Principles of Finance: Unit 5, Discounted Cash Flow Analysis

Discounted cash flow analysis…à la Shmoop.

CoursesFinance Concepts
Principles of Finance
FinanceFinancial Responsibility
Personal Finance
Finance and EconomicsPrinciples of Finance
LanguageEnglish Language
Life SkillsPersonal Finance
SubjectsFinance and Economics

Transcript

00:20

it relates to the amount of cash that will you

00:24

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

00:27

will flow will be higher lower or the same like

00:29

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

00:31

to be All of this is mapped against the background

00:33

of what a safe investment e a u s treasury

00:37

bill would produce with high levels of certainty in that

00:39

same period And that treasury bill return has already adjusted

00:43

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

00:47

will be So the treasury bill is a base case

00:49

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

00:52

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

00:56

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

00:59

bill number but okay dcf modeling is the big kahuna

01:02

of financial valuation tools is largely what the pros used

01:06

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

01:08

walk you through the nitty and the gritty of how

01:10

you do a fully ugly dcf model in warning this

01:14

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

01:16

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

01:19

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

01:22

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

01:24

with cash flows but you can imagine this system applying

01:27

to the value of stocks or bonds or lottery tickets

01:30

or a random celestial events And most importantly for this

01:34

set dead end or dying rich relatives Yeah all carry

01:37

the structure of time and risk discounting such that they

01:41

could be plugged into a dcf model And yes uncle

01:44

larry as this applies to you too you will die

01:46

in a few years or in twenty and by then

01:49

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

01:52

what will inflation make that one hundred million dollars in

01:54

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

01:57

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

02:00

pity for the young male crystals who had to die

02:03

Or worse to donate them for this project Uncle larry

02:06

phones you at three In the morning You barely make

02:08

out his words But you know he had a drug

02:10

problem for a long time Brilliant man but you know

02:13

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

02:15

dead his lawyer Honest How sends you a registered letter

02:19

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

02:22

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

02:25

of cash now and we have pretty high certainty of

02:27

a payout Like we trust how we know him He

02:29

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

02:32

uncles moe and curly are ill A swell Hey sir

02:36

Minds is that each will die in subsequent years and

02:39

each will leave you one million dollars And then the

02:42

lawyer tells you that your grand daddy warbucks was going

02:45

to leave his fortune toe larry moe and or curly

02:48

But that if none of them are alive well you

02:50

get all fifty million dollars of his estate and it

02:54

looks like granddaddy has at least two years left in

02:56

him So your crystal ball comes out It says that

02:58

Your best guess as to the amount and timing of

03:01

your cash flows Looks like this are so t plus

03:03

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

03:06

likely curley dies You get a million there and in

03:08

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

03:11

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

03:14

you get that fifty All right but you need to

03:16

have a present value for all fifty three million dollars

03:20

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

03:23

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

03:26

over to them getting cash today for that future dough

03:29

So that right away you can go live your life

03:32

have fun enjoy things and get that place in malibu

03:35

with the entryway water slides All right Well you need

03:37

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

03:41

value so that you can negotiate with the bank to

03:44

sell them those flows and get your cash today So

03:47

then how do you discount that flow of dough back

03:50

to today While the formula runs like this start with

03:52

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

03:55

And their brethren good government bonds and t notes and

03:59

so on And you look through the bond quotes online

04:01

and you know it that well today u s government

04:03

paper coming do exactly in one year yields one point

04:06

five percent and get that anywhere online and quotes for

04:09

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

04:12

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

04:15

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

04:17

two and a half there and government paper coming due

04:19

in four years When you expect daddy warbucks to die

04:22

and leave you all fifty paper today you could buy

04:24

and get three percent per year yield That tells you

04:27

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

04:30

the market is likely pricing in modest inflation and maybe

04:34

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

04:37

the market has thus done a whole lot of the

04:39

homework for you already In pricing of these otherwise crazy

04:42

complex issues in calculation inflation and risk adjusted returns into

04:47

the future In addition to that risk free rate Well

04:50

we have tto add that curly moe in Well gee

04:53

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

04:56

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

04:59

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

05:03

just the risk of the us government defaulting on its

05:05

promises payday loans and so on Well how do we

05:08

matthew lee at tribute numbers too quantify that risk and

05:12

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

05:16

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

05:19

lays claim to the money or the estate in the

05:21

inheritance laws change after the socialist candidate gets elected from

05:25

california and caps inheritance amounts at a million bucks after

05:29

that Well the government then keeps everything what They have

05:31

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

05:34

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

05:36

a tail in a fifty shades brand blindfold leftover from

05:40

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

05:42

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

05:46

The lawyer called and told you in writing that you

05:48

are the sole heir and you definitely get a million

05:51

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

05:54

you just have to have the time value of your

05:56

money which you equate to u s government bonds certainty

05:59

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

06:03

that million dollars from uncle larry police is a state

06:06

at the rate of one point five percent adding no

06:09

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

06:12

t bill rates and that flow to you is valued

06:14

as a million dollars divided by the quantity one plus

06:17

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

06:20

just one year away that sometimes he iterated just one

06:23

And that equals about nine hundred eighty five grand So

06:25

if someone offered you that amount to buy you out

06:28

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

06:31

neutral but likely take the cash because you know a

06:33

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

06:36

and the window is tickling you the cash out right

06:39

Well under the second cash flow we have to discount

06:41

uncle curly You stand to inherit a million bucks from

06:43

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

