he so the usual rules apply tell you when the quizzes are done you can come pick them up so there's still some quiz twos and quiz ones left I'll take the quiz twos into my office and as I said you don't pick them up I don't care but the quiz 3es will be out there as soon as they're done so let's um let's let's talk about option pricing as I said option pricing tends to be one of those things that's kind of mysterious people do it all the time they use models but they don't understand the building blocks and I said there are two building blocks for option pricing models one is replication the second is arbitrage let me repeat again what the process says Fisher black and Marin SCH said since you can create something that looks just like the option by combining the underlying asset neither borrowing or lending that has exactly the same cash flows that's a replication it has to trade at the same price that's arbitral the easiest way to see option pricing play out is actually what's called an Arbitrage pricing model so let me show you what an Arbitrage pricing I'm sorry with the binomial pricing model let me explain what a binomial pricing model is let's assume that prices follow a very simple process at every point in time they can jump to only one of two points that's a binomial part so let's say the stock price right now is 50 Next Period it can go to either 70 or 35 that's t equal to 1 tal to 2 if it goes to 70 it can go to 100 or 50 if it goes to 35 tal to 2 it can go to 50 or 25 right now you're at this point in time the stock is 50 two periods from now there are three different prices the stock can be 100 it can be 50 or it can be 25 very simplistic model but let's assume I sold you a call option with a strike price of four and we're going to try to value that call option so right now the stock price is 50 I'm selling you a call option the strike price of 40 if you exercise the option right away what are you going to get what's your profit going to be you're going to buy the stock at 40 sell it at 50 you're going to make $10 right but you got two periods to play the game so it doesn't make sense for you to exerise but let's carry it forward to t equal to two if you take the option with the call op if you take the $40 strike price if the stock price goes to 100 you're going to make 60 if it goes to 50 you're going to make 10 and it goes to 25 you're going to make minus5 no you're not going to make minus5 explain again why with an option you're not making minus5 what's going to happen if the stock price goes to 25 10 when it expires out of the money it's worthless you're not going to exercise the option why would you want to buy a stock at 40 if it's trading at 25 that's where the Right comes in so I know what the cash flows are going to be on this call option at T equ to here's what what I want to do I want to create a replicating portfolio that has exactly the same cash flows as the auction by combining the underlying stock and either borrowing or lending because it's a call option it's going to be borrowed so let's go to the stock PR with the stock price is 70 stock price is 70 I know it can go to either 100 or 50 I know the call is going to be worth either 60 or 10 so I'm going to go outad and borrow B Doll for the moment human me because B is just n and I'm going to buy know shares of stock let's call it Delta shares of stock two and not I don't know how much I'm going to borrow I don't know how many shares of stock I'm going to buy but I know what I want the cash flows on this position to be if the stock goes to 100 so 100 * Delta minus 1.11 * B if the stock goes to 100 has to be equal to 60 because that's what the call is worth and the stock goes to 50 50 * D minus 1.11 * B has to be equal to 10 remember High School I don't know which grade you did this in simultaneous equation you have two equations and two unknowns you work hard enough and long enough there should be no unknown that's what I do I solve for the equation and I end up with a Delta of one and it borrowing of $364 you say what does that even mean if the stock goes to 70 and I go out and borrow $364 and buy one share of stock I will create a position that is exactly the same cash flows as a call option the strike price of for how much is that going to cost me well one share of stock cost me $70 I borrow $364 so from my pocket I've got to come up with $33.95 it'll cost me $33.95 to create the replicating portfolio or the replicating position and because you you have Arbitrage you can't have a different price the call option if the stock price goes to 70 has to be equal to 3396 as well I go down to the stock price of 35 here the stock can either go to 50 or 25 if it goes to 50 the Call's worth 10 if it goes to 25 it's worth nothing again I ask the same question how much will I borrow and how many shares are the underlying stock I go through the the simultaneous equations again and I with Delta of 04 and B of $9 in one c what does that mean if I go out and borrow $91 and buy4 shares of stock and don't even ask me how you buy4 shares of stock let's assume you could you will create a position that is exactly the same cash flow as the call that position will cost me $4.99 that then becomes the value of the call if the stock go 35 so I know what the call is going to be worth if the stock price goes to 7 3396 I know what the call is going to be worth if it goes to the stock price goes to 435 it's $4.99 I move back in time to t0 and I ask exactly the same question how much would I need to borrow and how many shares the underlying stock will I need to buy to end up with 3396 if the stock goes to 7 or $4.99 if the stock goes to 35 and if I solve for that turns out that if I borrow $216 today and I buy 827 shares of stock I will create a position that replicates the call all the way through the life of the option because it'll be self