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The Email Chronicles (Valuation - Fall 2012)

The emails for this class will be collected in this file. Have fun with them!

Date Email sent out

I restrained myself from sending you emails all summer but the respite is over... the torture begins again (http://www.youtube.com/watch?v=7edeOEuXdMU) I am sure that you are finding that break is passing by way too fast, but the semester is almost upon us and I want to welcome you to the Valuation class. One of the best things about teaching this class is that valuation is always timely (and always fun...) Just as examples: Are Facebook and Groupon bargains, now that their prices have plummeted? Will Apple get to be the first trillion dollar company? What is the value added by the Kardashian sisters? If you have not visited my blog, I put my thoughts down on these issues (though I am still working on the Kardashian valuation) over the summer:

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... If you want to get a jump on the class, you can go to the class web site

2. Syllabus & Calendar: The syllabus for the class is available 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.

3. 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...

4. 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". http://www.stern.nyu.edu/~adamodar/New_Home_Page/public.htm

5. 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... As for Blackberry, fuggedaboutit... Dead technology walking!!!!!!!! I am looking forward to seeing you in a few days (The first day of class is September 5, 10.30-12 in KMEC 2-60).. I think we are going to have a lot of fun (at least, I am... ).

Until next time...

9/2/12 Hi!
The first session of the class is almost upon us (Wednesday, September 5). For those of you who have not checked your schedule, it will be in KMEC 2-60 from 10.30-11.50. There is little that you absolutely have to do before the class, but if you are one of those Type A personalities who needs to get a jump on the class, go ahead and browse through chapter 1 of any of my valuation books. If you have none of them, you can skip even this formality. Looking forward to seeing you in class. Until next time!

So, have you classified yourself yet? Are you a proud lemming, a "Yogi bear" lemming or a lemming with a life-vest? While you are pondering that life-changing question, I do have some information about the class.

1. Please do find a group to nurture your valuation creativity, and a company to value soon. If you are ostracized, please let me know...

2. Just to restate what I said in class this morning, you can pick any publicly traded company anywhere in the world to value. The non-US company that you value can 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. 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 2006) and then visit the SEC website (http:www.sec.gov) (for US listings) and download 10Q filings... If you can, also try to get to a Bloomberg terminal (find one, if you have never used one before) and print off the following pages for your company- BETA, DES (first 10 pages) and FA (income statement, cash flow and balance sheet numbers).

3. The web cast for the first class is up. You can get to it by going to
Take a peek. I think it is of superior quality... When you open the link, you can watch either the video or the slides. I also have posted the video on two other sites.
a. Lore: This is the site where I will manage your weekly challenge submissions. So, please accept the invite I send you to this site.
b. Apple iTunes U: This is my first try here. If you have an Apple iPad, iPod or iPhone, you can access the site by going here:
I am curious to know how the interface works and whether you can actually watch the video. I don't have my iPad with me at school. So, if you can try it and give me your feedback, I would appreciate it.

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 the webcast page (linked above). I did screw up on the date for the third quiz in the syllabus (it is correct on Google calendar). The third quiz is November 28.


I don't mean to bury you in technology, but I am tempted. As we go through these next 14 weeks, I would first and foremost love to see you in class. To help me with names (I am terrible with them), could you please bring your name plates with you to Monday's class? If not, just write in on cardboard and stick it in front of you. I promise I will not embarrass you but it will help to make the discussion richer and deeper (I have no idea what that means but it sounds good..)

On the technology front, I hope to keep four channels going and I would love your feedback on what works and does not. You are of course free to ignore all of them and partake of the class the old fashioned way - by coming to class and reading emails.
1. School website (http://www.stern.nyu.edu/~adamodar/New_Home_Page/equity.html)
It is old fashioned, I know... but it still will work as the central clearing spot for everything to do with the class. The webcasts, lecture notes, past emails and links to data/websites that you will be here.

2. Lore (used to be called Coursekit)
I am still experimenting with Lore and have all of your email addresses up on the site. I have sent out invitations to you and you need to accept. If you don't remember getting an email, never fear. I will send a reminder email to you by the end of the week. I will use Lore for three things:
a. Keep track of weekly challenge submissions. They are not graded but I like to know how many are trying
b. Enter your grades on quizzes and the project. You can therefore check and make sure that your quiz scores are correct and that I have not missed anything
c. Start discussions on topics related to the class. I just started a discussion on bias in valuation. Please feel free to jump in and respond or start a discussion or post a news story for others to respond to.
I will also post the lecture notes and webcasts here for those who prefer to get your stuff here or if the school website goes down (as it seems prone to do nowadays)

3. Apple iTunes U
I had sent a cryptic message about Apple iTunes U and if you have never used it, you probably had no idea what I was talking about. If you do have an iPad or iPhone or iPod, here is how you can see the class (in all of its glory or lack of it) on the device:
Step 1: Download the Apple iTunes U app. It is free.
Step 2: Open the browser on your device (iPhone, IPad) and enter the link below (or you can open this email on your device email program)
Step 3: The Valuation class should show up on your app bookshelf.
Step 4: Click and explore. It is pretty neat.

4. YouTube
I am using a site call Symynd to provide access to the class resources to anyone who is interested in valuation. This site converts the webcasts into YouTube videos and provides access to the material. You can get to the site by going to:

I am not a great fan of limited access and if you do have a friend, relative or acquaintance who may be interested in taking the class in real time (albeit for no credit), please do pass the information on to them. The more, the merrier! Until next time!


Not much to do for this class this first weekend, but a few bookkeeping notes.
1. Lore invites/joins: First, please do make sure that you are on the Lore/Coursekit site for this class. If you have not accepted my invitation, not received it or joined the class late, you can join the class by going to:
It should take only a minute to do, but it will help me keep track of submissions a little better.

2. Lecture note packet 1: We will be getting to the first lecture note packet towards the end of Monday's session. If you have bought the packet from the bookstore, please do bring it with you. If you have downloaded it, do so as well. If you have not downloaded it yet, you can do so by clicking one of the two links below:
For one slide per page: http://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/packet1b.pdf
For two slides per page: http://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/packet1bpg2.pdf
You don't have to print it, if you have a device that will let you look at the lecture notes. (An iPad or tablet works fine...)

3. Monday's class: As I mentioned in class, while I do not take attendance, I would like to see you in class. We will start with a pre-class quiz (about 5 minutes). To get a jump on the quiz, I have attached it to this email. Please look at it before you come to class and don't forget to bring your name plates with you.

4. Past emails: As you can see, these emails will start piling up. If you have missed any of my prior emails and want to catch up (either because you joined the class late or just do not read emails from me, when you get them), you can see all the emails that are sent out by going to:

Until next time!

Attachment: biastests.pdf


A few reminders before tomorrow's class.
The Project: Please do find a group and pick a company, not necessarily in that order. For the company, you have a lot of freedom to make your choices, since you are not constrained to have companies within the same sector in each group. The only requirements are that as a group, you choose at least one growth company, one money losing company, one non-US company and one service company. I want to emphasize again that there are no bad or uninteresting companies, but some companies will be more challenging than others to value, and the trade off is that you will learn more.
Name plates: If you do have name plates, please bring them to class tomorrow. If not, if you could write your name on something and bring it with you, I would be much obliged.
Start-of-class test: Just in case you have not seen it yet, I am attaching the test that we will start tomorrow's class with. It is easy and should not take more than a few minutes. So, give it your best shot.
Until next time!

Attachment: biastests.pdf

9/10/12 Hi!
Following up on today's class, I have attached the solutions to the bias quiz that we started the class with. Please take a quick look at it when you get a chance. Better still, pick up a few valuations and think about the appraiser's bias in each case. Thinking about the group project, I hope you have found a group. If so, great... Move on to picking a company, if you have not picked one already. If not, I am starting to put together an orphan list of those who are groupless. Could you please email me and let me know if you want to be part of that list? Until next time!

In the first session, I mentioned that I would post a valuation each week, with my assumptions and a spreadsheet, and that I would like you to give a shot at valuing the same company, using my spreadsheet and your variations on my assumptions. I know that some of you have never done valuations before and are uncomfortable leading into the water before you have learned how to swim. But take a shot at the numbers anyway. Initially, you may not make big changes in my numbers and play it safe but you will get more comfortable challenging me and making bigger changes as we go along.
The first company for this weekly series is Facebook, perhaps the biggest news story of the year. I valued Facebook on the day before its IPO and again a couple of weeks ago. The spreadsheet containing the August 2012 valuation is attached. In coming up with this estimate of value, I used Facebook's most recent 10Q and 10K. You can find them by clicking below:
Most recent 10Q: http://www.stern.nyu.edu/~adamodar/pc/blog/Facebook10Q.pdf
Prospectus (S!): http://www.stern.nyu.edu/~adamodar/pc/blog/FacebookS1.pdf

A post I had on Facebook in February explains the assumptions that I used in my initial pre-IPO valuation:
Here is my post on the day prior to the IPO:
Here is my more recent post, after the earnings report:

So, here is your challenge. Using the spreadsheet and making your own judgments, come up with a value per share for Facebook today. After you have come up with that number, please go to this shared Google spreadsheet and enter your number.
Since it is an open, editable spreadsheet, please do not mess up the numbers that others in the class might have already entered by the time you get there. Let's see how many valuations we can get on this spreadsheet by next Tuesday. Until tomorrow!

Attachment: Facebook August 2012 Valuaton


We will start tomorrow's class with a test on matching cash flows and discount rates and I hope it will provide a foundation for one of the first principles of valuation. So, please take a look at the table and see if you can pick the right "discount" rate to apply to these cash flows. Here is a hint. Start with the very last line item on the table (net cash flow) and see how it is computed. Therein lies the answer. On that mysterious note, good night and I will see you in class tomorrow! Until next time!

