Session 4: DCF Big Picture and First Steps in Riskfree Rates

hey Michael what year were you in the NBA program chair I can't hear you that's okay probably muted

so are you talking to me Michael Reef yeah what year were you yeah what what year 78

78 you preate me then so glad you're in the class hope you're enjoying I'm thank you put the guys stay care than

so is this the tech MBA group so I know Julian email that he Us in the tech MBA so know Jessica is little group

okay so any Tech questions we have I will turn to you right she's also part of the group but she's trying to distance herself yeah

okay so today we're going to start on the meat and potatoes part EV valuation discount rates risk free rates so today's start of the class test is going

to be about risk free rates even if you've never run into this issue or question think from from a common sense perspective so I want to pick some

somebody in this class who is Brazilian any Brazilians in here okay yeah what's your name John John's Brazilian and he's going to Value Brazilian company and I'm going to give

him two choices he can value the company in Brazilian r or in US dollars right the risk-free rate in Brazil indas and for the moment we talk about where you get that number it's a little messier

than getting a risk free rate in dollars is 7 and a half% the risk- free rate in US dollars is 2 and a half% so you can do a dollar valuation or re evaluation

very different risk free rates in which currency do you think you will get a higher value for your company whatever terms you want ultimately it's a value in the price so

you can do I'm glad that's that's a slam dunk because you should get the same right but you see where you can run into this question a 7 and a half% risk free rate

the discount rates in re terms are going to be much higher right if the discount rate is higher in a discounted cash flow valuation should the present value be lower so tell me John what's happening

that's offsetting the effect of the higher discount rate higher okay tell me why you say the same items to the same people and why do

exchange rates change I'm trying to get you to the core reason which is inflation it's inflation inflation is

the driver of risk free rates the driver exchange rates and if you're consistent that's something we're going to talk about today it doesn't matter which currency you value a company and you should get the same value and thank God

for that imagine being an equity research analyst you put had a recommendation on an Indian company said buy if you do everything in Indian rupees sell if you do everything in US

Dollars I can either buy or sell I can't do both so we talk about the rules you have to follow and how people fail those rules and then you get two different numbers because in most cases in

practice when you switch currencies you get a different answer so there's something in the process that you're not doing right now you talked about nominal or real that's a very Brazilian thing thing

to say a very Latin American thing to say because in most of the world we think in nominal terms right so when you get a salary offer from Goldman Sachs

you don't ask nominal or real not but in Latin America if you got an offer you might be very interested if it's in bolevard that you make sure it's in real terms rather than ninal

terms so when inflation was high in Mar of Latin America they did one or two things they did everything in US dollars so so they didn't have to deal with inflation in R and pesos or they did

things in real terms what does real terms mean your revenues can grow only if you sell more units the price is going to stay at constant dollars so your cash flows are

going to be lower in real terms but then your discount rate also has to be a real discount rate in the same inflation you're taking away inflation is going to be the star of the

show today it's going to keep popping up and it's a good thing that it keeps popping up because it reminds us of what drives interest rates so we're going to go back to that

core here's a followup question during the last decade t- Bond rates were at historic lowest it was the lowest 10-year t- bond

rate decade in the last century of course if you watch a lot of cnvc the reason is very simple right what kept rates low last the last decade

the FED did did it such a convenient reason the FED didn't how did it do it quantitative easing you know qe1 QE2 Titanic whatever else they had to do

essentially the FED did it it is to me the most damaging thing that's happened interest trade discussions is this belief that the FED sets rates and it's

deeply embedded because we keep getting told that because you started this year there a group of people on CNBC talking about what rates will do for the for the rest of the you know what they talked about the FED would raise rates the FED

would lower rates as if the FED controls and so we're going to dig a Little Deeper as to why that's not true but again the conventional wisdom is and

every time the fomc meets the whole world comes to a standstill right it's like the movie conclave they close the doors and you

wait for the smoke to come out say like a new PP rates are going up maybe different color smoke red smoke rates going up Green Smoke rates are going down Yellow Smoke we're not quite

sure why because we're convinced at the fomc's rate setting let me start set the stage for that discussion remember last September

the fomc Met does anybody remember what they did they cut rates by 50 basis points which for the FED is like going crazy it's a big cut usually it's 25 years big

cut now I remember the headline the next day fed low as interest rates I'm sure people say this is great my mortgage rate is going to go down my credit card rate is going to go down your company the borrowing rate you know what rates

did for the rest of the year the actual rates that you and I run into they went up the t- bond rate actually increased by 80 basis points between September and December the table

rate went up mortgage rates went up you're saying why because the FED sets none of those rates in fact what's the only

rate that the FED sets fed funds rate have you ever borrowed at the FED funds rate other I want you guys to try get online this evening see if you can borrow the FED funds rate I can

guarantee it'll be a lost time because what exactly is the Fed funds rate it's the uh rate Banks loan to each other overnight overnight it's an overnight in

that's the only rate the FED sets could it influence other rates Maybe if it's credible credible central banks affect

rates because the signals they send might tell you something about what's happening to inflation or the economy describe the FED as a wizard of

ODS remember the moveie the Wizard of O the wizard has no powers but where does the power come from the perception that the wizard has powers the fed's power

comes from the perception that the FED actually affects rates So today we're going to get past the mystery what is it that causes rates to change over time why were rates low

in the last decade the Fed was a side play it was not the lead player in those RS which brings me to a final question this is one that I got as repeatedly

over the last decade during the last few years there have been at least two maybe three currencies where the risk-free rate has actually become negative and that freaks

people out and I don't blame that when was the last econ class you took where people talked about negative interest rates econ is always a positive rate and all of a sudden you look around and the push back often came from

anal saying I can't do valuation anymore and here's why when risk free rates become negative play through what happens to your discount rates they all get really low and if the RIS gets really low they said the value has to go

through the roof I can't value companies anymore because everything is blowing up course is that true though when rates get negative I mean European companies must be must have been trading at

infinite values right in the last decade Euro had a negative risk rate in September 2019 John what did you say when with the r that that adjusted for the fact that

rates were high in real that your cash flows grow at a higher rate in real right when you live in a negative risk free rate World ises it sending you some

messages about the future of the economy in that country and inflation that country you're probably living in a deflationary shrinking economy this is

not great news so I gave you the benefit of giving you low discount rate but then when you do your cash flows I'm going to say you got live in the same world you came up within the discount rate so

we're going to talk about what happens in negative cre rates it's going to be okay if you stay internally consistent Bas like so add like 2% just reduce the

FL NE if they're mature companies you can have a negative growth if you have deflation you sell the same number of units your cash flows are going to be negative

right the this notion that everything grows at a positive rate is only in a valuation textbook are there companies that shrink out there how come we never

see these companies being valued I ask appraises when was the last time you valued a company where re us go down over time never done it how is that possible it's because

psychologically I don't think we can handle it it seems almost inhumane to give a company negative growth rate so what do we do replace with a positive growth rate we paint this nice story and

then we give it this negative of course things are going to blow up somebody back there a question Yeah question about sort of different currencies and risk-free

rates what about probability of for like the country Sovereign and we hold off on that because that's something I think the question you're asking is how do I get a risk free rate in Venezuela and

