Session 10: Terminal Value

every day okay so see a few more quizzes here if

you haven’t picked yours up so you get a chance to pick up your quizzes very quickly I forgot to make copies I’m sorry started the class test but I’ll put it online so you can download it today we’re going to actually finish our discussion of growth and talk about the really big number in every discounted cash flow valuation which is the terminal value a number that scares a lot of people hugely misunderstood hugely misused so I’m going to ask you some questions related to the terminal value that will come back to and talk about a little more today hey here’s the first one we’ve kind of talked around this we might even have talked specifically about it and terminal value is the number that we use to clerk to put closure on a discounted cash flow valuation and I’m going to list four different ways in which you can estimate terminal value and if you’re doing an intrinsic valuation I’d like you to tell me which of these four ways should never be used ever to get a terminal value first is a liquidation value yep why but what if that’s the most realistic endgame for your company what if there are no more years what if i have a royalty trust you know the royalty trust is basically the oil reserve i sell the oil from the ground 15 years of oil and the oil is all done there’s nothing left but this hole in the ground right you’re right liquidation value might not be the right way to value coca-cola but if i gave you a finite life investment and at the end of the investment the cash flows end and the project ends and the company’s wound up liquidation value is the cash flow it is an intrinsic cash flow hey so liquidation value might not be seen very often in discounted cash flow valuation but it is consistent with intrinsic valuation if your company doesn’t have life left at the end of the closure period stable growth model obviously you see a lot of it right you have seen a growing perpetuity model I actually listed the equation we did corporate finance a growing perpetuity is I’m sorry growing annuity model I’m sorry growing annuity model not a growing poverty model growing annuity model is when you have a cash flow that will grow at X percent a year for 30 or 40 or 50 years there’s actually an equation that will give you that well we almost never use it but can we use that in a intrinsic valuation let’s suppose I get to your tent and I say you know what this company will keep going but it’s not going to go forever it’s in a technology which eventually is going to get wound up maybe 30 40 50 years it’s using a growing annuity model consistent with an intrinsic valuation okay why should companies go forever in fact you could argue a growing perpetuity is the unrealistic assumption we all I’m saying is we get caught up in this growing perpetuate equation is the only way to compute terminal value it might not be liquidation value is okay a growing annuities okay that’s the way your company’s structured I’ve kind of given away the answer it’s the only way you should never compute terminal value applying a multiple and here’s the tragedy almost every investment banking valuation the terminal value comes from using a multiple six times a bit five times earning two times revenues you name it hey if you do that please don’t call this a discounted cash flow valuation it’s a discarded cash flow valuation and drag the drag component of the cash flows while I’m distracted by the cash flows you slip in six times a bit out you got huh by looking at what other companies in the space traded now which is a pricing and a multiple there’s nothing wrong with that it’s a forward pricing but it’s not an intrinsic valuation so when you see this kind of casual evaluations the biggest number comes from using a multiple got by update look by obtained by looking at

companies trading today it is really not an intrinsic valuation so let’s assume that you decide to go the perpetual growth right Joseph yep exactly it’s a relative valuation there’s nothing wrong with that right so I’ve used 15 times earnings to get the value fire five years from now that’s fine you’re doing a pricing you’re just doing a forward pricing rather than a current pricing the forecast period is kind of a non player in the game right because it’s that’s why i said it’s it’s really a pricing and drag because what you have in the front of the cash flows the cash flows look like that matter but they really don’t because it’s all coming from that multiple it’s just a way in which is slipping a pricing and make a claim that it’s an intrinsic valuation now let’s assume you decide to go with the perpetual growth rap right so let’s make this very simple let’s assume that you are doing an intrinsic valuation and you decide that this company has a hundred million dollars in after-tax operating income and cash flow every year forever with no growth let’s keep it simple let’s assume this company is a cost of capital of ten percent what’s the terminal value what kind of cash flows is 100 million every year forever is a perpetuity right what’s the present value of a perpetuity it’s guys come on you’re four months away from graduating right the present valuable perpetuity is the cash flow divided by the discount rate right which is a hundred divided by point 10 which is a billion dollars yet so you’re not happy it’s too low what have I told you this company will grow 2% you’re forever remember the terminal value got in the previous page this sounds like a slam dunk answer but go along with me will the terminal value go up go down not change any of the above actually can be it cannot be none of the above it’s got to be one of the three so let’s leave it at the fourth plausible answers right because you say none of the above I then we’re into the one of those mats territories as the numbers remember that man those math classes with math professor talk about numbers that don’t exist and you’d go wrap your head around that concept hey so increase decrease no change or any of the above go with it what seems like they are the obvious answer it’ll increase right in fact if I ask you mathematically what the answer is what do you do you take the well it’s now a growing perpetuity so what do you do you take the 100 million / point 10 / point minus point 0 2 which is 1.25 billion this is Magic I just increase the terminal value by 250 million if I make the growth rate 6% it becomes 2 billion by make it six percent it becomes 3 billion this is how you can really consider mean you could talk about value announcements right there right what am I missing when it there must be something I’m missing with no discount rate is it is still the same business you’re growing in the same business ready in other words what’s in my numerator the previous example I said your after-tax operating income is also your cash flow and why was able to do that what’s your growth rate zero if you have a growth rate of zero how much do you need to reinvest nothing so the reason I was able to assume my earnings were equal to my cash flows is because I had no growth what have I done I’ve thrown growth into the equation right that’s a good thing but that growth has to come from some ways and efficiency it’s not going to work why because it’s forever so what has to happen you have to reinvest how much what does it depend on let’s see if what’s a intrinsic equation for growth return on capital x reinvestment rate rights if you do it do a little algebra if I tell you the growth rate is 2% your reinvestment rate is going to be a function of what your return and capitalist let’s try one let’s say the return capital is exactly ten percent how much do you need to reinvest to get to a two percent growth rate two percent is my growth rate ten percent is my return on capital my reinvestment rate therefore has to be 0 point two or twenty percent right so let’s see if you took a hundred million you took our 20 / said you’re going to end up with 80 million in cash flows 80 million / point 1 0 minus point 0 2 is 1 billion I thought growth was good nothing happened you think what if I try four percent growth if you try a four percent growth forty percent of my 100 million leaves so my cash flow becomes 60 million 60 / point 06 is still a billion so the value doesn’t change when growth changes what