Attachment: Start of class test (Kennecott)


We started the session with a discussion of the right discount rate to use in valuing Carborandum, but the broader lessons I hope that you left with are: (1) consistency in matching cash flows to discount rates is critical and (2) even the big name investment banks and consulting firms can make fundamental errors in valuation. We spent a great deal of time trying to nail down the concept of a risk free rate and how best to measure it. The best way to cement these concepts is to try them out. Here are some suggestions on where you can get the updated data (to mirror what I used in class today):
A. Government bond rates
1. US treasury rates: Available all over the place, starting with the Wall Street Journal. You can also go to the source: http://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield
2. Euro government bond rates: My preferred source for this is the Financial Times market page. You can get it by going to: http://markets.ft.com/RESEARCH/Markets/Government-Bond-Spreads. Use the yields and ignore the spreads.
3. Local currency government bond rates: This is a gold mine. I hope it does not disappear. http://www.tradingeconomics.com/bonds-list-by-country
B. Default spreads:
1. Dollar/Euro denominated emerging market government bonds: http://markets.ft.com/research/Markets/Bonds (Go to the bottom of the page, pick high-yield emerging market bonds and pick the most recent date)
2. CDS spreads: If you first want to read a very short description of the market, start here: http://aswathdamodaran.blogspot.com/2010/02/credit-default-swap-cds-market.html
The sovereign CDS spreads can be found for individual countries online, but I cannot find a (free) online comprehensive list. CNBC has a partial listing of 5 year CDS spreads (not 10 years): http://www.cnbc.com/id/38451750
If you can get access to a Bloomberg terminal, you can get the spreads by typing in WCDS. I have attached my mid-year print out of the CDS spreads (if you cannot get to a Bloomberg)
3. Lookup table: This is available on my website but I have attached the table as well. This was last updated in January 2012.

If you find yourself fascinated by risk free rates, you should seek some therapy but in the meantime, here are a couple of papers that I have written on the topic that explains my thinking on the topic.
Here is my first attempt at putting my thoughts down: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1317436
This is a paper I wrote prior to the S&P downgrade and after the 2008 crisis: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1648164
Hope they don't bore you to death... or put you to sleep... One final reminder. There is no class next Monday. So, you have lots of time to catch up, if you are behind, or get ahead, if you so desire. Until next time!

Attachments: Sovereign CDS spreads (May 2012), Default spreads for sovereign ratings classes


As promised (or threatened), I have attached the first weekly challenge for the class. It is a simple test of consistency and how it plays out in valuation. Please give it your best shot. As I mentioned in the first session, the objective of the weekly challenge is not to trip you up. It is not graded but I think that doing it (or trying to) is the best thing you can do each week to test out your concepts for the week. When you are done, please go to the Lore website and submit your answer. You have until Sunday, when I will email you my answer/analysis. Until next time!

Attachment: Weekly challenge #1


Sorry to intrude on a long weekend, but that is exactly why I thought I would take advantage on three separate issues;
1. Valuation of the week: The valuation of the week is still waiting for your response. If you have already forgotten, I sent you my valuation of Facebook in August 2012 on Tuesday and asked that you give the valuation your best shot. I also asked that you enter your valuation output into a Google spreadsheet. If this entire discussion is coming out of left field (and you have no idea what I am talking about), go to the webcast page for the class:

Look right below session 2. You will see my Facebook valuation as well as the shared Google spreadsheet. The shared Google spreadsheet has six valuations: mine and five others. I think that we have more than 5 people in the class. So, give it a shot. It will take only a few minutes and you can tell people you valued Facebook (and you can use my spreadsheet as yours).

2. Weekly challenge: Stay on the same webcast page and if you scan down, you will see the weekly challenge for the week. This is due on Tuesday and please use Lore to submit your answers. If you are not on the Lore class site yet, here is the invite. Don't use this if you are already on the Lore roster. (You can test to see if you are by logging into the site and then trying to submit your challenge solution).

3. The Big project; At this point, you should have a group and hopefully have picked a company or are getting close. Assuming that you do pick a company sometime over this weekend, here are next few tasks:
a. Choose a currency that you will be doing your valuation in. The most logical currency is the domestic currency for the company.
b. Estimate a risk free rate in that currency. (If you have trouble, watch session 3 again)
c. Download the annual report for the company. I have found that typing in the company name.com brings up the home page for the company and the annual report is usually online. If it is in a foreign language, see if you can find an english version.
d. If you have a US company, type in http://www.sec.gov, and download the latest 10K and 10Q for the company.

Congratulations! You are now caught up officially with the class. Go out and have a great weekend!


Hope you are enjoying the weekend. I am attaching the newsletter for the week (you will get one of these each week for the rest of the semester). I will be honest with you on its contents. If you were in class and/or watched the webcasts, there is very little real news here. It just lets you know where we stand in the class and where we will be going next week. It may get more useful as the semester gets more chaotic. You can browse through it when you get a chance and I will also put it online.

P.S: Don't forget to try the weekly challenge and the Facebook valuation...

Attachment: Newsletter #1


Hope your weekend has been fun! Well, it is time for me to post the solution to the weekly challenge. To those who tried it this week, thank you for giving it a shot. To those who did not, there is always next week. Even if you did not try it, please take a look at both the challenge and the solution. Until next time!

Attachment: Solution to first weekly challenge

9/17/12 Hi!
As the class goes on, I will become increasingly delusional and act as if you are where you are supposed to be on the big project. So, operating under the delusion that you have found a group, picked a company and printed off an annual report/10K or 10Q, I thought that I would talk a little bit about how best to use these financial disclosures. In my view, financial disclosure forms have become data dumps and one of the biggest challenges in valuation is separating out the information in these forms from the numerous distractions. To help in this endeavor, I put together a webcast, using Procter & Gamble as my example, with the valuation set in early September 2012 (last week). I used P&G's 10K, which came out in August 2012, and covered P&G fiscal year (July 1, 2011-June 30, 2012). Rather than bog you down with huge attachments, you can go to this link:
The webcast and the associated documents are in the first row. I apologize for the fact that the webcast is 35 minutes long, but you can fast forward, if you get bored. As you can see, I will be posting more of these "tools" webcasts in the coming days. In fact, the next webcast will be on creating trailing 12-month financials, if your company's 10K ends in December. I hope you find them useful and if you can think of any mechanical aspects of valuation that you would like to see one of these on, please let me know. Until next time!

For those of you who tried the valuation of Facebook last week, thank you for trying. In fact, I will leave that valuation up and you can continue to work on it, if you have not already, and post to the Google shared spreadsheet. For this week, I decided to turn to a "story" and a "stock" that is big right now. The iPhone 5 is due in stores in a couple of days and the frenzy is well under way. Apple's stock price just hit $700 and has a "Buzz Lightyear" feel to it... Rather than do another valuation of Apple, I decided to focus on the value of just the iPhone franchise. In valuing the franchise, there is a key element that I had to incorporate, which is that it is a short life cycle: my thirteen-year old son views my iPhone 4, which is two years old, as ancient... The key to valuing the franchise then becomes estimating the likelihood that Apple can keep renewing this incredibly profitable product every 2 years or so. So, start wit this blog post on the iPhone franchise:
Then, use the attached Excel spreadsheet with my valuation of the iPhone franchise to make your own estimates. Once you are done, go in and enter your numbers into the Google shared spreadsheet (https://docs.google.com/spreadsheet/ccc?key=0Alt0SdORYnWadGdGSDYxalo4dzB5bGJDTlpnTW1kYVE). Have fun with it! Until next time!

Attachment: Valuation of iPhone franchise (Excel)


One of the messiest aspects of valuation is dealing with different currencies and different country risk exposures. The weekly challenge for this week is a simple extension of what we have been doing in class on riskfree rates and equity risk premium. Please do try it and submit your answer on LORE, when you are done. I will post my answer on Sunday.

Attachment: Weekly challenge #2


We are little more than halfway through the discussion of equity risk premiums but the contours of the discussion should be clear after today's class:

a. 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
Scroll down and look towards the top of the table of downloadable data items.

b. Country risk premium: The last few months should be a reminder of why country risk is not diversifiable. As you see markets are volatile around the world, I think you have a rationale for a country risk premium. You can get default spreads for country bonds on my site under updated data. If you are interested in assessing and measuring country risk, to get from default spreads to equity risk premiums, you need two more numbers. The first is the standard deviation for the equity market in the country that you are trying to estimate the premium for. The second is to estimate the standard deviation in a traded country bond in question. The two standard deviations should yield the relative volatility. If you have access to a Bloomberg terminal, these numbers are easy to get. If not, you will have trouble... If you have trouble finding either number, just multiply the default spread by 1.5 to get a rough measure of the country risk premium.

As for other sites that look at country risk, here is one that you may want to look at. It is the site maintained by Professor Campbell Harvey at Duke who does very good work on country risk:
If you want my estimates of country risk premiums, check under updated data on my website.

c. Company risk exposure to country risk: My concept of lambdas for countries is a work in progress. I have a paper on the topic that you can read, if you are so inclined:

d. Implied equity risk premiums: I am attaching the excel spreadsheet that will allow you to compute implied equity risk premiums. I am using the numbers that I used at the start of September 2012 to come up with an equity risk premium of 5.75%.

Please try to update the implied premium, using today's numbers for the S&P 500 (easy), 10-year T.Bond rate (easy), growth rate in earnings for next five years (Try to find a number on Yahoo! Finance.. If you cannot, leave it at 6.56% ) and just leave the updated dividends and buybacks from the spreadsheet (since these were updated a month ago). Follow the instructions to get the updated equity risk premium. We will explore it further in class on Monday.

Attachment: Implied equity risk premium spreadsheet for September 1, 2012


I hope the week was a good (and productive one). Next week is also a short week, since we have no class on Wednesday (but we do have class on Monday). Just to prod you (and harass you), I want to check on where you are on the project. Assuming that you have picked a company, joined a group and downloaded the financials, I had suggested last week that you estimate a riskfree rate in the currency that you will be doing the valuation in. If you have doubts about how to do this, the weekly challenge for this week (emailed to you on Wednesday) is a great way to get a solid understanding. Once you have a risk free rate, here are your next few steps:
1. Get a geographical breakdown of the countries/regions of the world that your company operates in. It should be in your annual report or financial disclosure forms somewhere. If you cannot, them's the breaks...
2. Get the total equity risk premium and country risk premium for the countries/regions: If you want to do this yourself, the weekly challenge will give you a template. If you want to take a short cut and use my estimates of country risk premiums, that is fine too.
3. Get a weighted average of the country risk premiums: You can use revenue weights of the country/region to compute the weighted average.

Finally, I hope you have had a chance of updating the implied equity risk premium spreadsheet that I sent you with Wednesday's email. If you have not, I have attached it again. All you have to do is update the S&P 500 and the US treasury bond rate and use the goal seek (instructions on spreadsheet). Until next time!

