Dollar Auction

  

Categories: Econ, International, Banking

Economists make a lot of assumptions when they make their models. One of the biggest and most common assumptions they make is that people are rational. We’d like to think that people, capable of building cities and atomic bombs...of building a global civilization...and of destroying it in under a minute...are rational creatures.

The dollar auction runs where two people are bidding on a dollar. The winner will get the dollar, and the loser will have to pay up whatever their last bid was. So players aren’t only trying to win, they’re also trying to minimize what they might lose. Once the bidding goes above $1, it makes sense to keep bidding. For instance, if your last bid was $0.95, and the other player’s bid was $1, then it would make sense for you to bid $1.01 to avoid losing $0.95. If this kept going, with infinite bidding, then each player would bid one cent through eternity.

Like the Prisoner’s Dilemma, this game shows that the rational choice doesn’t always lead to what appears to be the most rational outcome, especially when people aren’t working together, and instead are working in their own self-interest. For instance, it’s not rational to bid more than $1 to earn $1, but each player in the dollar auction is incentivized to keep bidding one cent more when it passes the $1 mark. If they worked together and said “okay, this is silly, let’s stop” it would lead to a more “rational outcome,” but how would they decide who's the last person to bid, i.e. the winner?

Related or Semi-related Video

Finance: What is Discounted Cash Flow?9 Views

00:00

Finance allah shmoop What is discounted Cash flow money air

00:07

gets your money on sale discounted money Yeah kind of

00:11

sort of like that but how can cash be discounted

00:15

and what is flowing anyway Is this like a scene

00:17

from huck finn goes to wall street so the cash

00:20

we're talking about here is cash in the future Got

00:23

it Your company the spice in ator ink sells a

00:30

product that takes any item of food and runs it

00:33

through a processor which makes it pumpkin spice flavor You

00:37

are hated by starbucks everywhere So spice in aitor is

00:40

going to make ten grand by the end of this

00:42

year Fifty grand by the end of next year and

00:45

for five hundred grand by the end of the following

00:48

year and a million bucks by the end of the

00:51

next All right that's not revenues that's profit Or at

00:54

least so you you think it's going to earn a

00:56

million bucks you estimate you guess you hope All right

00:59

Well the value of a company in professional wall street

01:01

he circles is the sum of the parts of its

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future cash flows or cash profits than discounted back for

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risk Meaning it might not actually earn that million dollars

01:11

in four years and time What if those forty years

01:14

or ten years or two years Alright all this means

01:17

that spice in ator ink earning half a million bucks

01:20

in three years is an estimated number It's not certain

01:24

it's hope for begged for prayed for even at least

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in the red states but there is risk It doesn't