what did I just assume that led my terminal value to stay unchanged in other words my return on capital is equal to my cost of capital think in capital budgeting terms if you take a project that is exactly the cost of capital what’s your net present value for the project it’s zero what happens to your company if you take a project with the net present value of zero nothing what if you take 100 project with a net present value of zero nothing thousand nothing if you get that you crack the code and what drives terminal value the terminal value is not driven by what you assume about growth it’s what you assume about excess returns in perpetuity that drive your terminal value if you assume that you weren’t exactly your cost of capital it doesn’t matter what the growth rate is so the next time somebody tells you oh that terminal value equation is so change the growth in look how much it changes they’re not getting it you can’t just change the growth rate this isn’t some math game this is a real business if you change the growth rate you have to think through the consequences of what will it mean in terms of reinvestment what will it mean in terms of cash flows and will my value go up at the only scenario your terminal value is going to go up is if your return on capital forever is greater than your caustic apple in fact if you have a business that owns less than its cause to capital if you increase the growth rate in your terminal value you’ll actually lower the terminal value you can add value do nothing to value or destroy value so the right answer here is any of the above of course you got to cross out the none of the above any of the above it’ll be increasing depending on what you assume about return on capital in perpetuity so that’s the message i’m going to try to reinforce today because if you get that you can you can basically break down terminal value Jordan right right if you take technology that’s constantly getting cheaper and cheaper and cheaper isn’t it plausible you could have a company there’s getting more and more me ask you a question is it getting cheaper and cheaper just for you or is it getting cheaper and cheaper for everybody in your space okay you know what’s going to happen next right the prices you charge your consumers in a sense it got cheaper cheaper just for you and everybody else lived in a world with cause for increasing that’s a huge competitive advantage you can then charge the same price as ever as everybody else and walk away this huge profit a benefit that accrues to everybody is a benefit that accrues to nobody and that’s I think part of the problem is when you hear stories like no this company you know what what happens if this you have to kind of add to the torrent it happens only to this company not to the rest of the space so what happened the technology space is your cost of your inputs keep going down but your output price also will go down because competition will keep pushing that down internet service company that same process right unless it’s something unique to you there’s going to be a price war that’s coming sooner or later and it happens at every one of these businesses where you have an underlying economics that’s driving the cost of your inputs down the cost of your out the price that you charge your output also goes down so everybody ends up in a sense in the same position they were before the cost structure started imploding on you so you got to look for other edges to kind of to get that gain on return on capital ever with now let me take that back I mean in fact let me ask the broad and jordans question his question was in evaluation can capex converge on depreciation can I set net capex 20 I can if I assume what about growth zero growth if you give me that growth you can make capex the what I can’t let happen is for you to keep telling me that operating income will keep growing up going up two percent to you but that you will have no reinvestment to go with it because mathematically though the company would blow up on you your return on capital go to infinity sigue don’t get caught up in the accounting depreciation number the question we are asking is can I keep generating more income with the same acid base the same invested cap in my acid base and the answer has to be no because if I can keep generating more income from then this is this is a goldmine business and unless I can find a way to keep everybody else up so the only scenario you can get away with that is if the government somehow grants me a monopoly lets me charge whatever price I want while having the economics of the business kind of work in my favor for the rest of attorney and if that’s the case and of course that company should be what they’re almost an infinite amount of money because that’s a money machine and that’s why it’s so difficult to think of a scenario I mean I try every year I try to think of it perhaps this outlandish example of a company

that can grow in perpetuity without reinvesting every time I try run into a brick wall somewhere along the way the logic breaks down because it’s very difficult to make that argument and carry its logic I mean you almost have to be in a world where only your company moves and everybody else is kind of static because if everybody is moving your advantages will start dissipating any other questions yes no that’s not what I’m saying I’m saying if you make that assumption then terminal value the growth doesn’t matter if you choose to make a different assumption then have a good reason for it tell me a story about comparative advantage in the long term it doesn’t make a reinvestment go to zero it means you can reinvest less to deliver the same growth rate so if you have a brand name company where you say brand name is this huge long-standing competitive advantage it’s going to last 100 years I’m valium Campbell super coca-cola i’m going to leave the return on capital above the cost of capital even after i get to your 10 i’m okay with that but the new reinvestment rate will then reflect that higher return on capital getting you will get a benefit from growth in perpetuity but that benefit is not unbounded right you still have a reinvestment you guard to bring it every time I grow a little faster I will increase that value but there is a cap to that growth rate because it’s forever it cannot be higher than your risk-free rate that cap can’t disappear so we talk about constraints we’re going to put on the terminal value that keep it from running away from you because if it runs away from you’ve lost control of your DCF yes yeah we go are you doing an analysis in normal terms you’re doing them in real touch okay so you’ll growth is at it at the inflation rate and you have to reinvest to keep your existing capacity at so your capacity stays fixed but your old machines have to get replaced with new machines when they run out right inflation helped you on the price level when you replace your machines what you have to pay more as well in other words you can’t draw on the inflation on the revenue side and say it doesn’t happen in the car side because that would be like this great company if you can pull it off all the more power to you but if everybody in your sector has that benefit your prices are going to start to come down you’re going to start to see that in your margins and your revenues what I’m trying to say this is perhaps categorical I’m almost never dis dogmatic about anything if you have growth in your terminal value then you have to every investment now if you assume a high return on capital I can live with that if you can justify that high return on capital hey so that’s the that’s the message i hope to deliver it’s not that everybody has to earn a return on capital equal to the cost of capital that’s too dogmatic for me but if you assume perpetual growth I want to see how you deliver that growth because if I don’t make you think about that and growth becomes this mathematical number that you just change and move towards your cause to capital u terminal value just explodes out on you so let’s take pick up where we left off on wednesday we were talking about growth and we were talking about how to estimate growth using fundamentals right and reviewing very quickly every single approach that we talked about dependent on two things how much you reinvesting how well are you reinvested so Christie helped me out again when we talked about how much you are reinvesting how do we measure that what are you how did we measure the reinvestment rate what do we do we took the net capex plus change in working capital and / by the Onyx right and we measure how well you reinvested joseph we took the earnings and / the invested capital book value of equity but both those measures worked only because we had positive earnings right if you have negative earnings we see already how this these approaches are going to break down because you have negative earnings what’s your reinvestment rate going to look like you take and reinvestment divided by negative number its negative your return capital will be negative number two will be negative you think this is very convenient negative times negative is positive but if you take a negative number and you grow it at a positive wrecked I know this sounds incredibly convoluted negative number growing is going to become a more negative number what I’m trying to say is the normal way we get out of a problem when you have when you’re valuing companies the values to lowes we hire use a higher growth rate that no longer works if you’re losing money and that’s at the core of why we run into trouble with money losing companies because we’re trained to play with the growth rain and it’s not working so one easy way out is replace a negative number with a positive number right which is what we