financing once I put that position together if the stock goes to 70 it's going to be worth 3396 I can fund the new replicating portfolio stock goes to 35 it's worth $4.99 which which essentially funds that as well that position right now would cost me $19.42 I have essentially created the replicating portfolio and with Arbitrage that will then become the value of the call option today remember you weigh only $10 for exercising today what's the extra $942 for that's a Time premium on the option b the binomial approach to options came about 10 years after black shorts you know why it was created because people tried to explain black shs in classrooms it was very difficult for people to see where the replication was and where the Arbitrage was the only problem with the binomial first I'm giving a choice only one of two prices at every point in time imagine a real stock and a real market and take of all the possible prices that Twitter could go through go to in the next second so I'm simplifying Life by making it only two choices to make that even a possibility I've got to make time really short if I make it a day there's no chance maybe if I make it a millisecond there's a chance it could be binormal but then I face a second problem let's suppose I asked you to draw a binomial price distribution for an option with a 3mon life and you decide to break three months down into seconds forget about milliseconds into seconds I'm going to ask you a rhetorical question don't give me a mathematical answer how many seconds are there in three months a lot of seconds right if you decide to draw a binomial tree with tiny little branches let's suppose you get a magnifying glass out you get a really sharp pencil it's say I'm going to draw a binomial tree and you make these tiny branches and you draw the entire tree take a look at what that binomial tree will look like look like a really dense Pine Tree on its side right basically it's it's going to be tiny branches going flip the tree over hang in there for a moment I'm going to there's there's an end to the story flip the tree over on its base so it's going to look like a triangle smooth out the outsides you know what the triangle is going to look like it's going to look like a normal distribution if you take the binomial distribution as a t as T gets really small you make the price change is small that's called a continuous distribution the binomial distribution converges on the normal distribution over time the black schs model is a limiting case of the binomial model if price changes are continuous they're small as as price changes as time gets smaller the buying nomial option pricing model becomes the black schs model what do you gain when you get the black schs model you no longer have to draw the tiny branches you got the normal distribution and a normal distribution can be characterized with an average and a standard deviation that's what the black schs model buys you but it does so at a cost it's built on the presumption that price changes are continuous is that a good assumption though are price changes because I'll describe to you how the world would work if price changes were continuous if you have a stock like Twitter trading at 43 you know how it gets to 40 54 it goes 43 4301 4302 it moves in small increments there are no price jumps in a continuous distribution so right at the at the start you can see it's an unrealistic assumption but what does it get you it gets you normal distribution and makes your life simpler so the original black shorts was was built on the normal distribution but it's still built on replication Arbitrage and in the original black schs the value of a call option is a function of five inputs s which is the value of the underlying asset K which is the strike price R which is the riskless rate T which is the life of the option and sigma which is the standard deviation or Sigma squar which is the variance of the log value of the underlying asset you know why we use log values because we take stock prices what's the lowest value price can take can't drop below zero right the highest value can be we want a normal distribution to have any sh of getting a normal distribution if you take the log of zero you know what you get you get minus infinity it gives you a chance of using the normal distribution that's why people when they use black shoulds models if they have to estimate volatility if they want to do it right have to use log prices there are shortcuts you can use give you just as good an answer but the original black schs was built on using log prices because it was built around the normal distribution skrt and sigma but last session if you remember I said there was six variables that determine the value of an option what's the missing variable what does the black should model not have it doesn't have dividend you know why it doesn't have dividence it was because when black ands were trying to solve for this model they ran into a bit of a brick wall they had the model set up the the equations written but nobody in finance had ever seen an equation like this one it required the use of what's called stochastic calculus and nobody in finance a stochastic calculus rumor has it that a physics PhD at the University of Chicago was wandering by Marin Scholl's office and he came in and looked at that equation it said we do that all the time in physics and he wrote out the solution from physics and so the Nobel Prize should really have gone to Fisher black Mar and Schultz and an unknown PhD student in physics but basically they were running into so much trouble that they said let's act like there are no dividends in fact the original black schs was designed to what to Value what are called dividend protected options he's saying what's a dividend protected option remember if you the reason we worry about options is in the day the dividend