Discounted cash flow analysis…à la Shmoop.

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it relates to the amount of cash that will you

know flow and the risk that the number we're guessing

will flow will be higher lower or the same like

there's risk we don't know what the number is going

to be All of this is mapped against the background

of what a safe investment e a u s treasury

bill would produce with high levels of certainty in that

same period And that treasury bill return has already adjusted

for the gumball experiment in everyone's gases toe what inflation

will be So the treasury bill is a base case

important element in the math of dcf models what's kind

of two things really it's a safety of payment thing

and it's also inflation adjusted all in that won t

bill number but okay dcf modeling is the big kahuna

of financial valuation tools is largely what the pros used

To attach a given value to a company we're gonna

walk you through the nitty and the gritty of how

you do a fully ugly dcf model in warning this

will hurt but you won't die from trying it Well

we're focused here on money we expect in the future

but discounted back for time and risk got it it's

key elements dcf model We're gonna work through an example

with cash flows but you can imagine this system applying

to the value of stocks or bonds or lottery tickets

or a random celestial events And most importantly for this

set dead end or dying rich relatives Yeah all carry

the structure of time and risk discounting such that they

could be plugged into a dcf model And yes uncle

larry as this applies to you too you will die

in a few years or in twenty and by then

you'll have what a million bucks twenty one hundred And

what will inflation make that one hundred million dollars in

twenty years worth today All right it's time and risk

All right we're moving on crystal balls Yes You feel

pity for the young male crystals who had to die

Or worse to donate them for this project Uncle larry

phones you at three In the morning You barely make

out his words But you know he had a drug

problem for a long time Brilliant man but you know

fried his brain Well a week later you learn he's

dead his lawyer Honest How sends you a registered letter

informing you that you'll be receiving one million dollars in

a year That's a million bucks We have the flow

of cash now and we have pretty high certainty of

a payout Like we trust how we know him He

didn't joke around How also in tones that your other

uncles moe and curly are ill A swell Hey sir

Minds is that each will die in subsequent years and

each will leave you one million dollars And then the

lawyer tells you that your grand daddy warbucks was going

to leave his fortune toe larry moe and or curly

But that if none of them are alive well you

get all fifty million dollars of his estate and it

looks like granddaddy has at least two years left in

him So your crystal ball comes out It says that

Your best guess as to the amount and timing of

your cash flows Looks like this are so t plus

one it's one year today's million bucks and people too

likely curley dies You get a million there and in

three years mode eyes and won't say in four years

we're guessing on daddy warbucks after they're all dead Then

you get that fifty All right but you need to

have a present value for all fifty three million dollars

that's involved here Meaning you want to go to a

bank It's called a fact door and pledge that money

over to them getting cash today for that future dough

So that right away you can go live your life

have fun enjoy things and get that place in malibu

with the entryway water slides All right Well you need

to discount back those future flows of cash to today's

value so that you can negotiate with the bank to

sell them those flows and get your cash today So

then how do you discount that flow of dough back

to today While the formula runs like this start with

the risk free rate That's those t bills we mentioned

And their brethren good government bonds and t notes and

so on And you look through the bond quotes online

and you know it that well today u s government

paper coming do exactly in one year yields one point

five percent and get that anywhere online and quotes for

free and then government paper in two years That's when

the next guy dies yeah that's two percent government in

three years you have the next guy dies Well that's

two and a half there and government paper coming due

in four years When you expect daddy warbucks to die

and leave you all fifty paper today you could buy

and get three percent per year yield That tells you

that we're living in a normal yield curve environment and

the market is likely pricing in modest inflation and maybe

a fed rate hike that's modest into the future Well

the market has thus done a whole lot of the

homework for you already In pricing of these otherwise crazy

complex issues in calculation inflation and risk adjusted returns into

the future In addition to that risk free rate Well

we have tto add that curly moe in Well gee

Dw don't die at least they don't die on time

Or maybe yeah you're not really their sole heir That

is there's risk involved in receiving the cash flows beyond

just the risk of the us government defaulting on its

promises payday loans and so on Well how do we

matthew lee at tribute numbers too quantify that risk and

it's not just risk of malaria in curly not dying

but it's other risk like some other aer materializes and

lays claim to the money or the estate in the

inheritance laws change after the socialist candidate gets elected from

california and caps inheritance amounts at a million bucks after

that Well the government then keeps everything what They have

a lot of pensions to pay so there's risk there

How do we quantify it While there's a donkey and

a tail in a fifty shades brand blindfold leftover from

the party last night Right We'll each risk has to

be individually assessed So let's review larry is already dead

The lawyer called and told you in writing that you

are the sole heir and you definitely get a million

dollars no matter what there's almost no risk here so

you just have to have the time value of your

money which you equate to u s government bonds certainty

death and taxes So you're going to safely discount back

that million dollars from uncle larry police is a state

at the rate of one point five percent adding no

risk premium to it You're just going to get government

t bill rates and that flow to you is valued

as a million dollars divided by the quantity one plus

zero point one five to the first power because it's

just one year away that sometimes he iterated just one

And that equals about nine hundred eighty five grand So

if someone offered you that amount to buy you out

of the inheritance from larry well you'd in theory be

neutral but likely take the cash because you know a

bird in the hand and it's likely that the ferrari

and the window is tickling you the cash out right

Well under the second cash flow we have to discount

uncle curly You stand to inherit a million bucks from

curly but not for two years and minor detail He's

not dead yet and there is risk he doesn't die

At least not any time soon where all the banana

peels laying around should be there Well there's risk he