do and we normalize numbers when we replace a negative earnings but let’s look at the more difficult scenario what if you’re valuing a young startup or infrastructure company that’s building toll roads it’s got negative earnings not because it’s a badly managed badly run company but because of where it is in the process right so your task is to make the negative earnings into positive earnings you also want to make sure that as you’re doing this you’re taking into account the fact that these companies still have to grow they grow their revenues rather than the operating income and to create the growth they have to reinvest so all the rules we talked about still apply but we no longer have that nice neat equation to use to compute how much is reinvest so I’m going to suggest a three-step process and this is a process i follow repeatedly when I value young startups but pretty much with any company when you have a negative number in your earnings keep moving up the income statement till he hit a positive number sounds like desperation done but it is the expiration time right and often the first positive number you going ahead is revenues good we have something to work with now right so we start with revenues and we grow revenues first top-line growth why because if you have negative earnings that’s where you got to go with top-line growth so you got small revenues going into big revenues second stuff what do you have right now you’re losing money right you have negative margins I know this sounds incredibly simplistic but you got to make those negative margins into positive margins so the second big number you’re going to focus on is what’s my target margin going to be what margin do I think my company can earn assuming it turns a corner and becomes a healthy company now that’s a tough number i’m not saying it’s easy but that number has to be estimated and you in a sense have to coax your company from where it is today losing money to that money-making entity so you got to make negative margins into positive margins to think about your your your modern now you have revenues now going from small to big numbers your negative margins have become positive margins you almost a you now have positive earnings then I’m going to ask your third question you made a small revenues in the big revenues yet revenue growth did you reinvest enough to sustain it because just like everywhere else to grow you have to reinvest and here I’m going to introduce a ratio you might not have seen so far it’s called the sales to capital ratio what it is is revenue / invested capital the way to think about this is how much additional revenue do i get for every dollar of additional capital i put into this business the higher that number the more efficiently you’re delivering revenues so you’re in a business like technology you might say i can deliver six dollars of revenues for every dollar of capital if you’re in the auto business you’ll be lucky to get a dollar fifty in revenue for a dollar in dollar fifty and revenue for every dollar in capital using how’s that going to help me it’s actually very simple I’m going to take the change in revenue every year I’m going to use the sales to capital ratio to figure out how much you would have had to reinvest in that year and that’s going to become my reinvestment net capex and change in working capital all consolidating the number so three-step process revenue growth makes more revenues into big revenues the target margin makes you negative earnings into positive earnings the sales to capital ratio allows you to estimate the reinvestment every year using why don’t you just use capex depreciation and working capital from last year you take a young startup you look at capex depreciation working capital as to you might as well and not looked at it it’s a completely noisy useless number because there’s not much there so the more you can tie things to your revenues the better off you are because that’s going to be the driver for growth is you have to start with revenue growth and work done so I’m going to take an example this is way back in time fact these numbers look hopelessly optimistic in hindsight but this was when serious had bought XM radio and the whole world looked like it’s in front of them everybody was going to have satellite radio in their cars and this was the future so I’ll plead guilty to the numbers being over optimistic but actually with the numbers i got my estimates i actually ended up with the value which was one-half of the market price if I was being optimistic the market has been twice as optimistic so I take you through the process here’s what serious look like when I sat down to value them there are a hundred and eighty seven million dollars in revenues tiny revenues and in operating loss of 787 million we are in trouble right your operating loss isn’t almost four times your entire revenue so there and it’s not surprising why that was because they were spending the money on infrastructure to kind of set up for future growth and was showing up as losses my task is laid out for me right to value serious first step is I’ve got to make the small revenues and big revenues so here’s what I did I projected out revenues of about nine billion in 10 years you say how do you

come up with nine billion their revenues came primarily from advertising so I looked at the entire radio advertising market i looked at the big players i tried to decide and this was my judgment on what portion of the market would end up with serious that nine-point-oh 35 billion reflects the collection of subscription revenues and advertising revenues that will become their base using but that’s an estimate of course it’s an estimate you think there’s somebody out there including somebody at Ceres who actually has knees listener in an envelope somewhere they know what nobody knows it’s your estimate versus somebody else’s what I’m trying to say is be willing to be wrong because you’re not willing to be wrong you will never get started and branding these companies get started then you can come back circle back and say maybe that number was too high so I’m essentially making small revenues in the big revenues I made the small company so one-third of my problem is now solved I’ve made the company into a big company at least in my spreadsheet I’ve got a second really big problem right minus for twenty percent operating margin if that stays at minus for twenty percent I know exactly what the company is worth it’s worth noting it’s going to go out of business so I spent some time trying to get this number and I’m not sure I got the right number I want to get a sense of what the operating margin is going to look like for serious once it gets to steady state I know it’s going to lose money next year two years or maybe even five years out so the second step in the process is I projected a target margin and here i use the margins of the largest players in this business clear channel in fact is the biggest player its margin is close to twenty percent i assume that they would converge on twenty percent so you can see assumptions are piling on top of assumptions but I’ve got to keep moving otherwise I’m not going to get to the end of the value so my operating margin goes from minus 4 22 + 19 point six percent say how do you come up with the middle numbers I actually use a very simple algorithm see if we can figure out what it is how did I get from minus 4 22 minus not a second decimal point I must be doing something spectacularly precise right there’s a very simplistic algorithm Esther how I got from your 02 01 your 12 you’re too what do it it’s actually a step but it’s actually a preset step so the spreadsheet actually filled out the 10 years where am i right now minus 4 20 right where do I want to be plus 20 what’s the distance between the two for 40 right i divided by 2 I told you it’s simplistic for 40 divided by 2 is a two twenty percent improvement there’s my improvement in year one now I met minus 200 I want to be at plus 20 what distance to 20 I took half the distance so each year all I’m doing is taking the half saying why half why not in fact in this spreadsheet I said it to have because I feel optimistic that margin will improve le quickly and then I let you change it change it in what sense yes since evaluation is the new disagree with me I have to show you the number that you can show your disagreement and so let’s say you came to me and said you know what you’re being way too optimistic about the pathway to profitability that’s what this is right it’s going to be a lot more rocky then my suggestion use make the half into a quarter you know what that’s going to do I’m going to still end up at plus ready but I’m going to lose a lot more money for a longer period it’s about it when you do these valuations of small companies you have to keep the doors open to your input so if somebody says you are wrong about that you’re not scramming so what do I change your so if somebody I don’t know this business somebody says you’re being way too optimistic that this business will improve that much I’ll make a half into a quarter i’ll still lose money but I lose money for a longer period and I will lose more money for the earlier years the last thing I want to be doing with a company like serious like uber is sitting there in your three asking what would the operating margin be in your three because I know exactly what that’ll cause you’ll cause my hair to fall out it caused me to free card and I’ll stop doing the valuation so I want to keep my eyes on that end game here the end game is this is the number that I’m most worried about the nineteen point five seven the middle numbers have a much lesser impact on value and I’m willing to concede them to you if you made a stand and said I think the improvement is going to be one-third or one quarter so take it the effective value is going to be relatively small so if you look at my last column that is my operating loss by yer and you can see initially I’m expecting it to actually get worse before it gets better why because they’re growing fast and as they grow fast the loss is kind of explored out on you as the margin improves the operating loss becomes an operating profit so my revenues come first my MA comes next what’s the one what’s the one thing I haven’t dealt with yet this