is paid the stock price drops roughly the amount of the dividend right what if I could also adjust your strike price by exactly the same amount you'd be protected that's what the original black shs was designed to do but the reality is there are no dividend protected options that I know of anywhere in the world it's an unrealistic assumption but it allowed them to saw for the original black schs the original black schs the value of the call is the stock price R not an expected future stock price the stock price de times n of D1 and I'll come back and talk about the intuition behind whatever n D D1 and N of D2 here n of D D1 minus k e minus RT I tell people that when you first start using the black schs model there all these virgent buttons on your calculator that you've never touched exponential natural log all of those come into play because e minus RT is just the present value Factor K minus RT is the present value of the strike price why because the original black shows again to simplified life was designed to Value what are called European options this is unfortunate because we attached to geography it's got nothing to do with geography you have European options and American options you know what the difference between the two options is what sets European options apart only on on the the last minute of the last day you can exercise only at expiration American options can be exercised anytime up to experti forget about all the math if I gave you two exactly equivalent options one is the European option but the other is an American option which one should trade for more the American because I give you everything the European option has plus the right to exercise early 95% of the time you might not use it but so a black Schultz model is designed to Value European option it's not a huge problem because as I said it'll give you a lower bu and American an option can add on you can modify black schs to reflect that but basically because you can't exercise till expiration what the black schs model is saying is look you have to pay the exercise price but not till two years from now so we're going to take the present value e minus RT is the present value Factor if you don't have an exponential button on your calculator you can just take the strike price and take a traditional present value and you get pretty close to the same number time n of D2 now let's talk about D1 and D2 D1 and D2 is this m this is what throws people when they use the black show what the heck is that D1 and D2 by themselves are difficult to explain they reflect all of the inputs that's a stochastic calculus yielding D1 and D2 but I can give you some intuition behind n ofd1 and n of D2 n ofd1 and n of D2 are areas under the normal distribution usually when you see normal distributions in statistics books it'll give you the height of the distribution n of D1 is an area of the distribution in fact if youve ever seen an N of D1 table it stretches from zero to one you know what that tells me n ofd1 and n of D2 are probability measures in fact n of D2 in option pricing is called the risk neutral as or is measured as the risk neutral probability that your option will end up in the money let me repeat that again so when I say the N of D2 in this option is is 75 I'm saying there's a 75% chance that s will be greater than K that's something we're going to come back and use when we talk about real options because that is something that you can actually use for economic significance of talking about what is the chance this option will actually pay off so both n ofd1 and n of D2 are probabilities that reflect all of the inputs more but embedded in the black shs is that replicating portfolio remember the binomial we solve for this as B and Delta in the black schs it's in there you just don't see it if you look at a black schs model here's what the replicating portfolio that comes out of the models if you go out and buy n of B1 shares of stock that's called the option Delta and borrow the present value of the exercise price time nd2 you've essentially created the replicating portfolio in the black schs model so if you break the black schs model down it tells you what the replicating portfolio is if you ever been around option Traders or were still option researchers they use a lot of Greek words notice Delta gamma Theta everything in option pricing is about that replicating portfolio and how it changes as different dimensions change so for instance if the stock price changes the option Delta will change if the life of the option changes the option value that's called the option Theta as the variance changes the option valuable change that's called the option Vega so basically every single aspect of option pricing is built around that replicating portfolio and from a practical perspective you might have heard of people trying to hedge option positions the way you hedge an option position is you get the replicating portfolio and then you create essentially a counterweight to the option because you know that if you sell the replicating portfolio and you bought the option you've effectively created a riskless position so there's going to be this temptation to plug numbers into the black shoulds get a value and walk away but the real value of the black shoulds you start breaking down what the replicating portfolio is and what it tells you about where the value of the options coming from any questions so this table that you see there is a normal cumulative normal distribution table it's actually a table that I would Supply to you if you ever have to price an option and a final exam because you can't use your calculator to get this you can use a computer because there is a cumulative normal distribution function in Excel but on a calculator it's almost impossible to get a cumulative distribution so that table has to be an input if you're going to Value