06:46

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

06:50

At least not any time soon where all the banana

06:53

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

06:55

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

06:58

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

07:00

a ton of money and that the two million he

07:02

said he was giving you was really two million yen

07:05

not dollars And on and on and on tons of

07:07

other risk including the one where he donates his money

07:11

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

07:14

big fan of So in this case you attribute a

07:16

very high risk like twenty five percent per year calm

07:20

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

07:23

But how do you calculate that flow of a projected

07:25

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

07:28

receive a million dollars in two years and the two

07:32

year government paper rate is two percent Plug in the

07:35

same formula you just did for larry and you get

07:38

a million dollars divided by one plus the quantity of

07:41

the risk free rate of two percent or point zero

07:43

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

07:47

Take the Numbers 1 by 1 here You know where

07:48

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

07:52

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

07:54

than one to discount back the future amount Then we

07:57

have the point o two thing there which is the

07:58

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

08:02

Then we have to add the risk premium point two

08:05

five or twenty five percent per year to get a

08:07

total of point two seven as the total risk free

08:10

plus risk adjusted discount rate against that million bucks two

08:14

years from now And the to the second power thing

08:18

right there exists because the event is to compounded years

08:22

away Iterated twice So the summary formula for this one

08:26

is a million over one point two seven to the

08:29

second power or a million over one point six one

08:32

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

08:35

think about that for this event your neutral substitution point

08:39

or value in taking cash today versus waiting two years

08:43

teo hope to get that million bucks is a bit

08:45

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

08:48

discounting there but it makes sense because the death of

08:51

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

08:54

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

08:57

bucket kick or that there will even be doa at

09:00

that point to give you in fact the twenty five

09:02

percent number well maybe way optimistic and whatever it should

09:06

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

09:08

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

09:11

gonna move on to the third cash flow Mo is

09:13

sick luckily financially for you he liked the whoopee cushions

09:17

from around the world You sent him each year on

09:20

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

09:23

and everyone else that you are his sole heir He

09:26

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

09:28

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

09:31

an iron lung three years from now the union nurse

09:34

should pull the plug and let him go off to

09:37

the big stooge in the sky in relative peace So

09:40

your discount rate for the mo money is way lower

09:43

than for the curly money That is the risk premium

09:47

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

09:49

less And you think about that risk is being just

09:51

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

09:55

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

09:58

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

10:00

the cash flows looked like this eventual money A million

10:03

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

10:06

the government treasury paper coming due in three years at

10:09

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

10:11

percent The duration is three years or three iterations So

10:15

the formula then looks like this We have a million

10:17

over the quantity One plus the quantity point o two

10:21

five plus point Oh five All to the third power

10:23

there All right well simplifying We get a million over

10:26

one point Oh seven five to the third and again

10:29

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

10:32

the president value of your million box in three years

10:35

in this case is eight hundred six grand And this

10:38

is kind of interesting for dcf geeks Anyway this money

10:41

which comes three years from now has ah higher present

10:45

Value than the curly money which comes only two years

10:48

from now Why risk way less risk way higher present

10:53

value Last calculation for this problem Grand daddy warbucks you

10:58

know that gee dw is likely to name you sole

11:01

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

11:04

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

11:07

term life insurer uses So what do you know You

11:10

use it too He could die in four years Or

11:12

ten or twenty Hi Standard deviation Yeah You know you

11:15

know he wants you to have the money So without

11:18

a lot to go on while you just apply a

11:20

ten percent risk premium to the risk free number two

11:23

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

11:26

we go Terminal value Fifty million dollars government risk free

11:29

rate for guaranteed payment for years from now three percent

11:32

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

11:35

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

11:37

million over the quantity One plus the quantity point Oh

11:39

three plus point one all to the fourth power which

11:42

is the same as fifty million over one point one

11:45

Three to the fourth which equals fifty million over one

11:47

point six three for about thirty point seven million box

11:50

ish the present value of your getting fifty million box

11:54

from g w four years from now discounted back for

11:57

risk in times about thirty million dollars that is fifty

12:00

million dollars in four years with risk adjusted in this

12:03

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

12:07

what is your total value of your family financially speaking

12:12

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

12:14

a nine eighty five k discounted back curly with six

12:17

fourteen mo was eight o six and g g w

12:21

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

12:23

discounted the cash flows Now all we have to do

12:25

is adam up and they add up like this and

12:27

they come to in about thirty three million and change

12:30

and note that the terminal payment of that discounted fifteen

12:33

million well it dwarfs the other flows at least a

12:36

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

12:38

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

12:41

stocks or equity investments that eventually gets sold that is

12:45

An equity investment will produce cash for three or four

12:48

or five or more years and then it will get

12:51

sold for twenty times earnings or whatever that eventual multiple

12:54

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

12:57

and that eventual sales price probably carries the most risk

13:01

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

13:03

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

13:07

so out so you think about the time value decreasing

13:10

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

13:14

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

13:18

a joke when it comes to dcf models our own

13:20

got assessment of the risk of adventure has a lot

13:23

more to do with the eventual outcome than getting the

13:26

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

13:28

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

13:30

guessing is involved here And unfortunately for you however well

13:34

moe curly and g w just signed up his trial

13:38

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