revenue going from one eighty seven to nine billion is going to take some reinvestment right so here’s the last piece of the puzzle I took the change in revenue every 0 based on my revenue growth in this sector did you look at this area it’s a pretty infrastructure heavy sector the sales too invested capital ratio is a dollar fifty which means for every dollar fifteen additional revenues would look like businesses are reinvesting about a dollar see what I’m going to do that in your one to get the additional revenue of 375 million you divide by 1.5 oh there’s my reinvestment in your one so each year I’m taking the change in revenue in that year and dividing by myself to invest in capital ratio and this is why I said if you have a high sales too invested capital ratio that’s an advantage because it means you can get more revenue for Less reinvestment Jordan in fact I’ve heard arguments in both sides which is there are people who say well initially want you get the maybe in some sectors you might actually be able to get more revenues with relatively little reinvestment but as the business gets more competitive like uber you might actually see a decreasing or you might have low upfront high you the question asking is why is it 1.5 every year doesn’t have to be if you have enough information to finesse it and say large companies have much so within the sector look across companies may be there are differences in sales invested capital by size of the business and you can use that then to have different numbers as you go through time so that approach of using sales of capital is kind of flexible enough to allow you to change numbers as you go along to reflect economies of scale or whatever else you think will happen within the business yes it’s the same definition that we use for return on invested capital right which is what that plus equity minus cash never ever when you are asked to do invest in capital and this is just my personal you don’t go with the asset side of the balance sheet you will get into trouble do you see what i mean by the asset side of the balance sheet you stop plant and equipment and then he said what do i do it good well you’re going to run into all these roadblocks that oh my god what do we do next whereas we go with the debt plus equity minus cash it’s far simpler it’s far more consistent but it’s all book value book value that plus book value equity minus cash so that’s what the invested capital is because when you do return on capital which is the analog when you have a mature company it’s based on book value as well because that’s what you put into your business if you have a great business you can invest 100 and get back 350 so it measures the efficiency of your investment so if you can get great growth with relatively little reinvestment the only way I can show that is by allowing you to use book value when you do reinvestment hey if you’re a business will return on capital is equal to cost of capital guess what’s going to happen then the book value is going to converge on market value you’re going to gain nothing from this additional growth and things are going to start to dissipate under you okay so three big numbers revenue growth target margin sales investment capital and if you look at most of my evaluations online their rest on those three big numbers and I want them to rest on three numbers rather than 35 numbers because then you can say I don’t like that number i like that number i don’t like that number that way you can focus on what he can change and see the effect on evaluation so revenue growth measures your growth potential the target margin measures your profitability potential your sales the capital ratio measures the quality of your reinvestment hum or the quality of your growth it’s are basically the same thing now one of the nice things about doing a discounted cash flow valuation is as you create this company on your spreadsheet and its really I mean you’re playing God right here essentially you’re taking a small company in making this huge profitable company you could please should stop it as a question am i comfortable with the company I am creating on my own spreadsheet you see what I mean by that because it’s easy to get carried away you can create some astronomically wonderful companies on your spreadsheet without even thinking about it so one thing I do to kind of keep myself i would say honest because i’m not that honest but it leads to be accountable to myself is I take that reinvestment which we think about in free cash flow is that what you take art of your earnings to get to cash flows but that reinvestment actually serves another purpose because its book value it’s also the change in your invested capital as a company in a year-to-year basis you see where I’m going with this if you take serious they had invested capital on their books of 1.65 seven billion at the start of the period so the book value of equity plus book value of that minus cash for series of the stock each year that I reinvest it adds on to the capital invested so I can keep track of that and because I’m

assuming an operating income from the margin i can divide my estimate of the operating margin with my estimate of the invested capital in this company I think of it as an imputed return on capital that I’m assuming for the company saying what he planned to do with it see that 15.8 1% in your 10 I have to be comfortable with that if I want this valuation to stand if I look at that 15.8 1% and said you know what that’s way too high my spreadsheet is sending a message to me saying go do something about it because I created this this isn’t some company that’s been no thrust upon me this is a company I created I have to be okay with my own creation if I created a Frankenstein this is my last chance to kill it before it comes to life I was ok with the 15.8 1% the reason I was ok so I looked again at Clear Channel and the other companies in the sector and the return on cap in the sector was roughly sixteen percent I said you know what 15.8 one percent is a pretty good return on capital but in this business because infrastructure is so expensive and difficult but there’s always a flip side to a negative right the negative in a toll road infrastructure companies what you have to reinvest a lot to get in the business what’s a positive you have to reinvest a lot to get into the business you see how this is going to help you later down throat is when you get to your 10 a year 15 you make this company a steady-state company you can draw on that and say it’s going to be difficult for others to enter the company I mean last to a week and a half ago when i took technology companies and i broke them down bye bye age on my web on my blog I actually broke and only one in five technology companies is less than Ted it’s an aging sector there are about forty percent of all technology companies are older than 25 years you think that’s not that long I mean I described this as technology companies age in dog years that 25 year old technology companies like a 75 year old consumer product company okay and the life cycles of technology companies are short much shorter than the more intense they grow faster it go quicker than most manufacturing companies because they don’t need that capital investment they can grow with red they can scale up easily that’s an advantage right but you know what makes it a disadvantage is they can other companies can also scale up quickly which is the reason they can’t last for as long as building an AT&T 100 years ago did so in this case that’s effectively what this imputed return on capital is setting is hey are you okay with this if I receive let’s say this had become this has been one hundred and fifty-eight percent it’s too high right so what’s the number i would go change if i end up with two higher return on capital in your 10 why i’m ending up to a higher return capital i’m not reinvesting enough right what’s the number that gives me my reinvestment my cells the capital ratio if I make the 1.5 into 1.2 my return capital is going to decrease there’s a feedback loop in your DCF that it makes sense for you to watch because it tells you hey maybe you’ve been too optimistic about reinvestment or not optimistic enough and the way to see that feedback loop is by keeping track of that return on capital over time any questions so let’s bring all of these different growth measures into one picture okay so the first thing to ask when you think you sit down to estimate growth is what i’m estimating growth in is a growth in earnings or is a growth in operating income if its growth in equity earnings you can always take the lazy way out and look at what analysts are projecting is growth with all the baggage that comes with it you can go with historical growth which is really makes your valuation into a modeling exercise or you can do fundamentals if you decide to go the fundamental road with the equity otic you have to decide whether you going to focus on earnings per share or net income if its earnings per share with stable return on equity you’re going to do the retention ratio times return equity if it’s a changing return equity at the deficiency component if you do net income with stable to turn equity all you do is replace retention ratio with the equity reinvestment rate reminder again all that’s different is an equity reinvestment rate is not capped at a hundred percent in Florida at zero it can be more than a hundred or less than zero and the same thing with operating income if you have negative earnings three-step process revenue growth target margin sells invested capital if you’re clear about your pathway when you sit down to value company you’re not going to be because I think one of the reasons is people think that by having 16 different estimates of growth so say hi and let me take the analyst estimate historical let me all throw it throw it all in a pot I’m going to end up with a better estimate that’s not the best way to estimate growth