Boulevard great question it's going to be quite that is probably the worst possible currency to even try but I want to set up at least a structure that if you wanted to try it I'll put you on the

pathway so let's turn back I think we were on slide eight of your packet because those are all question oh the last question that that I kind of skipped was these people who complain

explained to me about negative risk free rates and that valuations should blow up you know what the solution to that was right if any of you worked in appraisal and you got your stuff from duffen

Phelps or from croll now for a while towards the end of the last decade both t- Bond rates have become low and Euro they suggested that you

normalize rates I'm good friends with um the people who wrote that croll and the and I said guys you're doing serious damage to valuation by suggesting that

people normalize rates first what's a normal t-bond rate what is normal I mean how do we Define normal it's average over time over what

time you tell me how old you are I'll tell you what normal looks like to you if you say normal t- rate is 6% you've been in the market way too long you

probably started in the 80s you tell me a normal rate is probably 5% you probably start in the ' 90s you tell me it's 4% you probably started the early part of the century you tell me it's 3% 2 there are people who say rates look

abnormally High I don't even have check their birth certificate to know when they were born you were probably 25 years old of course rates look abnormally High because

you've lived in a world with 2% rates and that's all you know this notion that normal is some number that we all agree on is just fuzzy and it's already you're saying you're opening a door and I'm going to argue you don't want to open

that door in valuation so if you remember where we left off last class we were talking about valuing equity in a firm and I suggest two Pathways right what's the

first one if I want value Equity cash flows to equity discount at the cost of equity I get a value for Equity right Leon what's your other way to Value

Equity I'll start you off you value take cash flow to the firm you discounted the cost of capital you value the entire firm and then you subtract our debt you get value for Equity so two ways to get put a number in

equity I want to start on that process dividends can be a special case it's not so if you want to use dividends it's still Equity versus

firm if you worked in valuation you've probably seen firm valuation a lot more than Equity valuation and I'll talk about why we T end up valuing the business rather than Equity it's a little more flexible it gives you more

choices you value the firm and then you have to subtract out debt to get to Value record and a very very practical question let's say you valued a business and you're thinking about what kind of

debt to subtract and I'll give you the choices you can subtract out the long-term debt in the company you can subtract out total debt in the company you can subtract out

whatever you call debt in your cost remember this is not the first time you're encountering debt to get a cost of capital you to come up with debt to come up with the the weights you can subtract out the debt you included in

your cost of capital or maybe you go to town you're a conservative analyst that terrifies me what do you do you want to subtract the biggest number you can so you subtract

out everything account payable current liabilities let's take the one item that shouldn't be on the list let's rule it out what's one thing that you shouldn't do don't do d right because again being

conservative is not a virtue in valuation right I'll give you the most conservative estimate of value which is your company's worth nothing okay we've got that out of the

way let's talk about coming up with realistic value so it's really between a b and maybe C is a subset of the first two you know why I picked the first one

a I've seen investment Banks value companies and subtract out only long-term debt only in an investment banking world do you think that you can borrow money shortterm and not have to

worry about it what I would suggest as a remedial exercise for them is they be for forced to borrow money from a money lender perhaps with mob

ties for two weeks and then tell the money lender it's only a two we loan what are you making such a big deal about it those broken knees that you

emerge with after that you will it's all debt right so long-term debt this is an exercise in fut it's all debt what you saying what's the

difference between B and C until 20 19 accountants had a blind spot on debt anybody know what that blind spot was a big item of debt that they weren't counting

yes leases were treated as not debt there's some ownership test that they did but if you're a retail company like Walmart could have billions of dollars in commitments which never struck me as

making sense so for the last 35 years in my book in my classes in my valuations I've converted leases to debt when I compute the cost of capital

now of course it happens on the balance sheet so when I do cost of capital my total debt included leases which actually lowers your cost of capital a little bit because you have

a higher debt mix which raises your present value right you're saying this is good I'm going to put remember I've got the firm value what do I need to subtract out I need to subtract our debt

but in my world the debt I subtract out is the debt with leases in it if you decide to include something as debt in your cost of capital you have the

obligation to subtract that debt out when you get to the last stage otherwise you end up with these inconsistencies so if you're looking for the right answer the closest thing I can get to a right answer is C we'll talk about some Escape

hatches on that one so let's say you do this right you value The Firm you subtract our debt the same debt you had in cost of capital come up with the value V you take the same firm you take

cash flows to equity you discount them at the cost of equity and let's say you do both right should you get the same value for the

equity we'd like to right again because we get if we don't we have all kinds of side issues it's actually one of the most difficult exercises in valuation to go

through to take a real company value the equity directly value the firm and come up with the value of equity and have the two numbers match up because you're making implicit

assumptions that you don't even think about so let's start the process with a very with a hypothetical example where I made up the numbers I'll tell you up front

I've cooked the books on this example to deliver the answer I want which is the same Equity value and remember we talked about weekly challenges this week's weekly challenge I'm going to give you a challenge where I'm going to take give

you the numbers a very simple company to Value so don't worry no elaborate Excel spreadsheets needed and I'm going to ask you to Value the company's Equity twice once by take and the numbers are not going to match up and and I'm going to

say tell me why why they're not matching up what do I need to do to match them up get the process started it's going to be a little confusing right now but that process has to get started so here's what I'd like to do I'd like to take a

company I'm going to give you cash flows to equity that cash flows left over at debt payments let's say the only debt payment is interest expenses get a tax benefit you take that you add the two up

you get the cash flow to the firm the cost of equity for this firm is 13.625 oddly precise but there's a reason again I said I made up the numbers there's a reason I have to be

oddly precise the company is borrowing 50% of its capital at a 10% rate pre-tax and it faces a 50% marginal tax rate so remember if you

borrow money at 10% you have a marginal tax rate of 50% you're in effect borrowing money at 5% the market value of equity is 1,073

million the Precision in the numbers actually should give away implicit assumption so I want to start thinking about what it is that's making me it's always nice to work with nice round numbers why am I coming up with 1,73 and

the amount of debt is 800 mil so I'm going to try it both ways first I'm going to take cash flows to equity and I'm sorry I somehow lost the that should be raised the power so when you look at

this this should be raised to the power two raised so the last numbers 2 3 four and five should actually be power so basically I'm raising the power I'm discounting cash flows to equity at my

cost of equity the present value that I get is 1 173 million that was easy compan is perfectly fairly valued

then I'm going to try it by taking the cash flow to the firm and discounting the cost of capital remember the cost of capital is a weighted average of my cost of equity 13.625 and my after tax cost of De of 5%

my cost of capital is 99.94% I discount the cash flow of the firm at the cost of capital the value that I get is 1,873 m