Attachment: Implied equity risk premium spreadsheet for September 1, 2012


Hope you that you have some fun planned for your weekend. To add to the fun, I am attaching the newsletter for the week. As always, nothing earth shattering there, but please browse through it when you get a chance. And in case you have not done it yet, the weekly challenge awaits (also attached) and submit your solution on lore.com.

Attachments: Newsletter #2, Weekly challenge #2


I hope you had a chance to try the weekly challenge. Otherwise, try it now (it should take only about 5 minutes) and then check your answer against the attached solution.

Attachment: Solution to Weekly challenge #2


By now, you are probably tired of equity risk premiums and I don't blame you. Today's session, though, was all about implied equity risk premiums and what causes them to change over time. Other things remaining equal, higher cash flows and higher expected growth push up the ERP, whereas higher stock prices or a higher riskfree rate pushed the ERP down. If you get a chance, please play with the equity risk premium spreadsheet to check for yourself.
As for the inputs into the model, there is not much suspense. Here is where you can get them:
a. Level of the index: Almost everywhere
b. Cash flows on the index: For the S&P 500, I go to the source:
Click on the S&P 500 and then on index announcements. The most recent release on the buybacks/dividends on the index should be there somewhere. The only problem is that S&P updates these numbers on December 15, March 15, June 15 and September 15. So, you will have to leave the numbers unchanged during those months where there are no updates.
You have a choice on which cash flows to use in computing your premium: Current (trailing 12 month), average over last 5 years, average over last 10 years.
c. Expected growth rate: The easy route is to do what we did in class and get the data from Yahoo! Finance, where you will find it in any company's Yahoo page (under analyst estimates at the bottom of the page ). The better way to get it is to find a Bloomberg terminal, find the index in question (S&P 500 in this case) and type in EE. You will get expected earnings at least for the next 2 years and you can extrapolate from there.
d. Riskfree rate: Use the ten-year default free rate in the currency in which your expected growth/cash flows are denominated. For the S&P 500, this would be the 10-year US treasury bond rate.
If you want to carry forward and compare the equity risk premium to the bond default spread, here are the places you can go to get those numbers:
a. For the bond default spreads, visit my favorite macro data source (FRED, the Federal Reserve data site in St. Louis)
Click on categories first, then on interest rates and then on corporate bond rates. Finally, click on Moody's. You will see Baa rates going back to 1919 (Isn't that awesome?) You have to subtract out the ten-year bond rate and if you want to get that, you should find that on FRED as well. There is a iPhone and iPad app for FRED that you should download. It is free and you can download directly into Excel...
b. For the cap rates, you should try this site:

I am sure that there are better sources, but most of them require you to pay money. I am cheap..

If after all of this, you still want to read more about equity risk premiums, here is the link to my magnum opus (or something opus), the annual update I do on equity risk premiums:
Download the paper and browse through it. You will see much that is familiar.

That is about it for today. We started on the discussion of betas in class and will continue a week from today. There is no class on Wednesday (September 26). Until next time!


In a break from high growth - the first two weekly valuations of Facebook and the iPhone franchise had growth potential, I am turning my attention to what should be a boring, mature business but is anything but in today's environment. A few months ago in the aftermath of JP Morgan's immense trading loss, I posted on whether buying stocks after a sharp downturn was a good investment strategy:
I am sorry that the post is so long, but you can skip forward to the section I have on JP Morgan. At that time, the stock was trading at $35 and I argued that the stock looked undervalued and that I would buy at $35. There is a valuation attached to the blog post from June 2012.
The bank has since assimilated the loss, taking an after-tax charge of $2.734 billion against first quarter earnings and released its most recent financial statements. I have attached pdf print outs of the Yahoo! Finance summaries for the last 4 quarters of the income statement, balance sheet and statement of cash flows. The stock has risen to $40.55. I have also attached an updated valuation from today for JP Morgan. I will not spoil the suspense and tell you what my current estimate of value is, but take a look at the spreadsheet.

Change the assumptions that you think are unreasonable. The key numbers are your ROE, beta and expected payout ratio. Once you have your estimate of value per share, go to the shared Google spreadsheet and enter your numbers. As with the previous two valuations, I will leave this one online for you to revisit over the rest of the semester.

Hope you have a great rest of the week. Until next time!

Attachments: JPM Income statements, JPM Cashflow statements, JPM Balance Sheets, JPM Valuation


I am sorry but I forgot to send this email out yesterday, with the weekly challenge. This weekly challenge is aimed at nailing down the implied equity risk premium concept and will allow you to see if there is a relationship between the implied premium and interest rates/ default spreads. As always, try to submit your submissions on Lore. I know that some of you have had issues doing so and I am working on fixing the problems. The solution will be posted on Sunday night. Until next time!

Attachment: Weekly challenge #2a, Supporting data for weekly challenge #2a


A couple of quick notes. First, if you have tried the valuation of the week (JP Morgan), there was a little glitch in the model. I have attached a new version of the valuation... It has already been fixed online. If you have no idea what I am talking about, check the webcast page for the class:
Second, I am attaching the newsletter for this week. I know it is a day early but I am leaving for a Parent's weekend (for my college sophomore) and may not be able to send it tomorrow. In the meantime, please do try the weekly challenge (see the webcast page again) and have fun! Until next time!

Attachment: Newsletter #3


I hope that you had a great weekend and that you did get a chance to try out the weekly challenge that I sent out earlier in the week. As always, you can try it still and check out the solution which is attached. We will continue with our discussion of discount rates tomorrow. So, come ready to talk about betas, synthetic ratings and costs of debt/capital. I have attached the start of the class test, in case you want to get a jump on it.

Attachment: Solution to weekly challenge #2a, Start of class test for betas


So, we are close to done with the discount rate part of the class. Reviewing and recapping what we did in class today, here are some suggestions:

1. Bottom up beta: I gave you my rationale for bottom up betas and why they beat regression betas every single time. I did put together a list of 10 questions that you may have about bottom up betas
Nothing earth shattering, but it may still be useful.

I also mentioned that I have bottom up betas for the US, Japan, Emerging Markets, Europe and Global. You can find them by going to the updated data section of my site:
If you want to estimate bottom up betas on your own, you should try Capital IQ or the Bloomberg terminals. It is very simple to screen and download the data on your own. If you have never used Cap IQ's screener, I have a webcast on how to use the screener that may or may not help:

2. Cost of debt: The cost of debt is the rate at which you can borrow money at today. If your company has a bond rating, you should be able to find it online or on one of the ratings agency websites. If your company has no bond rating, you can use my synthetic rating spreadsheet, which you can find here: http://www.stern.nyu.edu/~adamodar/pc/ratings.xls
If you want to update default spreads, try http://www.bondsonline.com and check on default spreads. Remember that it will cost you $45 for each snapshot (the most recent spreads)

3. Estimating market value weights: The market value of equity for publicly traded firms should be simple to compute. Just remember to count all shares outstanding of all types to get to market cap. To convert book value of debt to market value, treat it like a bond and value it.

Finally, if you are interested in reading my take on how the dividend cliff may affect the equity risk premium and stock prices, go for it. And try out the spreadsheet...

Until next time!

Attachment: Synthetic ratings spreadsheet


Remember the story about Microsoft that I started the class with. I used it to illustrate the effect of bias on valuation and mentioned that I had found Microsoft to be expensive at every stage of its life as a public company. Well, the times they are a'changing. The market cap for Google just exceeded that of Microsoft yesterday and if Microsoft were fighting Apple for dominance, it would be 'no mas' moment for Microsoft. Microsoft's market cap of $ 240 billion is about a third of Apple's market cap. In fact, the pounding of Microsoft in the markets and in the press is so intense that even I, as a lifelong hater of Bill Gates' dark empire, feel sorry for the company. That may explain what I found when I plugged in the numbers for Microsoft into a spreadsheet that I devised a few months ago to estimate how much growth is worth in a publcily traded company in order to compare it with what you pay for that growth. You can get the background on what I am doing on the spreadsheet by reading this blog post:

Once you have read the post, take a look at the attached valuation of Microsoft. I have kept things simple (ignoring leases and R&D, two items that we will talk about tomorrow), taking the numbers from the most recent 10K (july 2012-june 2013) I know I am giving away the punch line, but here is what I found. (Note that I am adding back the goodwill amortization of $6 billion back to the operating income since it is entirely for a past mistake and is a non-cash meaningless accounting number) If I value Microsoft as a no-growth company, the value that I get is $273 billion for the equity, about $87 billion higher than the existing enterprise value. I must be missing something or Microsoft is an incredible bargain. Thinking about this boggles my mind, since selling Apple and buying Microsoft for my portfolio is akin to shedding my Jedi roots and going over to the Evil Empire. I may have to dig out my Darth Vader costume... So, save me from this fate and tell me what you see in Microsoft and enter your numbers in this shared Google spreadsheet.

Until next time!

Attachment: Microsoft 10k, Microsoft valuation (September 2012)


After mopping up the last loose ends of cost of capital (how to convert from one currency to another, dealing with hybrids), we spent the bulk of today's class talking about the base from which all cash flows are estimated - accounting earnings. In particular, we emphasized two issues: one is the need to work with updated numbers, and how trailing 12-month numbers are generally better than the last annual report and the other is the inconsistency of accountants when it comes to categorizing expenses into operating, financial and capital expenses. In particular, we focused on two key adjustments:
1. Operating leases: Lease commitments are contractually fixed, tax deductible and failure to make payments carry consequences. Thus, they are debt, though we can debate about whether they are closer to unsecured debt than secure debt. The process of converting lease commitments to debt requires two inputs: a table of future contractual commitments and a pre-tax cost of debt. I have attached the rating spreadsheet I sent you last week that converts the lease commitments to debt. If you are computing synthetic ratings, having leases can throw off that rating, this spreadsheet should do the trick. Feel free to tweak it if you want. I also have an extended paper on the consequences of converting leases to debt, which you can read if you are so inclined by going to:

2. R& D: If capital expenditures are expenditures designed to generate benefits over many years, R&D is super cap ex. We talked about the process of converting R&D from operating to capital expenses and why we care. It is not that it changes our cash flow for the current period but because it provides us with answers to key questions that you need to answer in valuation: (a) How much is the company investing for future growth and (b) What return is the firm making on these investments? I am also attaching my R&D conversion spreadsheet.

Until next time!