choose a path and take your process all the way down that path to come up with an estimate of growth that you’re comfortable with then use the feedback loop in your own valuation to decide whether you’re okay with your own assumptions any questions about growth can you have a company with negative growth sure your negative growth you might have negative reinvestment rate so what does that mean you’re shrinking your company you’re liquidating your company every year that’s okay in fact there are many companies where I wish that happened right because basically the company’s worth more as a smaller company rather than a bigger company so leave open that door that your expected growth rate can in fact be a negative number yes you could and it’s in fact a fairly simple assumption to bring in right because it’s the end of the game so when I project margins always do pre-tax operating margins that way I can leave open the door that tax rates can be different but I’ll tell you one reason doesn’t even have to be a change in the tax code it can be changing geographical mix of your revenues right so if you are telling me more of your revenues come from Asia that is consequence for my tax rate so do everything on a pre-tax basis bring in the tax rate at the end of the game and it’s with everything else you can make your judgment calls on whether that number should be a fixed number number from last year a number that you think would be very different in the future so now let’s talk about the terminal value none big number of course and in fact we need it because without it what kind of sunk right because the company can go on forever this is your way of putting closure that’s what a terminal value does and as we said earlier while there are different ways the one way that should never be used in a terminal value calculation is using a multiple if you’re doing an intrinsic valuation you can do liquidation value you can do stable growth model either in perpetuity or for a finite time period when I value private businesses I tend to use liquidation valued by the businesses because many private businesses it’s really unrealistic to assume that this business will go on forever it’s usually the life of the least you own a store when the lease ends the business might have so leave open that door again of liquidation value don’t shut it that quickly because there might be some businesses we’re better off valuing based on a liquidation value rather than making assumptions about perpetuate ease so let’s talk about the rules that you need to follow to make sure your terminal value doesn’t run away from you so if you follow these four rules I promise you you will control your terminal value doesn’t mean you’re always going to be comfortable with the number but you will at least know what’s driving your number where it is first assuming you go with the growing perpetuity model remember that that growth rate has to be less than or equal to the growth rate of the economy in which operate which means that that number is going to be a function the inflation of the currency you decide to do the valuation and because higher inflation currencies you’ll have a little more leeway it’ll also reflect the assumptions you’re making about whether this company is going to stay a local company or a global company because I’d might affect the growth rate in fact I have introduced this this this rule before but I will introduce the gain in the context of terminal value when you get de terminal value use your risk-free rate as a cap on your growth rate in perpetuity that’s really bad news for you and US dollar terms of your terms right now right because what have I just said that your growth rate today if you’re doing evaluation in US dollars cannot exceed what it’s at eboard rage right now two and a quarter percent it actually went up fairmount and Friday two and a quarter percent you think that’s terrible you doing it in yours just be glad you’re not doing it in yours right Neuros what’s your it’s going to be about half a person you think that’s awful that’s so pessimistic you know why I’m forcing you to be pessimistic with your growth rate did that half a percent help you elsewhere an evaluation when you did your cost of capital you are celebrating the half of it looks like such a low risk free rate miss it wonderful no keep your risk-free rate i’ll come back and hold you accountable somewhere else what will kill your valuations you leave the risk-free rate at half a percent and decide to use a three percent nominal growth read new numerator because that’s what europe has grown at historically that i promise you will deliver to higher value for your company because in a sense you’ve made incompatible assumptions within your own valuation so if somebody i see why should the risk-free rate do you have anything to do with the nominal growth rate you can give them a long drawn-out economic ads so which is a risk-free rate is expected inflation plus an expected real interest rate and the growth rate in the economy is expected inflation plus an expected real growth rate but there’s a simpler explanation which is if your help by one you’ve got to kind of cut back on the other so the low risk free rate is helping you on the disc contract and

this is why only when you talked about risk relates i said don’t try to normalize the risk-free rate i’ll give you a way to kind of keep things in sick this is way of keeping things in sync is by setting the growth rate at less than or equal to the risk credit and just be glad you’re not doing things in danish krone right heard about in Denmark what’s happened if you borrow money in Denmark this is almost so mind-boggling you can’t even wrap your head around it the bank sends you a check every month you borrow money they send you a check every month you lend money you send a check out to the guy you’ll earn money to this is something fundamentally wrong with this process right hey there is created in Denmark is less than zero I don’t even know what to make of it but it means i don’t have value a Danish company I better factor that in somewhere along the way and that basically will show up both there’s a lower discount rate in a much lower growth rate so keep that as a cap but that’s a cap it doesn’t mean every company has to go at 2.25 percent right your company can grow it to it can grow at one it can go at half get into a zero percent of you forever can it go 2-1 percent do forever what happens to a cash flow if I said the growth rate at minus 1 percent do forever so peaks in your terminal year and then it gets smaller and smaller and effectively disappears right which is actually the way life cycles look in practice so leave open the possibility that your company might be that the company that actually has negative growth rate in perpetuity it’s ok you can have minus 1 percent growth forever or minus 2 percent growth forever after your 5 it essentially is a way of saying my company peaks in my terminally and then get smaller so that’s the first rule any questions on that so make sure your growth rate does not exceed your risk-free rate yes let’s let’s pause that when you say improve your business where does it show for a mature company first it live shows a higher return on capital so that’s a higher return on capital story that’s the story you’re saying even if you assume it’s a permanent higher return on capital the way it’s going to show up is with that same growth rate now you will get a much lower reinvestment rate you will stood reward these companies but the way that reward is going to manifest itself is not by giving them a higher growth rate but by giving them a lower reinvestment rate now I have terminal value if you believe that that high return capital will lead them to read by s’more and grow faster then give them a growth theory so what that’ll mean is you’ve introduced a growth period for mature companies that might otherwise have been mature companies already so you have the levers under your control it does it doesn’t have to show up as you greet AG in your terminal value it can show up as a longer growth period a higher return on capital lower e the lots of places we can reward companies if we believe that the lower is free rate is helping them that’s right that’s a high growth period right so basically all that means is you will have a five-year pit window or a three-year window whatever your QE window will be will become a high growth period the only note I would add is what Jordan race yesterday which is if you have low risk free rates you’re not the only one your comparators are getting it and my fear is you could be building these high growth pills for every company when in fact collectively companies are all borrowing at the lower rate there’s three investing all at this what they think is this better return on capital they all produce more stuff and then it’ll Carranza who’s going to buy all this stuff so that’s I think one of the concerns I have with giving companies this little bonus from lower discredits is we all partake in those lower as credits okay and that I think will mean that the benefits are going to be a lot smaller than we think they are collectively for companies so any other questions on so if you pick a higher inflation currency will get more leeway in your growth rate but your caustic apple also be higher yep so what so tell me what your concern is with you see you growth in that emerging market currency will be higher so what do you already have to do then to do a dollar valuation convert it back into so