01:29

happen Maybe there's thirty percent on that produces three hundred

01:32

grand in profits instead of five hundred grand but ten

01:35

percent odds It produces a million dollars instead of that

01:37

five hundred grand and years out So calculating that risk

01:41

and then discounting it in the value of the company

01:44

Today is a big part of valuing a business parts

01:48

that's the risk side But then there's the time side

01:51

you have to think about as well If you had

01:52

a company you were certain would make half a million

01:55

dollars in profit thirty years from now you know like

01:58

shmoop well that wouldn't be as impressive or valuable as

02:02

a company You were equally certain would make half a

02:05

million dollars in profit next year So that's the time

02:08

component let's add up the notional value of this company

02:12

just as an illustration here Alright Your company's spice in

02:15

ater at the moment has no cash your debt and

02:17

is for illustrative purposes on lee So don't get all

02:20

technical on us and wine about details Try to glean

02:23

a concept here okay So spicy nature will make ten

02:26

thousand Dollars this year in profits it's january now in

02:29

twelve months were eighty percent certain it'll make ten grand

02:31

in profit All right now if we bought the safest

02:34

bond in the world a one year u s treasury

02:37

bond we get three percent interest We fight a discount

02:41

on a thousand bucks Okay that number's serves as kind

02:44

of a bassline whenever we do these kind of analyses

02:47

the u s treasury paper is in generally riskless question

02:51

how much riskier is our company Above and beyond the

02:55

t bill I even company makes that ten thousand dollars

02:58

like could it only make five thousand sure couldn't make

03:01

nothing couldn't lose money Sure couldn't make way more than

03:05

ten grand maybe twenty thirty forty grand Regardless there is

03:08

risk here So the value of that ten thousand dollars

03:11

a year from now carries what is called a risk

03:15

premium tacked onto that three percent figure We're gonna divide

03:19

by it So adding risk premium makes the present value

03:23

less All right let's say that extra risk is pretty

03:26

high like twelve percent That company produces meaningfully less than

03:30

ten grand and profits All right well we discount back

03:32

that One year from now figure of ten thousand dollars

03:36

to be less right Well here's the math you take

03:39

the amount expected to be earned Yes that is the

03:42

cash flow ding ding ding and you divide by one

03:45

plus the quantity of the risk free rate that t

03:47

bill three percent thing plus the risk premium which we've

03:51

guest is in twelve percent So what is the risk

03:54

adjusted and discounted cash flow of ten thousand dollars expected

03:58

or estimated a year from now worth today Well it's

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ten grand divided by the quantity one plus point zero

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three plus point one teo or divided by one point

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one five to the first power for this one year

04:09

away and it looks like that which equals a bit

04:12

under eighty seven hundred bucks So wow Interesting It means

04:16

that the risk of getting that ten grand a year

04:19

from now is high In fact it is worth roughly

04:22

thirteen hundred bucks less today Because of that risk or

04:26

set another way our analysis would suggest that you'd be

04:29

risk neutral if you took a cashier's cheque today for

04:32

eighty seven hundred bucks versus waiting a year and getting

04:36

that Ten grand pay then But if you did wait

04:38

well you'd have a very nice fifteen percent ish return

04:41

on your invested money All right Welcome to risk people

04:44

This is investing Wanna one's order and no extra charge

04:48

from the kindly loving people it's mum inside All right

04:51

And as you'd guess you can get to the total

04:53

value of the company by adding up and then discounting

04:57

future years cash flows of this company in the same

05:01

way when we have the ten grand number already What

05:04

about the fifty k two years from now Well since

05:07

we are comp pounding investment returns we make a call

05:11

too Exponents land with e ticket there all day passed

05:15

And to discount the odds of that fifty k coming

05:17

to us two years from now we apply a similar

05:20

calculation on lee Now we think that the odds of

05:22

fifty k in two years are even riskier than they

05:25

were before Will attach a seventeen percent risk premium toe

05:29

actually getting out fifty grand a profit out of our

05:31

product And we have to discount it back on top

05:34

of the safe or risk free rate of three percent

05:38

Well how's that work well we have fifty thousand bucks

05:41

coming to us We think and hope and pray two

05:44

years from now We then divided by one plus point

05:48

zero three plus the risk premium of point one seven

05:52

squared or to the second power Why Because it's two

05:56

years of compounding away not one Remember I kind of

05:58

mumbled that one year to the first power thing was

06:01

clever on Alright that's Fifty grand over the quantity One

06:05

point two square or fifty grand over one point four

06:08

four or carrying a present discounted value of fifty k

06:12

divided by that one point four four which is a

06:14

little under thirty five grand Well if we carry this

06:17

forward a year and there's even more risk for the

06:19

fur five hundred thousand bucks we expect in three years

06:23

Well then we get something like a risk premium of

06:25

say twenty two percent tacked onto the safe rate of

06:28

three percent or twenty five percent total And we discounted

06:32

back three years or cubed if it looks like this

06:36

Five hundred thousand dollars divided by the quantity one plus

06:39

point oh three plus point two two to the third

06:43

power Or that's five hundred thousand dollars over one point

06:47

two five cubes Which is almost to telling us that

06:51

the present value of that highly suspect five hundred k

06:55

in profits supposedly coming in from spice in ator was

06:59

about five hundred thousand over too or just over two

07:03

hundred fifty grand in present value today Got it Well

07:07

same holds true for that million dollar year and calculate

07:10

the discounted cash value of that million bucks four years

07:14

from now you follow the same pattern and add in

07:16

the million bucks divided by the quantity one Plus you

07:19

know all the other crap in there Yeah So if

07:22

we're getting the total discounted cash flow valuation of the

07:25

company we just add everything up including a sale of

07:28

the company at the end Like if we sold it

07:31

for two and million dollars six years from now we

07:33

discount that back with some you know premiums and someone

07:36

loaded in so that ten million's not a sure thing

07:39

at all We have to assume our guests or dark

07:41

board with blindfolds on the value of the company overall

07:44

will hold for five years from now And yeah that's

07:48

How This kind of cash flow works at least the

07:50

one point overs you're learning here So just be careful

07:52

when you throw that dart You don't want to force

07:54

your business partners to rock and ipad shit no matter 00:07:57.755 --> [endTime] how much that looked cool Oh

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