an option but this is to Value an option where there is no dividend or there's complete dividend protection and as I said that's unrealistic so I'm going to give you a version of the black shows that you're going to see more frequently in this class because many of the options we're going to Value are going to have dividend like components that reduce the value so for instance if you own an oil Reserve every time you extract oil from the reserve you're actually reducing the value of the reserve if you own a patent and you wait a year to exercise the patent you're giving up some of the value that's like a dividend and there's a version of the black shoulds that adjust for divid it does make some simplifying assumptions to get there but if you can tell me what the dividend yield is on the underlying asset dividend yield would be 2% 3% whatever it is I can create a version of the black schs where I take D1 and D2 you're wondering what the question mark is for whatever reason it seems to taken the sigma and made it into question mark so that's really a sigma wherever you see the question mark so it takes the original version of the black schs and it brings in the dividend yield into the D1 and D2 so it's a dividend yield adjust version of the black strolls and it allows you to value options on underlying assets which do have a divid mod so you need know you don't need to really solve or derive an option pricing model but you need to understand the basics of option pricing models if you get if you want to use them in real options any questions on option prices so now there are people in option pricing with purest and when you use a black shoulds model for instance value real option you're pushing the limits of the black schs model here's why I told you the black schs model is designed to Value European options which means the option doesn't get exercised till expiration one of the options we're going to talk about is the option to develop an undeveloped oil Reserve so let's say you have the rights to this reserve for the next 20 years you have an option for the next 20 years would you want to wait till the last minute of the last day of the 20th year to start developing a reserve that would be a waste right because you can't get all the oil out in a second so the essence of real options is you almost always will want to exercise early if the option goes in the M that's true for patterns it's true for un develop reserves so the argument purus make is you shouldn't be using a black shs model you know what I agree but I'll continue to use it anyway and here's why if I wanted to use a binomial model to value these reserves what would I have to do i' have to draw these little branches for the rest of Eternity I will use the black shs model and accept the fact that I'm going to get a lower bound on the value and I'm making assumptions about continuous prices it could get me into trouble but the alternative of actually going through a binomial model is just horrifying I just can't get to an end game it's not worth it in fact um if you take the binomial model there are no probabilities in the binomial model but you attach it probabilities to the branches you get what's called a decision Tre if you don't want to use option pricing models you can actually arrive at roughly the same conclusion by using decision trees the nice thing about decision trees is you're not bounded by two outcomes you can have three choices four choices now the way I you know option pricing models are like you know they're they're intimidating so when you present option pricing models to finance people even if they're experience Finance people their eyes glaze over so I tell people don't bring out option pricing models unless you absolutely have so if you go into a pharmaceutical company and you bring out an option pricing model everybody is looking at the black shoulds model saying I don't get this decision trees though everybody should be able to relate to statistics it's probability it's much more you know much more intuitive so if you if you can get to an option pricing value using a decision tra why use option pricing model in the first place so fil that away as something you can do and this is actually an an example of how a decision free would work now I'm using a drug to treat diabetes and essentially you're right here you're trying to decide whether to develop the drug and then it goes through each state so it's perfect when you have sequential risk as you do in a drug company and you don't know what the outcomes will be it allows you to kind of back into the value of the option through the decision trees and probabilities rather than using an option price so file that away I'm not going to go through decision trees because that requires know basic statistics and probability but often you can get the same values that you get with an option pricing model if you're willing to flesh out the entire decision so now let's talk about the three tests that we're going to run on every real option that I'm going to present so whenever I present a real option to you the first question you need to ask is is there really an option am I misusing the option pricing mod so I'm going to draw the pay diagram so you can see the option I need to tell you what the underlying asset is I need to give you the strike price describe the option second stop you got to make sure that this option has economic value and remember the key word there is there exclusivity if there is clearly there is an option value if there isn't there is no option value but often you fall somewhere between those two extremes and third I'm going to ask can I use an option pricing model to Value this real option and there because I'm using either a binomial or black shoulds which is built on replication Arbitrage the underlying asset has to be traded the option has to be traded