I subtract the debt magic I get match but I I I told you I've cooked the books here I've fixed the problem get the same answer there are assumptions I'm making here that lead me to the same

answer and that's what the weekly challenge about digging out what those assumptions are so for the moment I'm not going to dig deeper because it does require that you understand cash flows equity and cash flows and cost of

capital a little bit more and we'll get there so the first principle in valuation is do not mix match cash flows and discount if you have cash flows

equity for God's sake don't discount them back at the cost of capital I don't care how well you estimated the cash flows you've laid waste to your valuation if you have cash flows of firm

pre-b cash flows do not discount them back at the cost of equity the casualness with which people talk about the D and the CF terrifies me because they think if you have a d and a CF you

have a DCF but there are so many combinations of D and CF that don't work make sure you got them matched up because you know exactly what's going to happen you saw that with the kenot

case right the carand valuation you take cash flows to equity and discount them at the cost of capital you're going to overvalue equity you take cash flows to firm and discount them at the cost of equity you're going to undervalue equity

so on this page put a big X on the page because this is not what you're supposed to do in a quiz you might be in a hurry you might end up on this page and start doing things you shouldn't be doing I've taken every possible mismatch I can

think of and played through so I said what if I took cash flow equity and discount the cost of capital no surprise I get the kard effect the value of equity is too high if I take cash flow of the firm and discount the cost of

equity I get a value of the equity that's too low because I'm attaching too higher discount rate to the cash flows I even looked at the possibility that if you take cash flows to cash flows of firm at discount the cost of

equity you don't even know what you're doing you might forget to subtract out the debt I've seen it happen in practice because it's like a mix of you know fish and

fowl you have no idea where it ends up know so you end up with a value that's we spend so much time getting the cash flows right and getting the discount rate before you do all of that

stuff start the question what are the cash flows I'm trying to estimate what's the discount rate that matches up to it so let's set the stage for valuation what I'm going to do in the next few

minutes is show you big pictures of valuation for the moment don't get caught up in the details of how I compute free cash or Equity free cash to the firm or dividends I wanted to focus on what I'm trying to do in all of these

models the dividend discon model a free cash Equity model what I'm doing in common and where I'm diverging so here's what you have in any discounted cash

flow model you have expected cash flows in the future right that cash flows require a starting point and a growth rate you have a discount rate for those

cash flows and you have closure you know what I mean mean by closure you can't estimate cash flows forever so what do you do you stop at a point in time you estimate a number of course it can't be a random

number we're going to talk about how to do it right and how you can mangle that number but that's basically the structure for every valuation if you're doing an intrinsic

valuation there's only one way you can apply closure which is to assume that at the end of year five or year 10 or year 15 your cash flows grow at a constant rate

forever what does that buy you it buys you an infinite Series in mathematics and 200 years ago mathematicians solve for the value of that series we stole that equation we act like we invented it

in valuation but this is the famous terminal value equation cash flow in your six which becomes just a equation you plug numbers into but to do that you have to assume your cash flows grow at a

constant rate forever let me finish that thought though if you're telling me cash flow is grow at a concentrate forever it has to come with a cap right what's a cap

with cannot be greater than you're jumping too far ahead so let's do the first step it cannot be greater than the nominal growth rate of the economy in which you operate why because if you grow faster

than the economy forever you're going to become the economy then what right I we will talk about how you come up with the normal growth rate in the economy because who the heck knows what the

growth rate in the economy will be years from now and there are suggestions I will make on how to deal with that estimation question but the core assumption that you cannot grow fast in

the economy becomes one you have to make so I'm going to show you the three variants of discounted cash flow valuation the dividend disc model the free cash Equity model and free cash

refer model yeah estimate only because once you get to stable gr what the what the what's you can estimate for once you get to mature

growth you can keep going it doesn't change your value but why create pain for yourself when you don't have to so let's talk about the three models right so you guys are going to do the

dividend discount model you're going to do the free cash FL Equity model and this part of the class is going to do free cash flow The Firm first I ask you what's your cash flow you give me dividends your job was easy right you looked at the actual dividend your job

is to forast those dividends in the future so how how how are you going to go about doing that in practice what do dividends come out of they come out of income so you're probably going

to start by forecasting income if you're lazy you might just apply today's payout ratio why lazy because that will change as your company's growth decreases so you're projecting out earnings growth

net income growth and a payout ratio how long do you have to do it until your earnings start to grow at a constant rate forever because then the payout ratio is fixed so that's your job in dividend discount but the problem with

the dividend discount model is you're focused on what companies actually pay out we know beyond the shadow of a doubt that companies do not pay out what they

can afford to it's not even debatable that's a pretty categorical statement how do I know that with apple what gives them away so if I ask Apple C phones I've been paying out everything I

can afford to how do I know he's a liar look at his cash balance you got 250 billion in cash how the heck did it show up on your balance

sheet it's a direct consequence that you could have paid dividends I'm not saying you should pay it out I'm just saying that means that if I focus on the dividend discount model for Apple I'm

going to undervalue the company so the free cash Equity model is just a potential dividend model I say look I'm not going to look at what Apple actually pays out I'm going to look at what they could have paid out sounds

like it's going to be complicated it's one of the simplest exercises in valuation is estimating what they could have paid out because what can you pay out as a business whatever's left over over after every

other need has been met right it's right there on your statement of cash flows that becomes your free cash Equity since of focusing on dividends you look at free cash load Equity you have to project those free cash load equity in

the future so you're projecting out net income just like the dividend people but instead of estimating a payout ratio you're estimating how much of the net income you'll have to reinvest back into the company it's like a free cash FL

Equity version of a payout ratio you project out free cash FL Equity until again n income in both these cases though the cash flows you're discounting are cash flows to equity so the discount

rate is going to be the cost of equity so now let's turn to you guys you're doing a free cash flow to the pre-b cash flow you're going to pre projecting out free cash for the firm in the future you

can no longer start with net income why not pre-b net income don't go together right what the problem net income it's after interest expenses you got to climb the income statement it's going to come

with consequences usually go to operating income operating income is earnings before interest in taxes if there was an account in the room you probably going netp Abit is not operating I you know

frankly my world the two are the same it's operating income you're going to act like you pay taxes on the operating income why act because you pay taxes on taxable income after interest expense but I'm acting like you have no

interest expenses that's why this is called an unlevered cash flow you're acting like you have no debt then you subtract out reinv investment so to project out free cash on the firm I have to project operating income saying

what's a big deal operating net it can be a big deal and we'll talk about why the growth rates in the two will almost never be the same you subtract out the reinvestment you come up with free cash flow how long do you have to do it until

your operating income starts to grow at a rate that's a stable growth rate sounds familiar right all I'm doing in all three approaches is picking a cash flow making sure I get a discount rate

that's consistent that cash flow and doing it for as long as I need to before I get to stable growth I like to think in valuations in pictures okay so if you looked at my

Invidia valuation I take an Excel spreadsheet but Excel spreadsheets are almost mindboggling and bankers do it deliberately you show a spreadsheet

where do you even start right so I am exposing myself when I do pictures because it kind of brings your focus on what is he assuming that I

don't agree with so it is a risk but I want you to take that risk operating everything is so don't let this word volatile even enter into the

picture what does that mean they move around if you don't have a direction on that just let it go right if you're volatile and you see a trend that's your

job is to estimate what the trend is you do all company even a mature Oil Company are earnings going to be volatile why cuz o o prices change unless you have

some crystal ball that tells you which direction they're changing worrying about oil price volatility is going to get you nowhere right so don't let volatility stop it's always going to be

the case in statistics when something keeps moving around how do you work with it you average it out so use statistics to it so here's my first picture it's a dividend discount

model picture it's really adding nothing to the previous page but it kind of highlights what I'm trying to do as start with existing divs by looking at net income in the payout ratio and then

