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Val emails


The emails for this class will be collected on this page, arranged chronologically. Since I send quite a few, you can target it on a specific month by going here:

Have fun with them!

Email content
I am sure that you are finding that break is passing by way too fast, but the semester will soon be upon us and I want to welcome you to the Valuation class. As I looked at the class list, I see lots of familiar names from corporate finance. So, you do know what’s coming. I will bury you with emails, and here is the first one. One of the best things about teaching this class is that valuation is always timely (and always fun...) Just as examples: Is it time to sell Tesla? Was WeWork worth any money ever or was Softbank delusional, and if the latter, what does that make Oyo? How much does a Super Bowl add to an NFL team’s value? You will find the answers to these and other questions on my blog:

1. Preclass work: I  know that some of you are worried about the class but relax! If you can add, subtract, divide and multiply, you are pretty much home free… In are you have forgotten your accounting, I have added my version (which would probably not be approved of by your accounting professor) of an accounting class to my website:
If you want to get a jump on the class, you can go to the class web page:

2. Class Logistics: Normally, we would meet on Mondays and Wednesdays in Paulson Auditorium, but with COVID still wreaking havoc on our lives, we will meet virtually (on Zoom) at the scheduled time (Mondays and Wednesdays, 2 - 3.20 pm, from February 1, 2021 to May 10, 2021. I don’t take attendance, but I would really, really like to see you in the live sessions, with cameras (and clothes) on, but I understand that some of you are in time zones where this will be difficult to do. Never fear, because the classes will be recorded and available on three platforms:
a. My website: The recordings of the sessions, with all of the material (slides, links, other) that I use during the session will be available on the webcast page for the class: 
b. YouTube Channel: There is a second option, if your broadband connection is not that great and you are watching on a Tablet/smartphone. There is a YouTube playlist for this class, where all class sessions will be loaded.

  When you get a chance, check it out.

3. Syllabus & Calendar: The syllabus for the class is available on the website for the class and is also linked here:
and there is a google calendar for the class that you can get to by clicking on

For those of you already setting up your calendars, it lists when the quizzes will be held and when projects come due. 

4. Lecture notes: The first set of lecture notes for the class should be available in the bookstore by the start of next week. If you want to save some money, they can also be printed off online (if you want to save some paper, you can print two slides per page and double sided). To get to the lecture notes, you can try
Please download and print only the first packet on discounted cashflow valuation. If you want to save paper, you can download the pdf file on you iPad, Android or Kindle and follow along... 

5. Books for the class: The best book for the class is the Investment Valuation book - the third edition. (If you already have the second edition, don't waste your money. It should work...) You can get it at Amazon or wait and get it at the book store... If you are the law-abiding type, you can buy "Damodaran on Valuation" - make sure that you are getting the second edition. Or, as a third choice, you can try The Dark Side of Valuation, again the second edition, if you are interested in hard to value companies.. Or if you are budget and time constrained, try "The Little Book of Valuation". Finally, if you really want to take a leap, try my newest book, Narrative and Numbers at 
You will find the webpages for all of the books at http://www.stern.nyu.edu/~adamodar/New_Home_Page/public.htm. If you want a comparison of the books, try this link: http://people.stern.nyu.edu/adamodar/New_Home_Page/valbookcomp.html 

6. Valuation apps: One final note. I worked with Anant Sundaram (at Dartmouth) isn developing a valuation app for the iPad or iPhone that you can download on the iTunes store: http://itunes.apple.com/us/app/uvalue/id440046276?mt=8 
It comes with a money back guarantee...  Sorry, no Android version yet…  

I am looking forward to seeing you in three weeks on Zoom! Let’s hope that the world holds together until then! Until next time!
I know that week one is approaching and one of the themes of this class will be that while your valuation looks like a collection of numbers, the story that holds these numbers together is the glue. Consequently, to get a handle on valuation, you have to learn to navigate that space between stories and numbers and your skills have to be broad. I know that you are still on break and that the last thing you want to do is reading, but if you do get a chance, please read this post that I have on my blog:
The post was triggered by the awe I felt, looking up at Brunelleschi’s Duomo in Firenze this summer, but the thoughts are all investing/valuation thoughts. In fact, I wrote a book on connecting stories to numbers and here is the post introducing the book (which became available about two years ago).

If you did get a chance to read my long email last week (and I would not blame you if you skipped it), you probably missed the link to the lecture note packet that I said was available at this page:

Also, if you missed the first email, the email chronicles will record them for posterity and you can find them by going to this link:

That is about it for the moment. If you want to get ready for the class, start by keeping up with the business news for the next week. See you in two weeks in class,. Specifically, the first class is scheduled for February 1, 2021, from 2 pm - 3.20 pm, NY time.See you next week in class. Until next time!

It’s been a week and while not a whole lot has happened, I thought I should check in ahead of next week’s class. First, if this is the first email you are reading, then you should catch up with the two earlier ones, which are available at the link below:
If you are wondering about the logistics (exams, projects etc.), we will start the first class with the syllabus, which will also lay out the themes for the class:
As you go through the syllabus, you will notice mention of a project and you can find the details of that project here:
Once we are through the syllabus in session 1, we will turn to an introductory packet (of about 20 pages). The link to that package is below:
Please have this ready for the first session. The rest of the class will be covered in the lecture note packets, and I sent you the link to the first one last week (but here it is again):

Having drowned you with all of that stuff, let me hit with you some pre-class reading (and I don’t think it is too painful). I don’t do much academic research and am supremely uninterested in writing for an echo chamber. Much of what I have written that is original or different has be initially (at least) on my blog.  I spend the first few weeks of each year, talking about the data that I update on my website:
The first two updates are on my blog. Please browse through them, because they are relevant for class:
  1. https://aswathdamodaran.blogspot.com/2021/01/data-update-1-for-2021-data-look-back.html 
  2. https://aswathdamodaran.blogspot.com/2021/01/data-update-2-for-2021-price-of-risk.html 

The first class will be a week from today (Monday, February 1, from 2 pm - 3.20 pm, NY time) on Zoom. The Zoom link for all of the classes (all 26 sessions) is below:
Please download and import the following iCalendar (.ics) files to your calendar system.
Join Zoom Meeting

Until next week!
As we head into the last weekend before class, I am sending this as a collective email to all of my classes (Corporate Finance, MBA Valuation and Undergraduate Valuation). So, please be careful before you replay all, since roughly a thousand people are in the three classes put together. When I start class on Monday, it will be my 37th year teaching and I am thankful that I still look forward to the day. There is no other profession where you can start with a fresh slate every few months, even though you may screw it up in the subsequent days and weeks. The class times on Monday (February 1), just in case you need a reminder, are:
  • Corporate Finance, from 12.30 pm -1.50 pm, NY time
  • Valuation (MBA), from 2 pm - 3.20 pm, NY time
  • Valuation (Undergraduate) from 3.30 - 4.45 pm, NY time
As you can see, there is only a sliver of time between the classes (ten minutes), and if I seem like I am in a rush to get out, once class ends, that is the reason. Please come to the zoom class, unless the time zones work too much against you or you have life and death commitments. 

I last emailed you just four days ago, and for those of you are wondering how much can happen in four days, the evidence is in front of you. We have had three big market movement days (two negative, one positive) in the last three days, and if you are thinking about places to hide from risk, you may want to start by reading my third data post for 2021:
If you did not get a chance to look at the first two, they are linked at the bottom, and one of them gives you my market view (I would not pay for it, but its free…). The even bigger story is the frenzy around GameStop, with Reddit traders taking hedge funds to the woodshed. The story has legs because it has shades of David versus Goliath, and it feeds into many of the populist and political themes that have surrounded us for the last decade. I normally don’t write reactive posts, but this one was big enough that I did it anyway:
As you read this post, you will see that I am not a fan of hedge funds, most of which are run by people who bring nothing to the table, while charging obscene fees and delivering sub-standard returns. That said,  I am not sure what the end game for Reddit investors is, either. I have offered four choices, and given my opinion, but you be the judge! Until next time!
We are officially rolling. If you enrolled in the class in the last couple of days, you did miss the first two emails but they are already in the email chronicle, in case you are interested:
Email chronicles: http://www.stern.nyu.edu/~adamodar/New_Home_Page/eqemail.html
This chronicle will be updated at the end of each week to include all emails sent up until then. 

If you were able to make it today’s class, thank you, and the slides that we used for the class should be at the links below:
Syllabus: http://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/eqsyllspr21.pdf 
Introduction to Valuation (Slides for Wednesday’s class): http://people.stern.nyu.edu/adamodar/pdfiles/eqnotes/Valintrospr20.pdf 
I mentioned the project for the class, but only in very general terms. You can find the specifics at the link below:
Project: http://people.stern.nyu.edu/adamodar/pdfiles/eqnotes/eqprojspr21.pdf
A quick note about today's class.  During the session, I told you that that this was a class about valuation in all of its many forms – different approaches (intrinsic, relative & contingent claim), different forums (for acquisitions, value enhancement, investing) and across different types of businesses (private & public, small and large, developed & emerging market).  After spending some time laying out the script for the class (quizzes, exams, weekly tortures), I suggested that you start thinking about forming a group and picking companies. To get the process rolling, here is what I have done
1. Group: Please do find a group to nurture your valuation creativity, and a company to value soon. If you are ostracized, or feel alone, I will create an orphan list and make sure that you are adopted.
2. Company Choice: Once you pick a company, collect information on the company. I would start off on the company's own website and download the annual report for the most recent year (probably 2019) and then visit the SEC website (http://www.sec.gov) (for US listings) and download 10Q filings. (You can pick any publicly traded company anywhere in the world to value. The non-US company that you value can have ADRs (but does not have to have ADRs) listed in the US but you still have to value it in the local currency and local market. You can even analyze a private company, if you can take responsibility for collecting the information.)
3. Webcast of today’s class: The web casts for the first class are up and running in all of their variations (Zoom recording, downloadable video, downloadable audio and YouTube). You can access it by going to:
4. Lecture Note Packets: Please download the first lecture note packet, when you get a chance. You can either download it as a powerpoint file (though powerpoint bloats file size or as a pdf file)
Powerpoint slides: http://www.stern.nyu.edu/~adamodar/pptfiles/val3E/valpacket1spr21.pptx 
PDF version: http://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/valpacket1spr21.pdf 
5. Post class test: To review what we did in class today, I prepared a very simple post-class test. I have attached it, with the solution. Give it your best shot.
If you did not get the syllabus, project description and the valuation intro in class this morning, they are all available to print off from this site. I will also be sending out a post class test and solution after each session that should take you no more than 5-10 minutes to do. It is a good way to review the class and I hope that you find it useful. Sorry about the length of this email, but there will be more to come (I promise!). Until next time!

Attachments: Post-class test and solution.

As promised, the first valuation of the week is up, and as promised, it is GameStop. Given the trading frenzy on the company, it is the talk of markets. To get a picture of what I think about the frenzy, you can start with my blog post from last week. (I know that I sent you the link, but here it is again).
In the link, I have a best case valuation of the company of about $47. I have a base case valuation of the company that is more reflective of the troubles in its business model and the difficult it will have in pivoting to becoming an online retailer primarily or a gaming platform:
If you are wondering where the base year numbers in my valuation are coming from, you can click on the link below to get historical data on the company going back to 2001:
Here is what I would like you to do. Download the spreadsheet that I have for valuing the company. There are four primary drivers of value
a. Revenue growth rate (in 2021 and a growth rate beyond); I used 10% for 2021, 2% thereafter & my revenues move slowly to about $ 7 billion in 2021)
b. Target operating margin, measuring the profitability part of your story (I used 5%, lower than the industry average for online retail (5.84%), but much higher than the negative margins posted by GME in the last three years)
c. Sales to Invested capital, measuring the capital intensity that will be needed for them to deliver growth. A primarily online retail story will need less, and a gaming platform or growth in stores will require more. (I assume that any growth that happens will be online, and I use the average sales to capital of 1.80 ratio of online retail firms)
d. Failure probability: reflecting the likelihood that the company does not make it as a going concern. I used the bond rating to estimate the chance of failure to be 12%
Change what you want, leave all else alone and come up with your own value. Then, please go to the Google shared spreadsheet and enter your inputs. Let the games begin:
Until next time!

Today's class started with a test on whether you can detect the direction bias will take, based on who or why a valuation is done. The solutions are posted online on the webcast page for the class. We then moved on to talk about the three basic approaches to valuation: discounted cash flow valuation, where you estimate the intrinsic value of an asset, relative valuation, where you value an asset based on the pricing of similar assets and option pricing valuation, where you apply option pricing to value businesses. With each approach, we talked about the types of assets that are best priced with that approach and what you need to bring as an analyst/investor to the table. For instance, in our discussion of DCF valuation and how to make it work for you, I suggested that there were two requirements:  a long time horizon and the capacity to act as the catalyst for market correction. Since I mentioned Carl Icahn and Bill Ackman as hostile acquirers (catalysts), you may want to look at Herbalife, the company that Ackman has targeted as being over valued and Icahn did for being under valued. See if you can get a list going of how each is trying to be the catalyst for the correction... and think about the dark side of this process. We will be starting on the first lecture note packet on Monday. So, please have it downloaded and ready to go.