Attachment: Synthetic ratings spreadsheet, R&D conversion spreadsheet


I am sorry to send another email in such a short time span, but two quick notes. First, I had mentioned a couple of references on forensic accounting. I have attached two below. There are much more detailed books on forensic accounting but they are mostly written for forensic accountants, not investors:

Second, this week's weekly challenge builds on much of what we have done this week in class and is great review for the next quiz. So, please try it and post your solutions on lore.com. I will send you my solution on Sunday.

Attachment: Weekly challenge #3

10/4/12 Hi!
I had mentioned in class yesterday that I planned to put a webcast on constructing trailing 12-month numbers (to accompany the 10K webcast from a couple of weeks ago). I don't mean to insult you, if you already know how to read a 10K or estimate trailing 12-month numbers. If you do, please skip these webcasts. If you do think that it may help, you can get to the webcasts by going to:
Please download the supporting material as well. The webcast on the 10K is about 35 minutes long and the webcast on the trailing 12-month numbers is about 16 minutes. Hope you find it useful! Until next time!
10/5/12 As the weekend approaches, I have to play the role of the Grinch and inform you that your first quiz is next week. Here are a few things to keep in mind:
1. Material that will be covered: The quiz will cover cover the first 8 sessions of the class. In terms of the lecture notes, this will include the introductory packet and the first 135 pages (or so) of lecture note packet 1. Thus, it will cover the consistency requirements in DCF valuation (currency, equity vs firm etc), and two of the key inputs into DCF valuation (discount rates and cash flows). With discount rates, take care to review how to get risk free rates in different currencies, estimating equity risk premiums for mature and emerging markets, estimating the cost of equity for multinational companies and costs of debt/capita. With cash flows, please do review how to update earnings and clean up for accounting inconsistencies, as well as the tax rate, cap ex and working capital issues that we will cover on Monday.
2. Chapters in the book: If you are using the Investment Valuation book, the key chapters that will be covered by the quiz are chapters 7-10. If it is one of my other valuation books, it will be the chapters on discount rates and cash flows. There are problems at the end of each chapter that you can try. If you don't have the book, not a big deal... see below for practice quizzes.
3. Past quizzes: All of my past quizzes are online and you can find them, with the solutions, at the following link:
As you work through the quizzes, remember that some of these quizzes covered growth as well. You can ignore the growth problems.
4. Weekly challenges: If you have worked the weekly challenges every week, you are already pretty prepared. If you have not, you do have the weekend to try them and make sure you try the latest one that I posted on Wednesday.
For those of you who were in my corporate finance class and are wondering why there is no review session, it has generally not been needed in this class. However, if the quiz is a disaster, we will rethink that proposition. Until next time!

Hope you had a chance to try weekly challenge #3. Solution is attached in two parts - the solution itself and the synthetic ratings spreadsheet used to estimate the cost of debt. Until next time!

Attachments: Weekly challenge # 3 Solution & Synthetic rating


Today's class covered a lot of topics, some related to cash flows and some related to growth. Let's start with the cash flow part first. After addressing what tax rate to use on operating income, and concluding that using the effective tax rate for the near term and the marginal tax rate in perpetuity, we also took a closer look at reinvestment. I argued that capital expenditures should be defined broadly to include R&D and acquisitions, for consistency reasons. If you want to count the good stuff (growth) that comes from these investments, you have to also count the cost. To get from cash flow to the firm to cash flow to equity requires us to bring in cash flows to and from debt. While borrowing more can make your cash flows to equity higher, they also make your equity riskier, raising the cost of equity. The net effect of leverage on the value of equity can be positive, negative or neutral, depending on the firm and where it is in its borrowing cycle. On growth, we started with historic growth and quickly dispensed with the notion that it is a fact. Depending on how it is estimated (arithmetic vs geometric) and over what period, you can get different numbers. It is also thrown off when a company's earnings go from negative to positive and generally becomes lower as companies get larger. While you can use analyst forecasts of growth, they have historically not done much better than time series forecasts, perhaps because analysts wear multiple hats.

One final point. As you work through the past quizzes, you will notice a lot of problems that deal with country risk and cost of equity. You will notice that in some of these questions, the answer uses the weighted equity risk premium approach, where you compute the equity risk premium for the risky country or countries, and multiply by the beta. In others, I use the more elaborate lambda approach, with lambda estimated by dividing the proportion of revenues in the country (for the company) by the proportion of the average company in the market.
Cost of equity = Risk free rate + Beta (Mature market premium + Country risk premium(s)); the equity risk premium can be a weighted average across multiple countries.
Cost of equity = Risk free rate + Beta * Mature market premium + Lambda(s) * Country risk premium(s)
Which one should you use? If you are given the data on what the average company makes in an emerging market, I am nudging you towards using a lambda approach. If that is not given, use the more conventional beta approach.

As for the quiz, it is in the first 30 minutes of Wednesday's class. There will be class after the quiz. So, please hang around, if you finish early. IF YOU WILL NOT BE MAKING THE QUIZ, I NEED TO KNOW BEFORE 10.30 ON WEDNESDAY MORNING. If you are, it is open-book, open-notes but no laptops or connectivity.


I know that you are busy, getting ready for the quiz. (Humor me... I like to preserve my illusions). However, when you are done with the quiz, you may want to take a look at this week's valuation: Research in Motion. RIM is a case study of how quickly a growth company can go from “star” to “dog”. A few years ago, its “Blackberry” franchise was viewed as an entrée to high growth and high margins, and the company commanded a market cap in the tens of billions and a reputation as a well managed company. By last year, both its franchise and its reputation were in the dust heap and I had a harsh post on the company that you can read by clicking below:

Well, the company is back in the news. About ten days ago, RIM announced its second quarter earnings, reporting an operating loss of $235 million on declining revenues. Terrible news, right? Well, the stock price jumped 18% on the announcement, which led to this blog post on the power of expectations earlier today:

So, this week, I have valued Research in Motion, using the updated data through the most recent quarter. The valuation does deal with some issues that I have not dealt with in my earlier valuation but that we talked about in class last week:
(1) RIM has an operating loss (and negative operating margins) for the last year and has long term structural issues to overcome.
(2) RIM still has R&D expenses (which I have chosen to capitalize), which affects our estimates of operating income and book capital and
(3) There is a very real chance that RIM may not make it to become a going concern. I have attached a likelihood of 20% that RIM will fail but I may be too optimistic.

Take a look at the valuation, in conjunction with the most recent 10K and 10Q, and make your own estimates. In particular, try changing the revenue growth rate and see what that does to your valuation (I promise you that you will be surprised). Until next time!

Attachment: RIM valuation, RIM 10K, RIM 10Q


The quizzes are done and can be picked up on the ninth floor of KMEC. For those of you unfamiliar with the convention, the quizzes are on the table right at the entrance to the finance department. They are in alphabetical order, face down. Please take your quiz and do not mess up the order. The solution and distribution are attached. If you cannot read them, they are also online on the webcast page for the class. I will be out of my office today. So, if you have issues with the grading, you can either come by tomorrow morning or on Monday.

Attachments: Quiz 1 solution, Grade Distribution


Hope you are having a great weekend. With the Yankees in the playoffs, I am. Two quick notes. First, I forgot to send the weekly challenge on Wednesday. If you get a chance, try it anyway, but if not, just take a look at it. Second, the newsletter for the week is attached.

Attachment: Newsletter #5, Weekly Challenge #4


The heart of today's class was the discussion of terminal value. We began by ruling out using multiples to get terminal values, at least in the context of intrinsic value. To keep terminal values in check, you have to follow four basic rules/principles:
1. Constrain your terminal growth rate to be less than or equal to your riskfree rate (which is a proxy for long term growth in the economy)
2. Don't wait too long to put your company into stable growth (and try not to push past 10 years)
3. The key input in your terminal value computation is your return on capital (and excess return assumption). If your return on capital = cost of capital, your terminal growth rate does not add any value.
4. Give your company the characteristics of a stable growth company in terms of excess returns and cost of capital.
As for which model is right for you, use a firm valuation model if you believe that debt ratios will change over time or are not sure and reserve the dividend discount model for desperate times (when you lack the inputs to compute cash flows)/
Try the attached challenge (think of it as a weekly challenge tailored to this session) to understand the mechanics of the interplay between growth, excess returns and terminal value.

In the final part of the class, we talked about two big loose ends - cash and cross holdings. Just in case, you have nothing to do, you may want to browse through this paper on the topic. (It is one of the loose end papers from my sabbatical year).

Attachment: Weekly Challenge #4a


Now that you have had the requisite period to mourn, celebrate or not care about quiz 1, you should be turning your attention to the DCF valuation. Anyway, I thought I would lend a helping hand:
1. Model building versus Model borrowing: This is not a modeling class and I am fine with you borrowing and adapting my models. If you decide to build your own model, keep it simple. Please do not use investment banking valuation models that you may have borrowed from a prior, current or summer job. Not only do they add detail, where you need none, but they often have fundamental mistakes built into them.
2. Which model should I use? First, go through the slides from a couple of sessions ago where we developed a roadmap for picking the right model. Once you have decided whether you want to use dividends, FCFE or FCFF, here is my suggestion. For companies where operating margins are not likely to change dramatically, use one of the ginzu models on my website. They are versatile and will do a lot a great deal of your dirty work (capitalizing R&D, converting leases to debt, taking care of management options) for you. For companies where margins are likely to change over time or companies with negative earnings, use the higrowth.xls spreadsheet (even if you do not expect high growth). In particular, stick with the following choices:
a. fcffginzu.xls: if you are doing a FCFF valuation of a firm that has positive operating income and you do not expect dramatic shifts in margins (and return on capital) over time
b. fcffsimpleginzu.xls or higrowth.xls: if you are doing a FCFF valuation for a money losing firm or want to allow your margins to change over time.
c. fcfeginzu.xls: if you are doing a FCFE valuation of a firm that has positive net income and you do not expect dramatic shifts in margins and leverage over time
d. divginzu.xls: for financial service firms
You can find all four of these under spreadsheets on my website.