I project those numbers out until I get to stable growth and then I discount those dividends back at the cost of equity for the moment we haven't addressed how you come up with future payout ratios cost of equity that's what

the rest of the classes for what I get is a present value I'm done it's the value of equity in the company with free cash or Equity models I do something very similar but I replace dividends with these potential dividends free cash

Equity I go through the same exercise of projecting free cash Equity still focused on that income and I discount back at the cost of equity I get a value

equity and then I get to free cash to the firm and I require a mindset shift first my cash flows are pre-ad cash flows so when I ask you about growth and you're valuing the firm I'm not asking

for growth in earnings per share or growth in net income I'm asking for growth higher up you're saying why would they be different as a general rule As you move up the income statement

your growth rates have to get a little lower you know why why does a 3% Revenue growth translate into a 5%

operating income growth become a 7% net income growth and a 9% per share growth calb let's start with the first one why would uh why would Revenue growth not show up as operating income

growth could be like economies scale operating leverage right fixed costs right all cost Scala and operating income and net income what causes those two numbers to diverge

it's interest expenses another fixed cause right interest expenses don't grow so net income will grow and why would earnings per share especially at us companies grow at a rate faster than net

income for shares number of shares right if you do Buy Backs the number of shares will decrease I see too many people valuing firms doing firm valuation you where they get the growth rate by going

to Zach or going to IBS what do they do they actually take sside equity research analyst forecast of growth and they report great resource

but here's the problem what's the metric that most Sal side Equity reserve and you ask them about what's a metric that they that they estimate growth in it's earnings per share growth you take that

earnings per share growth you make it your operating income growth you've already set yourself on the path of overvaluing your company not all growth rates are created

equal going to come back and look at that more carefully but you can see how I move the way I think about almost every measure has to change so I get

future free cash of the firm I discount them back at the cost of capital I value the operating assets of the company sounds mysterious right you know

all I valued are those assets whose income is showing up in my operating income so let me reframe the question if I'm buing Apple I take free cash with the firm discounted the cost of Apple

and I come up with the present value what have are not counted yet why not why is Cash not in there because the interest income from

cash shows up where I told you that somewhere in this class your accounting soft tissue is going to come back and bite you it's it so if your financial

statement everything starts to swim together I want you to fight through that and at least look at a few expenses show up below the operating income line interest income shows up below the op

which means if I valued Apple I haven't valued the $200 billion in cash they have that's not Penny change I've got added on is there anything else any other assets that companies might own

whose income doesn't show up as part of operating income go ahead K asss be very careful if I'm JP Morgan

and I own that building on 277 Park like unoccupied un vacant which is very rare right I mean so most real estate is used for operations I can't add that on

because that'll be double counting but what happens if you own 5% of another company that's treated as a minority holding and the income from those Holdings show up below the operating

income Line This is a nightmare because if you have companies with lots of cross Holdings you now have to bring them in so what's big deal what if they have 2155 cross Holdings I'll let you de deal

with that in your mind think about the nightmare that creates I haven't valued them yet I add them on then I subtract out debt and own I call these the loose sense in

valuation the reason is when you take the cash flow and you discounted the cost of capital you he a sigh of relief you say I've done my work and then the Mischief begins because there's so many

things you can do between that firm value and Equity value that can get you into trouble we're going to spend 2 s just in that space so in terms of sequence here's what I'd like to

do I want to start by looking at the process of valuation so I forgot to ask the question how many of you have picked a

company already okay Leon I'm going to make you my guinea pick so you picked a company have you started the valuation yet good this is exactly where I want you to be

so where are you going to startop what are you going to to start with but to get the top line you have to have so you're going to download last year's income statement and that's

become so much e so much easier than it used to be right especially if you you remember to get your Capital IQ account going in which case you can download every year of data for the last 10

years I think one of the problems with having all this data is we don't know what to do with it we're drowning with all this data and if you take an accounting class you compute 200 different ratios and you have no idea whether you're coming or going after

those ratios so here's what I want you to focus on when you look at the past Financial date of your company you're trying to answer three questions the first is you're asking how quickly has

this company grown over those 10 years right it's a pretty simp you're doing this because you want to frame the future but you might as well step and the metric I would like you to focus on

when you think about growth is revenues not earnings not operating net income why because can a mature company

grow its income by 15 20% yeah you have accounting you can have Cost Cuts the different reasons for growing I want you to focus on the top line so Leon got that you would focus on the top line that's going to answer your growth

question but growth is only a piece of the puzzle right for that growth to manifest as cash flows below you have to first make money so the second question

I'm going to ask you is how profitable has this company been over the last 10 years and there there are three measures of of profitability that I want to look at again I might be stressing your

accounting here but if you go back and look at a financial statement You' see all three the first is called the gross margin Vera what's or Nikita what's a

gross margin what does it measure so but the problem is in a county class you look at a cogs first you say what the heck is a cogs right what is it measure though in in in Broad

economic terms in business story terms what is a gross margin measure you're basically measuring unit economics right you know what unit

economics is how much money do I make on the next unit that I sell gross margins are what's going to give it away so let's take a software company let's say you get on the Microsoft website and you

order a copy of or you become an Office 365 subscriber they charge you $69.99 or $89.99 instantaneously what do you think happens right after you do it you think

there's a little gnome at the Microsoft headquarters who running around creating an extra copy of Office 365 just for you how much does it cost Microsoft to create that extra copy nothing take a

look at gross margins for software companies as Sky High because if you're a Manufacturing Company you can be the most amazing Manufacturing Company in the face of the Earth but to sell a car

what do you first have to do you have to make the damn thing right so when you see gross margins for Tesla of 80% you know that somebody's

making up crap you've heard of Kathy woods and Arc if you want to see what happens when people have lost connection or never

made connections with being in a business start to these are very smart people say what's wrong with 80% margins I've seen other you're right you've seen other companies but they're not

companies that make cars if you make 30% gross margins as an automobile company you're a hero so look at your gross margins

because you're trying to understand the unity economics of the business your company's in because that's going to frame your story then you look at operating margins operating income what does that tell you

this is the economies of scale story right every Company claims to have economies of scale but if you truly have economies of scale what clue are you looking for in those 10 years is to see

if you have economies of SC Calum if a company so what are you going as revenues increas in other words your costs have to grow at a slower rate than revenues Uber kept claiming that

economy was scale for the first 11 years of the existence it was a complete lie and it was right there in front of us right the cost kept growing at the same rate or a higher rate than

revenues so operating margin is going to tell you something about economies of scale so when when you grow your company that'll become the basis for whether you think the margins can keep improving is

have the economies of scaled run out you still have it and then you look at net margin the least informative of the three margins what separates operating from net

margin how much money you've borrowed so you take Invidia they're almost exactly the same number why is that Nvidia has less than 1% debt it's

almost entirely an equity funded company you take caret the two numbers are going to be very different right grow margin again but you're looking at the past and it's not how profitable you're just

looking at parts of the business model that are feeding into profit so how much are you growing how much are you you know what how profitable are you have you been and

third you ask how efficiently are you growing growth is good right but the good side of growth is your revenues grow you but there's a bad side to growth which is to get that

growth what do you have to do you have to put money back into the business in what depends on your company if you're an automobile company you have to build plant and capacity if you are