Attachments: Post-class test and solution.

Each week, I will use the Thursday email to prod, nag and bug you about the project. So, without further ado, here is where you should be this first week:
  1. Find a group: The groups are yours to create and you should try to have at least 4 people in a group and not more than 8 (that limit is for your own protection).  If you are being ostracized and no one wants you,  you can add your name to the orphan list for the class: https://docs.google.com/spreadsheets/d/1bVHle6DwwbeNWrZHRvPInd_dSckAddDH_veHcZyS3Nc/edit?usp=sharing 
  2. Pick a company: This will require some coordination across the group to make sure that you meet the minimum criteria (at least one money loser, high growth, emerging market, service company). In making this choice, remember that you can value any business you want, public or private, small or large, listed in any market. There are at least a couple of entrepreneurs in the class who are valuing their own businesses and  quite a few valuing privately owned family businesses. Once you have picked a company, please enter your company name in the Google class master spreadsheet: https://docs.google.com/spreadsheets/d/1ZTPRdD65dYPoWuG05UH0vSto1jrNGNstGwvdTPo2qAE/edit?usp=sharing 
  3. Annual Report: Find the most recent annual report for your company. If you are valuing a private business, just ask for income statements and balance sheets for as long as you can get them (I will assume that you know the owner or better still, you are the owner).
  4. Public filings: If your company has quarterly reports or filings pull them up as well. 
In doing all of this, you will need data and Stern subscribes to one of the two industry standards: S&P Capital IQ (the other is Factset). As MBAs, you should have access to Capital IQ on the Stern Dashboard, but you need to ask for access, I have attached a pdf file that shows you how. Until next time!

Attachment: Cap IQ Access


I know that it is still early in the class and office hours are not on your mind, but they will be soon. Let me start with my office hours, which are scheduled as you know, from 11 am - 12 pm, NY time, every Monday and Wednesday for all three classes. Since NYU classes is finicky about how zoom sessions show up in classes, I had to create the session in my corporate finance class (and will show up to those who are enrolled in the class on their Zoom stream) but not in the valuation classes. Consequently, I am sharing the details of the zoom session just for my office hours (since the meeting ID is the same for all of the sessions, all you have to do is incorporate this into your calendar and it should show up every Monday and Wednesday):

Weekly: https://nyu.zoom.us/meeting/tJcqde6grTguE9fPlW_auZIONu4fKwRdN2Es/ics?icsToken=98tyKuCrqTktEteWtBCERowqB4joKPzztnZbj_pbrBPSPCFGWCrZGPcWNJloItz-

Join Zoom Meeting

Meeting ID: 937 2783 3493

TA Office hours and review sessions
In addition, your TAs will have both office hours each week, and a review session, where they will cover problems from past quizzes and exams, related to the material of the week. I have scheduled the Zoom sessions for those, and they should show up on NYU classes, when you log on. Sorry for this convoluted and messy email, but there are some things that are more complicated online than in physical locations. Until next time!
A few quick notes. The first is that I did put up an in-practice webcast today. It is a very basic webcast on how to read a 10K, using P&G as my example. The links are below:
Downloadable video:  http://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/Reading10Knew.mp4 
YouTube Video:   https://youtu.be/UzUJzdn7c2w?list=PLUkh9m2BorqmRAGzJb5OIvTAKZZu9HWF- 
P&G 10K: http://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/PG/Reading10KPG.pdf
P&G Valuation (excel spreadsheet): http://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/PG/P&Gvaluationfixed.xls
It is a very old webcast,and I need to do a newer version, but I am way too lazy.

Second, for those of you who have already valued GameStop (the first valuation of the week), thank you! For those of you who have been putting it off, there is still time to add your input to the crowd:
If you scroll to the right, and towards the top, you will see the average and median values that the crowd has estimated. 

Finally, for those of you who are late to this party, we have run out of beer and chips, but you can read all of the emails that I have sent so far in the class:
If you read them all, it is the equivalent of drinking a six-pack. So, please don’t drive or operate heavy machinery! Until next time!
I hope that you are enjoying your first weekend back at school. I will intrude with a couple of notes. 

1. Teaching Fellows/Review sessions: Just a reminder about the TAs for this class. There are two:
They will have office hours and a review session each week. The times and zoom links are on NYU classes.
2. Newsletter:  The first newsletter for the class is attached. As I said, there is usually not much news in these newsletters. Think of it more as a timeline for the class, telling you where we went last week and laying out our plans for the week ahead. If you get a chance, take a look at it. 

Finally, we will be starting with the first lecture note packet in class on Monday. Please have it with you for class. The pdf version can be found here:
Have a great weekend! Until next time!

Attachment: Issue 1 (February 6)

2/7/21 I am taking a break from the Super Bowl since I really don’t much care for half time shows. I hope that you are enjoying the game. First things first. This week, we will be delving into the mechanics of discount rates, starting with the risk free rate and then moving on to the equity risk premium. They are both central to valuation and we live in unusual times, where the former, in particular, is doing strange things.

Second, we will be starting off tomorrow's class with the question of firm versus equity valuation. I am attaching the cash flow table that we will be using for the start-of-the-class test as well. If you get a chance, please take a look at it before you come into class. The question is at the bottom of the page. Until next time!
Today's class started with a look at a major investment banking valuation of a target company in an acquisition and why having a big name on a valuation does not always mean that a valuation follows first principles. We began our intrinsic value discussion by talking about the weapons of mass distraction. If you want to read the blog post I have on the topic, try this link:

After setting the table for the key inputs that drive value - cash flows, growth, risk, we looked at the process for estimating the cost of equity in a valuation. In particular, we broke down risks into different types and argued that only some of these risks belong in discount rates, if investors are diversified. Next session, we will start with a discussion of risk free rate, a foundational number that will drive the rest of our calculations. I have attached a post class test for today, with the solution, but I think that four of the questions relate to risk free rates, which we have not covered yet. So, if you want to wait until Wednesday’s class, you might have an easier time. Until next time!

Attachments: Post-class test and solution

Airbnb was one of the highest profile IPOs of last year, and as the IPO approached, and before the bankers priced it, I posted my valuation for Airbnb, with my story:
You will notice that for an IPO valuation, there is an added input for IPO proceeds and IPO share count, but the bottom line is that I valued the equity of Airbnb at about $35-40 billion. As with any IPO, the numbers all come from a prospectus and I have a link to the final prospectus that Airbnb filed on December 2:
Now that Airbnb has been public for a while, I have updated my valuation to reflect its public status:
Note that barring a few minor changes (updates to the riskfree rate and discount rate), not much has changed and my value for equity is still around $36 billion, but my value per share has dropped because the existing management options have become a much bigger drain at a share price of $200/share. In fact, the market’s assessment of equity value is about $1 billion, well above my estimate. It is also worth noting that I am not one of those who discounts the value of sharing economy companies. I own Uber and would love to own Airbnb, but I am having trouble stretching my story to get to the value that the market is attaching.

There is a very real possibility that I am missing something significant. So, here is what I want you to do. There are five drivers of value for Airbnb (one more than GameStop):
a. Gross Billings growth rate (in 2021 and a growth rate beyond); I used 40% for 2021, kept it high from 2022-25 and then dropped it down to 2% over time.
b. Revenue as a share of gross billings: This is the percentage of the gross billings that Airbnb gets to keep. It is currently around 12.5% but I expect it to rise to 14%.
c. Target operating margin, measuring the profitability part of your story (I use 25%, reflecting my expectation that Airbnb is going to evolve to look more like Booking.com, an intermediary, than a hotel company)
d. Sales to Invested capital, measuring the capital intensity that will be needed for them to deliver growth. I use the company’s current sales to invested capital ratio of 2.65.
2. Failure probability: reflecting the likelihood that the company does not make it as a going concern. I assess a failure risk of 10%, reflecting their money losing status, but also factoring in their evolving business model and low debt.
Change what you want, leave all else alone and come up with your own value. Then, please go to the Google shared spreadsheet and enter your inputs. Let the games begin:
Until next time!
We started the class with a discussion of risk free rates, exploring why risk free rates vary across currencies and what to do about really low or negative risk free rates. The blog post below captures my thoughts on negative risk free rates:
If you want to see my updated perspective on risk free rates, try my blog post from today:

We just started on the discussion of equity risk premiums but the contours of the discussion should be clear.Historical equity risk premiums are not only backward looking but are noisy (have high standard errors). You can the historical return data for the US on my website by going to
Click on current data, and look to the top of the table of downloadable data items. Finally, The post class test and solution are attached. We also embarked on assessing country risk. I won’t drown you in the details, but you should also be able to look up equity risk premiums by country at the data link. 

One last note. It is Wednesday and time for the first weekly challenge, and it relates to the consistency of equity versus firm valuation. I have attached it and will post my solution by Sunday night. Until next time (which won’t be until a week from today. Monday is a university holiday!)

Attachments: Weekly challenge #1, Post-class test and solution.

By now, you should have a company picked, and if so, you can start thinking about at least the first two pieces of your discount rate calculation, a risk free rate and an equity risk premium. 
  1. Riskfree Rate: Currency is a choice and you can choose to value your company in any currency, though the currency in which your financials are reported is a good place to start. Of course, if that currency happens to have a 100% inflation rate, you may rethink your choice. Once you have the currency, follow the template for computing a risk free rate. If your currency does not have a default free entity issuing it, you may need sovereign default spreads for ratings classes, and you can find them on my website. Here are some useful links:
    1. Government Bond Rates (in local currency): https://tradingeconomics.com/bonds 
    2. Sovereign Ratings: https://www.moodys.com/login?ReturnUrl=https%3a%2f%2fwww.moodys.com%2fviewresearchdoc.aspx%3fdocid%3dPBC_186519%26lang%3den%26cy%3dglobal (You will be asked to register, but it is free… And worth the giving up of your privacy. If you are worried about your privacy, that train has left the station anyway…)
    3. Sovereign CDS spreads: Try typing in SOVR into a Bloomberg terminal
  2. Equity Risk Premiums: I went through my calculation of country risk premiums in class and we will return to this calculation net week, with implied equity risk premiums. In case, you are truly bored over this long weekend, you can read an annual update paper that I write on equity risk premiums every year. I am still working on this year’s version, but you can download the 2020 version by going to the link below: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3550293 

That’s about it for the moment. Enjoy the long weekend, and until next time!

2/12/21 Since this is a long weekend and you have nothing to do (just kidding), I have put up two valuation webcasts. The first one is on risk free rates and the second on implied equity risk premiums. We have not done the latter yet, but we will be talking about it in class next week:

Risk free Rates
Additional material:

Implied Equity Risk Premiums

The webcast uses the February 2013 spreadsheet, but I have tweaked the spreadsheet a little bit and the cell numbers have changed in the updated version, but the process remain the same. I have attached the February 2021 version to this email. I hope that you get a chance to watch one or both! Until next time!

Attachments: Implied ERP spreadsheet from February 1, 2021


1. First things, first. Your newsletter is attached for the week.

Attachment: Issue 2 (February 13)

2. Company choice & groups: I was checking the valuation master sheet:
I notice that a lot of you have not picked a company yet. If you have already and have just not entered the company name (not symbol), please do so. 

3. Orphans up for adoption: If any of you are in groups that would like an extra person, please check this list:
If you can add someone to your group, I would appreciate the gesture. Thank you!
I hope that you had a good weekend. Two quick loose ends to tie up. First, I hope that you had a chance to watch the in-practice webcasts on the risk free rate and implied equity risk premium (I know you probably were busy doing more fun stuff, but no harm asking). Second, I sent you a weekly challenge last Wednesday. I don’t know whether you had a chance to try, but it is still not too late. I have attached the solution to that weekly challenge (and the weekly challenge, in case you have no idea what I am talking about). 

This week is a short one, since we have only one session and we will turn our attention to equity risk premiums, talking about forward-looking estimates and we will then move on to the cost of debt and capital. So, if you are shaky about any of those concepts, I hope that you are rock solid, by the end of the week. 

Finally, since we are in the midst of this discussion, you may find my last data update post on my blog useful:
In fact, if you have not read the first three updates, and have time on your hands, please do so. Until next time!