Let me clarify, though, what I would like to get from you when you turn it in:
1. Each of you can turn in your valuation individually. You do not have to submit as a group.
2. All I want is a base case valuation of your firm. It will be easiest if you submit the excel spreadsheet containing your valuation and include your assumptions page in the same spreadsheet.
3. There is no hard copy required and you can submit your DCF valuation spreadsheet electronically. But please do the following:
In the subject enter: "My perfect DCF Valuation". Do not deviate from the script or my filtering program will dump your email into my general email pile.
In the email text, specify the name of the company that you are valuing (yes, there are people who have submitted valuations of unnamed companies), the price per share that the stock is trading at on the day of your valuation and your estimate of value per share.
4. Your DCF valuation will not be graded. I will review the valuation and send you back your own spreadsheet with my comments embedded in the spreadsheet. Some of the comments will be suggestions (which you are free to ignore) and some will be stronger than suggestions (and these should probablyy not be ignored).
5. If you don't get back your valuation within 48 hours of submitting it, please send me another email to let me know. My filtering program sometimes works in mysterious ways.
6. If you get done before October 26, go ahead and send your valuation in early.
So, don't freak out about this deadline. It is more feedback on your valuation than judgment day... Until next time!

10/17/12 Hi!
Today's session was a collection of the remaining loose ends. First, we looked at practical ways around the problem of valuing cross holdings. In the absence of information to value subsidiaries on an intrinsic basis, you can fall back on using market value (if the sub is traded) or use an approximation (Price to book, to estimate value). Second, we looked at the cost of complexity and argued that complex companies are worth less than simple companies, though measuring complexity is difficult and deciding how to incorporate it in value is even more so. Third, we looked at debt, not only at the cost of capital stage (where we define it narrowly to be interest bearing debt and lease commitments) but at the last stage (where we define it more broadly to include underfunded pension obligations and potential legal liabilities). We finally turned to the question of how best to deal with employee options, and argued that the fully diluted approach will understate value of equity per share and the treasury approach with overstate it. The best way to incorporate options is to value them as options and reduce equity value. If you are interested, I have a paper on dealing with employee equity compensation (options and restricted stock):
Until next time!

I know that I am pushing my luck but I have the weekly challenge for this week attached. It relates to our discussion today about employee options. I am also attaching the option spreadsheet that corrects for dilution in valuing employee options. Give it a shot and I will post both this weekly challenge and the terminal value challenge on Lore for submission. Until next time!

Attachment: Weekly challenge #5


I know that this is going to sound like a nag, but that is because it is one. Your initial DCF valuation is due a week from today and I am happy to say that about ten of you have already exercised your option to submit early (with early feedback). I am glad to say that all ten have followed my suggestion on subject matter for the email: "My Perfect DCF Valuation". In case you have been putting this off, I have put together a to do list that may or may not help get the job done.

1. Pick a company
2. Collect financial information on the company (10Q, 10K annual report, news stories...)
3. Estimate key inputs to DCF valuation
a. Discount rate
- Bottom up beta for the company
- Riskfree rate in the currency
- Equity risk premium (including country risk premium)
- Lambda, if necessary
b. Cash flow
- Earnings in most recent period (Operating and net income)
- Effective tax rate
- Capital expenditures (including acquisitions)
- Depreciation
- Capitalize leases, if necessary
- Capitalize R&D,if necessary
c. Growth rate
- Historical growth rate
- Analyst estimates (if available)
- Fundamental growth rate
* Return on equity or capital
* Reinvestment rate
d. Terminal value
- How long a growth period..
- Growth rate forever
- Excess returns in stable growth
4. Pick a DCF model
- Dividends
5. Loose ends
- Cash and marketable securities
- Cross holdings (and minority interest)
- Any other assets?
- Management options
5. Put the numbers into either one of my ginzu models or your own.
- divginzu.xls: if you are valuing a bank or financial service company
- fcfeginzu.xls: if you are valuing a company with stable debt ratio & stable ROE
- fcffginzu.xls: If you are valuing a company with unstable or changing debt ratio & stable ROC
- fcffsimpleginzu.xls or higrowth.xls: If you are valuing a company with changing debt ratio & changing margins (or losses right now)
6. Estimate the value per share
7. Compare to market price
8. If necessary, revisit the inputs and reestimate value
9. Send your valuation model to me by emai, with "My Perfect DCF valuation" in the subject head
10. If you don't hear back within 24 hours, email me a reminder.


I know that you are busy with your DCF valuations. I will keep a running tab of the count:
DCFs turned in so far: 14
DCFs yet to come: 160
On a completely different note, the newsletter for the week is attached.

Attachment: Weekly Newsletter #6


Hope your weekend was a good one... I know that last week was busy and I did send out two weekly challenges. If you got a chance to work on one or both of them, thank you! If you did, here are the solutions:
Solution to terminal value challenge:

Solution to management option challenge:

As with the other weekly challenges, even if you did not get a chance to do them, please take a look at the solutions. Until next time!

Attachments: Solution to terminal value challenge, Solution to management option challenge


We started today's session by looking at how changes in the macro environment can affect an intrinsic valuation for even a mature company, using 3M to illustrate the case. We followed up by valuing the S&P 500 using a dividend discount and an augmented dividend discount model, emphasizing the connection between valuing an index and making a call on the equity risk premium. We then turned our attention to value young companies early in the life cycle, using Amazon in 2000 to bring out some of the key issues. Finally, we closed with the valuation of a mature company - Hormel Foods - with the possibility of a transition.
Each of these valuations is available as an Excel spreadsheet and you can get them by clicking below:

Con Ed: A Stable Growth Dividend Discount Valuation: www.stern.nyu.edu/~adamodar/pc/eqegs/coned08.xls
3M: Pre-crisis valuation: www.stern.nyu.edu/~adamodar/pc/eqegs/3Mprecrisis.xls
3M: Post-crisis valuation: http://www.stern.nyu.edu/~adamodar/pc/eqegs/3Mpostcrisis.xls
S&P 500: A Dividend Discount Model Valuation: http://www.stern.nyu.edu/~adamodar/pc/eqegs/sp500.xls
S&P 500: Dividends augmented with buybacks: www.stern.nyu.edu/~adamodar/pc/eqegs/sp500fcf.xls
S&P 500: Dividends augmented with buybacks, fundamental growth: www.stern.nyu.edu/~adamodar/pc/eqegs/sp500fcfwithfundgr.xls
Amazon.com in January 2000: A Valuation of a Company on the Dark Side: www.stern.nyu.edu/~adamodar/pc/eqegs/amazon2000.xls
Amazon.com in January 2001: http://www.stern.nyu.edu/~adamodar/pc/eqegs/amazon2001.xls
Hormel Foods (Status Quo vs Optimal value, Optimal capital structure): http://www.stern.nyu.edu/~adamodar/pc/eqegs/hormel.xls, http://www.stern.nyu.edu/~adamodar/pc/eqegs/hormelrestr.xls, http://www.stern.nyu.edu/~adamodar/pc/eqegs/hormelcs.xls
Until next time!


I know that you are busy on your own valuations and may not have time to look at this, but I am going to put this on anyway, since some of you are struggling with working with different currencies. The company that I am valuing this week is Ambev, the Brazilian beverage company, and a company that I have valued half a dozen times over the last 12 years. In fact, it was called Brahma, when I valued it the first time around. For the first decade, I valued Ambev only in US dollars, primarily because I was unable to come up with a riskfree rate in nominal $R. I have actually valued Ambev in both US $ and R$ and if you get a chance, compare the two valuations. While the two valuations are not identical, they yield very similar values and the differences are actually mechanical and can be made to go away. Start with the US$ valuation first and then focus on the numbers that are different in the $R valuation. You can change the inflation rates and see what effect it has on your value. (I have also attached the page from Bloomberg summarizing Ambev's financials.... you can get these for any company by working with the FA output page and creating your own detail. This is my standard page that I like to use for any company). Until next time!

Attachments: US $ valuation of Ambev, R$ valuation of Ambev, Ambev financials


Another class, another dozen DCF valuations. I know that we went through a blizzard of valuations but I was trying to use each one to illustrate a point, rather than delve into the details. We started with declining and distresses companies, arguing that the biggest challenge with declining companies (Sears) is overcoming the resistance to forecasting negative growth with negative reinvestment rates and with distressed companies (Las Vegas Sands), it is the factoring in of the risk that the firm will default (and go out of business). We then used emerging market companies to illustrated the broad lessons of valuation - that you should scalpel rather than a bludgeon to deal with country risk, that cross holdings create valuation headaches and that governments can affect value positively or negatively (nationalization). We then moved on to valuing companies in different sectors, starting with financial service companies, where I argued that the banking crisis of 2008 created a breach of trust, which has led to a reassessment of how we value financial service companies, with less trust in dividends and more care paid to regulatory capital. We then looked at companies with intangible assets, using Amgen to illustrate the effect of capitalizing R&D on value.

As with the last session, you can get your hands dirty by getting into the excel spreadsheets that contain these valuations:
Valuation of a company in decline (Sears): http://www.stern.nyu.edu/~adamodar/pc/eqegs/sears.xls
Valuing of a distressed company (LVS): http://www.stern.nyu.edu/~adamodar/pc/eqegs/LVS.xls
Valuing an emerging market company: http://www.stern.nyu.edu/~adamodar/pc/eqegs/embraer2008.xls
Valuing an emerging market company with corporate governance issues (Tube Investments):
Status Quo: http://www.stern.nyu.edu/~adamodar/pc/eqegs/tubeInv.xls
New investment improvement: http://www.stern.nyu.edu/~adamodar/pc/eqegs/tubeInvHigherMgRet.xls
Existing asset improvement: http://www.stern.nyu.edu/~adamodar/pc/eqegs/tubeInvHigAvgReturn.xls
Valuing cross holdings in emerging market companies(Tata companies)
Tata Steel: http://www.stern.nyu.edu/~adamodar/pc/eqegs/tatasteel.xls
Tata Chemicals: http://www.stern.nyu.edu/~adamodar/pc/eqegs/tatachemicals.xls
Tata Motors: http://www.stern.nyu.edu/~adamodar/pc/eqegs/tatamotors.xls
Tata Consulting services: http://www.stern.nyu.edu/~adamodar/pc/eqegs/tcs.xls
Valuing financial service companies
Valuing a bank in the "pre-crisis" days (ABN Amro): http://www.stern.nyu.edu/~adamodar/pc/eqegs/amro03.xls
Valuing an investment bank just before crisis (Goldman Sachs): http://www.stern.nyu.edu/~adamodar/pc/eqegs/goldman.xls
Valuing a bank in the middle of a crisis (Wells Fargo): http://www.stern.nyu.edu/~adamodar/pc/eqegs/wellsfargo2008.xls
Valuing a bank with FCFE: http://www.stern.nyu.edu/~adamodar/pc/eqegs/DBk09.xls
Valuing a company with intangible assets (Amgen): http://www.stern.nyu.edu/~adamodar/pc/eqegs/amgen.xls
Until next time!