Uber what do you have to do acquire customers if you're a pharmaceutical company invest in R&D my definition of reinvestment is far broader than capex on a statement of

cash flows it's whatever you have to do to get that growth you saying why do you care cuz growth can destroy value if if you invest huge amounts to get growth

that's not that much you grow but you're destroying value and I'm trying to look at this company is it a company adding or destroying value how much is it how efficiently is it delivering growth what I'm trying to get you out of is this

mindset of I'm looking at the at the numbers I'm going to compute ratios you're looking at past financials to get an understanding of the business unit economics economies of scale and where

debt is a burden on the company because it's going to frame your story going forward so I'll give you my definition of free cash with the V and we'll talk about each of these items more later on you start with operating income which comes

from revenues STS operating margin you act like you pay taxes you're saying why should I pay taxes well you know unless you want to be in jail you have no choice but to

play I mean you might try to minimize the taxes and you know but there has to be a tax effect and then you subtract out reinvestment and in in traditional

know valuation textbooks is defined as capex minus depreciation net capex investment in long-term assets and change in working capital re investment in short-term assets we're going to shred those assumptions past what you

see as capex and depreciation and working capital we're looking to what you're putting back into the business shred in what sense what did I say Uber's biggest reinvestment was

acquiring customers it won't show up as capex in a statement of cash flows I will treat it as capex why because I don't have to follow accounting rules I I have to look at what drives valuation and this is how you grow I've got to

bring it in so now you're ready right so Leon has looked at the how many years of data do you have in new company five five years he's looked at the last five years and he's formed at least a preliminary sense of how quickly it's

growing it might be a money is it a money losing company so the margins so if it's a money losing company there's no point there is a point right you're looking to see at least if it's moving in the right direction if you start at -

73% you're - 91% that's not a good sign -73 going to minus 35 maybe you can frame the story better and then you're also looking at the high Growth Company what are they

investing so now you're ready to tell your story I'm going to give you two Pathways first let's start with the more General Pathway to value a company to estimate free cash for the in the future you have to start with revenues right so

to get future revenues what do you have to do you have to project out Revenue growth say can I just use the growth over the last 10 years you can but pray and hope that this doesn't work in every

company you do because then I really don't need you CH GPT could probably do it right it's completely mechanical the reason I want you there is you might

look at a company with 30% growth over the last 10 years and say the stories changed it's going to grow at only 5% you have to tell me what why the stories

Chang but you start with Revenue growth second stop you got to estimate operating margins going forward Leon has negative operating margins if he

believes they will stay negative for ever his job got very simple right he's got the D valuation he's going to tell me the equity is worth nothing and I'm perfectly okay with that but if it's a

company that has promised what do you expect to happen you expect the margins to improve and there's a question I'd like you to answer it's not an easy question to answer which is once you get

through this pay what will your operating margin look like what's going to feed into it the unit economics now do you see why I I want cuz if you're a software company and you say my steady

state is going to look like it's 45% that's okay but if you're a Manufacturing Company 15% might be all you Aspire for you can look at industry averages But ultimately it's your choice

to make and then there's a third question a third link you got you got revenues you got operating margin that gives you operating income you now have to estimate how much you will have to

reinvest to get the growth rate and here your ambition is actually going to cut against you do you see what I mean by that the more you think you can grow the more you will have to reinvest doesn't mean it's a bad thing someone ask you

how much will you have to reinvest tied to your Revenue growth that's all I need to get the free cash of the firm re so if you look at my my my base spreadsheet for valuing companies that I use on

almost every company there's Revenue growth level there's a margin level there's a sales to Capital level which just basically ties your reinvestment revenues I'm done I've got my free cash for the firm you're saying warant you

breaking what's the point of breaking it into more detail what exactly am I going to bring in unless I have something new to add so I get my free cash flow how long

do I have to do it until your company becomes a mature company say what if that's 50 years could happen I never go past

that why not because there aren't companies out there that don't grow for more than 10 years but the exceptions not the rule the median growth period for us Growth Company for a US company

in the 208th Century in the 21st century been 3 to 5 years 10 years is already at the 90th percentile and you know what I'm asking as an investor I'm saying I'm going to put you at the 90th percentile

if you can grow longer that's icing on the cake I want it for me imagine putting in a 50-year growth period for inor and finding it fairly valued

congratulations you got the value but what has to happen for you to break even it's got to grow for 50 years selling AI Chips To whom martians maybe that's in

your story but if you make your base story that this will be the greatest company in the face of the Earth that's like signing One S and saying he's going to hit 75 home runs

and win has a World Series every year for the next 10 years anything less is now a negative surprise that's not a great place to

be and to Discount these you need a cost to Capital lots of details but let me set the intuition up for the cost of capital there are two ways I can raise money borrowed money or for Equity let's

start with the easy one the cost of Deb is the rate at which I can borrow money longterm today I'll talk about the longterm later on why we make it longterm so you're a banker you're lending me money I'm trying to figure

out what interest rate you're charging so help me out here before you even embark on that exercise what's the first thing I have to get out of the way Brazilian US dollar I have to tell you in what currency right because it's

going to be very different if I'm boring so let's say it's an US dollars so you're lending me money today what's the absolute lowest rate I can

expect to see on a long-term borrowing 4.5 4.6 which is what the t- bond rate is and if would you lend me money at that rate if you're a banker and you

went around lending money at 4.5% you're not going to be a banker for very long right you're not going to be a bank for very long why cuz people default so as long as banking has been

around you can go back to the 1500 and the RO setting up the banks what do you do you start with the risk free rate and you add a spread we can dress the spread up but it's a spread for covering

defaults a credit spread a default spread we'll talk about how to estimate it better but you're trying to estimate a cost of debt but before I leave the cost of debt there's one more stop

governments around the world have made it much better for us to borrow money than to use equity why because debt brings a tax benefit

interest expenses tax reduction so if I borrow money at 8% and I have a 30% tax rate in effect I'm borrowing money at 5.6% that's the easy part of the capital

equation cost to debt after tax cost to debt rate at which I can borrow money longterm today turn to equity and now I'm going to potentially face a nightmare you guys are all Equity

investors in my company right you bought My Equity because you hope to make a return you know what the cost of equity is the number you had in your head when you bought my shares this is the first

of The Nightmare to estimate the cost of equity I've got to read your months it's say I can don't worry I cannot if your mind is wandering you're okay but let's say I read each of your

minds what's the second problem I'm going to face France did you all of you get together in a bar and agree on a number before you got no each of you came from your

different places different risk verions each of you is a different number right so if you think about a stock like Invidia how many people own shares in in I'm not expecting a precise answer a lot

of people with very different numbers and for 70 years in finance we've struggled with this how do you come up with one cost of equity for a company where there are thousands of people

investing in the company so let's see how we've resolved this problem you're not going to like some of the assumptions we make let's say Ravi owns a th000

shares and France owns a million shares whose mind do I care about more you're done right let's say France owns a million shares

but he's a Founder SL investor he can't trade because he gives up control then but Gabrielle owns a million shares but he trades those shares who affects prices

more in corporate finance we call those investors the marginal investors and you know what evaluation you have to do in value company you got to look at look at risk through their eyes you're saying

but I feel a lot more risk that's your problem because that risk was entirely avoidable right if you wanted to you could have bought an index fund you chose to not

diversify the market doesn't reward that kind of risk so when you do cost of equity you got to act like your black rock or vanard the two largest investment in Nvidia are Vanguard and

black rock they're saying so what how many what companies does Vanguard own really the question should be what companies does Vanguard not own

right it's a supremely diversified investor so what what does that mean when they look at Nvidia the risk they see is the risk it adds to a portfolio we've just

essentially had finances biggest breakthrough entire discipline came from this breakthrough Harry Marco it's in the 1950s that the risk of a company is not the risk of it standing alone but

the risk added to a portfolio when you use a beta whether you like it or not this assumption is following you because in C estimating the cost of Equity we estimate the cost

of equity to that Diversified investor to get there start with the same risk re rate we start with the cost of debt with 4.5% the beta will measure on a relative

basis how risky you are relative in what sense beta is a scaled around one when I tell you beta of a stock is 1.2 I've already told you that it's riskier than

average 1.2 times a relative risk measure and then you multiply the relative risk measure by the price of risk in the equity Market say what the heck is a price of risk in the equity