I need to be able to borrow and L at the risk fre you can see with each test I'm raising the ante and it's getting more and more difficult to meet the test so we're going to go through a series of options but let me lay out first how we're going to approach it we're going to start by looking at options and projects Investments valuations okay then we're going to move on to options and capital structure how when companies borrow money there is an optionality in not going all the way up to your optimal debt ratio and then we're closing off by looking at options when you look at distressed equities equities and companies where there's a lot of debt the company might not make so let's start with the first one options and Investments when we do corporate finance classes at least the very basics of capital budgeting we estimate the cash flows in the project we come up with the discount rate we take the present value and we compute a Net Present Value the rule is very simple right if the net present value is greater than zero you accept the project if it's less than zero you reject the that's perfectly good advice but I'm going to build on that the fact that you have a negative Net Present Value in a project doesn't end the discussion if I now said if I gave you the rights to this project for the next 10 years how much would you pay for it even though the project has a negative net Pres value now you might still pay for the rights because things can change the Net Present Value can become POS that's your option to delay we're going to start for that we're going to use the option to delay to talk about why patents and nonviable Technologies and undeveloped reserves for an oil company can be valued as options second stop we're going to look at options to expand what is that your initial project might have a negative Net Present Value but to the extent that it gives you the right to a second project which right now is not viable but could become viable in the future you have an option to expect that's the example I talked about last session I talked about marot opening 10 hotels in China with a license to open 500 more if things work out that second decision is the option to expand and the third is the option to deliver which is if you enter into a long-term project and you start to see the cash flows coming well below expectations it's nice to be able to walk away from your mistakes because that essentially means you're not bound to getting those negative cash flows of the remaining life of the project I'm going to argue that the option to delay the option to expand and the option to abandon sometimes projects that look bad using a static analys with traditional cash flows and npv might be projects that you would still add onto your portfolio because the options tilt the SC so let's start with the option to delay as I said when you do a project analysis take cash flows you discount back at a discount rate you come up with the Net Present Value all it tells you is that that project is not a good project today that you shouldn't take it but if you get the rights to this project things can change like what the investment you might need to make on it could be a green energy project where technology changes the economics of the project the cost might become much lower it could be that the market itself is changing that what looks like a small market today could become a big Market in the future future so if you think about the rights to this project what you have essentially is a bad project but the option to delay means that this project could become a good project so let me draw the payoff diagram for the option to delay and start delineating what the underlying characteristics are so you have the option to delay if you decide to take this project there is an investment you got to make in the project right now the present value the cash flows are less than the investment so it's an out of the money option but you got 10 years to it over those 10 years the present value of cash flows could actually change the market could get bigger May might be able to charge higher prices if the present value of cash flows exceed the initial investment you're going to take the project and you're going to claim the net present value is it possible though that 10 years from now you look back and say I wish I hadn't bought the rights absolutely in which case what happens you lose whatever you pay for the option it's like any other out of the money option there are no guarantees but you buy it because there's a possibility that this project would become a good project that's what the option b was captured so I'm going to use two examples to illustrate the option to that the first is when you get a patent and if you're familiar the way the US is and around the globe increasingly countries are bought into it is with a patent you get the exclusive rights to do something for the next 15 the next 18 the next 20 years right not obligation so once you file a patent you're not required to produce a product so let's assume that you have a product patent and it's going to cost you I whatever that's 100 million 10 billion whatever it's going to cost you to develop the patent into a commercial product let's say you do a capital budgeting today based on what you know about the pro the product today and you come up with the present value of cash flows of V if V is less than I the present value of the cash flows is less than the cost of developing the spend in a commercial product you're not going to develop it wouldn't make any sense you're going to sit and wait remember you have 15 or 18 or 20 years left in the P if we stays below I for the rest of the 15 or 18 or 20 years you throw it in the trash can and say I wish I hadn't bought that B that option but if V increases over time above I at some point in time you will exercise the option