This week's weekly challenge is truly a two-minute affair and relates to a conundrum we face when valuing firms. The standard approach is to estimate free cash flows to the firm and discount them back at the cost of capital, with the weights being based on the market values of equity and debt. After discounting the cash flows, though, we end up with intrinsic values for equity and debt that may be different from the original market value. While this inconsistency bothers quant types, it does not bother me in the least because they measure different things. The cost of capital measures what it will cost you to acquire the firm today, and you have to pay market prices to do that. The intrinsic value measures what you think the business is worth. However, there are cases where you might want consistency and it is very easy to do within Excel, using the iteration box in calculation options. Try it on the weekly challenge.

Attachment: Weekly Challenge #6, Daimler valuation

10/25/12 Hi!
As I mentioned in class, we will be moving to packet 2 next week and I would like you to have a copy. If you are getting it at the bookstore, it should be available already or very soon. If you followed my prescription and decided to download it and print it off already, I am really sorry but you may have downloaded the wrong packet. To see if you have, check the cover page. It should say September 2012. If not, I have cost you a great deal of ink and I will reimburse you for the ink and the paper (I am not kidding... Send me the invoice). Anyway, to cut through the confusion, I have the direct link to the right packet:
http://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/packet2b.pdf (for one slide per page)
http://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/packet2bpg2.pdf (for two slides per page)
I am truly sorry again for messing up.... Until next time!
10/26/12 Hi!
Thank you for getting your DCF valuations in. The good news is that they are all stacked up, ready to go, in my smart mailbox. The bad news (though you might not view it as such) is that I may not get your DCF back to you until Monday. On a different note, I had mentioned in class that I was going to give a talk at Baruch on private equity and that it would be on iTunes. It is now up and running. If you are interested, you can watch (as if you don't get to listen to me enough in class, but just in case you are having withdrawal symptoms over the weekend) by clicking on the links below:
Sorry. It is a little long (I am long winded...) and it is in two parts. Make sure you watch part 1 before part 2.... You can also get the powerpoint slides by clicking below:
Have a great weekend before the big storm hits.... Until next time!

Looks like this storm will be a big one but that is no reason for me to give up on routine. I am attaching this week's newsletter.... Hope you get a chance to browse through it. Next week is lecture note packet 2.

Attachment: Weekly newsletter #7


By now, I am sure that you have heard that there will be no class tomorrow. Once you get over the heartbreak, please check out the solution to the weekly challenge for the week. It is trivial but it does yield a neat little trick.

Attachment: Solution to weekly challenge #7

10/29/12 Hi!
As I was thinking about the canceled class this morning, I worked out how much each of you is paying for the session. At a cost of $150,000 for your MBA and the twenty classes that you take over the two years (I may be wrong on one of both of these... ), I am estimating that you are paying about $7500 a course and about $300/session. So, Stern should be refunding you $300 for today's canceled class. There is almost chance of that happening. So, I decided to do my part to make up for at least a portion of the cost. I made a webcast of the rest of packet 1 (I was tempted to start on packet 2 but the session was about 40 minutes and I thought this may be the limits of your attention span). The webcast is at this link:
Assuming that you have power, you can download the session and watch it. It covers lecture note packet 1, pages 285-End. I hope you stay safe toda

Windy out there.... Hope you are staying safe and that you have a chance to watch the webcast that I sent out a link to this morning. By now, you should have received back your DCF valuation back. If you have not, please send it again to me. Rather than make myself into an all-knowing oracle (which I am not), t thought I would take you through the process I used to diagnose your DCF valuations.

Input page checks
Step 1: Currency check: What currency is this company being valued in and is the riskfree rate consistent with that currency?
Right now, if you are valuing a company in US dollars, I would expect to see a riskfree rate of about 3.5% here.. though some of you used 30-year bonds rates which would give you a slightly higher value). if you are valuing your company in pesos or rubles, I would expect to see a higher riskfree rate, (Watch out for the tricky ones.. a Mexican company being valued in US dollars or a Russian company in Euros.. Your riskfree rates should revert back to 3.5%, if this is the case)
Step 2: ERP check: Is the equity risk premium being used consistent with where the market is right now and where this company has its operations?
If you are analyzing a company with operations only in developed markets, I would expect to see a number of about 5.5-6% here... That is because the current implied premium in the US is about 6% (january 2012) or 5.52% (March 2012). If you are using a premium of 4.56% (which was the premium in january 2010, you will over value your company. If your company is exposed to emerging market risk, I would expect to see something added to the mature market premium. While I begin with the presumption that where your company is incorporated is a significant factor in this decision, it should not be the only one in this decision. Coca Cola and Nestle should have some emerging market risk built into them.
Step 3: Units check: Are the inputs in consistent units?
Scan the input page. All inputs should be in the same units - thousands, millions, billions whatever... What you are looking are units with far too many digits to make sense. (Check the number of shares. It is the input that is most often at variance with the rest, usually because you use a different source for it than the financial statements)
Step 4: Normalization check: If earnings are being normalized, what is the normalized value relative to the current value? If reinvestment numbers are off, should they have been normalized as well?
In some cases, we normalize earnings by looking at historical average earnings or industry average margins. While this is perfectly defensible, you want to make sure that the normalization is working properly. Thus, if earnings of $ 3 million are being replaced with earnings of $ 3 billion, you want to make sure that this company has generated earnings like these in the past. You may also want to consider an alternative which is to allow margins to change gradually over time rather than replace current with normalized earnings.
As a follow up, check the reinvestment rate for the firm. If it a weird number (900%, -100% etc.), it may be because something strange happened in the base year (a huge acquisition, a dramatic drop in working capital). A better choice may be to average over time.

Output page checks:
a. High Growth Period.
Start by checking the length of the growth period and the cash flows during the growth period. In particular,
- Compare the FCFF (or FCFE) to the EBIT (1-t) (or Net Income). Especially if you are forecasting cap ex, working capital and depreciation independently, compute an implied reinvestment rate
Implied Reinvestment Rate = 1 - FCFF/ (EBIT (1-t) or 1 - FCFE/ Net Income
Thus, if you have after-tax operating income of 100 and FCFF of 95, your implied reinvestment rate is 5%
- Look at the expected growth rate over the period. Does it jive with your reinvestment rate? (If you see a high growth rate with a low reinvestment rate, the only way you can justify it is by calling on efficiency growth. For that argument to make sense, your current return on capital has to be a low number... See the attached excel spreadsheet that computes efficiency growth.

- If you are forecasting operating income, cap ex, depreciation and working capital as individual line items, back out your imputed return on capital:
Imputed Return on Capital = Expected EBIT (1-t)/ (Base Year Capital Invested + Sum of all reinvestment through year t-1)
If you see this number taking off through the roof or dropping towards zero, your reinvestment assumptions are unreasonable.
b. Terminal value
Start by checking to make sure your growth rate forever does not exceed your riskfree rate. Then follow up by
- Examining your reinvestment rate in your terminal year, using the same formula we used in high growth
- Backing out your implied return on capital (ROC = g/ Reinvestment Rate)
- Checking against your cost of capital in stable growth (you don't want to get more than 5% higher than the cost of capital and you do not want to set it lower than the cost of capital forever)
I have a spreadsheet that can help in this diagnostic:

One common error to watch out for is estimates of terminal value that use the cash flow in the final year, grow it out at the stable growth rate. That locks in your reinvestment rate from your last high growth year forever.
c. Cost of capital
As a general rule, your cost of capital should be consistent with your growth assumptions. Thus, you should expect to see betas move towards the stable range (0.8-1.2) and your debt ratios to rise towards industry average. Thus, your cost of capital in stable growth should be different from the cost of capital in high growth.
d. Final value of equity
Check for danger signs, including
- Cash and cross holdings becoming a huge percentage of value
- Options either being ignored or being a huge number

Market Price
As a final sanity check, look at the current market price. If your value is not even in the ballpark, go back and repeat all of the earlier steps...

Try it out with your own DCF valuation and then offer to do it for a friend... Then, take your toolkit on the road. Pick up a valuation done by an investment bank or equity research analyst and see if you can diagnose any problems in them. You are well on your way to being a valuation guru.
I have also attached a full set of diagnostic questions that you can consider in the context of valuation to this email.

Attachment: Valuation post-mortem


I hope you made it safely through the wind and the rain. We have no power but other than that, no other issues yet. Anyway, as you know, classes have been canceled for tomorrow. I am planning on doing a full 80-minute webcast that I will try to upload by tomorrow (but may have to wait until I have power and broadband...). Please try to watch the webcast sometime before class on Monday. Monday is also the day of the quiz and it will cover the rest of packet 1 (DCF valuation from estimating growth all the way through the Dark Side of Valuation). It will not cover relative valuation, which is the topic for tomorrow's webcast. If you take a look at the prior quiz 2s (under exams & quizzes on the website for the class), you will notice that many of them cover some pieces of relative valuation. The more recent ones are focused just on DCF valuation, with a particular emphasis on the loose ends - valuing cross holdings, cash and options. Please review your notes on these.

One final note. There will be no company valuation of the week, but I have a valuation assignment from an unconventional source: the ABC show, "Shark Tank". I don't know whether you have ever seen this show, but is one where entrepreneurs pitch their business ideas and four sharks (including Mark Cuban) have to make instantaneous assessments of the value of the idea/business and bid on it. Here is one episode:
I would like you to play the role of a shark and assess the value of the first pitch on this episode, which is for a scrub sponge. Unlike the other sharks, you will have the luxury of time to make the assessment. You can explore what the potential market for sponges is and if you can, build a spreadsheet on the value of the sponge. If you have questions, you can look at this paper I have on valuing young and start up companies.
Stay dry! Until next time!


I have heard from enough of you to know that Monday's quiz may pose logistical problems for those who have no power and have had to abandon their homes. So, as the all-knowing oracle, I will move the quiz to Wednesday. I have also decided not to put the webcast that I made for today's class online. Instead, I will do the revolutionary thing and teach it in person on Monday. We will get a little behind in the class, but let me work that out. In the meantime, stay safe and warm! Until next time!


I know that most of you have already downloaded packet 2. If you have printed it off already, stay with that packet but I did go through the packet tightening and shortening it. The new packet is attached to this email. You can download it to your laptop or iPad but you don't have to print it.... I also tried to put it online but the server is not letting me upload big files (yet).. I will keep trying.