Market hey when you put your money into stocks I hope you expect to make more than five 4.5% why because you can make 4.5% effortlessly right so to get you to

invest in equities I've got to at least promise you more I might not be able to deliver it's called the equity risk premium it's a fancy word for you think that price of risk changes over time I

we had a twoe period where each being tested right first came deep seek then came tariffs who knows what the next week will bring this next 15 weeks each of us is going

to find the price of risk changing and so is every so when the price of risk in the equity Market changes what happens stock prices change we're going to talk about

estimating Equity R scrims and betas but the cost of equity comes through that process I a cost of equ in a cost of debt I take a weighted average based

on Market valuates as opposed to what let go of your accounting self because in an accounting statement a bance sheet that's a shareholders Equity

that's book Equity Let It Go in valuation it's always market value weights and those weights can change over time so if I'm valuing in I can start with 99% Equity 1% debt but

nothing stops me from changing the debt ratio which means that your cost of capital can also change over time in fact you're probably not going to see me value a single company where the cost of

capital stays the same over time because the company story of course it's got that's the process evaluation and as you can see the steps the way I'm going

to break them down is I'm going to start by looking at the past don't give up on that are some of you going to have more of a past than others absolutely a valan Coca-Cola you have a lot of history you

can look at the Levi St lift example you saying that's unfair my team member is 85 years of date I have only three hey it's not it's it's it is what

it is you got to live in the world you're in three years of data is what you have learn what you can from the past obviously you will learn less than the Coca-Cola person were but your job is to First estimate risk and disc

contract we're going to start with that then we're going to move to talking about future cash flows and this is where the rubber meets a road because you have to leave your comfort zones right you got to talk about the

future and then we're going to talk about this closure this termin value number because it comes with a lot lots of constraints and lots of misconceptions and then at the end I'm going to talk about tying up the loose

SS what should you subtract out what do you do with cash cross Holdings so let's get the process starting with the discount rate does the

discount rate matter in a DCF you say of course it does d in the DCF that said though it doesn't matter as much as you think it

does in most valuation one of the things I think I see that I think is not productive is how much time people spend

estimating discount rates and how little time they spent estimating cash flows my rough estimate is a typical valuation 80% of the time is spent estimating

discount rates 20% of the cost of capital I'm going to make a general statement when I've screwed up on evaluation and I've screwed up on lots of them it's almost never because I got

the discount rate wrong it's because I've got the cash flow wrong we need to shift our Focus from discount rates to cash flows so I will talk about discount rates but as a class

goes on I want you to put it in perspective and when you look at that discount rate the consistency rules apply one we've talked about Equity versus FM make sure you're consistent the second we've kind of started on

currency you estimated cash flows in real your discount rate is to be in realiz pesos got to be pesos dollar it's got to be in dollars and third if you choose to do your valuation in real

terms your discount rate also has to be real so step back to think about a discount rate you need it of course so in a discounted cash flow valuation the discount rate is doing all of the heavy

lifting in terms of C conveying risk your cash flow doesn't do it's an expected cash flow and if you break the discount rate down you got a risk-free rate in the currency of your we talk about a cost of

equating you need a relative risk measure I'm not even going to call it a beta because then you're already jumping into capm I don't need it I just need a measure of relative risk and I'm going to leave the door open that if you don't

like Bas in the ca maybe there's a different measure of relative risk that works for you and need an equity risk premium now of course if this were a financial Theory class which it never

has which SP the next 3 weeks talking about different risk and return models in finance I don't have the time for that and it's not the point of the class but if you think about risk and return

models and finance are all built around that so before we embark on this process of thinking about risk and bringing to discount rates think about uncertainty

in general it's been a subtext for this class right you look into the future you're going to feel uncertain what do I do about it here's what I'd like you to start with whatever company you pick Leon's company I'd like him to make

what's called a risk profile start listing everything you're uncertain about you know how long that list is going to be in fact the qu the really everything in that valuation is uncertain even your risk free rate you

might find as uncertain if you're doing a valuation in Russian rubles and then when you're done with the list you're going to have like 35 items and you say what the heck am I going to do and that's when you get

overwhelmed which is one reason most people don't try to Value companies too much uncertainty so here's the first step to dealing with uncertainty in a more healthy way when I look at uncertainty I think of it as going into

buckets let's talk about the first bucket uncertainty can either be estimation uncertainty or economic

uncertainty just take in video what's the estimation uncertainty that maybe the gross margin is off instead of 74 should be 76 and if I did more work I could finesse

it maybe the revenues need to be adjusted for something that was prepaid that's estimation uncertainty you know what economic uncertainty is is how will

the AR Market develop what will deep seek do to the market the reason I divide it is doing more research spending more time collecting more data

what which are the two kinds of uncertainty are you going to be able to reduce estimation uncertainty economic uncertainty is economic uncertainty and here's the bad news 80

to 90% of the uncertainty you face an evaluation is economic uncertainty and you know how it's going to manifest right when you're done with evaluation especially if you're a

numbers person you're going to feel the urge only I collected more data if only I looked up more stuff I will feel more

comfortable you're welcome to try it out but I'll wager that two days of data collection later you're going to feel even less comfortable than you were because you you know you're just taking

something that doesn't matter in trying to finesse and that's why I call it the karmic point in valuation where you said there are someone certainties I worry about and some I don't economic

uncertainty I say okay it's that it's going it's going to affect my valuation nothing I can do about it second classification uncertainty can be micro uncertainty or macro uncertainty micro

uncertainty is uncertainty related to something the company does its management does if youing Tesla what are your micro uncertainties probably send you to therapist if you thought too long

about it starting with Elon and electric you know whether they're Tesla 3 the new Tesla 3 is going so forget about the Cyber truck you all these things that

are micro but are there you know micro uncertainties yeah inflation could go up interest rates could change the economy could go into recession he's saying why divide into micro and macro you know

which of these two uncertainties show up in your discount rate at least in the traditional Finance view of the word what do we say about risk that you building risk that a diversified

investor would find which is risk you can't can't diversify a away it's just micro uncertainties micro uncertainties average law of large numbers so you can have a company with

lots of micro uncertainties and a low discount rate anybody think of a good example of company lot of micro uncertainty low discount rate is a biotechnology company

risky young farmer company yeah but what kinds of risk are you thinking about that a drug would not make it through the pipeline which is the quintessential example of a company