doesn't name you soul oeiras Well by the way and

there's risk that it turns out he owed other people

a ton of money and that the two million he

said he was giving you was really two million yen

not dollars And on and on and on tons of

other risk including the one where he donates his money

to the society of booboo which you know he's a

big fan of So in this case you attribute a

very high risk like twenty five percent per year calm

pounded that this whole inheritance thing with him doesn't happen

But how do you calculate that flow of a projected

guest at two million dollars in two years Well you'd

receive a million dollars in two years and the two

year government paper rate is two percent Plug in the

same formula you just did for larry and you get

a million dollars divided by one plus the quantity of

the risk free rate of two percent or point zero

two plus the risk premium to the second power let's

Take the Numbers 1 by 1 here You know where

the million came from That's The inheritance amount with one

in there is because we're dividing by a number greater

than one to discount back the future amount Then we

have the point o two thing there which is the

risk free government paper rate That's what it's currently yielding

Then we have to add the risk premium point two

five or twenty five percent per year to get a

total of point two seven as the total risk free

plus risk adjusted discount rate against that million bucks two

years from now And the to the second power thing

right there exists because the event is to compounded years

away Iterated twice So the summary formula for this one

is a million over one point two seven to the

second power or a million over one point six one

two nine for about six hundred fourteen grand So let's

think about that for this event your neutral substitution point

or value in taking cash today versus waiting two years

teo hope to get that million bucks is a bit

more than half the eventual amount That's a lot of

discounting there but it makes sense because the death of

your dear uncle isn't certain and neither is the notion

that you'll receive all the dough when he does finally

bucket kick or that there will even be doa at

that point to give you in fact the twenty five

percent number well maybe way optimistic and whatever it should

be called given that we're in the business of betting

on death here it's like a life insurance company we're

gonna move on to the third cash flow Mo is

sick luckily financially for you he liked the whoopee cushions

from around the world You sent him each year on

his birthday So he's already told you and his lawyer

and everyone else that you are his sole heir He

put it in writing certified it and he's tired of

suffering So he's also left instructions that if he's in

an iron lung three years from now the union nurse

should pull the plug and let him go off to

the big stooge in the sky in relative peace So

your discount rate for the mo money is way lower

than for the curly money That is the risk premium

You'll add to the risk free rate here is way

less And you think about that risk is being just

five percent Why not zero risk premium Well because there's

always curveballs in life and you can't predict him and

you want to be conservative in you're discounting So then

the cash flows looked like this eventual money A million

box risk free rate two point five percent that's for

the government treasury paper coming due in three years at

current market prices and the risk premium there's just five

percent The duration is three years or three iterations So

the formula then looks like this We have a million

over the quantity One plus the quantity point o two

five plus point Oh five All to the third power

there All right well simplifying We get a million over

one point Oh seven five to the third and again

that's a million over one point two four ish So

the president value of your million box in three years

in this case is eight hundred six grand And this

is kind of interesting for dcf geeks Anyway this money

which comes three years from now has ah higher present

Value than the curly money which comes only two years

from now Why risk way less risk way higher present

value Last calculation for this problem Grand daddy warbucks you

know that gee dw is likely to name you sole

heir And every actuarial table you've read shows him dying

in exactly four years That's the over under number Every

term life insurer uses So what do you know You

use it too He could die in four years Or

ten or twenty Hi Standard deviation Yeah You know you

know he wants you to have the money So without

a lot to go on while you just apply a

ten percent risk premium to the risk free number two

do you're discounting here and you get the numbers Here

we go Terminal value Fifty million dollars government risk free

rate for guaranteed payment for years from now three percent

a year Compound it risk premium here's ten percent years

to event for and the formula then it's for fifty

million over the quantity One plus the quantity point Oh

three plus point one all to the fourth power which

is the same as fifty million over one point one

Three to the fourth which equals fifty million over one

point six three for about thirty point seven million box

ish the present value of your getting fifty million box

from g w four years from now discounted back for

risk in times about thirty million dollars that is fifty

million dollars in four years with risk adjusted in this

case today you're estimating is worth thirty mil So then

what is your total value of your family financially speaking

Of course well we'll just adam up larry gave you

a nine eighty five k discounted back curly with six

fourteen mo was eight o six and g g w

was thirty point seven million there All right so we've

discounted the cash flows Now all we have to do

is adam up and they add up like this and

they come to in about thirty three million and change

and note that the terminal payment of that discounted fifteen

million well it dwarfs the other flows at least a

this point So this is a structure you'll see a

lot when you're valuing payout of bonds and more commonly

stocks or equity investments that eventually gets sold that is

An equity investment will produce cash for three or four

or five or more years and then it will get

sold for twenty times earnings or whatever that eventual multiple

is and you'll discount it back for time and risk

and that eventual sales price probably carries the most risk

or at least aton of risk so it'll carry a

big discount value and it's usually calculated a decade or

so out so you think about the time value decreasing

a lot of that sum to today's values Note also

that we've used imprecise numbers here Why Because precision is

a joke when it comes to dcf models our own

got assessment of the risk of adventure has a lot

more to do with the eventual outcome than getting the

third decimal correct so don't do it It makes you

look like you don't understand that a whole lot of

guessing is involved here And unfortunately for you however well

moe curly and g w just signed up his trial

subjects for elon musk snu eternal life company so well 00:13:42.739 --> [endTime] let's Just hope you kept your receipts No