  1. Weekly challenge #1
  2. Solution
Moving right along, it is time for the valuation of the week, and this week’s company bears no resemblance to your first two. It is Heineken, the Dutch brewer, with a worldwide brand name. The reason that I am focusing on the company is not because I like its product, but because this is a valuation that I did in September 2019, in Euros, when the risk free rate was negative in that currency. Begin by reading this post on negative interest rates from 2016:
You can continue by reading this piece that provides the background for the company and my valuation:
You can download the historical data on the company here:
You can download my valuation here;
You are welcome to update the valuation to include the additional quarter of information that has come out, but not much has changed. Try playing with the risk free rate/stable growth rate combination, and I use the word “play” deliberately, since you are messing with first principles when you do so. When you are done, you can enter your number and an updated price into this Google shared spreadsheet:
If nothing else, this will give you bragging rights, since 99% of people who do valuation for a living have not only never valued a company with negative risk free rates, but many in this group will claim it cannot be done. You can say it can and will be done. Until next time!
I am sorry to hit you with a second email on the same day, but this one is about getting data for your company, In the next week or two, we will delve into estimating betas for your company, and if you have access to a Bloomberg terminal, you can pull up the beta page for your company. If you have used a Bloomberg terminal before, you will easily find your way on it, but just in case you have not, I have put together a webcast to help you:
While I look at only a couple of commands (HDS, to get ownership lists, and BETA, to get the beta page) in this webcast, I have a document that lists out all of the Bloomberg commands I use:
If you are in New York, and you can go into school, you can find the Bloomberg terminals in the building:
If you are not in New York, and you don’t have access to a Bloomberg terminal, never fear. All of the data that you get from a Bloomberg, you can get from other sources, and I will send you those links on Thursday. That’s about it. Until next time!
n the session today, we started by doing a brief test on country risk premiums. After a brief foray into lambda, a more composite way of measuring country risk, we spent the rest of the session talking about the dynamics of implied equity risk premiums and what makes them go up, down or stay unchanged. We then moved to cross market comparisons, first by comparing the ERP to bond default spreads, then bringing in real estate risk premiums and then extending the concept to comparing ERPs across countries. Finally, I made the argument that you should not stray too far from the current implied premium, when valuing individual companies, because doing so will make your end valuation a function of what you think about the market and the company. If you have strong views on the market being over valued or under valued, it is best to separate it from your company valuation. I am attaching the excel spreadsheet that I used to compute the implied ERP at the start of February 2021. Play with it when you get a chance. Post class test and solution attached.

Building on the theme of cross market risk premiums, I have attached the weekly challenge for this week, and it includes a data set. Don’t be intimidated. It is actually a lot of fun, once you start playing with the numbers. Until next time!

Attachments: Implied ERP spreadsheet for February 2021, Post class test and solution, Implied premium challenge & data

2/18/21 First things first. By now, I hope that you are in a group and have picked a company. If you have, you should be able to complete two basic tasks related to discount rates, estimating risk free rates and equity risk premiums. Along the way, you have to get comfortable with how to estimate implied equity risk premiums, and to further you on that path, I posted a webcast on equity risk premiums last week. Take a look at it (it is on the webcast page for the class: http://www.stern.nyu.edu/~adamodar/New_Home_Page/webcasteqspr21.htm), when you get a chance. Also, please do try this week’s challenge, since it will give you perspective on equity risk premiums and how they relate to riskfree rates and default spreads. Until next time!
If you remember, we started this discussion in class by looking at how to measure company risk exposure to country risk, using Embraer, Ambev and Coca Cola, using revenue weights, and then looking at Royal Dutch, where we used oil production weights. In this week’s valuation tool’s webcast, I look at estimating a company’s risk exposure to country risk.
Webcast: https://youtu.be/D3IGn6tH03c?list=PLUkh9m2BorqkNIdjpZY2kI0qzRbEv5F5L
Slides: http://people.stern.nyu.edu/adamodar/pdfiles/blog/ERPforCompany.pdf
Supporting data: http://www.stern.nyu.edu/~adamodar/pc/datasets/ERP&GDP.xls
Of course, the table you see in this webcast with GDP and ERP is an old one, and you can get the updated version here:
Give it a look, when you get a chance. 

On a different note, I had sent you a YouTube video on how to use Bloomberg to get basic data on your company. For those of you wondering how I got a Bloomberg terminal installed in my home, I did not. What I used instead is a really neat interface called Bloomberg Anywhere that you can use to make your terminal mimic a Bloomberg. If you are in New York, and can access a terminal at Stern (I sent you the locations), you should, but I have learned (thank you to Houss El Marabti) that you too have access to Bloomberg Anywhere, as a Stern student. I have attached the instructions on how to use it in the document below, but keep in mind that there are only a handful of connections that Bloomberg allows at any one time. (Read the document to the end to see why). Given that constraint, you should plan your Bloomberg expedition with purpose, and be ready to get the stuff you need quickly. For the moment, I would like you to get on, if you can, and print off three Bloomberg pages for your company as soon as you can:
  • BETA: Just print the default page (which will be a 2-year weekly beta against the local index)
  • CRPR: which will give you the bond ratings for your company, if it is rated
  • DDIS: which will give you the maturity distribution for your company, if it has debt, with an average maturity
If you play this right, it will take only a few minutes, and if you don’t have a printer, just take pictures of each of these pages. Until next time!

Attachment: Student instructions for Bloomberg

Last week, we continued on our discussion of discount rates by looking at how best to estimate the equity risk premium. This coming week, we will complete that discussion and start on the meat and potatoes part of valuation, which is cash flows. In the meantime, attached is the newsletter for the week

Attachments: Issue 3 (February  20)

This week, we will complete our discussion of hurdle rates and move on to murkier territory, where we estimate earnings and cash flows.  I hope you had a chance to try the weekly challenge. If you did, the solution is at the link below.
Give it a glance, if you have the time!
2/22/21 n today’s class, we started by reviewing the pitfalls of regression betas. They are backward-looking, noisy and subject to game playing. We went on to talk about bottom up betas, focusing on defining comparable firms and expanding the sample. I did make a big deal about bottom up betas, but may have still not convinced you or left you hazy about some of the details. If so, I thought it might be simpler to just send you a document that I put together on the top ten questions that you may have or get asked about bottom up betas. I think it covers pretty much all of the mechanics of the estimation process, but I am sure that I have missed a few things.
In the next session, we will talk about cost of debt.

Attachments: Post class test and solution

My valuations of the week are usually on individual companies, and this semester, we have already looked at Airbnb, Heineken and GameStop. This week, I am doing something different, but one where every investor has a stake in the outcome. I want to value the S&P 500 index, using the same principles that allow me to value a company. You can start with a blog post at the start of this year, where I valued the S&P 500:
Read to the end of the post for the valuation, but it is a simple one based upon expected earnings and cash flows on the index. My valuation of 3360, at the start of the year, was about 12% below the index level, but that reflects my assumptions. They are in this spreadsheet:
Please download the spreadsheet, and change the assumptions that you feel comfortable changing, valuing the index as of today. Note that, if nothing else, you can update the riskfree rate to what it is today and the index level. Once you are done, you can enter the numbers in a shared Google spreadsheet:
In today’s class, we started with the cost of debt and computing debt ratios for companies and how to deal with hybrid securities.. If you are interested in getting updated default spreads (on the cheap or free), try the Federal Reserve site in St. Louis:
These are spreads on indices created by rating, updated daily. Neat, right? We then moved on to getting the base year's earnings right and explored several issues:
1. To get updated numbers, you should be using either trailing 12 month numbers or complete the current year with forecasted numbers. In either case, your objective should be to get the most updated numbers you can for each input rather than be consistent about timing.
2. To clean up earnings, you have to correct accounting two biggest problems: the treatment of operating leases as operating (instead of financial) expenses and the categorization of R&D as operating (instead of capital) expenses. The biggest reason for making these corrections is to get a better sense of how much capital has been invested in the business and how much return this capital is generating. I know that we have not covered R&D expense capitalization fully in class, but I think you can still try it.  Post class test and solution attached as is the weekly challenge.  You will get another email later tonight about the first quiz. So, stay tuned.

Attachments: Post class test and solution

2/24/21 The first quiz is coming up and I wanted to cover some logistical details.
1. Quiz location and timing: The quiz will be on Wednesday, March 3. It will be accessible online on NYU classes from 4 am - 2 pm, New York time, and it is an hour long exam. It is open-book, open-notes and you can even use your laptop. The questions, unlike previous quizzes (see below), will be multiple choice and the quiz is 10% of your grade.
2. Quiz coverage: The quiz will cover everything through the end of cash flows (about slide 157); growth is not on this quiz. It will therefore include the big picture sessions on valuation, discount rates and cash flows.
3. Past quizzes: I am posting the links to the quizzes from just the past few years. While there are older quizzes you can cover, these are much more relevant for the quiz at hand.. If you do run into a growth question, skip it.
As you work through these quizzes, please do remember that these quizzes are open ended and were meant to be taken in a classroom. While the questions on your exam will be roughly equal in difficulty, the fact that they are multiple choice is both a plus an a minus. The plus is that right answer should be one of the multiple choices. The minus is that all of the other choices may work, if you make a mistake on a step.
4. Quiz review webcast: I have a webcast from a prior semester that I have put together where I take you through the material that will be covered on the quiz. It is about 35 minutes long and it may help you get ready for the quiz (or not)… 
5. Additional office hours: I will be having extra office hours next week. I am still working out the times, since I want people on different time zones to be able to join in, but I will let you know as soon as I have them nailed down, with a zoom link. I hope that you find this useful.
I was going to remind you of the project and working on it, but if you are turning your attention to the quiz, you may be checking out the links I sent yesterday for the past quizzes and solutions. Since the link I sent yesterday included only a subset of the quizzes and stopped in 2016, I decided to update the files and create new links. Try these for all the quizzes through 2019, and remember to work backwards, since the earlier quizzes may have slightly different coverage:
Past quizzes: http://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz1.pdf 
Past quiz solutions: http://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz1sol.xlsx
I hope that you find some time to not just review the lecture notes, but work through the practice problems. In fact, it is the working through problems, using the lecture notes as a guide, that will provide the deepest learning.
 know that you have big and fun plans for the weekend and it is my job to ruin them. If you feel the urge to catch up on your project, I am going to give you the capacity to do so by posting not one, not two, but three in-practice webcasts:
1. Trailing 12-month numbers:  In the webcast for this week, I look at how to compute trailing 12 month earnings from a 10K and a 10Q: 
The most productive use of the webcast is to print off the most recent annual and quarterly report for your company and work with your company’s numbers.
2. Converting leases to debt: I have also posted a second webcast on converting leases to debt which takes you through the process of which numbers to use in this conversion and how to deal with loose ends (like the lump sum that is often given for past 5 years).
3. Converting R&D to capital expenditures: We have net covered how to capitalizet R&D expenses in class yet, but you can get a jump on the process with this webcast. I use Microsoft from a year gone by to illustrate this concept:
Incidentally, to add to your stress, I just want to remind you that the first quiz will on Wednesday (March 3). It has been brought to my attention that a handful of you have back-to-back-to-back classes all day that day, and that you might not be able to squeeze an hour in, during the window that I gave you (4 am - 2 pm). Since the valuation class runs from 2-3.20, I think that the best solution is to move the window an hour, so that it runs from 5 am - 3 pm. Since there will be class that day, I obviously would prefer that you finish the quiz before the class starts, but if the only time you can take it is from 2 pm - 3 pm, you can watch the recorded session. 

On a different note, I don’t know whether you had a chance to read Charlie Munger’s remarks this week:
I won’t pick a fight with a 97-year old, and I like the fact that he has no filters, but I think Charlie is plain wrong on his assertion that 2-3 stocks are all you need in a portfolio. It is particularly rich coming from him, since Berkshire Hathaway has dozens of holdings in its portfolio and even more so when you factor in that the S&P 500 index has outperformed Berkshire Hathaway’s investment returns for the last decade. On Tesla and Bitcoin, though, Charlie has a point.

I know that you are busy and I have a guess about what you are working on. I have attached the newsletter, on the odd chance that you may want to take a look at it. I As you prepare for the quiz, try not to  drive yourself into a frenzy. It is just a quiz, just 10% and if you do badly, you can make it go away. That said, it is better to do well than badly. So, good luck and see you in class on Monday.

Attachment: Issue 4 (February  27)

In tomorrow’s session, we will continue on the path of estimating earnings and getting to cash flows. Along the way, we will have to deal with tax rates, capital expenditures, working capital and other potential pitfalls. Nothing that we do is particularly difficult or hard to understand, but the details will pile on top of each other. Also, if you have not had a chance to check in, the March update for the S&P 500’s ERP is up:
It is at 4.56%, down from 4.80% in February, but the T.Bond rate surged to 1.43%. 

On Wednesday, you will take the quiz online, and it an hour long, and unlike prior quizzes (which were in class, and 30 minutes), these will be multiple choice or calculated answers, where you will get all or nothing on the question. As mentioned before, the quiz will be accessible during the day for about 9 hours (and I will send you the specifics on Tuesday). If you have enrolled with the Moses Center for accommodations, I have incorporated those into your quiz times as well. Also, the quiz is open book, open notes and you can use your laptop. If you want all quizzes that I have given from 1997 to 2019, you can get them at the links below:
Quizzes: http://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz1.pdf
Solutions: http://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz1sol.xlsx

I think it is over kill, but whatever makes you happy.