I am sorry for the last minute changes but the storm has thrown us about 2 sessions behind schedule and I want to get the material that matters into the remaining sessions. I hope that you are doing well and I hope to see you tomorrow morning in class (As of right now, NJ Transit is still not running trains into the city and the gas shortages make it dangerous to drive in... So, I am looking at my options). Worst case scenario... I will do a full webcast and see if I can get it to you. I will let you know by early tomorrow morning... Seat of the pants is getting really worn out... but that's all I have...

Attachment: Lecture note packet 2 (condensed)

11/5/12 Hi!
It is good to be back in the classroom again (at least for me...) and I thank those of you who made it to class for being there.. I know that it could not have been easy. And for those who were not there, I hope that you are safe. Today's session laid the groundwork for relative valuation (or pricing). All relative valuation is built on three steps: (1) identifying "comparable" assets that have been traded, (2) standardizing the price to allow for comparisons and (3) controlling for differences. While relative valuation often gets short shrift in valuation books and classes, it remains the more used approach to valuation and deserves a place in the arsenal of anyone doing valuation.
The key, then, is not to avoid using multiples/comparables but to use them with discretion and good sense. In today's class, we laid out the four steps in the process of deconstructing and understanding multiples, and got through the first two and a portion of the third. We began with the definitional tests: is the multiple consistently defined and is it uniformly estimated?For a multiple to be consistent, its numerator has to be in sync with its denominator and for it to be uniform, it has to be estimated the same way for all of the comparable companies. In the second step, we looked at the distribution of multiples and noted several features: multiples can never be normally distributed (because they cannot fall below zero), there is bias introduced when a multiple cannot be computed and that companies are similar more than they are different. For the third step, where we try to extract the variables that determine a multiple, I suggested a simple approach. Use a stable growth model (equity or firm) and do algebra to extract the variables that drive that multiple. We tried this on PE ratios and extracted the three variables that determine it: the payout (or potential payout) ratio, the expected growth in earnings per share and the cost of equity. Generically, these measures capture the quality of growth, the level of growth and the risk in that growth.
The second quiz is day after tomorrow and nothing that we covered today will be on that quiz. It will cover only discounted cash flow valuation (and the portion of packet 1 that we did not cover for quiz 1). Until next time!

First, a confirmation. The quiz will be in the first 30 minutes of class tomorrow. Please let me know ahead of time, if you will not be taking the quiz.... Second, I know that you are busy right now, but when you do get a chance, please take a look at this week's valuation of the week. As you probably read, Disney announced its intent to buy Lucasfilm for $4.05 billion. The link below includes the news story:
Since Lucas Films is a privately owned business (owned 100% by George Lucas), we have no access to its financials. However, the sale does not include Skywalker Ranch (the 4700 acre ranch owned by George Lucas in Marin, which is where Lucas Films is located).

Looking at the acquisition and the accompanying announcement that there would be three new Star Wars movies coming out over the next decade, it seems to me that this is not an acquisition of a company but a franchise. The Star Wars franchise is the most successful movie franchise in history. In fact, take a look at the accompanying excel spreadsheet which lists out revenues from the franchise. My estimate is that the total revenues from the franchise over time is $26 billion and I may be being conservative because this article suggests that it is really about $ 33 billion.
Note that these are revenues and that you have to estimate operating income and cash flows to get a sense of value.

Here is the exercise for the week, though. Assume that all that Disney is buying is three more Star Wars movies and the residual income from all past Star Wars movies. I have a spreadsheet that you can use to value the Star Wars franchise (past & present). My estimate of value is about $3.2 billion, lower than the $4.05 billion but I am not considering any interesting synergies that may come from this combination (new rides at the theme parks. a combination of Pixar magic and Star Wars characters....). I gave it my best shot. Why don't you give it a try? When you are done, you can enter your estimate of value into the shared Google spreadsheet.
Until next time!

Attachment: Star Wars franchise valuation


The quizzes are ready to be picked up. I have also put copies of the solution and the grade distribution next to the quizzes (and attached them to this email). As a class, well done! I know that the last two weeks have been tough and I thank you for putting in the work (as you clearly did), getting ready for this quiz. We will skip the weekly challenge this week. You have had enough challenges for the week already. Until next time!

Attachments: Solution to quiz, Distribution


I will keep this short. I hope you had a chance to pick up your quiz last week. If not, it will be there until Monday (at which point I will take it into my office). The newsletter for the week is attached. One final note. The mystery project will go online on Monday and will be due a week from Monday. It is a group project. Until next time!

Attachment: Weekly newsletter #8


I know that the storm has thrown all your schedules into chaos and that it is tough to get back into the rhythm of class. For those of you still waiting to return to your homes or get power, that is doubly hard. I don't want to seem like I am piling on but my coping mechanism has always been to get back on task and I am afraid that I will drag you along. So, this week, we will continue with lecture note packet 2 and finish the section on multiples. Since understanding how to value companies using multiples is such a fundamental part of valuation practice, there are two things you can do that can further that understanding:
1. Mystery project: As I noted in yesterday's email, you will be getting the mystery project tomorrow and it is really an exercise in relative valuation, with a foray into statistics. It is a group project, but there is something that everyone can take away from the process.
2. Relative valuation portion of your DCF project: On your big project (on which you have already done your DCF valuation), it is time to move to the next part which is relative valuation. You can pick a multiple to value your company (and we will go through how best to make that choice in class), define your peer group and control for differences (which we will cover tomorrow). It is not a time intensive exercise and it is a great way to get that part of the project done soon.
So, see you in class tomorrow! Until next time!


As promised (or threatened), the mystery project is ready for you. It is a group project, due a week from today (Monday, November 19 at 5 pm). The assignment is a pretty straightforward one, and the write up should be brief and to the point. Be creative, use statistics as a tool and don't be afraid to be different.... I have attached the project description and the data that you will need (it is also online on the webcast page for the class and under the main menu for the class... will also be posted on Lore and iTunes U)

Attachments: Mystery project description, Data for mystery project

11/12/12 Hi!
Today's session was about backing up and filling in the pieces of the relative valuation puzzle. Last class, we looked at how to back out the variables that underlie individual multiples, using a DCF model as a starting point and some algebra. Today, we looked at a series of relative valuations, starting with beverage companies, working our way through trucking, retail, banking and internet companies. Through all the examples, the key was checking for valuation fundamentals: a cheap stock is one that not only trades at a low multiple (of earnings, book value or sales) but does not have disqualifying factors (high risk, low growth, low return on equity or capital).
We looked at both subjective and quantitative ways of controlling for differences on these dimensions. If your statistics was a little rusty, you might have been intimidated by the multiple regressions but trust me when I say that it is easy to get back to speed on the basics. We ended the class with a market regression for PE ratios. In fact, if you want to see the entire spectrum of market regressions (for US, emerging market, Europe, Global) across multiples, click on the link below:
Until next time!

So, we've all eaten the company's yogurt but the company itself is on the appetizer plate for Nelson Peltz. Here is the news story on the Peltz move:
The motivation seems unvarnished. Peltz wants the company to cut costs, be more focused on its core businesses and return more cash to its stockholders (you could have written that script without reading the news story). The motivation for the targeting is easy to see and it is that the stock price for the company has stagnated for the last 5 years.

In this week's valuation, I have tried to do two things. One is to compute the optimal debt ratio for Danone to see if there is potential for value enhancement from increasing the debt ratio. The other is to do two valuations of Danone: one that I am titling the status quo valuation, with things the remaining the way they are and one that I call the Peltz valuation, with higher leverage and a combination of a higher return on capital (and lower reinvestment rate). Take your best shot at any or all of these and when you are ready, you can enter your numbers into the shared Google spreadsheet:
Until next time!

Attachments: Capital structure analysis for Danone, Valuation of Danone: Status Quo, Valuation of Danone: The Peltz Effect

11/14/12 Hi!
In today's class, we completed the discussion of relative valuation by looking at market regressions of more multiples - PEG ratios, PBV ratios, EV/Sales multiples. In the process, we noted the importance of checking for linearity in the regression and the commonality of companies across the globe on the drivers of multiples. We also looked at a simple technique for coming up with companion variables for multiples: dividing net income by the denominator for equity multiples and after-tax operating income by the denominator for enterprise value multiples. We closed the discussion by looking at choosing a multiple: the cynical view that you pick a multiple that best fits your story, the "quant" approach of picking the multiple with the highest R-squared and the "qualitative" approach of picking a multiple that reflects what managers in the sector focus on.
We then started our discussion of private company valuation by noting that motive matter in private company valuation. We then began he process of valuing a private-to-private transaction by positing that using the beta to come up with a cost of equity will understate the cost of equity for an undiversified buyer. Instead, the total beta allows you to capture the firm specific risk in the cost of equity and capital. We also looked at the impact of the key person on value and began with a discussion of liquidity and its effect on value.
Finally, please give the mystery project a shot as soon as you can. Until next time!

If you get a chance, try this weekly challenge. It should help cement the relative valuation concepts.