the first thing is if it’s a pure inflation difference it’s driving the girl trade your exchange rate has to change for it drink if it’s real growth that you’re getting in Asia then you have to do what I suggested earlier give them a growth periods if you believe that coca-cola gets a new lease of life the cars entering Asia the way to reflect that is by giving them a growth window where they grow faster because they’re growing in Asia but after that there is no benefit you get from having higher inflation currencies delivering more of your growth rate because by the time you converted back into the domestic currency in which you’re doing the valuation that benefit will disappear so if you have higher growth in emerging markets and it’s higher real growth give them a higher growth window don’t put them in terminal value yet hey but once that growth is ended the rule still applies Cheney the questions so that’s the first rule here’s the second one don’t wait too long to put your company into stable growth what’s too long I am obviously talking on no 25 year 30-year windows it’s almost mind-bogglingly long I have never done it this kind of cash flow evaluation with longer than a 10 year growth window so play devil’s advocate saying but there are companies that have grown for longer than 10 years right so Nathan Microsoft IBM Google then think about it why are we able to name these companies because of the exception rather than the rule right you don’t ever want to value a company to be the exception right from the start because then what’s your upside i mean the analogy I would give it some book that some guy who runs in the center field twenty-one-year-old runs inside of here in Yankee say we said that’s the next Mickey Mantle hey yourself setting yourself for 15 years of disappointment right your best-case scenarios ‘is Mickey Mantle you I told you so no surprises here you can’t value a company to be the next Google let me take it back you can value a company as if it’s an ex Google and invested in on that basis but then pray and hope that it is the next Google because everything beyond that will now be a negative surprise so when you think about growth periods and you start saying should I use five should i use ten should i use 15 especially with these promising companies box right it’s going to go public sooner or later north box does it basically provides in the storage space it’s a fastest growing young company out there so quickest I think to a billion dollars and revenues of any of those companies including goober you say well that’s a great company i’m going to use a long growth beer and you said five ten i’m going to show you a graph that might short you later okay that might sober you up on the growth bridge but just be cautious about not allowing for these extended growth periods which you cannot deliver and remember it’s not growth that drives value it’s what kind of returns and capital you can make with that growth rate right so if you can grow for 50 years or 80 years it’s not going to create value unless you earn a return on capital greater than the cost of capital what the first session I talked about narratives qualitative analyses knowing what a business done knowing what its competition is this is the place that shows up the stronger and more sustainable the competitive Vantage’s for your company so there is a use for that corporate strategy class you talk right so if you can make it practical here’s where it comes in think about the compared advantages think it through the process because if you believe your company is strong and sustainable competitive advantages the way it shows up is as a higher return on capital and you can essentially give them a longer growth period because of that so when you think about putting your company into stable growth that’s what you’re thinking about don’t think about what the growth rate was last year how promising things look ask yourself what the competitive advantage of this company so whether it’s uber or box this is a question that’s tough to answer right this is a young company is what will their competitive advantages be but unless you grapple with that question it’s going to be very difficult for you to come up with a sensible value for your company fact let’s say you know let’s say go but what do you think it’s compared to advantage is going to be instead we and we know right now it’s a first player in many of these it’s in Moore city but think through the game five years out you got all these car sharing companies what’s going to make if you think uber is going to be the special one where it’s competitive advantage is going to come from one is capital which is obviously play the problem though is with capital and I was talking to somebody from uber very high up last week and is complaining there’s too much capital coming into young startups you know why it’s complaining because lift just got an influx of capital and using the capital lift is cutting prices in la if you’ve taken

over in LA it’s 92 cents a mile which is obscenely low which is you drive 45 minutes in LA in the taxi an uber it cost you twenty eight dollars that guy’s not even butt lift is comment because so capital again is an advantage if you have it and nobody else does so Hooper’s down into the spring st. tomorrow and let the bubble bush let nobody else be able to get capital because they’ve got three billion capital that makes them but capital is a dangerous game you have three billion in capital you think that’s your advantage how much is Apple have 170 billion there are players with a lot more cap cash in their pockets so if that’s their advantage then it’s going to wither away all you need is a big player like Google to come into the game with electric cars throw 10 billion in and there goes your capital advantage brand and and they’re working on it right what’s and in terms of car sharing what’s the brand thing is you hit that app it’s midnight you’re the corner you you could be mugged at any time you want the card to get there within five minutes ago my God where is it where is it where is it so part of the branding is is it reliable and part of the reason those stories over the last six months you’ve heard about uber is so troubling is if you decide that part of the bed is you want a nice safe ride you might say those stories of making it be unfair to uber but they have to deal with it they have to deal with it really quickly because we’re undercuts that advantage they have what else and lets me specific what exactly but how will the show us what a network effects what does that mean the more users you have it actually gets you easier to get additional users right the classic incremental effects is if you think about ebay network effect is you want to go where everybody else is because otherwise what are you going to get from auction item so that’s a classic network benefit lot more cars a lot more cars you have a lot more drivers so basically there’s a network effect but is it a local network effect our global network effect it’s a local network effect which means you got to fight this out city by city it could be uber in New York and lift in LA which actually will affect how much you value the company at because it will mean what so think through these things because it might be qualitative but it’s going to determine how long you let this company grow what kind of return on capital you give it and what you will do to this company when you make it at steady state company so it is true that there are some firms that own excess return yes sir let me asking question this Trevor collecting know the answer to that question you think no nobody does that’s what all I’m saying is we’re all in a state of uncertainty you have to make your best judgment with the information you have in front of you that’s all you can do if you put the weight of the world on your shoulders that I have to get this right you’re never going to complete the evaluation you’re right it’s a lot of uncertain you have to make judgments but if you wait two things settle down to make your judgment everybody will know by that right so this is part of the process of being first in to these young companies is whether you’re thinking through this process a little more seriously than everybody else and I’ll tell you your biggest advantage why most people investing in uber is it because they’ve taught through these networking benefits it’s because they want to be there when it goes public they’re in there like sheep for the same reason the sheep are there because the other sheep are there and if it’s going to go public they don’t want to be left out and it is true when working with very little but we’re working against people working with nothing at all so it’s you have to do the best you can and you’re going to be wrong and you know what the best way to deal with being wrong is don’t put all your money nobre have 20 and it’s a diversification the classic reason for diversification actually gets stronger when you have companies like uber because it’s hubris to say I know uber is going to be the winner i’m going to put all my money and over how do you know right so everything we talked about in the context of diversification becomes you have to talk about it in spades when you have a company like uber and in fact the reason i brought up this issue of return on capital is Mackenzie actually has a very specific it’s pretty dogmatic when you get to stay steady state a mature company mature companies are required to earn a return on capital e equal to the cost of capital so in McKinsey valuations there is no growth in the terminal value so if you look at the McKinsey book which actually came out about the same time as my first valuation book look at the terminal value