specific risk when a VC invest these young young farmer company uses a 40% discount rate I have to take a second look I mean I look at what is that what exactly you building in there Microbus

is macro and there's a third group a of risk where I divide risk into discrete risk and continuous risk I'll take the

easy half of that continuous risk is risk that affects you every moment of every day if you're a US company with European operations every moment of every day your value changes why because

every time the exchange rate changes your cash flows change right but if you are a US company with operations

in a country with fixed exchange rates things look really stable until they don't you've traded off continuous

uncertainty for discrete a devaluation a revaluation which of these two risks do you think is easier to bring into valuation or deal with this business continuous uncertainty or discrete

uncertainty continuous is far easier in finance we've studiously avoided discrete uncertainties so when you talk about valuation people act like there's no nationalization risk no failure risk

we can't do that we can't look away from this so discret try that out take your company and think about risk and put them into these buckets which essentially kind of gives

you the big picture question so when you look at a company and say it's risky I'm not going to let you stop there I'm going to say what kind of risk are you talking about the reason I ask is not because I'm inherently curious It's

because I want to figure out it's a risk that it's going to affect my discount rate or not second I'm never going to ask you what would you like as a hurdle

rate you're going to say 15% 18 but you can't do that you're a market taker when you enter the public markets I don't care what you would like to make I'd like to be able to

fly but I'm not going to jump out of a window saying I can fly not if I'm sayane what you like as a hurdle rate is kind of irrelevant I've seen people doing these things I used to 15%

discount rate why because I like 15% discount rates I need to make at least 15% okay I'd like to eat 5,000 calories and remain the same weight it's not going to work you can't put an

unrealistic expectation up front and allow it to and finally the the diversification effect don't make it any more mysterious than it

is how does diversification work I it's a law of large numbers right basically that when you have company specific that cut in both

directions that averages are so as we go through this class we're going to come back to them but as you as I said if it's a finance class you can go through mods I'm going to do a

two-minute review of the evolution of risk and return model and finance some of you might remember this in my corporate finance class the oldest risk and return model in finance textbooks is

the capital asset pricing model the risk free rate is a starting point for every one of these models so that's not any different but in the capital asset pricing model everybody ends up looking like

Vanguard why because there are no transactions cost and no private information everybody gets supremely Diversified and risk is measured with one number the beta against that market

portfolio amazingly simple model it's St it staying power tells you how compelling it is to have a simple model 1964 1978 Steve Ross said y said

multiple source of Market risk why are we all trying to capture the One beta see Arbitrage pricing model allows for multiple Market risk factors in a bait against each one but the factors themselves were

unnamed Factor one factor two is a statistical model which never caught on why because no compan is going to jump onto the bandw I'll use Factor 2

model if you put names on the factors interest rates yield curve GDP growth you've gone from an Arbitrage pricing model to a multifactor model and then in

1992 Jee farmer and Ken Fred perhaps the most widely quoted paper in active investing and finance said why are we even trying to build a model why don't we let the market tell us what's

risky you how will the market they took 5050 years of returns looked at what kind of companies on high return small cap companies low pric to book companies and they said those must be measures of risk you see why it's a leap of faith

because you're assuming markets must be right over long the long term I call these proxy models for risk you've given up on measuring risk if you're a small company I say you're

risky it's a bludget but you can see why people went that R ultimately in all of these models though you need a risk-free rate to get started so I'm going to use the cap I'm

not partly because I'm going to continue to use it in this class because I think there are ways in which you can use it better but if you decide to go with an Arbitrage or a multiactor model everything I say about RIS rates with

the cap will carry over there everything I say about a single B you multiply by five for an Arbitrage pricing model and everything I say about Equity risk premiums you now have multiple risk

premiums the same thing will apply so I need a risk free rate I need an equity risk premium and I need a beta which of these three should be the slam duunk

RIS free rate when I did my MBA it's a long long long time ago how much time we spent on the RIS free rate 2 minutes I was told to use the US

Treasury rate as a risk free rate and we moved on shows you how dollar Centric my MBA class was and also how much trust there was that if you have a US Treasury it must

be risk-free both are kind of shaky at this point in time but today you can't pass is by in 2 minutes because the world has become

Messier so what I'd like to talk about is what a risk free rate is and you're going to find maybe the next discussion too much on the risk fre rate but I don't think we have a choice but to

delve it so I'm going to give you what I'm looking for when I'm looking for a risk-free rate I want to find an investment where I know exactly what I'm

going to make guaranteed pile that away so when you say I'm going to make 4 % at the end of the period I come and look at what you made you're always going to make 4% so if you think about what you need for

that to be true first The Entity issuing the security can have no default risk not even a tiny bit because we have default risk to call it risk-free is absurd right second there

can be no reinvestment risk what am I talking about if you have a 10-year time Horizon even if you believe the US Treasury has no default risk is a one-year T risk free if you're looking

at a 10-year time rizon tell me why it's not because at the end of year I have to invest in a table and two and I don't know at what rates so onee tble is not risk free if I'm

looking at a 10year time Horizon a 10year t-bond is not risk free if I'm looking at a oneyear time Horizon because it's price risk we just made the water more murky

right because for me to tell you what the risk free rate even is in US Dollars the first thing you need to tell me is over what time Horizon there's no such thing as a dollar risk free rate that just floats on its

own so here's what I'm going to do I'm going to talk about three things here first it's time Horizon matter second currency clearly plays a role and third

just because you have a government bond rate doesn't mean you have a risk fre rate unfortunately much of the world you told Government Bond rate must be some

of you worked in appraisal work in India value companies the Indian government bond rate in rupees becomes your rree rate but that implicitly assumes that

there's no default risk for a government when it issues Bonds in the local currency there's actually a logic that backs it up right why should governments

at least in theory never have to default in a loc on a local currency Bond you print the money right but here's the fact that works against that

you know that half of all Sovereign defaults government defaults in the last 50 years have been local currency Bond default defaults governments choose to default

even though they could print the money say why they be stupid enough to do it when you print money to pay off debt it's true you didn't default but did you create another consequence you have inflation you're

caught between a rock and a hard place right you want inflation often hyperinflation or do you want it to fall and what Latin America has start us and let's face it everything we know about Sovereign default Latin America is start

us it's like the Bible of sovereign default everything that's happened there is that it's easier to come back from default than it

is from inflation I went to Brazil for the first time in 1997 to teach valuation class to days every question I was asked was a question about inflation nobody cared about return on capital or

growth it's why because it was 5 years after hyperinflation and they were de PTSD basically everything inflation it took 15 years before the

Brazilian government could issue 10 bonds and R because nobody would buy R bonds long term they all at issue bonds and dollars this morning I was looking at

I'm going to put a post up on U pricing you know what the highest p ratio Market in Latin America is right now

