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Principles of finance ah la shmoop discounted cash flow analysis

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Okay this whole thing is a big fat example Time

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Yes whale of a tale Our company produces cash flow

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today and we bet it will produce it in the

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future But in our future there is uncertainty mainly as

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it relates to the amount of cash that will you

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

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will flow will be higher lower or the same like

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

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to be All of this is mapped against the background

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of what a safe investment e a u s treasury

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bill would produce with high levels of certainty in that

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same period And that treasury bill return has already adjusted

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

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will be So the treasury bill is a base case

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

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

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

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bill number but okay dcf modeling is the big kahuna

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of financial valuation tools is largely what the pros used

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

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walk you through the nitty and the gritty of how

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you do a fully ugly dcf model in warning this

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

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

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

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

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with cash flows but you can imagine this system applying

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to the value of stocks or bonds or lottery tickets

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or a random celestial events And most importantly for this

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set dead end or dying rich relatives Yeah all carry

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the structure of time and risk discounting such that they

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could be plugged into a dcf model And yes uncle

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larry as this applies to you too you will die

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in a few years or in twenty and by then

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

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what will inflation make that one hundred million dollars in

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

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

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pity for the young male crystals who had to die

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Or worse to donate them for this project Uncle larry

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phones you at three In the morning You barely make

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out his words But you know he had a drug

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problem for a long time Brilliant man but you know

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

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dead his lawyer Honest How sends you a registered letter

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

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

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of cash now and we have pretty high certainty of

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a payout Like we trust how we know him He

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

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uncles moe and curly are ill A swell Hey sir

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Minds is that each will die in subsequent years and

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each will leave you one million dollars And then the

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lawyer tells you that your grand daddy warbucks was going

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to leave his fortune toe larry moe and or curly

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But that if none of them are alive well you

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get all fifty million dollars of his estate and it

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looks like granddaddy has at least two years left in

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him So your crystal ball comes out It says that

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Your best guess as to the amount and timing of

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your cash flows Looks like this are so t plus

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

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likely curley dies You get a million there and in

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

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

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you get that fifty All right but you need to

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have a present value for all fifty three million dollars

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

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

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over to them getting cash today for that future dough

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So that right away you can go live your life

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have fun enjoy things and get that place in malibu

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with the entryway water slides All right Well you need

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

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value so that you can negotiate with the bank to

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sell them those flows and get your cash today So

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then how do you discount that flow of dough back

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to today While the formula runs like this start with

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

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And their brethren good government bonds and t notes and

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so on And you look through the bond quotes online

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and you know it that well today u s government

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paper coming do exactly in one year yields one point

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five percent and get that anywhere online and quotes for

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

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

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

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two and a half there and government paper coming due

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in four years When you expect daddy warbucks to die

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and leave you all fifty paper today you could buy

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and get three percent per year yield That tells you

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

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the market is likely pricing in modest inflation and maybe

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

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the market has thus done a whole lot of the

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homework for you already In pricing of these otherwise crazy

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complex issues in calculation inflation and risk adjusted returns into

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the future In addition to that risk free rate Well

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we have tto add that curly moe in Well gee

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

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

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

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just the risk of the us government defaulting on its

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promises payday loans and so on Well how do we

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matthew lee at tribute numbers too quantify that risk and

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

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

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lays claim to the money or the estate in the

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inheritance laws change after the socialist candidate gets elected from

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california and caps inheritance amounts at a million bucks after

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that Well the government then keeps everything what They have

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

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

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a tail in a fifty shades brand blindfold leftover from

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

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

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The lawyer called and told you in writing that you

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are the sole heir and you definitely get a million

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

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you just have to have the time value of your

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money which you equate to u s government bonds certainty

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

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that million dollars from uncle larry police is a state

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at the rate of one point five percent adding no

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

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t bill rates and that flow to you is valued

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as a million dollars divided by the quantity one plus

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

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just one year away that sometimes he iterated just one

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And that equals about nine hundred eighty five grand So

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if someone offered you that amount to buy you out

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

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neutral but likely take the cash because you know a

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

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and the window is tickling you the cash out right

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Well under the second cash flow we have to discount