Attachments: Weekly challenge #3, Solution & Synthetic rating

We continued our discussion of cash flows, by first putting to rest some final issues on earnings, including the tax rate to use in computing after-tax cash flows and dealing with money losing companies. In the process, we did look at what to do about accounting fraud, and while the answer is not much, there may be a role for forensic accounting. To be honest, most forensic accounting books are designed for valuation morticians, but here are a couple that you may find useful:
We then moved on to examine broad questions about what to include in capital expenditures and working capital, before putting the cash flow topic to rest by working out debt cash flows and cash flows to equity. Next session, we will continue with a discussion of growth rates but remember to take your quiz earlier in the day first; the class will start at the scheduled time, but I will give you a break and go for only an hour. 

Atttachments: Post class test and solution

By now, I know that you are pros at taking quizzes online, but I do know that you still worry about whether you will find the quiz tomorrow and how exactly the process works. To help along the way, I have created a 20-minute demo quiz, with four questions from what the quiz will cover. If you get a chance, go on NYU classes, take the quiz (it will be review) and submit it, to make sure that the process works smoothly. The score on the demo quiz will not count, but it may give you some peace of mind.

On a different note, today is the day that you get the valuation of the week. Rather than hit with you another company valuation, I thought I would try something lighter.So, let’s have some fun. I have always been a Star Wars fan, and like other fans, I was a little worried when Disney bought Lucas Films (and with it the rights to the Star Wars franchise) for $4 billion a few years ago. Disney was explicit about its plans at the time, and said that it planned to produce three major Star Wars movies, continuing the story, and three side stories (like Rogue One) filling in history. I went to see Force One in December 2015 and wrote this post on my blog about what I thought the value of Star Wars was at the time;
I assigned a value of almost $10 billion to the franchise, with a big chunk coming from the side products (toys, software, apps) coming from the franchise. You can download the spreadsheet that contains the valuation here:
When I wrote the post, Force Awakens had been out in theaters only a few days and I estimated box office revenue of $2 billion for the movie. Rogue One, of course, had not been released yet and I estimated revenues of $1 billion. Force Awakens is now one for the history books, with global revenues of just over $2 billion and Rogue One crossed the $1 billion threshold.
Updated box office for Force Awakens: http://www.boxofficemojo.com/movies/?id=starwars7.htm 
In addition, the eighth Star Wars movie has come and gone, with the Last Jedi, as has the next add on movie on Hans Solo:
Updated box office for The Last Jedi: https://www.boxofficemojo.com/movies/?id=starwars8.htm 
The final movie in this trilogy, The Rise of Skywalker came out in 2019. You can get the updated box office numbers for all of these movies here:

In addition, it looks like Star Wars is going to be central to Disney Plus making inroads into the streaming business. The Mandalorian was the most-watched series last year, and those Baby Yodas sold out for Christmas (merchandising again) and Wandavision looks like it is going to be a hit as well. That adds a value stream that did not exist a few years ago. Armed with this additional information, here is what I would like you to do. Go into the spreadsheet and reestimate the value of the Star Wars franchise. It may be only tweaks but give it your best shot. Once you have a value, go into this shared Google spreadsheet:
Enter your numbers and lets see how the distribution of values evolves over time. And since this is a Star Wars post, might as well end with some good advice from Yoda: Have fun, you must!

In this session, which occurred after the quiz i, we started on our assessment of growth rates, starting with historical growth rates, before looking at analysts estimates of growth and why they do not carry more predictive power (given that analysts often are immersed in company-specific knowledge and have access to management). We then looked at tying growth to two fundamental questions: (1) how much companies reinvest and (2) how well. The way we measure these can vary depending on whether you look at earnings per share, net income or operating income. The weekly challenge for this week, if you feel up for it, centers on fundamental growth. Try it, if you get a chance.

Attachments: Post class test and solution, Weekly challenge

I know that you just finished your first quiz and that you are probably in no mood for valuation. On the quiz itself, a couple of notes:
  1. On question 3, I had asked for the approximate risk free rate in Egyptian pounds, which is just the differential inflation added to the US T.Bond rate. I was just trying to make your life easy, but some of you did the more precise calculation (where you multiply (1+ T.Bond rate) by (1+ Inflation rate in Egypt)/(1+Inflation rate in US) and then subtract one). Since this is clearly correct, I have modified the solution check to treat that answer as right. So, if you did this and you check your quiz score, you should see a point added on.
  2. On the questions asking for a percentage answer, I had tried to explain what the computer had as answer by asking you to enter 8.15 as your answer, not .0815, if the answer was 8.15%). Some of you did add a percent (entered 8.15% in the box.. Instead of just 8.15) to the end of your answer, and computer algorithms are very stupid in some ways and those answers were treated as wrong. That is absurd. If you were one of those people, please let me know and I will go in and manually fix your score.
In sum, though, if you did well on the quiz, congratulations. If you did badly, make it your freebie (the lowest quiz out of three gets dropped out), Either way, do not spend too much time celebrating or regretting and move on.

Speaking of moving on, this would be a good week to take your company’s annual report apart and estimate the free cash flow to the firm and equity last year as well as accounting returns. If you have the historical data for your company, you can not only estimate historical growth in earnings per share but in other metrics as well (net income, operating income, revenues). While I almost never do a valuation based upon historical numbers, I find it useful as a platform for understanding the company and devising my story and forecasts for the future. If you want to see historical growth rates of all companies, broken down by sector, please visit this link:
Scroll down to historical growth, and you should see the data not just for US companies, but broken down globally and regionally. All these growth rates are in US dollars.
3/5/21 I am testing your patience at this point, but I am going to go on anyway. In the session after the quiz (yes, there was class after the quiz), we looked at the link between fundamentals and growth, and in particular, at how much of a role accounting returns (ROE and ROIC) have on assessing both growth rates and the value of growth. The scariest aspect of these numbers is that they are entirely driven by accounting choices, which can create biases.  In this webcast, I look at the process of estimating accounting returns, using Walmart as my example:
Webcast: http://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/ROIC.mp4 
Walmart 10K (2013): http://www.stern.nyu.edu/~adamodar/pdfiles/cfovhds/webcasts/ROIC/walmart10K.pdf
Walmart 10K (2012): http://www.stern.nyu.edu/~adamodar/pdfiles/cfovhds/webcasts/ROIC/walmart10Klastyear.pdf
Spreadsheet: http://www.stern.nyu.edu/~adamodar/pdfiles/cfovhds/webcasts/ROIC/walmartreturncalculator.xls
An updated version of the return calculator is attached. In case, you are interested in learning more about returns on capital, you should first seek out a psychiatric evaluation, and if you pass, try reading this awesomely boring paper of mine on the topic:
If nothing else, I can guarantee you that if you have sleep problems, this paper will get rid of them.

Attachment: http://www.stern.nyu.edu/~adamodar/pc/returncalculator.xlsx


This may be your weekend to forget valuation, but I am afraid that I have to intrude. The most recent newsletter is attached. 

Attachment: Issue 5 (March 6)


 the coming week, we will complete the last pieces of intrinsic value, talking about growth in all of its forms tomorrow and the terminal value on Wednesday. This is hard to believe but we are close to half way through the semester. So, if you have not picked a company, you should. If you have, you should have the financials. If you have the financials, you should be working on the valuation. I think you get the picture. I have also attached the solution to the weekly challenge. If your reaction is what weekly challenge, I don’t blame you. 

Attachment: Weekly Challenge #4 solution

For this week, I thought I would switch gears and value a very different company from the ones that we have valued before.  I look at Aramco, a company that became the most valuable public company (in terms of market cap) over night, when it had its IPO last year. The place to start this valuation is with the Aramco IPO, a document written by bankers for bankers, and hence thoroughly boring:
You can follow up with two posts that I wrote at the time of the IPO:
1. http://aswathdamodaran.blogspot.com/2019/11/a-coming-out-party-for-worlds-most.html
2. http://aswathdamodaran.blogspot.com/2019/11/regime-change-and-value-follow-up-post.html 
The excel spreadsheets containing my valuation of Aramco is here:
Obviously, much has happened since then, as oil prices have plummeted and then come back again, and if you want to do an updated valuation of Aramco, you can use the updated financials, but you may just want to look at the mechanics of this valuation, since it illustrates how much flexibility there is in valuation models, allowing them to be adapted to meet pretty much any set of circumstances.

In today’s class, we talked about the loose ends in valuation, i.e., all the things you do after you have discounted cash flows back at the discount rate and why they matter. We started with cash, the simplest and most direct of all assets to value, and talked about why investors may attach a premium or discount to the cash balance of a company, arguing that discounts reflect a lack of trust in management. I mentioned a paper that looks at how the market discriminates across companies, when it comes to valuing cash balances. We then moved on to cross holdings, and why they are difficult to incorporate into value, and to other assets that you may consider adding on, because we have not considering them yet. On the latter, the key component to remember is not to double count an asset, by first counting its cash flow and then the value of the asset itself.  Finally, I attach a weekly challenge for this week, built around terminal value. Please try it when you get a chance. It is simple but it will reinforce some key components of what we did in class.

Attachments: Post class test and solution, Weekly challenge

We are reaching the end of the intrinsic value details, and before I talk about the project, I wanted to let you know that the second and third packets for the class are available to download. You can find the links to the pdf versions of the files below:
Packet 2: http://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/valpacket2spr21.pdf
Packet 3: http://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/valpacket3spr21.pdf
The links are also accessible from the webcast page for the class.

I hope that you are also moving forward on your project. As I mentioned at the start of the class, I will be glad to give you feedback (without a grade) on the intrinsic (DCF) value for your company, if you can get your DCF spreadsheet to me by April 2. While I will not be able to tell you whether your valuation is right or wrong, I can at least tell you whether there are inconsistencies. You are welcome to use any of my spreadsheets, with the most general one being the fcffsimpleginzu that I use on most of my valuations of the week. 
The spreadsheet comes with add-ons that you may or may not need. Thus, there is a lease conversion worksheet, but if your company follows IFRS or GAAP can capitalizes leases, you can turn it off. There is an option worksheet that converts employee options into a value and recomputes value per share. Use what you want, turn off whatever you do not. If you want to build your own spreadsheet, you can do so, but remember my admonition about less is more and please do not (under any conditions) use a spreadsheet you picked up at an investment bank, since fundamental flaws are baked into it.
This week, we talked about some of the checks that you have to run on terminal value, to make sure that it is not running away with your valuation.  In this webcast, I look at ways in which you can take your terminal value number and diagnose it for problems.

he newsletter for this week is attached. In case you have time on your hands, I took the fourteen posts that I wrote about the COVID crisis playing out in markets last year, and made it a paper (too long and verbose, but that’s my weakness). If you are interested, you can read the paper here:
I hope that you find it not too painful to read. It is too personal and theory-agnostic to be an academic paper, but writing is my form of therapy. 

Attachments: Issue 6 (March 13)

During today's session we finished the last loose ends in valuation and started on connecting stories to numbers. If you find the Zoom session tiresome to watch, you may prefer this Google talk version that I did a few years ago on the same topic:
It is a little easier to get through and covers the topic.

The DCF is due by late Friday (April 2) (try to get it in by 5 pm, but if not, 6 pm or 7pm..). If you can get it in earlier, all the better. A few notes on the submission:
1. Individual, not group: This portion of the submission can be done individually and should be done individually rather than as a group, The feedback is specifically for you.
2. Submission content: An Excel spreadsheet will do, with notes embedded on your story and any specific assumptions
3. Submission subject: Use “My Perfect DCF” in your subject
Remember that this DCF is for feedback, not a grade, but work on it as if were your final valuation. That way, the feedback will be more focused and perhaps more useful.  To put a bow on this part of the class, I have a blog post that you may find enjoyable about dysfunctional DCFs. 