Argentina in any just word nobody should ever lend to Argentina ever again right this country that makes an art form of default every three or four years but guess what every every fth year it's

back again it's amazing people almost have amnesia the bottom line is just because you have a government bond rate doesn't mean you have a risk free rate so I'm

going to present you with a series of fairly simple questions which I think can lead us to think about risk- free rates better let's say you're valuing a US company in US dollars or any company

in US Dollars and you want a risk free rate I'm going to give you some choices for the risk free rate and as I go through them I want you to cross out the choices that don't apply because I'm going to come back and ask you why you

cross them up so I could use a 3-month table R why not short a time for what so given what I'm doing right which is value companies

when you value companies how long you estimating cash flows no that's not true I stop after 10 years but what happens after 10 years cash flows go on forever

so it's really really long time I don't even know how many zeros there are in thousands of years but no forever so too short ter how about a 10year

t-b maybe but a 30-year t-bond should be better than a 10e tond right I'll come back and talk about why I continue because if I purely if I

picking just risk R rates a 30-year Bond wins over a 10year bond because my cash flows continue forever you want a really long-term rate why not a tips rate you know what a tips rate is it's an

inflation protected t- Bond was about 2.26% when I did this why can't I use that if I'm valuing a company in US dollars because the minute you put a

currency on your cash flows you're doing things in ninal terms because you're doing things in real terms there's really no need for a currency the minute I say US Dollars it's a nominal cash

flow and I can't use a real discount rate what about the last two the highest the the the highest of these numbers why would I do that I'm a conservative person I'm going to go fine don't even go

there or the low to the numbers or some other thing there is of course an implicit assumption I'm making you know using any of these numbers which

is that the US Treasury has no default risk 20 years ago people say of course how many times in the last decade have we dance this

dance of the government might default this weekend it's not a financial default it's a political default actually in the US because you got this very strange

system of you come up to a debt limit if Congress doesn't pass no go on with you you it's a different kind of default but

we've planted the seeds of at least a possibility and you know where the seeds have taken ground right ratings agencies rate companies the US still has a AAA

rating from Moody but S&P and fit is now below AAA so we've now opened the door to default risk we'll have to talk about what to do if you want to bring in in for the

moment I'm going to keep the t-bond rate as my risk free rate and dollar but that could very well change let's move on step forward

anybody valuing a EUR European company who you value on on Swiss company right that's I'm going to cut because Swiss frank so that'll be easy get a Swiss

rank risk free right who you Val Juliet okay which is based where okay I want somebody with the European company no nobody's doing European you

haven't even thought about European companies there is a continent called Europe with a lot of companies if you're having trouble finding a company you might want to look there right so Jessica is going to pick a Spanish

company to Value I'm not pre picking but let's say you pick a Spanish company to Value you are doing your valuation in Euros right why because all your financials are in Euros might as well stay with Euros you want a Euro risk free rate so what did I say we're going

to do going to find a 10year government B yours I did but I have a bit of a problem you see what the problem is 1 2 3 4 5 6 7 8 9 10 10 governments all of

which issu 10year bonds all in euros and the rates are all different so Jessica help me out here which of these rates are you going to use in your Spanish company

valuation this is the statistical solution the only problem is what do we say why are these rates different in the first place they're all in the same currency what's the only reason for

differences there's more default risk right that's the only reason this is 1998 drma bonds and dut these are all Euro bonds so almost so I'm going to

come back to Jessica the only reason for the differences is higher default risk countries like Spain and Portugal and Italy have higher rates and I don't want default risk in there what is the rate

that it keeps as a shot of being risk-free here Jessica why not because it's German but because it's the lowest for much for all of the

Euros existence the German Euro bond has been the lowest rate but it's getting closer the Netherlands now has a rate very close because Germany has its own

set of economic problems now and budget problems so who knows a year from now and I put this graph up it might be the Dutch bond that has the lowest rate go with the lowest Euro bond rate as your

risk cre rate but just saying but I want to punish my Spanish company for being Spanish or my Greek company for being Greek I will give you plenty of chances to punish your company for being Spanish

or Greek just don't do it in the risk free rate you value a Russian company in US Dollars what should use as your risk free rate the USD bond

rate but it's a Russian company I know there are two other inputs to come right you need a beta and you need Equity risk premium I'll let you punish

your company there don't punish it in your Base number because then you're double counting risk the third example say you're valuing an Indian company in Indian

Rupees at the start of 2025 the 10year rupee bond rate you had it has to be rupees don't use a dollar bond rate or it has be was 6.8 out wager across India

people are valuing companies was that that is a risk creater but you do that you're assuming that there is no default risk and this don't take this as a patriotic slight

I'm not talking about India will default but I'm saying in that number there is the posibility some of it is for default and I'm going to help you on that road so I'm going to cheat and I'm going to

use a very simplistic measure of whether there's default risk I went to Moody's and I looked up the Sovereign ratings for India and if you ever visited that page every country has two ratings local

currency rating and a foreign currency rating foreign currency rating is when borrows in Euros or dollars the local and I was hoping I was praying I would

see a AAA under the rup under the local currency rating because they not have used to 6.82% and blame Moody if something went wrong what I saw instead

was a B3 rating at the start of 2025 a B3 rated Bond had a default spread of about

2.18% looks like I made that up and sometimes I do make up stuff but next session I'll talk about where I get those default spreads it's like an algebra problem right the government bond rate is 6.82% I'm worried that some

of it is might for default risk and to the degree that you believe this default spread number see what the risk free rate for India is going to be first let's say get a sense of

direction are you going to add the 2.18% or subtract out the 2.18% subtract out because you want to take out the default risk you subtract out 2.18% the risk-free rate you get in

Indian Rupees is 4.64% you know why I want to do this because later on you're going to punish this company by giving it an Indian Equity risk premium and guess what that

number is going to be high because India is a risky country and often it's the same spread that's driving that risk premium in most Indian company

valuations I think you double count India country Risk by using the Indian government bond rate and that's what I'm trying to push back against so pleas set up how I think

about spreads because in the next class we'll go through that this entire approach requires that come up with that 2.18% right there are three ways you can

get this spread one is if your country issues Bonds in US Dollars Brazil for instance issues 10year Bonds in US dollars at the start of 2025 that number was

7.75% the Indian government bond rate was 4.58% I'm sorry the US bond rate was 4.58% that difference 3.17% is the bond market estimate of the

default risk in Brazil until about 20 years ago this is the only choice you had you to find the only problem is there only about 15 countries in the world that

issue Bonds in B in dollars or Euros you can't do this we have rupee bonds you can't do this for India India does not issue dollar denominated 10year bonds the government

doesn't 20 years ago New Market opened up called The Sovereign CDs Market know that market is just a fancy way of describing a market where you can go by insurance against Sovereign

default so let's say you buy an Indian bond and you want to protect against default you can go to The Sovereign CDs Market buy a bond it's a market set rate

at the start of 2025 that number for Brazil was about 3.23% I actually comput a netted out number where I take out the US number

from it just to get a set but it's about 2.8 to 3 so basically that's what the Sovereign CD you why would that number ever be different than the Government Bond number it's liquidity trading this

is a much more liquid Market than the Government Bond is and this you can get for about 80 countries that's better than the 15 we had for government bonds but I still have a problem right there are about 900 countries where there is

no Sovereign CDs spread and no rating for those countries I use the lookup table which is you tell me your Sovereign rating I'll tell you what the spread

should be right the 2.18% came from looking at the B3 rating for India so you can look at the default spread so next class when we start we'll talk

about what if the three approaches can all be used I get three different numbers which you can for Brazil which one should I use I'll start with that come with the next class but I want you to start thinking about risk free rates

as something that's more than just you look it up in the Wall Street Journal it is a lot of worth at least in some currencies that