it’s no plat which is Mackenzie’s version of after-tax operating income inhabit x 1 minus t / cost of capital there’s no G so for the first 15 years or so in the McKinsey book was out people would email me saying how come there’s no G in the terminal value equation in the McKinsey book to which my responses why aren’t you emailing Mackenzie wait but they we had the same publisher so they must have thought we all hung hung out together somewhere now and the answer is very simple if you read the rest of the chapter they’re very specific and this is built into McKenzie DCF spreadsheets is once you get to steady-state your return on capital is equal to the cost of capital when the return on cap is equal to the cost of capital what we say happens a value growth it goes away there is no so might as well use a zero growth rate because you get the same terminal values using a two percent under three percent growth ray the only problem is Mackenzie itself has some research that undercuts that assumption it comes from a magazine called McKinsey quarterly which is actually one of my favorite magazine street because it’s actually it’s a great it’s free get on the McKenzie website register they do a lot of applied corporate finance and valuation work so here’s an example of a paper that they did so these are McKenzie consultants they get together they look at what the return on capital is for companies is relative the cost capital doesn’t go to the caustic Apple like to assume in the McKinsey they looked across companies and they found that while growth rates converging the growth rate of the economy in other words the assumption that growth goes to the risk-free rate is a reasonable assumption that the returns on capital of companies actually stayed above the caustic app for decades so that’s why I said I’m not dogmatic if you showed me a company and said in this company I think the return on capital is going to stay above the cost of capital I think Mackenzie’s own research backs it up if you’re valuing a brand name company or an infrastructure company that it’s okay to assume the return on capital is above the cost of capital even though your growth hits the stable growth rate in five years or ten years but think through that because I think that that’s an issue we run into end we’ve already dealt with this earlier but there are times you will be told that this is a special company the cash flows are growing at the inflation rate and they’re all you’re doing is placing old capex with new capex and maintaining capacity so it’s okay for capex to offset depreciation net capex is zero I think it’s hard coded into some investment banking DCFS capex equal to depreciation is hard court in the terminal value the reason of course it doesn’t work is if inflation is helping you when you sell stuff to people guess what it’s hurting you when you replace old assets which effectively means and even when the growth rate is equal to the inflation rate you can’t get away assuming that mid-cap x is 0 so that’s something that you constantly have to check your terminal value on find the Paris stop in the process check all your numbers to make sure your internally consistent I’ve used this this valuation triangle analogy before valuation triangle you have three sides of triangle your cash flows growth and risk and I said they have to be consistent so we have a high growth company you tend of high-growth hide reinvestment high-risk you make it a mature company which is what you’re in steady state you have low growth you have the reinvestment to go with that low growth which is low reinvestment but you also have to give the company a cost of capital of a mature company so if you have a cost of capital of twelve percent of fifteen percent right now it’s a risky company don’t leave that cost to capital a twelve to fifteen percent once you make the company and stable company because as it becomes mature its cost of capital will have to converge on that of a mature company so it’s not just a growth rate that changes it’s everything else and the reinvestment assumption that you make in steady state has to be consistent with your growth rate in the return on capital you’re assuming to the company so that’s the last big number in the valuations and think about you got cash flows you got growth rates you got discount rates and you’ve got the terminal value those four numbers will it be embedded in every discounted cash flow renovation so here’s how I’m going to bring this to closure I know that you haven’t started the DCF for your company I know I just noticed in my stomach in fact I know some of you haven’t even picked the company to do your DCF all you’ve thought about the company you’ve gotten very close you almost touched company but you haven’t got that so but somewhere in the next three weeks you will have to do a DCF and you’re going to go back and look through your notes and you’re going to be bamboozled but all the different DC of models which model do i use I want to take you through a very quick journey through all of these different models and talk about how you pick the right DCF model for your company notice how i phrase that I don’t say the right DCF model period because there is no one model it fits

every company so part of this process evaluation is picking the right company picking the right model so at this stage in the process we have cash flows you have a discount rate we have a growth rate you have to decide what cash flow you want to discount what are your choices you can discount evidence you can discount free cash or equity you can discount free cash flow to the firm what are you choices in discount rates you can use cost of equity you can use cost of capital what are your choices on growth you can have stable growth already in which case you’re done in five minutes you can have a high-growth peer and then stable growth a high-growth pin and a transition phase or a growth rate that varies every year so if you think about it your choices are in front of you and the question is how do you bring these choices together so here’s the first thing to think about should I value the business we should a value equity in the business deceive the first for candor already come to should I value the business travel when we did when we started this process what did I say if you do it right what happens you get the same value so this is a pragmatic charge which is going to be easier to do is it easy to value the business of value equity to value the business what do you need you need free cash flows to the firm right which are pre dat cash flows to value equity you need cash flows after debt payments which are after interest payments and principal payments so we went through that freak asteroid equity computational a couple of sessions ago and and there were two ways i computed one was this long way where i had to figure out principal repayments and new dead issues but i also gave you a shortcut right where you took the net capex times one minus debt ratio and to use the shortcut what did i say you have to assume stable dead there’s a tiebreaker if you have a company where you look at the decoration you’re okay with it being the debt ratio forever and it’s going to be a relatively small number of companies and free cash or equity works fine but if you have changing debt ratios doing free cash or equity becomes a nightmare see when would that debt ratios change well either you have a company very little debt now that you expect to increase its debt ratio over time or a company like Petrobras which is a huge amount of debt that has to decrease its debt ratio you’re better off valuing the phone so first fork in the road ask yourself does this company have stable leverage if it a stable leverage you can do an equity valuation if it doesn’t you’re better off valuing the entire business let’s say you decide to go the equity rod what are you two choices you can value based on dividend so you can value based on free cash for equity let me take away one of those choices if you can estimate free cash or equity never ever use a dividend discount model it’s lazy it’s sloppy and leave you with some strange numbers for companies let me take Berkshire Hathaway the dividend discount model what’s the value equity zero the company’s never paid a dividend absurd right but that’s because you’re taking the easy way out you’re looking at the dividend if you cannot compute free cash flow equity then you can say I have no choice I have to use a dividend discount model you think when would that be what do I need to compute freakish word equity I need to start with net income then I need cap X minus depreciation I need debt ratio and I need change in working capital right I can always do that at the financial statements in front of me when are you going to have most the most difficulty coming up with netgear exchange and working capital in debt ratio private company you might have a little difficulty but as long as you have the full financials for a private company I can do it but if you have a bank or an insurance company it’s a nightmare try it so already I give you the last vestiges of the dividend discount model it’s because you had no choice use the dividend discount model because you could not estimate free cash or equity that used to be my defense for using the dividend discount model for banks under 2008 I no longer use the defense I have to come up with a different answer now but that was the reason I say you know what i’m using the dividend discount model because i have no choice if you can estimate the free cash flow equity just use it its potential dividend you think but I had to make assumptions to get there it’s a cash flow right let’s write then the statement of cash flows so if you take the equity branch then look at when you can estimate freak asteroid equity if you can estimate free cash short equity go with the Freak nationalist equity so firm versus equity which one do you pick whether your debt ratio is stable or not if you go the equity route dividends with its free cash flow equity you can follow through on the branch now once you decide to do a firmer and equity valuation your dis country it kind of comes out of that choice right because if you are estimating cash flows to equity whether its dividends of free cash flow equity your discount rate always has to be a cost of equity if your cash flows are pre debt cash flows here this contract has to be a cost of capital if your cash