Attachments: Post class test and solution

3/16/21 In this week’s valuation of the week, I look back at a valuation I did two years ago, when Brexit was still up in the air in the UK and people were unsure about how it would play our, with as many as seven different options on Brexit, ranging from a No-deal Brexit to no Brexit at all. I tookeasyJet, a UK company that is particularly exposed to Brexit, because it gets so much of its revenues from the EU, which has stringent rules on who can or cannot fly between EU countries, and tried to value it under different scenarios. You can read my valuation thesis here:
If nothing else, you will see how scenarios can be used to deal with uncertainty. The valuations themselves are at the links below:
  1. No Deal Brexit: http://www.stern.nyu.edu/~adamodar/pc/blog/easyJetNoDeal.xlsx
  2. Messy/Delayed Deal Brexit: http://www.stern.nyu.edu/~adamodar/pc/blog/easyJetMessyDeal.xlsx
  3. Smooth or No Brexit: http://www.stern.nyu.edu/~adamodar/pc/blog/easyJetSmoothDeal.xlsx
Brexit may now be settled, and you may not care about easyJet, but review the write up and valuation anyway, since this approach may help you in valuing your company, especially if you feel that the COVIDmay have the same type of discrete consequences for your firm.
In today’s class, we continued our discussion of stories, and how critical it is to keep the feedback loop open, so that you can make your stories better. We also talked about how story breaks, shifts and changes. Since I talked about dealing with new earnings reports, I thought you may find these two posts of interest in how narratives shift, and with them, values:
Reacting to Earnings Reports: http://aswathdamodaran.blogspot.com/2014/08/reacting-to-earnings-reports-lets-get.html
Narrative Resets: http://aswathdamodaran.blogspot.com/2015/08/narrative-resets-revisiting-tech-trio.html 
We started with two conventional valuations, one of Con Ed, another of  3M. If you are still wrestling with the question of management options, I have a weekly challenge that may help you work through your doubts:
Of course, the stories on these companies has evolved since, but it should give you a taste of how narratives change

Attachments: Post class test and solution, Weekly challenge #5

 I know that your project DCFs are not due until two weeks from tomorrow, but if you decide to work on your DCF and even turn it in early, here is some general guidance.
  1. You will be turning in a spreadsheet, not a report.
  2. Your submission will be individual, not as a group.
  3. You will be submitting to me, as an email attachment. Please include the words “My Perfect DCF” in the subject.
  4. You are welcome to use any of my spreadsheets. The most forgiving and versatile of my spreadsheets is http://www.stern.nyu.edu/~adamodar/pc/fcffsimpleginzu2021.xlsxIt has updated equity risk premiums, as of yesterday, for both the US and other countries, and it gives you a way of inputting the effect of COVID on this year’s earnings and revenues. 
  5. Each of your valuations tells a story. Try to make it explicit and built it into your spreadsheet. In my spreadsheet, I have set up a worksheet to allow you to do this. Take advantage of that worksheet.
Don’t put too much pressure on yourself. This is only for feedback. Try your best. 

One final point. I know that this weekend is supposed to be a 3-day quiet weekend. I am not sure what that means but I won’t be sending you emails until Sunday night. Since I will not get a chance to email you tomorrow, I have the links to your valuation tools webcast for the week below, covering valuing employee options and how to value them. 
Welcome back from your non-break. I held back on emailing you but the newsletter for the week is attached. As for this coming week, we will continue to dive into valuations, starting with one of the S7P 500 tomorrow before embarking on the dark side of valuation. The second quiz is a week from tomorrow, which I know is the start of the passover week. If you cannot take it on March 29, for religious reasons, let me know and I will try to make accommodations. Also, if you want to try your hand at the possible, plausible and probable, you may want to take a look at ARK’s valuation of Tesla from a couple of days ago. Whether you are a bull or a bear on Tesla, I want you to take a look at what Ark is projecting and ask the questions that will help you draw a distinction between being optimistic and wandering off into fantasyland:

Attachments: Issue 7 (March 20)

3/22/21 In today’s class, we looked at how best to adapt valuation models to value companies on the dark side. Specifically, we examined how best to value young companies with limited information. If you are interested, try this paper on valuing young companies:
I also mentioned a blog post that you may find relevant for today’s discussion on how dilution in future years is already incorporated into value:

Next Monday, we will move on to the second quiz for the class. In case you are nervous about it, here are some specifics:
1. Quiz time and logistics: The quiz will be accessible from 5 am to 3 pm, NY time, on Monday, April 5. Since it is a one hour quiz, you will need to start by 1 pm to get done. We will have class from 2 pm - 3.20 pm, NY time. 
2. Content: It will cover the mechanics of DCF, starting with growth rates and terminal value and extended into the loose ends of valuation and the versions of the DCF we have used on the dark side. 
3. Review for the quiz: The links to the review for the quiz and the past quizzes are below:
3/23/21 First, before I sow more confusion, I want to clarify that the quiz is this coming Monday (March 29), not the following. I am sorry that I screwed up on the email yesterday. Second, in this week’s valuation of the week, I am going back in time, to  a valuation and pricing that I did of the Los Angeles Clippers, when Steve Ballmer paid $2 billion for the team. I explain how I value the Clippers and how I would value any sports franchise in this post:
You can find my valuation of the Clippers in this link:
You can do one of the two things in this week’s valuation challenge. 
1. You can take my Clipper valuation and make your own assumptions (there are relatively few) and value the Clippers as of June 2014. 
2. You can then follow up by trying to price the Clippers, a preview of the pivot that we will be making away from valuation in the weeks to come. To help, I have raw data on sports franchises below:
For MLB, NFL, NBA and NHL: http://www.stern.nyu.edu/~adamodar/pc/blog/SportsTeamData.xlsx 
For European soccer teams: http://www.stern.nyu.edu/~adamodar/pc/blog/eurosoccerrawdata.xls 
For IPL (Indian cricket) teams: http://www.stern.nyu.edu/~adamodar/pc/blog/IPLrawdata.xls 
The data is a little outdated and you are welcome to update them, if you want. If you are a fan, you can pick your favorite team and using the raw data in these spreadsheets, try to value and price your franchise.
If you are in the corporate finance class as well, this may be repetitive, but what the heck? I talked about Monte Carlo simulations and the use of Crystal Ball, in conjunction with Excel, to incorporate uncertainty into valuation. You have access to Crystal Ball through Stern, but you can also download a trial version here:
If you are thinking about incorporating this into your company’s DCF, the program will provide the mechanics, but it can be garbage in, garbage out.  If you get a chance, read this blog post, since it gives you a step by step approach to doing a Monte Carlo simulation:
There are two challenges you will face along the way. The first is one created by the inability of statistics classes to create either an intuitive feel for or a love of statistics. I cannot fill in that gap entirely, but if the only statistical distribution you remember from your statistics class is a normal distribution, read this quick and dirty summary of what the distributions mean and how to pick between them:
It will take about 20 minutes to read, but will help you when you get to choose between distributions. The second is coming up with parameters for the distribution, a data question, and the answer lies in looking at the data. For instance, if you are trying to get a distribution going on interest rates or exchange rates or commodity prices, you can use historical data, and the Federal Reserve has that data going back a hundred years in this amazing link (which I have sent to you before):
If it is cross sectional data (for instance, operating margins across software companies), there is no better place to look than on S&P Capital IQ (Remember the link I sent you to be able to get access… If not, I have attached it again).
I hope that you have had a good week. I know that some of you have turned your attention to the quiz, which is on Monday (March 29), and that is perfectly understandable. However, if you are working on your project, the DCF is due a week from tomorrow for feedback, but only if you want it. When you do submit it, a reminder to enter “My Perfect DCF” in the subject. In addition, if you are interested I just posted on how I see the rise in interest rates playing out on value:
It looks at why stocks can continue to rise, even when rates are inceasing, and how the cause of the rate rise can play a role in how markets react to it. 
I hope that you are well. If you are in the process of valuing your companies,   If you are using my spreadsheet (http://www.stern.nyu.edu/~adamodar/pc/fcffsimpleginzy2021.xlsx) to value your company, and are confused about some of the inputs, I did a webcast about a year ago on using the spreadsheet (albeit a slightly earlier version of it). You can find the YouTube link  below:
You can take my spreadsheet and adapt it, but if you do, please do not hard code numbers directly into the valuation. That will make it more difficult for me to decipher what is going on, and for you to change your mind, as you will later this semester. Instead, create extra rows or cells in the input sheet, and add your changes in there. (I give you an example during the video guide). Finally,  looking at coming week, you have a quiz on Monday (March 29). It will be accessible from 4 am that day to 3 pm, NY time, and will be an hour long.
Two quick notes. First, the newsletter for the week is attached. Second, we will be done with packet 1 this coming week and moving on to packet 2. Please download both packets 2 & 3 when you get a chance. The  links are on the webcast page, but I have the attached the pdf links below:

Until next time!

Attachments: Issue 8 (March 27)

3/28/21 The quiz will be accessible starting at 4 am, NY time, tomorrow (March 29), and ending at 3 pm, NY time. It is scheduled for one hour. There will be class tomorrow, and I understand that some of you will not be able to come to some or all of the class, if you take the quiz at their, but please do come to class, if you can make it. This week, we will wrap up our discussion of intrinsic value, by looking at the last parts of the dark side of valuation. 

In today’s session, we continued on the dark side of valuation with a look at mature companies on the verge of transitions, and how you have to value the status quo company and the restructured one to make a judgment on investing in it. Finally, we looked at declining companies, where your forecasts may have to show declining revenues and margins, and added a twist with distressed companies, where you have to follow up your DCF. In the last part of the class, we looked at the challenges in valuing emerging market companies, from country risk to currency choices to corporate governance and cross holdings. None of these are unique to emerging market companies and learning how to deal with them becomes central to valuing any company.

Attachments: Post class test and solution

The second quiz is now behind you, and you should be able to check both your grades and the feedback (with solutions) online. As you work on getting your company DCFs done, I don’t want to distract you too much, but my valuation of the week for this week uses a different approach to valuing a company than what we have used to value companies so far. Using the Uber IPO from 2019 as my case study, I introduce a different approach to valuation where I value what a rider is worth to Uber, and use that to build up to a valuation of Uber. This is a technique that I have used to value Netflix (see my September 2020 valuation), Spotify (at the time it went public) and Amazon Prime, and you are welcome to borrow and adapt it, if you are valuing a company that is user or subscriber based. The blog post for the Uber IPO, from April 2019, is here:
In that post, I link to two valuations of Uber, one top down (where I use the conventional approach) and one bottom up (where I value a rider and build up). 
Since I have been tracking Uber since 2014, you can also contrast how my story and valuation of the company has changed since my first valuation (which I went through in class). In fact, in September 2019, I bought Uber, based upon a follow up valuation. The post explaining that is linked below:
I still own Uber, having doubled down in March 2020, when they dropped to $14. So far, so good, but the story is still unfolding. Until next time!
In today’s session, we wrapped up our discussion of intrinsic valuation. For decades, we have valued banks using the dividend discount model, simply because getting cash flows is so difficult, but that approach is built on trusting management at banks to behave sensibly (paying out what they can afford to in dividends) and regulators to do the same. For me, that trust was breached in 2008, and I present a way of estimating FCFE for a bank, using investment in regulatory capital as my stand in for reinvestment. Next session, we will wrap up the valuation section and start on pricing. If you are interested in reading more about valuing financial service companies, try this link:
The Deutsche Bank post is here:
We also looked at valuing commodity and cyclical companies, and why capitalizing R&D can change the value of a pharmaceutical company. The last part of the class was our first foray into pricing, why price can be different from value and why pricing is so much more common than intrinsic value. Finally, I have extended the deadline for the DCF feedback to Sunday night, since I have other family commitments this weekend and won’t be able to look at your valuations until next week.

Attachments: Post class test and solution

4/1/21 No more prodding and nagging, I promise. If you do decide to turn in your DCF for feedback, the window will stay open until Sunday night. Until next time!
Next week, we will be on our way on pricing an asset or company. As you will notice in the discussion, you will find that pricing is more about data and statistics, though a front loading of finance gives you perspective. One of the tools that we will draw on is regressions. This week’s valuation tools webcast takes you through the process. I know that we have not gone into pricing yet, but if your statistics are a little shaky, please go through the webcast. I use the banking sector to illustrate my case but I hope that you find it useful for both your  project.  If you are solid on your statistics, you can skip this webcast, since you already know everything that I am saying. If you need a quick review of the process, I think it will be useful.
Start with the webcast:
Download the slides:
Here is the raw data:
And the descriptive statistics:

I hope that your weekend is a little less frenetic than mine, but I am definitely not bored. That said, I wanted to nag you about getting your DCFs in by tomorrow, for feedback.

Attachment: Issue 9 (April 3)


I can see from my mailbox that it has been a productive weekend for many of you. I apologize for not returning any DCFs turned in since Thursday, but I was on the road in Los Angeles, visiting my son and his family, and decided to take a few days off from being online. I will get them back to you this week. This week, we will also delve further into pricing, and get ready for some basic statistics and data analysis. 

4/5/21 In today’s session, we continued with our discussion of multiples, starting with the definitional test, where you check for consistency. During the session, we also played Moneyball with the data and then extracted the variables that determine each multiple and noted that they have asymmetric distributions, making averages untrustworthy and medians more meaningful.  If you are disciplined about following this process, you will find multiples much more useful and have an easier time controlling for differences.