and claim the net PR you could make this patent you can make it a technology essentially I'm saying you can have a non viable technology or a bad project today but the rights to that project can still have value because things can change so the underlying asset here is the project that comes out of the pattern or the product that comes out of the pattern the choice of when you develop it the contingency is going to come about if the cost of introducing the product becomes less than what you get as present value of cash flows of course that could if that never happens what do you lose you lose whatever you paid to acquire this what are the two ways companies acquire patents one is you can obviously buy them the other is but 90% of patterns don't come through Acquisitions comes through R&D one way to think about R&D is what you're paying to acquire options that's what a pharmaceutical company's R&D does it turns out options of course all your options end up being out of the money and never come in the money you're going to end up white you know that's that's bad or but essentially that's one way to think about why why companies do R&D it's to create options that you hope will have value in the future so let me let me look at let's look at how you would get the inputs to actually value this option everything I do in terms of trying to price an option I'm going to go back to an option pricing model and state it in terms of the inputs I need in an option pricing model to Val the option if I can somehow come up with these inputs I should be able to value a patent a nonviable technology a license anything that's not viable today but could be viable in the future you ready you've got not you got a patent on a product and I'm going to try to valuate an option what is the underlying asset it's the product that comes out the pattern right so when I ask you what is the S what is the value of the underlying asset you're going to take the present value of the cash flows from developing the patn today don't do any forecasting ask yourself if I develop the pattern today what would the cash flow look like you take it's like a traditional capital budget what you get as a present value will be S and while you're doing this you're complaining to me you know what you complaining about I feel so uncertain this is a patent it's a new product and I'm going to tell you that's a good thing that sounds like a weird thing to say but this is going to help you that you're uncertain so s becomes the present value the cash flows from developing the pattern today K becomes the strike price is the cost of actually developing the pattern so the factory might have to build of the commercial setup you got to set up that becomes the K in the morning is it possible that K is greater than S absolutely it's a patent it's a new product who knows whether it's viable today or not remember I told you the value that you get from the cash flows is you're going to feel uncertain I'm now going to let you put a number on how uncertain you feel the uncertainty you feel in that value becomes the sigma or the standard deviation of this option the more uncertain you feel about the future the higher the standard deviation will be in that value now of course the question is where do I get that there are two ways you can get it remember the Monte Carlo simulations we did earlier on when we valued companies in a Monte Carlo simulation you run 10,000 100,000 simulations you get a value but you also get a distribution of values we did that for X on for Royal Dutch okay when you get a distribution of values you can also give me the standard deviation from the distribution so one way in which you can get the sigma here is run Mont Carlo simulations on developing the pattern and give me the standard deviation you get across those VAR I've got the S I've got the sigma I've got the K how long does this option last you get a pattern you don't get it in perpetuity in the US I think it's 18 years 20 years whatever it turns out to be at the end of the 20th year it becomes F everybody else can enter the business so the life of the option becomes the remaining life of the pent and there's one more thing to factor in let's say that your patent becomes viable one your from now you still have 19 years left part of you says let's develop the patter but the other part of you says let's do some more homework let's assess how good the project is so there's this trade-off should I wait or should I develop and I'm going to introduce a tradeoff if you wait you might potentially increase the value of this product by knowing more getting a Market but if you wait what do you lose remember you 19 years of protection left by waiting you lose one out of the 19 years you give up some of the protection you have on the P that becomes like a dividend year to bring into the market so let's actually take an example of a real patent and this is very difficult to get when you're in the outside of the company because much of this is internal information a company I just got lucky here it's a company called biojet but it's a fairly large biotech company now but when I did this was a small biotech company and it had a drug working its way that had that had that had worked its way through the pipeline that had just that was very close to approval but they patented it's a drug called avenex to treat Ms potentially a big market and what I got lucky on is I got my hands on a capital budgeting project analysis that the company had done on developing the Dr if you ever ever seen a pharmaceutical company estimate cash flows in a drug it's kind of a scary and and morbid process because here's what they did they estimated the number of people in the US they projected initially they going to sell the drug only in the US the number of people in the US who suffered from Ms and they got a pretty good