flows are in one currency or discard rate isn’t being exactly the same currency and if you decide to go real in other words take inflation I’d make sure your discount rate is also real so you estimate cash flows your discard rate has to match up toy it’s not even a choice you choose the cash flow your discount rate gets use of you which brings me to that growth question let’s say you’re valuing anybody here valium Toyota know coca-cola McDonald’s the reason I bring these up and these are companies we are stretching to find any reason to give them high growth anymore McDonald’s is reported declining grow declining revenues on same-store so in a sense this is a company at best case scenario you might be looking at one percent growth maybe one and a half percent growth even in nominal terms you just hit the jackpot in evaluation why because if you have a company growing at less than the growth rate of the economy already what can you see that it’s already a mature company in which case you need only three numbers to value the company right close next year Kosta capital growth rate you’re done no spreadsheet needed you could probably do it in the back of an envelope right now and say I’m done with my evaluation can you take a look at it don’t do it now no but if you have a company that is growing at less than the growth rate of the economy it’s a mature company there’s a cost of capital that reflects that maturity you can essentially use a stable growth model you don’t need to wait till you’re ten to computer terminal value can do it right now and that’ll be the value today if you have a company with any growth then we talked about you know some reason to believe that a company might have rediscovered growth to low interest rates give them a growth window where you allow them to earn a higher return on capital and a higher growth rate this could be the case if you even if you have emerging market drop is you can say this company is rediscovered its youth at least temporarily give them a high-growth window and then drop them off to stable growth that’s a two-stage model if you have a company where the growth rate is thirty forty fifty percent you probably have to have a transition phase you know what i mean by transition phase it’s not going to go from 52 to overnight you might say over three or a four year period i’m going to let the growth decline so basically when you think about growth those are your choices you’re either already in stable growth you have a temporary high growth phase followed by stable growth or you have growth kind of changing over time so I think of this as the equivalent of playing in a Lego box it’s been a long time since we played with Lego but you know if you take LEGO pieces and you try to fit them together and they don’t go together you can try for the rest of eternity but they’re never going to fit but basically there are three pieces three compartments in my Lego box it’s a cash-flow Lego there’s the discount rate Lego in the growth Lego you put them together you got a DCF model so you can take out the cash flow to equity cash flow to the firm you haven’t seen these Legos if you guys should create these Legos so people can try them evaluation but every DCF model is just a collection of those three pieces and if you try to force a cost of equity with a cash flow to the firm piece things are going to start breaking so every discounted cash flow modeling system is this a collection of the assumptions you make of cash flows growth and rest take a look at your company to make a judgment and which one best fits your company yes any questions just well remember that right now US dollar risk free rate it’s 2.25 percent right so let’s say you’re sitting on the valley Procter & Gamble and basically investment ready to come up with four percent it’s not a high growth rate but it’s higher than two point two five percent right so when you’re talking about four five percent growth you’re talking about growth that’s close enough to the risk-free rate that you can bring it down to the risk reread without huge consequences you I’ll tell you well it’ll be ten percent is let’s say you have a pharmaceutical companies one blockbuster drug that’s creating growth and it’s going to expire in five years or seven years you know the minute the drug goes the growth goes with it that’ll be a classic example a license patents something expiring that basically said that happens then I’m going to bring the growth dig down to stay back row I know we’re reaching towards the end of the session but i want at least get started on the next piece which is what i call the loose ends and valuation sounds like a funny thing to say but at this point think of where we are we have cash flows you’ve discard the cost to cap will you come up with the present value this is what the heart of discarded cash flow valuation is right but it’s amazing how much stuff happens after you tell me you are done it’s what i call the loose ends it’s all this stuff you do after you tell me you’re done and i’ll give you the Genesis for this particular portion of the presentation I work incredibly hard like four and a half hours a week i get i get only five months off every

year but because i worked so hard every seventh year I get the whole year off with pay it’s called a sabbatical you guys probably have something similar in your jobs right now I don’t think so and people complain I even when your academics complain about they have no idea what the real world looks like but about nine years ago I’d a sabbatical actually reminds me I but not a sabbatical coming to you that I should have taken two years ago I should get back and check on this what about nine years of our sabbatical and people have these huge plant sabbatical write a book they’re gonna call here but at a single of vision on my sabbatical here’s what I wanted to do I want you to wake up an entire year with nothing to do so my sabbatical arrives and I’m very ostentatious about it probably too so I settle in my house i buy it to do list from from staples I put it about my little corner of my room where I not hang out at home and here’s where I think I got over the line so my kids come down to go to school and I point to my to do listen look I have nothing to do today piss them off nine okay and then I made my fatal mistake my wife came down and I said I have nothing to do today she said really and then I warned her up I take the dogs out for a walk i come back and there’s something i’m not to do listen what the heck happened here a whole year nothing to do something just pick up bok choy at the grocery store I don’t even know what bok choy look like assume there is to ask I spent two hours wandering around the grocery store looking for box I don’t even know which section to look at is it livestock is it not turns out to be ugly looking cabbage but after I finally come back and says pick up kids at school so it’s all these items showing up so after about the fifth or six items showing up in my to-do list I start to get desperate to put things to do on my to-do list to keep my wife away from my lips such a week I need somebody to give me something to do so I get this email from the editor of cfa magazine I’d even know there was a magazine called see a fair magazine so will you write an article for the magazine a one page article my original responsive are you kidding me I’m on sabbatical but then I did remember I needed something for my to-do list I said how yeah and right oh so in big letters on my to-do list right article for cfa magazine cannot pick up bok choy kids etc etc so I sit down to ride ride the article and not to tell you only took me a day to write the article but it’s the only thing I’ve ever written in my life that’s got me hate mail you know how difficult it is to get hate mail and valuation people don’t feel strongly enough I hate you for using bottom I Bader’s I hate you for using employ dreams never happens but this one actually got me some hate mail part of it was the title of the article it said stop the garnishing and I was talking about the process in valuation where people will be done with evaluation and then they would start to garnish in what sense do it at twenty percent for control now call fifteen percent of the liquidity at thirty percent for synergy I said you got to stop this because if you do this you’ll go to back into a number you want it in the first place the wave of hate mail starts coming in I might have used the word arbitrary somewhere in the necessary so arbitrary premiums and discounts all these appraisals started writing how dare you call it arbitrary we have this research that shows that the discount should be twenty-eight percent strange samples of crazy companies but I guess it’s some kind of study anyway but one of the emails actually struck home it said if you think what we’re doing in valuation is so wrong why don’t you come up with a better way of doing it cuz i’m not saying controlled is not what well i’m not sure why it’s always twenty percent I’m not saying liquidity doesn’t matter why is it always thirty percent so I said you know what you’re right I have 11 months left in my sabbatical here’s what I’m going to do each month I’m going to pick up a loose set and I’m going to spend the month thinking about how I would deal with that loser you’re saying like what first week I dealt with first month I dealt with liquidity the next was controlled so basically all these big things that people attach premiums or discounts for it’s actually one half of one of my books now it’s a the modern and valuation second edition the second half of the book is my sabbatical year it’s basically nine loose ends each of which I kind of dealt with as a chapter in fact you don’t have to buy the book because I took the chapters made them into quasi papers I don’t even really fix anything i just called it it and give it a different title supply that way the publisher doesn’t know that the whole chapter is on so he Gordon type in value of control you get chapped 11 of the book i took out any word chapter in fact i did to find and replace and microsoft words that find what chapter their place with paper it’s amazing how quickly chapters disappear papers show up right so you can get those that sabbatical your kind of play out on but that’s what the loose ends are so and wednesday when we what we’re going to do is we’re going to spend time on those no sense and here are some of the things we’re going to talk about what’s the value of cash so we’ve dealt with that already

ashes cash is it you have a billion dollars in cash in the hands of a company would you sometimes discount the cash in the hands of some companies and attach a premium and others I think so we talk about that when you talk about cross holdings we’re going to talk about other assets that you might want to bring into evaluation you have a headquarters building in Tokyo or Beijing or Shanghai that’s gone up in value should you be adding the value of the real estate your discounted cash flow valuation so we’re going to go to a series of loose ends and talk about tying them up but we’re going to use the process from this kind of cash flow valuation to reason our way to how best to deal with these loose ends so I’ll see you on Wednesday you for that