10:48.800
i is equal to 1.

00:10:48.800 --> 00:10:51.980
You're going to
square this thing.

00:10:51.980 --> 00:10:54.620
And then you're going to divide
it by-- we squared, right?

00:10:54.620 --> 00:10:58.700
You divide it by n squared.

00:10:58.700 --> 00:11:01.570
And this might seem like a
more-- out of all of them,

00:11:01.570 --> 00:11:04.750
this actually seems like
the simplest formula for me.

00:11:04.750 --> 00:11:06.240
Where you essentially
just take--

00:11:06.240 --> 00:11:09.230
if you know the mean
of your population--

00:11:09.230 --> 00:11:10.840
you just say, OK,
my mean is whatever

00:11:10.840 --> 00:11:12.440
and I can just square that.

00:11:12.440 --> 00:11:14.122
And just put that
aside for a second.

00:11:14.122 --> 00:11:16.080
But first, I can just
take each of the numbers,

00:11:16.080 --> 00:11:17.990
square them, and
then sum them up,

00:11:17.990 --> 00:11:21.020
and divide by the number
of numbers I have.

00:11:21.020 --> 00:11:22.440
I don't know if I
wrote-- no, I've

00:11:22.440 --> 00:11:24.010
erased the last set of numbers.

00:11:24.010 --> 00:11:25.420
But we could show
you that you'll

00:11:25.420 --> 00:11:26.480
get to the same variance.

00:11:26.480 --> 00:11:28.480
So to me, this is almost
the simplest formula.

00:11:28.480 --> 00:11:30.822
But this one's even
faster in a lot of ways

00:11:30.822 --> 00:11:32.780
because you don't really
have to even calculate

00:11:32.780 --> 00:11:34.470
the mean ahead of time.

00:11:34.470 --> 00:11:36.780
You can just say,
OK, for each xi

00:11:36.780 --> 00:11:38.950
I just perform this operation.

00:11:38.950 --> 00:11:40.954
And then I divide by n
squared or n accordingly.

00:11:40.954 --> 00:11:42.370
And I'll also get
to the variance.

00:11:42.370 --> 00:11:44.760
So you don't have to do
this calculation before you

00:11:44.760 --> 00:11:45.730
figure out the whole variance.

00:11:45.730 --> 00:11:48.188
But anyway, I thought it would
be instructive and hopefully

00:11:48.188 --> 00:11:50.870
give you a little bit more
intuition behind the algebra

00:11:50.870 --> 00:11:53.370
dealing with sigma
if we worked out

00:11:53.370 --> 00:11:54.870
these other ways
to write variances.

00:11:54.870 --> 00:11:56.828
And frankly, some books
will just say, oh yeah,

00:11:56.828 --> 00:11:57.440
you know what?

00:11:57.440 --> 00:11:59.399
The variance could
be written like this.

00:11:59.399 --> 00:12:01.440
We're talking about the
variance of a population.

00:12:01.440 --> 00:12:02.940
Or it could be
written like this,

00:12:02.940 --> 00:12:04.726
or maybe they'll even
write it like this.

00:12:04.726 --> 00:12:06.350
And it's good to know
that you can just

00:12:06.350 --> 00:12:10.320
do a little simple
algebraic manipulation

00:12:10.320 --> 00:12:11.920
and get from one to the other.

00:12:11.920 --> 00:12:13.650
Anyway, I've run out of time.

00:12:13.650 --> 00:12:15.990
See you in the next video.