number then they estimated what percentage of those people go to a doctor and it's not 100% so you could have MS you never go to a doctor nobody diagnoses you just s through the crack so let's say 90% of those people go to a doctor then they estimated what percentage of those people get the right diagnosis and guess what that's not 100% either this is the scary part so let's say 90% of the people who go to a doctor actually get diagnosed so now we've gone from 100 to 90 to 81% then they look at what percentage of those people get assigned a drug to treat the MS you saying why would everybody get it because you have insurance of health health care cost and it could be at 60% of those people end up actually being on the drug so that brings the market down to about 60% of 81% now brings you down to 48% then they estimate the price they're going to charge for the drug and that's a choice right they can set it at a really high price but that'll lower the market because if you set it too high only 20% might take it and they estimate Revenue so they all gone through this process estimate flows the present value they got for the cash flows was 3,422 mil so think of that as the value of developing the drug today avanex um Biogen had never actually developed a drug on their own they've been around but they' licens drugs out to other farmer companies because actually producing a drug is a very expensive process in the US it's not just the manufacturing you got to set up sales teams you got this whole infrastructure has to be set and they estimated that the cost of doing that for avenex would be 2875 so let me pause right there if you develop the drug right now you get 3,422 million the cost of developing this drug is 2875 million if I take the difference between those two numbers which is 547 million what if I just solve for what is that so I've taken the present value the cash flow subtract out initial investment that's a Net Present Value right that is the npv of this project this 547 men file that away because I'm going to create some magic here remember they haven't developed the drug yet they have 17 years left on the drug so they could wait what will they gain by waiting they can check for side effects they can check to see if they can make the market bigger and let's say the uncertainty they feel about the C the 3422 is an estimate right you could be wrong in the cash I could have done a monal simulation here but I don't know enough about about Ms and how doctors behave to actually build that so I cheated to get an estimate of how uncertain I felt about the value I looked at publicly traded biotech companies and that's the cheating part and I looked at the standard deviation of their stock prices and it turned out that the standard deviation in stock prices or the variance in stock prices of publicly traded biotech companies is 224 you see why this is cheating because what I want is the uncertainty I feel about the present value of cash flows I'm using the variance in stock prices as aoxy for that uncertainty but it saves me a ton of time if I could do a monard simulation I'd probably get a much more sensible number but I'd need a lot more information to get the distribution's going so I've got 17 years left on this option I've got an SN a that suggests it's viable today and if I wait I know I'm going to lose one of the 17 years protection so I'm going to treat that like a dividend deal I'm giving up that value if I would I have all of the inputs for a black schs model if I plug in the values D1 D2 n of D1 and N of D2 the value that I get for aex valued as an option is 97 M and if you have MS this should terfy because here's what you fix right if Biogen develops a drug right now the npv is 547 if it waits and treats it as an option it's worth 97 mil and what's the rule with options don't exercise if the option has well and why should this matter to you if you have MS you've been waiting for this drug for 10 years it is viable but the company chooses to wait because it thinks the upside you're waiting exceeds the co the the whatever you give up in terms of that I'll give you the good news though Biogen did develop the drug almost instantaneously and I and I'll tell you why it probably happened here what am I assuming the cost of delay is one out of the remaining 17 years right but you see what the problem that assumption is I'm assuming that there's no other farmer company out there working on a drug to treat Ms what if I told you that MC was working on a drug and it's going to come out in four years I have a foure lead time but they're going to you know what my cost of delay will then become so being 1 over 17 and really only four years protection it's going to be become one over4 if I make the cost of delay 25% the value of the option drops below 547 million I would exercise it here's the bottom line if you live in a competitive pharmaceutical sector you're going to see drugs develop much more quickly because there's a cost to waiting the cost to waiting is high because somebody else might develop a drug but if you're a monopoly pharmaceutical company and you look around the Horizon and nobody else is going to develop a drug for the next 18 years you will wait because it costs you too much or you giving up too much value by developing the drug Right Way in fact what I did here was I actually calculated how long if there no competition at all that they wouldn't develop the drug for almost eight years so each year I recalculated the value recalculated the value the option and if they have no competition they would actually wait eight years before they develop the drug that's what I what I meant when I said it's really bad news if you have MS because the drug is out there it's viable but they're choosing to wait because there's no competition and what they give up by exercising early is too much relative