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uncle curly You stand to inherit a million bucks from

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

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

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At least not any time soon where all the banana

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

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

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

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a ton of money and that the two million he

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said he was giving you was really two million yen

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not dollars And on and on and on tons of

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other risk including the one where he donates his money

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

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big fan of So in this case you attribute a

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very high risk like twenty five percent per year calm

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

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But how do you calculate that flow of a projected

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

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receive a million dollars in two years and the two

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year government paper rate is two percent Plug in the

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same formula you just did for larry and you get

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a million dollars divided by one plus the quantity of

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the risk free rate of two percent or point zero

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

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Take the Numbers 1 by 1 here You know where

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

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

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than one to discount back the future amount Then we

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have the point o two thing there which is the

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

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Then we have to add the risk premium point two

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five or twenty five percent per year to get a

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total of point two seven as the total risk free

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plus risk adjusted discount rate against that million bucks two

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years from now And the to the second power thing

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right there exists because the event is to compounded years

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away Iterated twice So the summary formula for this one

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is a million over one point two seven to the

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second power or a million over one point six one

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

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think about that for this event your neutral substitution point

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or value in taking cash today versus waiting two years

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teo hope to get that million bucks is a bit

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

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discounting there but it makes sense because the death of

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

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

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bucket kick or that there will even be doa at

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that point to give you in fact the twenty five

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percent number well maybe way optimistic and whatever it should

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

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

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gonna move on to the third cash flow Mo is

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sick luckily financially for you he liked the whoopee cushions

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from around the world You sent him each year on

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

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and everyone else that you are his sole heir He

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

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

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an iron lung three years from now the union nurse

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should pull the plug and let him go off to

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the big stooge in the sky in relative peace So

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your discount rate for the mo money is way lower

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than for the curly money That is the risk premium

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

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less And you think about that risk is being just

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

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

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

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the cash flows looked like this eventual money A million

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

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the government treasury paper coming due in three years at

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

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percent The duration is three years or three iterations So

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the formula then looks like this We have a million

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over the quantity One plus the quantity point o two

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five plus point Oh five All to the third power

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there All right well simplifying We get a million over

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one point Oh seven five to the third and again

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

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the president value of your million box in three years

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in this case is eight hundred six grand And this

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is kind of interesting for dcf geeks Anyway this money

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which comes three years from now has ah higher present

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Value than the curly money which comes only two years

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from now Why risk way less risk way higher present

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value Last calculation for this problem Grand daddy warbucks you

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know that gee dw is likely to name you sole

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

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

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term life insurer uses So what do you know You

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use it too He could die in four years Or

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ten or twenty Hi Standard deviation Yeah You know you

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know he wants you to have the money So without

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a lot to go on while you just apply a

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ten percent risk premium to the risk free number two

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

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we go Terminal value Fifty million dollars government risk free

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rate for guaranteed payment for years from now three percent

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

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

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million over the quantity One plus the quantity point Oh

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three plus point one all to the fourth power which

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is the same as fifty million over one point one

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Three to the fourth which equals fifty million over one

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point six three for about thirty point seven million box

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ish the present value of your getting fifty million box

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from g w four years from now discounted back for

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risk in times about thirty million dollars that is fifty

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million dollars in four years with risk adjusted in this

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

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what is your total value of your family financially speaking

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

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a nine eighty five k discounted back curly with six

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fourteen mo was eight o six and g g w

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

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discounted the cash flows Now all we have to do

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is adam up and they add up like this and

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they come to in about thirty three million and change

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and note that the terminal payment of that discounted fifteen

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million well it dwarfs the other flows at least a

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

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

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stocks or equity investments that eventually gets sold that is

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An equity investment will produce cash for three or four

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or five or more years and then it will get

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sold for twenty times earnings or whatever that eventual multiple

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

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and that eventual sales price probably carries the most risk

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

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

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so out so you think about the time value decreasing

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

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

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a joke when it comes to dcf models our own

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got assessment of the risk of adventure has a lot

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more to do with the eventual outcome than getting the

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

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

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guessing is involved here And unfortunately for you however well

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moe curly and g w just signed up his trial

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

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