Attachments: Post class test and solution

I know that most of you have given up on the valuations of the week, but about a year ago, Kraft Heinz reported earnings with a trifecta of bad news, languishing operating numbers (flat revenues & declining margins), an accounting irregularity (with an SEC subpoena) and a massive impairment of goodwill, sending the stock price down by more than 25%. 
While companies reporting bad numbers is not uncommon, what made Kraft Heinz special is the pedigree of its lead investors, with Berkshire Hathaway owning 26% and 3G Capital (a Brazilian private equity group with an unmatched reputation for financial acumen and ruthless cost cutting. Investors who followed Buffett into the stock were not only shocked but claimed to be betrayed, that the oracle would mislead them. I wrote a post on why this unquestioning faith in Investment Gods is dangerous and delusional, and posted my valuation of Kraft Heinz. 
Blog post: http://aswathdamodaran.blogspot.com/2019/02/the-perils-of-investing-idol-worship.html
Valuation: http://www.stern.nyu.edu/~adamodar/pc/blog/KraftHeinz2019.xlsx
The financial information, including the most updated earnings report at the time of the post, can be found at this link:
I found the company close to correctly valued, with a value of $34.88, almost equal to the stock price of $34.23. The stock is currently trading at $40.70, roughly where you would expect it to be, given that valuation in 2018, and building in the expected price appreciation since. That said, you may want to revisit this valuation to see what you think of Buffett’s biggest blunder.  Talking about what’s coming down the road, as we enter the last few weeks of class, your third quiz is scheduled for April 26 and your final exam for May 12, if you want to mark those dates on your calendar. 
In this session, we continued with our discussion of pricing, starting with the analytics that drive PEG, PBV, EV/EBITDA and revenue multiples. During the session, I played the role of a naive equity research analyst, using sloppy pricing to push buy recommendations on stocks in a number of sectors, based purely on the level of multiples (low PE, low PBV etc.) and asking for pushback. In some cases, we just noted qualitatively the forces that may explain the stock’s cheapness (the beverage sector, for example) and in others, we used regressions. The bottom line, though, is that most companies that look cheap deserve to be cheap. The key to pricing is finding a mismatch between the pricing and the fundamentals (low PE & high growth, low PBB and high ROE, low EV to Sales and high margins). It is basis for much of equity research, and takes the form of screens. If you are interested, I have a post that expands on the notion of screening.
Since you have access to Cap IQ, you can try this out in any sector.

Attachments: Post class test and solution

4/8/21 I know that you have other things on your plate, but I will nag you about your final project nevertheless. If you have your DCF done, and most of you hopefully have (and I will get them back to you, if you have sent them to me for feedback soon), it is time to price your company. Go through the process that we went through in class of choosing comparable firms, finding a multiple that works and then controlling for differences (statistically or otherwise). Along the way, don’t forget that pricing is a pragmatic game. If it works, use it. To give you a sense of pricing, I I suggest that you read this excerpt that I found in a guide for appraisers trying to value a hotel on how to do it.
Another valuation rule-of-thumb used in the lodging industry is that each room of a hotel is worth 100,000 times the price of a Coke™ in the on-floor vending machine or in-room mini-bar. More formally:
Value = Coke™ price x Number of Rooms x 100,000
The Edgemore Hotel sells cans of soda for $1.50 in the room mini-bars. Thus, the value of the Edgemore by this “precise" valuation method is:
$1.50 x 300 x 100,000 = $37,500,000
We urge market participants to use this technique judiciously, as some properties seriously "misprice" soda in relation to property. (Really?)
No. This is not a parody but a real technique. If you don’t believe me, read the whole thing:
You may find it laughably simplistic, but in pricing, if it works, don’t fight it. 
4/9/21 If you have trying your hand at the pricing part of your project, you probably also are recognizing that this is an exercise in working with data sets. I have put up a webcast that is more statistics than finance about how to look at data and try to evaluate relationships between variables. I use the banking sector to illustrate my case but I hope that you find it useful for both your  project.  If you are solid on your statistics, you can skip this webcast, since you already know everything that I am saying. If you need a quick review of the process, I think it will be useful.
Start with the webcast:
Download the slides:
Here is the raw data:
And the descriptive statistics:
The newsletter for the week is attached, and as we move through packet 2, a reminder that the last packet is available for download on the webpage for the class:

Attachment: Issue 10 (April 10)

By now, almost all of you should have got your DCFs back, with my minimalist feedback. If you have not received feedback, could you please resend your DCF with “My Perfect DCF” in the subject. If you were expecting feedback on details (like beta or revenue growth rates), you were probably disappointed, but I thought that it might make sense to take you through my template for reviewing my spreadsheet, so that you can do it yourself on a future valuation.
1. Start by looking at your historical financials: The first place to start is by checking the inputs that you have for the most recent year and the year before. Here, for instance, are the numbers for Live Nation (which at least five of your were valuing) and Nio (which at least seven people are valuing):

Obviously, Live Nation  and Nio diverged in 2020, with the former having a horrifically bad year and the latter a really good one (at least in terms of growth). Note that Nio is incorporated in the US, but it is a Chinese company.
2. Check out the riskfree rate and cost of capital: The riskfree rate will reflect your currency choice for your valuation and your cost of capital will (or should be) in the same currency. I do have a worksheet that computes your cost of capital, but if you plan to use, rather than directly input a cost of capital, please make sure that you have picked the businesses and geographies for your company in that sheet.
Live Nation
Live Nation is being valued in US dollars, while Nio is being valued in Yuan. (See riskfree rates). The costs of capital are consistent, lower for Live Nation than for Nio. To check to see if your cost of capital is within bounds of reasonableness, remember that the median cost of capital in US dollar terms for a global company is 6-6.5%, and if you have a different currency, you can add inflation to it. If your cost of capital is more than 4% off the median in either direction, check your numbers to see if there is a mistake.
3. Check through the key inputs on growth, margins and reinvestment: The key inputs that drive your valuation are in the input sheet, and while they might be linked to a cell in default, you preserve and should use the power to change them to what you think best fits your story (see step 5):
Live Nation
You may need to revisit your numbers after you go through step 4, but you are not bound by historical data, industry averages or any other variable. These are your inputs.
4. Do a quick scan of the valuation output: Go to the valuation output page, and check out the following:
a. Revenues in your terminal year: One of the problems with growth rates in percent is that it is very difficult to figure out how the compounding plays out over time. To illustrate, take a look at the revenue forecasts for Live Nation over time:
The growth rates look high, but the revenue you have in year 10 is $8.5 billion, well below the revenues of $11.5 billion they had in 2019. That is a pessimistic story, albeit a plausible one, for the future, and if that is what you intended, you should leave it as is. If not, you should go back and change your revenue growth rate from years 2-5. 
For Nio, revenues are up, up and away, which makes sense given that it represents the convergence of two potentially big markets (China and electric cars)
Here the revenues increase to 340 billion Yuan in year 10. (In dollar terms, this would be about $50 billion). Again if that strikes you as too low (high) a number, go back and revisit your revenue growth rate. To get a sense of whether it is too high or too low, you should look at large companies in the sector and see what they generate as revenues.
b. Evolution of margins/operating income over time: In the table above, you also see margins changing for your two companies towards your target margin. How quickly it happens depends on the year of convergence that you pick. A lower number (as is the case with Live Nation) will cause a speedier convergence.
c. Imputed return on capital: If you go to the bottom of the valuation spreadsheet, you will notice an item that you probably overlooked when you did your valuation, but it will give you a snapshot of how your assumptions about growth, margins and reinvestment have played out in the company. For Live Nation, here is what you see:
The fact that your return on capital has trouble getting off the floor and even approach your cost of capital is troublesome, and it does look like you are reinvesting way too much, but more on that in step 5.
With Nio, the return on capital rises rapidly over time, but given its status as a first mover in China and presumed competitive advantages in that market, you may be okay with the 24.85%, but if you feel it is too high, you may need to work on your reinvestment, by lowering your sales to capital ratio.
5. Go to your stories to numbers worksheet: The most critical sheet on diagnosing your own DCF is your stories to numbers sheet. If you never even got to this sheet, clearly, you would not have been able to use it, since it will carry the default stories for GameStop or Boeing in there. For Live Nation, here is what you will see:
As you can see, the valuation yields a negative value per share and the culprit is also clear. It is your negative FCFF for the next 8 years. While each individual item has a storyline that makes sense, there is a fundamental contradiction in these forecasts. Since you are assuming that the company will not even make it back to 2019 levels, why do you need to be reinvesting such huge amounts in the future. Put simply, the sales to capital ratio is way too high, given your revenue story, and the easiest way to fix it is to go raise the sales to capital ratio to a really high number (I would use 100, in this case, since you never make it back to pre-COVID levels). In more moderate cases, where you make it back to pre-COVID levels over the next three or four years, you can use a high sales to capital ratio for those three years and then lower it to historic norms or industry averages. 

Finally, I know that a few of you built your own spreadsheets and I applaud you for doing so. If you found yourself pushed into using my spreadsheet, it is not because I am better at building spreadsheets than you are. I am not an Excel ninja, but I do know that spreadsheet building is a lot more work than you initially think it will be. In my experience, any spreadsheet you build takes about ten runs before you fix any remaining errors, and I wanted your focus to be on valuation, not Excel. So, feel free to abandon my spreadsheet and build your own, when you have the time.
In today's class, we closed the book on relative valuation by looking at how to price young companies, using forward multiples, and how to pick the "right" multiple for a valuation, with the answers ranging from cynically picking one that best fits your agenda to picking one that reflects what managers in that business care about.  It is amazing how widespread relative valuation is. I found this link recently on rules of thumb in valuation. Take a look at it.... especially the multiples mentioned
We then moved on to asset based valuation: liquidation valuation, accounting valuation and sum of the parts valuation. Specifically, we focused on when it makes sense to value a company by valuing its assets and what pitfalls to avoid. If you are interested in a more extensive assessment of companies like United Technologies, you may find this reading useful:

Attachments: Post class test and solution

I decided to go back in time to 2017 for this week’s pricing is of a Russian steel company, Severstal, because it helps illustrate the process of pricing and contrasts it with the intrinsic valuation, and may be helpful as you price your companies.  You can get the story of the pricing at this link:
You can see the  raw data for steel companies in this link, with an added worksheet for just the top 25 steel companies in market cap terms:
I used this raw data to estimate median values and compared Severstal to those values in this link:
Finally, I looked at the 25 largest steel companies and ran scatter plots and a regression. Even though you may not have the time to do this now, come back and take a look at it when you are working on your final project, if you get stuck on the pricing section.
In today’s session, we talked about the challenges of valuing private company, especially when the buyer is undiversified and cares about liquidity. We argued that you need to adjust for the lack of diversification in your discount rate (using a total beta). If you are interested, I do have total betas, by sector, on my website and you can find the data here:
We also talked about dealing with the lack of liquidity with an illiquidity discount, which should vary across companies, buyers and time. We also showed why the value to a private buyer will be lower than to a public buyer, and that this can lead to shifts in ownership of assets over time. I am also attaching the weekly challenges (two, but very simple) for the week.

Attachments: Post class test and solution

I know that this is meant to be a quiet weekend and I will try to play my role. There will be no valuation tools webcast tomorrow and I will not email you until Monday. If you do want to get a burst of activity in before the weekend, I have updated the market regressions for PE, PBV, PEG, EV/Sales and EV to EBITDA, by region, for the start of 2021. You can find the regressions by going to this link:
If you want to plug the numbers for your company into one of these regressions to get a market-relative pricing, try it.
4/20/21 I hope that you had a good break, and are ready for the sprint to the finish line. First on the list is quiz 3, which will cover all of pricing, asset based valuation and private company valuation (packet 2), which is scheduled for next Monday. The links are below:
The second is the final project, due on the last day of class (May 10) which you are mostly through, if you are done with your DCFs, and almost all through, if you are also done with the pricing. I will send you a to-do list this Thursday that covers the last segments. The final item on your to-do list is the final exam, which is scheduled for May 12. 

As you have gone through this class, you have also wrestled with the tax questions both in terms of inputs into value as well as broader question of how changes in the tax code play out as changes in value. I have a post on my blog on corporate taxes, with the proposed increase in US taxes as my starting point, that you may find useful:
4/21/21 Hi,
We started today’s class by looking at IPOs, and how to incorporate both the proceeds and the pricing considerations of bankers (who guarantee an offering price) as well as how VCs and PEs may look at firms during their transitions.  Along the way, we had a discussion of direct listings as a challenge to the IPO process and 
We then started on the real options discussion with an analysis of the two driving forces behind their value: learning and adaptive behavior, and then moved on to the three questions that need to be asked and answered before buying into the real options argument:
1. Is there an option embedded in an asset? (Look at the cash flow payoffs)
2. Does that option have value? (Is there exclusivity?)
3. Can you use an option pricing model to value that option? (Are the underlying asset and option traded)

The third quiz will not include real options.

Attachments: Post class test and solution

I won’t nag you about the project, though I will double up after the quiz. As you prepare for quiz 3, please keep your focus on packet 2, though remembering your intrinsic value basics can only help. 
  • One recurring question that some of you have had is about my use of (1+g) in some problems and not using it in others. Here is the simple rule. If you are given next year's number (earnings, return on capital, margin etc.), you don't need a (1+g) in the numerator. If you are given the numbers for the most recent year, you do need a (1+g) in the numerator. Thus, if I tell you that the expected operating income or margin or return on capital next year is X, you don't need to put the (1+g) in the model.)  
  • On private company valuations, please go through when we use total betas to estimate cost of equity and when we don’t (hint: it depends on the buyer of the company and how diversified he or she is). 
  • Some of the past quizzes have questions about voting/non-voting shares and options. Ignore those. They will be on the final exam, but not on this quiz.
  • Quiz review: To review for the quiz, you can use the following resources:
  • I will have office hours tomorrow (Friday) from 7 pm - 8 pm, NY time, if you have questions and issues about the material for the quiz or the project. The zoom link is  https://nyu.zoom.us/j/94650089910
I know that some of you have had issues with the multiple choice format on the quiz, especially with the fact that it is all or nothing. I sympathize, but I don’t think that the option of submitting your work with the multiple choice solutions is a fair one and here is why. There is an advantage embedded in a multiple choice test that you do not have in an open ended test, insofar as the right answer is one the choices available. In fact, while the other choices may be plausible if you make a conceptual mistake, a pure math error should not show up as an answer. Consequently, when you take a multiple choice test and you get partial credit, you are getting two bites at the same apple. 