to what they did one final piece of this puzzle Biogen as I said already had drugs out there but they'd licensed the drugs out in fact if you gave me a pharmaceutical company and you ask me to Value the traditional way of valuing it is to project out the revenues and the cash flows and some of your valuing from a company can value the entire company but let's say I want to build up to the value in a different way I can actually value a pharmaceutical company three slices the first is the value of the commercial products that they already have out there with the traditional discounted cash FL valuation the second is you value the existing patterns which have not been developed as options and the third is remember that have an R&D Department that's continuing to churn out pattern you can say what's the value of that adding SL I'll tell you up front I would not use this on a fiser you imagine how crazy you go you drive yourself if you took you know all of the pattern because it probably have hundreds of patterns and try to do an option on each one and then try to validate but if you gave me a small farmer company with one big drug that's just been approved and which ever patented and one commercial product this approach actually would give you a better answer because you're breaking the drug down the company down into its constituent Parts in a so the big question is how do you value R&D so I'm going to give this a shot with Biogen there two existing drugs at the time that I did this valuation want to treat Hepatitis B and another drug called Inon that they licensed out to other farmer companies when you license out a drug there are two ways you can license it one is you can get a fixed license F from the company or you can get a percentage of revenues the way barin had set it up is they got a fix license in fact the collective cash flows from the licensing on these two drugs was expected to be 50 million a year for the next 12 years it's contractually said so what's the only risk that Biogen faces on these cash flows it doesn't worry about revenues or how much they are it worries about default risk on the part of whoever has licensed a drug from so to take the to Value this 50 million I took the 50 million discounted back at the pre-tax cost of debt of the licensing companies you see why to use the pre-tax cost of De because these cash flows are like Bond payments they're contractual payments don't be so quick to jump on the cost of capit discount rate for every single cash flow fact let me ask you a question if Biogen had licensed this drug to Medicare and the government had promised to pay $50 million a year for the next 12 years what would you use as a discount you would use the risk fre it's the guarantor risk you worry about here because that's what determines the value so the present value is 397 million so I've got the value of aex which is their only pattern valued is an option I've got the value of the existing drugs 397 million what's the last piece I'd like to value Biogen continuing R&D and here I had to make a couple of assumptions I first assumed that I could project out what the R&D expense would be for the next 10 years so the R&D expense in the most recent year was 100 million I assumed it would grow at 20% for the next 10 years and 5% thereafter so I projected out the R&D expenses what's the value of R&D what's the value of any investment it's a Net Present Value that investment added on right so if your R&D earns a return on Capital equal to its cost to Capital you know what added value comes from already zero so all I had to do to Value R&D is make a judgment and I'm not saying it's easy to do on what the return on Capital would be so basically I assume that every dollar invest in R&D would generate a125 in value which turns out to be a return on Capital about 3% above the cost of capital that then is all I need but there is a substantial amount of uncertainty whether I can pull it off so let's say the discount rate for this tree is 15% so there's my R&D cost growing at 20% for the next 10 years and 5% thereafter there's the value of the patents that come out of the R&D that's an expected value of a125 for every dollar invested so there's my value patterns the difference is the added value and Beyond year 10 I assume they earn their cost of capital so I ignore the added value after you take the present value of that added value I estimate the value of Biogen continuing R&D to be 318 so three pieces to BU I have aex 97 million their existing products licensed are 397 million and the value Futurity the value that I get for biogents operating assets is 1.62 billion then I do add cash subtract our debt so it's a different way of arriving at the value of operating assets for a patent or a pharmaceutical company but you can see it's a lot more work and if you have dozens of patents don't even go down this path don't ever use this approach for big farmer companies to drive you crazy if a small farmer company with a single drug or two drugs and you want to Value them separately and add them together perfectly okay so I'll stop there and next session we're going to talk about uh using the option to delay to Value undeveloped Reserves the mar days it's I mean the next week I can understand this is two days after last so unless you're planning to miss the last I mean I I don't so plan the what I would say after you I have so it given that it's so close the last class I I pry yeah you're have no effect on your value so why would your value change the price nothing has changed nothing fundamentally has changed it's not like he's given a specific plan or what he wants to so there's nothing I would see that you change Basic Value the he's not taking private private business taking private to treated like public no total yeah oh yeah this is for you right it's do [Music] well take care [Music]