That said, I understand if taking multiple choice quizzes is not your ball of wax. Consequently, for the third quiz, there will be an open ended version, where you will download the quiz as a file, and send me your solutions as an excel file. A note of warning that this will require that you show all your work (which is a little more work on your part) and that you will no longer have the advantage of seeing the potential answers (as you would in a multiple choice quiz). If you would prefer this option, please go to the Google shared spreadsheet below and enter your name and email since I will have to let NYU Classes know that you will be taking this version:
The newsletter for the week is attached. As the clock winds down, deadlines are approaching. The third quiz will be on Monday (April 26). It will cover packet 2 (pricing, private company valuation and asset based valuation). So, keep that in mind as you review past quizzes. You can find them here:
Past quizzes: http://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz3.pdf 
Past quiz solutions: http://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz3sol.xlsx  
My suggestion, if you have limited time, is that you start with the most recent quizzes and work back since they will be more closely tied to the material for this quiz. The review session for the quiz is at the links below:
The quiz will be accessible from 4 am to 3 pm, NY time, and will take an hour. So, please get started by at least 2 pm. Finally, if you do decide to go with the open-ended question format for the third quiz, please let me know by tomorrow morning (9 am, NY time). 

I need some time to get the logistical details ironed out.

Attachment: Issue 12 (April 24)

In today’s class, we used real options to examine why the rights to non-viable technology can be valuable and why the values of natural resource companies are affected by both the level and variability of commodity prices . As a cautionary note, you are pushing option pricing models to breaking point when using them to value these options, but the key takeaway is that even if you do not value the options explicitly, understanding that they exist can alter how you behave as a business. It is also true that the information that you will need to value many real options will be accessible only if you work at the pharmaceutical or natural resource company, and consequently, you cannot apply it to your company (project), since you will not have that access. During the course of the class, there were a couple of places where I was guilty of not being as clear as I should have been. One was when we discussed why I used Merck’s pre-tax cost of debt in my present value calculation for Biogen’s license fee. Let me break down my rationale into multiple parts:
  • I use Merck’s cost of debt, since Merck is the one that has contractually agreed to pay the license fee and the risk is that they will not (if they default).
  • I use the pre-tax cost of debt, since there is no tax advantage that Biogen gets from Merck using debt. Using an after-tax cost of debt would have inflated the value of the license fee for a tax benefit that Biogen would not be getting.
The other issue is the cost of delay, where I use different approaches for different options (1/n for the patent, the CF as a percent of value for the undeveloped reserves). That reflects judgment choices, but ultimately, the question you are trying to answer is what you, as a company, will lose by not exercising an option (patent or undeveloped reserve) once it becomes viable. There is one potential application of options in valuation and that is valuing equity in troubled companies with lots of debt as options that you can try on your company, and it will be relevant if you are valuing a money losing company with a lot of debt.

Attachments: Post class test and solution

I hope that you have recovered from your third quiz and are ready for the last parts of the class. Before I talk about the latter, a few notes on the third quiz. I tried to be clever on problem 5 on NYU classes, and it ended up hurting more than helping. In problem 5, I had given you the cost of equity for public firms, in conjunction with their tax rates and debt equity ratios, and asked for the valuation of an all equity funded private company. To solve this problem correctly, you needed four steps:
1. Solve for the beta implied in the cost of equity = Beta = (Cost of equity - Riskfree rate)/ Equity Risk Premium
2. Solve for the unlevered beta = Beta/ (1 + (1- tax rate) (D/E))
3. Compute a total beta and cost of equity
Total beta = Unlevered beta/ Correlation Coefficient
Cost of equity = Risk free Rate + Total Beta * ERP
4. Value = FCFF/ (Cost of equity -g)
I had set up the problem to give full credit for this answer and one point out of two for an answer that skipped the second steps. Through the wonders of NYU classes, it gave full credit for the second answer and no credit for the first. If you checked your score earlier today, that was the issue. I manually went through the quizzes, checking the answers and giving full credit for the right answer. For those who skipped the levering, I considering changing the score back from 2 points to 1 points but decided that the retroactive score correction may not be fair. Suffice to say, both answers got full credit. I am sorry about the intermediate mix-up, but all’s well that ends well. With all three quizzes under your belt, the next big thing on your to-do list is the project. While I will send you a comprehensive list on Thursday, for the moment, your focus should be on pricing your company. That requires finding comparable companies, picking a pricing multiple and controlling for differences. While I did use regressions to do the last, recognize that you cannot fight the data. Hence, you may find that no regression works for your company, and if that is the case, you have to revert back to using the average or median for the sector. You can always try a different multiple and perhaps even a different set of comparable, but don’t fight the data. 
In today’s class, we completed our discussion of real options, starting with an analysis of why the option to abandon and financial flexibility can be viewed as options, and how to value them. We then turned our attention to distressed equity, and why stock in a highly levered, money losing firm can become an option, and why it matters for investors. Since the value of distressed equity as an option rests on having a lot of debt, you will not find much use for it on your project, unless you happening to be valuing a company where there is negative earnings or the threat of negative earnings and a lot of debt. If you do, you may find this spreadsheet useful in getting that option value:
If you are have trouble with figuring out where to get the inputs, I am sending you a preview of the very last valuation tools webcast, where I use Jet India (a company that I think has been put out of its misery) a few years ago, with the model:
Webcast: http://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/equityoption.mp4
Jet DCF: http://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/webcasts/DistressedEquity/jetindiaDCF.xls
Jet Equity as option: http://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/webcasts/DistressedEquity/jetindiaoption.xls 
As I said, don’t force your company through this, if it does not fit. Finally, I have attached a weekly challenge about patents that may help cement what we talked about in class. 

Attachments: Post class test and solution

If you have not started the project yet, please do. If you have already completed, kudos. If you are in the middle, here is the to-do list , just to keep you organized.

1. DCF Valuation
1.1. Consider feedback you got on your original DCF valuation and respond, but only if you want to.
1.2. Update macro numbers - riskfree rate to today's rate and equity risk premium. 
1.3. Update company financials. If a new quarterly report has come out, compute new trailing 12-month numbers, at least for revenues and operating income.
1.4. Review your final valuation for consistency
What you should include in your final report: A picture that shows your valuation (with the story embedded). That should include your key inputs, a summary of your projected cashflows, your key output (including value per share and price per share). If I were turning in a valuation of Boeing, for instance, here is what it would look like (If you are using my spreadsheet, this is already a worksheet in the spreadsheet that you can use to fill in your story.

2. Relative valuation/ Pricing
2.1. Collect a list of comparable firms (stick with the sector and don't be too selective. You will get a chance to control for differences later) and raw data on firms (market cap, EV, earnings, revenues, risk measures, expected growth)
(You can this data from Bloomberg or Cap IQ. The latter is a little more user friendly)
2.2. Pick a multiple to use. There may be an interative process, where you use the regression results from 2.4 to make a better choice here)
2.3. Compare your company's pricing (based on a multiple) to the average and median for the sector. Make a relative valuation judgment based upon entirely subjective analysis.
2.4. Run a regression across the sector companies. (Be careful with how many independent variables you use. As a rule of thumb, you can add one more independent variable for every 10 observations. Thus, if you have only 22 firms in your list, stick with only two.)
2.5. Use the regression to make a judgment on your company and whether it is under or over valued. (If you are using an EV multiple, estimate the relative value per share. This will require adding cash and subtracting out debt from EV to get to equity value and then dividing by the number of shares)
2.6. Use the market regression on my website to estimate the value per share for your firm. You can find the regressions here:
What you should include in your final report: Tell me what multiple you used in pricing (and why), the comparable firms you used (with sample size), how you controlled for differences (if you used a regression, give me a summary of what you found with statistical significance - t stats and R squared) and your pricing judgment. For example, if I were presenting a pricing for Boeing, this is what it may look like:
Multiple used: EV to Sales, because earnings are negative and EV to Sales has the highest R squared among the different EV multiples
Comparable firms: Global aerospace and defense firms (Sample size = 28 firms)
Control tool: I ran a regression of EV to Sales against operating margins across the 28 firms 
EV/ Sales =  0.83 +  6.51 (Pre-tax Operating Margin) R squared = 38.33%
(1.35) (4.56**)
(Numbers in brackets are t statistics with the two stars indicating significance at the 99% confidence interval)
Boeing’s pricing = 0.83 + 6.51 (.096) = 1.46 (I used expected future margins, since 2020 margins will be negative)
Boeing EV = 1.46 * $76,559 = $111,390
Boeing Pricing per share = $164.11 (I added cash and subtract out debt to get to equity value, before dividing by number of shares)

3. Option valuation (Monday’s class)
3.1. Check to see if your company qualifies for an option pricing model. It will have to be a money losing company with significant debt obligations (a market debt to capital ratio that exceeds 50%).
3.2. If yes, do the following:
3.2.1: Use your DCF value for the operating assets of the firm (not the equity value) as the S in the option pricing model
3.2.2: Use the book value of debt (not the market value) as the K in the option pricing model
3.2.3: Check your 10K for a footnote that specifies when your debt comes due. Use a weighted-maturity, with the weights reflecting the debt due each year. (You don't have to worry about duration)
3.2.4: Estimate the variance in firm value, using your own estimates or the industry averages that I have estimated and are built into the linked spreadsheet.
3.2.5: The value of equity that you get from this model is your option pricing estimate of value for equity.
What you should include in your final report: Boeing is losing money, but its debt is only $28.5 billion (about 25% of its value). So, the option to liquidate is not worth computing.
4. Bringing it all together
4.1: Line up your intrinsic value per share (from the DCF model), the relative value per share (from the sector), the relative value per share (from the market regression) and the option based value per share (if it applies)
4.2: Compare to the market price in May 2019  (the date will depend on when you get done)
4.3: Make your recommendation (buy, sell or hold)
What you should include in your final report: My DCF value ($160/share) and pricing ($164/share) are both higher than the current price. I am buying Boeing.

5. Numbers to me!!!!
Fill in the Google shared spreadsheet when you have the numbers for your company.
To provide some motivation beyond my pathetic begging, I will assign 5 points out of the 40 points on the project to just getting the numbers into the spreadsheet. (Please don’t enter random numbers)

6. Final Project write up
Write up your findings in a group report and submit as a pdf file. The report should be brief and need not include the gory details of your DCF valuation. Just provide the basic conclusions, perhaps the key assumptions that you used in each phase of valuation. There should be relatively little group work. So, you may not really need to get together for much more than basic organization of the report. The group report is due electronically by Monday, May 11, at 5 pm. A pdf format works best. You do not need to attach the raw data and excel spreadsheets). I am not a stickler for format but here are good examples of reports from previous semesters online.
Just to keep the over zealous from going over board, I am going to put a page limit of 20 pages for each report (for up to five companies). You can add two extra pages for each additional company to the limit; with 7 companies, the page limit is 19 pages. If you are doing your valuation individually, a page limit of 4 pages applies. Please do not attach excel spreadsheet. And no.. you don't have to do everything that these groups did. I just like the fact that the valuations were organized, presented in much the same format and were to the point. Of course, content matters
4/30/21 This is the last of the valuation tools webcasts emails. I just added webcasts on how to value patents as an option as well as valuing distressed equity, using option pricing models.For the patent valuation, here are the links:
Webcast: http://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/optiontodelay.mp4
Presentation: http://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/webcasts/optiontodelay/optiontodelay.pdf
Spreadsheet: http://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/webcasts/optiontodelay/productoption.xls
To value equity in troubled companies as options, I am going to send you the same links that I sent after class on Wednesday: I use Jet India (a company that I think has been put out of its misery) a few years ago, with the model:
As I said, don’t force your company through this, if it does not fit (money-losing, with a lot of debt). 
The countdown has begun. We have three sessions left in the class, nine days until the project is due and twelve days until the final exam (but who’s keeping count, right?) The last newsletter is attached and while it contains no real news, it is a ritual that I go through each week. As you work on your project, please do enter your final numbers in the Google shared spreadsheet:
If you get ambitious and want to work on getting ready for the final exam, here are the links
Webcast: https://youtu.be/_8HYZ-BaBSA
Slides: http://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/valfinalreview.mp4 
You can also find past final exams and solutions at this link:
Past finals: http://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/finals.pdf 

Past solutions; http://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/finals.xlsx

Attachment: Issue 13 (May 1)

Tomorrow, we will turn our attention to the many sins in acquisition valuation and as a precursor, I have attached a series of questions that cut to the heart of acquisition valuation and will form the backbone for tomorrow’s class. It is a great way to review the entire class while also getting ready for tomorrow’s class. So, please give it your best shot. Next Monday, in the last session, we will turn our attention to the last part of this class, where we will go inside companies and look at the levers to increase value. For those of you who will be in consulting, strategy or running your own businesses, you will get to see what drives value up (or down).  As you embark on the closing touches of the project, here are a few things to keep in mind:
1. Tweak your DCF, if you need to, estimate a value and let it go. This is an ongoing story and this your take, as of right now.
2. Do the pricing of your company, recognizing that your final pricing conclusions are going to be a function of the multiple you use, the companies you use as comparable firms and how you control for differences. If your R-squared is low, try alternatives, but at some point, adopt the karmic pose. It is what it is.
3. If the option pricing applies to your company, try it.
4. Make your recommendation and I will accept your judgment.
5. Go into the Google shared spreadsheet and enter the numbers for your company.

I know that this is shaping up as the week from hell for some of you and I share some (or all) of the blame. I will have my regular office hours this week (11 am - 12 pm, NY time) and will have two added office hours:
Wednesday, 7 pm - 8 pm, NY time: https://nyu.zoom.us/j/94870538854 
Friday: 7 pm - 8 pm, NY time: https://nyu.zoom.us/j/99755679472 

See you soon!

Attachments: Pre-class test for 5/3/21

I am sorry if you found today's session to be a downer. Don't get me wrong. Acquisitions are exciting and fun to be part of but they are not great value creators and in today's sessions, I tried to look at some of the reasons. While the mechanical reasons, using the wrong discount rate or valuing synergy & control right, are relatively easy to fix, the underlying problems of hubris, ego and over confidence are much more difficult to navigate. There are ways to succeed, though, and that is to go where the odds are best: small targets, preferably privately held or subsidiaries of public companies, with cost cutting as your primary synergy benefit. If you get a chance, take a look at a big M&A deal and see if you can break it down into its components. I briefly mentioned the InBev/SABMiller merger in class but if you want something more extensive, I am going to offer you the blog post that I did on it when it happened:
If you look towards the bottom on the post, you will see a YouTube video on the merger.
I go through the process of valuing control and synergy in a merger, and even if you don’t agree with my assumptions, the framework can still be useful. 

Attachments: Post class test and solution

I sent you the links to the final exam review over the weekend, but in case you missed it, here are the details:
1. When? The regular final exam is scheduled for May 12. It will be accessible from 4 am - 8 pm (16 hours), NY time, that day.
2. What will it cover? It is comprehensive and will cover everything in the class from intrinsic valuation to pricing to real options. That said, the material is interrelated. So, it is not as bad as it sounds. Like the quizzes, it will be open book, open notes. It will be also be open laptops and be two hours long. 
3. Is there an open answer option? Yes. As with the third quiz, if you want to take the open answer version, with its pluses and minuses, please sign up in the Google shared spreadsheet: 
4. Review session and past exams
The review session for the webcast is below, with the slides at the second link
You can also find past final exams and solutions at this link:
I hope these help.
In today's class, we started by drawing a contrast between price and value enhancement. With value enhancement, we broke down value change into its component parts: changing cash flows from existing assets, changing growth rates by either reinvesting more or better, lengthening your growth period by creating or augmenting competitive advantages and lowering your cost of capital. We then used this framework to compute an expected value of control as a the product of  the probability of changing the way a company is run and the value increase from that change (optimal - status quo value). This expected value of control allows us to explain why market prices for stocks rise when corporate governance improves, why voting shares usually trade at a premium over non-voting shares (and why they sometimes don’t).  

Final project nag. When you have the numbers for your company, please enter them in the Google shared spreadsheet:

Attachments: Post class test and solution

I hope that you are moving towards completion on your project. I am tracking your numbers on the Google shared spreadsheet, and if you have not entered them in already, please try to get your numbers in by Sunday (the earlier in the day, the better). If you already have your numbers in there, and want to change them, you have until Sunday to do it, before I download to prepare for the last class:
As you put the wrap on your projects, here are some final points to consider:
1. You cannot fight the data. Put simply, if no matter what you try, you cannot get any of the regressions to work, the message is that the pricing in the sector cannot be explained by the fundamentals on the ground today. That does not make pricing pointless but it can give you a pricing for your stock that is very different from your intrinsic value.
2. If your company is a young, money-losing company, plugging your company current revenues (tiny) and operating margins (negative) into a sector regression will give you absurd predictions for pricing (negative or very low EV to sales ratios). The reason is not mechanics, but perspective. Investors buying Palantir or DoorDash are not buying these companies for how much money they made last year, but based on how much they will make in the future. If you want to price these companies, you have to follow these breadcrumbs, and use your expected revenues and margins from a future year (remember that you have made these forecasts already in your DCF) in the regression to get a predicted pricing for the company. Remember to bring this back to today. As an example, assume that a regression you have for EV/Sales against operating margins yields the following:
EV/Sales = 0.80  + 15.00 (Pre-tax Operating Margin)
If you company current has a 10% margin, plugging that value into the ratio will yield an expected EV/Sales of -0.70, but if you expect your company to have $10 billion in revenues in year 10 and an operating margin of 20% (and a cost of capital of 9%), here is what you will get:
EV/Sales in year 10 = 0.80 + 15.00 (.20) = 3.80
Expected EV in year 10 = $10 billion (3.80) = $38 billion
Value today = $38 billion/ (1.09)^10 ; I am discounting back at the cost of capital, because it is enterprise value. If this were equity value, I would discount back at the cost of equity.
3. If your pricing and intrinsic value are very different, you have to choose which one you want to use for your final recommendation. DO NOT average the two. Bankers may do it, but it is very bad practice. When choosing, recognize that there is no right choice. It depends on faith (do you have faith in your DCF) and philosophy (are you a trader or an investor?). I will not second guess your recommendation. 
It is the final weekend of the class, and I wanted to remind you again to enter the numbers for your company, when you have them, into the Google shared spreadsheet:
I will check in on you, over the weekend, but the slides for the last day of class will be available only on Monday, since they use the data from this spreadsheet. I was scheduled to have office hours today on Zoom from 7 pm- 8 pm, NY time. Unfortunately, Spectrum, my internet provider, has decided to do maintenance work in the neighborhood and has cut off service for the rest of the day. I am truly sorry to leave you stranded, but if you were planning to come to office hours to ask a question, could you send it by email instead? I can answer the questions on my phone, since my cell service is holding up for the moment. 
Just a quick check in that won’t take too much of your time. The Google shared spreadsheet seems to be filling up nicely, but if you have not entered your numbers yet, here is the link:
The weekend is winding down and three final notes.
1. If you have not entered the numbers into the Google shared spreadsheet, please do so.
2. If your project is ready for submission, please submit it as a group (with all the group members ccd) and make sure that you put “The Grand Finale” in the subject.
3. Once I have all the spreadsheet numbers, I will put together the closing presentation to you tomorrow morning and get it to you before class. If you can make it to class live, I would really appreciate seeing you there. It will be a review, a celebration and goodbye wrapped in one.
I am sorry that I cut it this close, but your slides for today are available at
See you in a few minutes. 
Thank you for coming to class today, after I subjected you to a brutal weekend on the project. If you were not able to make it, the slides for the session are here:
We started with using Dante’s Inferno to illustrate layers of valuation hell, with different valuation sins putting you deeper and deeper in that space. We then used your findings on the project to review the basics of intrinsic valuation, pricing and real options. If you want to see the entire list of valuations of everyone in the class, please try the link below:
Your final exam is less than 48 hours away. I have sent the review session links before, but just in case you have lost them, here you go:
You can also find past final exams and solutions at this link:
One final point. If you want to take the open ended version of the exam, please sign up on the Google shared spreadsheet, by midday tomorrow:
I know that you are in the midst of getting ready for the final exam, and I am sorry to interrupt. There are three questions seems to be coming up on the real options problems and I am afraid that I have contributed to the confusion. So, here is some clarification:

1. What is the probability that S>K?   
As stated in class, it is N(d2) which is the risk neutral probability that S>K. In some of the problems, though, I have used a range from N(d1) and N(d2) as the range of probabilities. Let me explain why. N(d1), in addition to being an option delta, is also a probability that the option will be in the money. In fact, the only reason d1 is different from d2 is because you are uncertain about S
d2 = d1 - square root of the standard deviation
If you had a standard deviation of zero, N(d1) = N(d2). As the uncertainty increases, the gap between these two numbers will widen. Thus, you go from being certain about the probability to having a range. Having said all of this, N(d2) should be the point estimate on the probability that S>K. You can use the range to indicate that there is uncertainty about this probability.

2. What is the cost of delay?
        This is a tough one. Sometimes, I use 1/n and sometimes I use  the cashflow next year/ S and sometimes I use no cost of delay at all. Lets look at the conceptual basis. The cost of delay is a measure of how much you will lose in the next period if you don't exercise the option now as a fraction of the current value of the underlyign asset (It parallels the dividend yield. On a listed option on a stock, if you exercise, you will have the stock and get the dividends in the next period) . Thus, if you have a viable oil reserve, the cost of delay is the cashflow you would have made on the developed reserve next period divided by the value of the reserve today.
        Here is the overall rule you should adopt. If you have a decent estimate of the cashflows you will receive each period from exercising the option, it is better to use that cashflow/ PV of the asset as the dividend yield. If your cashflows are uneven or if you do not know what the cashflow will be each period, you should use 1/n as your cost of delay. If you will lose nothing in terms of cashflows by waiting, you should have no cost of delay.
        Let me take three examples. The first is the bidding for rights to televise the Olympics in an earlier quiz. There were two years left to the Olympics and you were trying to price the option. In this case, there is no cost of delay since you really cannot exercise the option early even if it is deep in the money. (You cannot televise the Olympics a year before they happen...) The second is the oil reserve option. Since the cashflows from the reserve tend to be fairly uniform over time (based upon the barrels of oil you would produce and the current price per barrel, it is easy to estimate the cashflows you would generate each year on the reserve. In most of the oil reserve problems, therefore, you would go with the cashflow/ PV of oil in the reserve as your cost of delay. The third is the patent examples. While you may be able to estimate the expected cashflow each year from commercialising the patent, these cashflows are more difficult to obtain and are less likely to be uniform over time. That is why many of the patent problems use the less preferred option of 1/n as the cost of delay, where n is the number of years left in the patent.

3. How am I going to estimate N(d1) and N(d2) and the option value?
If you were doing this by hand, as was the case with the old exams, and without a computer, I used to provide a table (which I have attached) that you can use. On this exam, since you have access to your laptop, I will do the dirty work for you with an option pricing model that you can input your S, K, r, t, sigma and dividend yield into, and the values of the call and the put will be calculated. In effect, you are being graded on getting these inputs right, not on whether you can put them into an option pricing model.

Attachment: http://www.stern.nyu.edu/~adamodar/pc/optlt.xls

I hope that you are done, and are celebrating. However, just in case you still care about grades, yours just went online. If you want to check how your grades were computed, I have attached a spreadsheet that should help. I know that this semester was a challenge. None of you signed up for an online class, and I am sure that you are all Zoomed out. And valuing a company in the aftermath of a full-blown market crisis is never easy. The good news is that if you can value a company in this environment, you can value it any setting. I appreciate your showing up for the online class and  the work you put into the class, and the patience you showed as I drowned you in emails, valuations of the week, weekly challenges and other torture devices.  I know that many of you are graduating and I that  hope your "job" brings you as much joy as mine has to me. If you enjoy what you are doing, you will never have to work a day in your life. Well, at least, I have not! 

You have my email address for life and you can bounce off any questions, queries or issues that you have with corporate finance, valuation or the most valuable sports franchises in the world (the answer to the last is always the "Yankees").  If you are not graduating, I will see you around school next Spring (I live the cushy life, teaching only in the spring and living near the Pacific the rest of the year). While I will not be teaching in the fall, I will be back teaching both corporate finance and valuation in the spring, and you can watch another entering MBA class endures the duress of unending emails, non-stop nagging and everything else that goes with this class. I could tell you that I hated doing it, but I would be lying. And just in case, you need a valuation fix... here are some links:

Twitter feed: @AswathDamodaran (Do your part to advance me to Lady Gaga or Kanye West status…) My children tell me that TikTok is the social media platform of the day. Perhaps, my next online valuation class should be on TikTok…. So, have a great summer and an even better rest of whatever life has in store for you!
5/14/21 I was going to add this on to my last email but I did not want to short change the work that Lorenzo and Javier did as the teaching fellows for this class. Not only were they ready to step in and answer questions on my behalf, they often did it better than I could have. If there were shortcomings in the class, trust me when I say that they were entirely my fault, and Lorenzo and Javier are blameless.  I could not have taught this class without their help.