Attachment: Weekly Challenge #8

11/16/12 HI!
I know that you are probably working on the mystery project and i hope this email helps clarify some issues:
1. Due date, format and submission: The due date is Monday, November 19, at 5 pm. Each group needs to submit one report and it can be done electronically. The format is simple: focus on your mission, picking the 5 cheapest and most expensive stocks and your "takeover" stock, explaining how you came to your decision (as briefly as possible). When submitting your report, enter "No mystery here" as your subject on the email.
2. Mission control: I know that I used multiple regressions and a few other statistical tools in making my relative valuation judgments. I would like you to do the same, but two notes of caution. First, the statistical tools are just tools. You have to make the final judgments. So, don't let the regressions pick stocks for you. Second, this is not a statistical exercise but an investment exercise. Put differently, don't make it the focus of the project to deliver a great looking regression with a high R-squared, if in the process you curtail your investment choices.
3. Outlier mania: Building on the last email, your best efforts at statistical analysis will be foiled by outliers. They do their thing: lower R-squareds and make your regressions look bad. You will be tempted to remove the outliers, but be careful what you do. if you eliminate just a couple of companies that are clearly off the charts (PE ratio of 5000...), you are on safe ground. If you find yourself eliminating 20 or 30 companies as outliers, I think you are undercutting your objective by eliminating those companies that would have emerged as your cheapest and most expensive companies.
4. Missing values: I know that there are missing values for quite a few companies on some of the variables. On a few of these variables (such as dividends), the missing values can be replaced with zeros but on many of them, they are really missing. Here again, you have to keep your overall mission in mind. You could, of course, use these variables in your regression/analysis and eliminate all companies that have missing values or your can replace these variables with close proxies that have no or fewer missing values. I think the latter makes more sense to do.
5. Relative, not intrinsic value: Remember that this is a relative valuation and not an intrinsic valuation exercise. So, avoid trying to do intrinsic values of companies or even coming up with inputs to intrinsic value; in fact, using any of the intrinsic value equations in the notes (PE = Payout ratio/ (Cost of equity-g) is really a stable growth dividend discount model value)will lead you down this path. This really should free you up in the following sense. In both DCF and relative value, the value of a company is a function of its cash flows from existing assets, expected growth rate, the quality of that growth and the risk. In DCF valuation, we have tight constraints in how we measure these; thus, risk is measured with a beta and captured in a cost of capital. In relative valuation, you have far greater freedom in how you define and measure these variables. Thus, you may decide to use return on equity (or capital) as a proxy for the quality of growth, the size of the company as a proxy for risk, the expected growth rate in revenues as your proxy for growth (please don't view these as recommendations, since I just picked them as examples).
So, let loose and have some fun with the data. The world will not end if you pick the wrong companies (and I don't even know what wrong is...)
Until next time!

I know that you are busy on your mystery project. If you do get a break, just browse through the paper at the link. It is well worth reading and relevant to our discussion of multiples:
I have also attached the weekly newsletter for this week. Until next time!

Attachment: Newsletter #9


Today, we began the discussion of private company valuation by looking at how we can fine tune the illiquidity discount, using either the restricted stock studies or the bid-ask spread data from public companies. We then looked at how the value of a private business is always higher to a public buyer than a private buyer and the logical consequences for private businesses over time. Next, we looked at how while the valuation of a private company for an IPO is very similar in structure to that of a public company, the use of the proceeds and the underwriting guarantee can affect the offering price. We closed the private company valuation discussion by looking at how VCs can value private businesses and how they fall between the private-to-private transaction and the private-to-public transaction.
We then started on lecture note packet 3 (please download it, if you don't have it) and the first steps in option pricing, as a prelude to our discussion of real options. We laid out the three basic questions that animate the real options debate: (1) Is there an option embedded in a decision? (2) Does that have option have significant economic value? and (3) Can we use an option pricing model to value that option? We will use the foundation we laid in class today to discuss the values of the options to delay, expand and abandon when we get back to class after the break.
One final note. The solution to last week's weekly challenge is online and attached. There will be no weekly challenge or valuation of the week this week. You deserve a break from valuation and my emails for at least a few days. Until next time!

Attachment: Solution to weekly challenge #8


I think that I have returned all of the mystery projects back. If you have not received yours, first please check with your teammates ( I tried to Reply All to get everyone on the list but a few did not have all of the group members ccd and I did forget on a few). There should be an attachment to the email, with your file and my comments on it. The grade is on the first page.

Looking over the mystery project, here are some of the overall impressions I have:
1. Multiple used: The two most widely used multiples were PE and EV/EBITDA. Here was the breakdown:
Mutliple used Number of groups
Trailing PE 8
Forward PE 5
EV/Sales 7
Combination 3
Sector multiples 3
FCFE/Price 1
Other 2

There were 37 groups overall. In making your choices, the following factors seemed to come into play: (a) the regression R-squared (higher R-squared) (b) differences in accounting standards across markets (led people to choose Revenue or EBITDA over EPS) (c) Number of firms that you would lose in the sample (steered away from multiples that cost you too many firms). I think that these are all legitimate factors. A few groups mentioned that they were using equity multiples because they were equity investors. I don't think that is necessarily the case. Equity investors can use EV multiples and back into a value for equity... There were three groups that used combinations of multiples and figured out creative ways to reconcile their choices. There were also a few groups that ran the regression within each sector and picked under and over valued companies on that basis.

2. Regressions: Almost everyone followed the script and ran the regressions... One thing I did notice is that some of you chose to stick with all of the variables in the regression, even when there was no statistical significance. Sometimes, taking a variable out rather than leave it is the better choice. About 20% of the groups reported regressions with dummy variables for emerging markets, but the statistical significance of that variable was marginal. The reason may lie in the types of firms that are in this sample. These are the largest market cap firms and most of them are multinationals. The fact that they are incorporated in emerging markets may therefore not matter very much. Five groups ran the regressions by sector or used sector dummies. While this makes sense, you have to be careful to make sure that you have enough data within each sector to sustain the regression. (The simple rule of thumb is that you can have one independent variable for every 15 observations. Thus, if your sample size is 35, you can have at the most 2 independent variables.

3. Recommendations: When picking under and over valued companies, what matters is the percentage and not the absolute difference. In other words, a company that trades at a PE of 10 with a predicted PE of 15, is more undervalued that a company that trades at a PE of 40 with a predicted PE of 50. Here is the list of companies that came through as most under valued:
Company # of Groups
Volkswagen 15
Statoil 13
Mitsui & Co 12
GM 10
Ford Motor 8
Hyundai Motor 7
Mitsubishi 6
Eni SPS 5
China Unicom 5
Note the dominance of the auto sector, with five auto companies making the list. Either the auto sector is a bargain or investors are wary about something in this sector.

For most overvalued, here is the list of the top few:
Company # of Groups
VMWare 20
Facebook 16
Hermes 16
Kinder Morgan 13
Enbridge 9
Anadarko 8
Merck KgA 8 (not the US Merck)
GE 6
The most overvalued companies were VMWare, Hermes and Facebook. Just a note of reference that Ford Motor made it to the overvalued lists three times as well.

4. LBO candidate: A good target for a leveraged buyout will be under valued, under levered, easy to takeover and badly managed. Almost all of you focused on finding an under valued company (which is good), an under levered company (makes sense) and a company easy to takeover (low takeover defenses), but the search on the fourth dimension (bad management) was all over the place. Some of you were looking for companies with high margins and others with stable cash flows. There was almost no consensus and each group had its own unique pick. As a general rule, control requires inputs that you can change and that indicates a firm with below-average margins. There was almost no overlap between the groups with no company being picked more that twice. I have a paper on LBOs that fleshes out what you may want to look for in a LBO candidate. f you get a chance, please browse through it.
Thank you for the effort you put into this project. Have a happy thanksgiving! Until next time!

11/21/12 Hi!
I know I promised you no more emails for the week, but I have to break the promise today. If you have looked ahead in your calendar, you have probably noticed that there is a quiz scheduled for next Wednesday. While I did consider moving the quiz to the following Monday, that would put it into the last two weeks of class and I would prefer not to squeeze more into those weeks. I know that this does not leave you much preparation time, but the quiz will cover packet 2 (relative valuation & private company valuation). Until next time!

I hope you had a great Thanksgiving! I did and I also kept my promise not to send you emails over the weekend. I know that the weekend is not officially over but the countdown to class has begun. This week, we will be covering real option applications in valuation, building on the basics of option pricing from last week. The last quiz is scheduled for Wednesday and it will cover packet 2 (relative valuation and private company valuation). As always, the past quizzes are a good place to start (and especially the more recent quiz 3s). The newsletter for the week is attached.

Attachment: Newsletter #10

11/26/12 Hi!
Glad to have you back in class! Today's class dealt primarily with one real option: the option to delay. In traditional capital budgeting, the value and viability of a project is measured at a point in time (today) by taking the present value of the expected cash flows and netting out the initial investment. The resulting NPV yields a very simple decision rule: if it is greater than zero, the project is a good one and you should be willing to pay to get it, and if it is less than zero, the project is worthless. While that bedrock principle is a good one, the exclusive right to a non-viable (negative NPV) project can still be valuable, especially in businesses with a great deal of uncertainty. This option to delay an investment was the basis for our examination of two key assets: the value of a patent and the value of undeveloped natural resource reserves.
With a patent, the option is to develop the patent into a commercial product, the present value of cash flows from development become the underlying asset and the remaining life of the patent becomes the life of the option. We used this process to value Avonex, a patented drug to treat MS, and came to three key conclusions. The first is that the option value can yield a premium on the discounted cash flow value, with the size of the premium depending on the uncertainty you face in how the cash flows evolve over time and the length of the patent life. The second is that exclusivity matters a great deal and that patents can very quickly lose their option value in competitive markets. The third is that a technology or a pharmaceutical company can be valued in three slices: a DCF value for its existing products, an option value for its undeveloped patents and an additional value for ongoing R&D.
With natural resource reserves, the optionality comes from the fact that natural resource prices are volatile and that companies have a timing choice of when to develop these reserves. Consequently, when oil prices are volatile, the value of undeveloped oil reserves, viewed as options, will increase. Since the underlying asset (oil, gold etc) can be traded, natural resource options come closest to meeting our requirements for using real options.
The quiz remains in its scheduled slot on Wednesday from 10.30 to 11. If you will not be taking it, please let me know before Wednesday at 10.30. Until next time!
11/27/12 Hi!
I hope that you are working your way through the quiz material or are already done. I just want to clarify one point on which I have been guilty of sowing confusion and that relates to when should have a (1+g) in the numerator of your valuation equations (all of the multiples will have this issue). 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. If the problem is ambiguous, I will accept either answer. Until next time!
11/27/12 Hi!
I know that you have no time for this right now, but when you get a chance, you may want to take a look at the disaster that goes by the name Hewlett Packard. A week ago, the company announced it was taking a write off of $8.8 billion on its acquisition of Autonomy that happened only a year ago. Not only was the amount of the write off large, but it was 80% of the price paid on the transaction. To confound matters, HP claimed that $ 5 billion of the write off was because of accounting improprieties at Autonomy. I am always a little wary when acquirers claim complete ignorance of accounting problems at targets, but I think this case may be a good "learning" moment. I posted this on my blog yesterday about the deal:
More importantly, I tried to estimate the effect of the accounting fraud (based upon the very limited information that we have) by valuing Autonomy at the time of the deal, with and without the accounting fraud. I have attached both spreadsheets to this email. My estimate of the accounting fraud effect on the pre-deal value was roughly $1.7 billion. You can play with the spreadsheet and modify it to allow for things I may be missing. Once you are done, go to the shared Google spreadsheet and put in your estimates:
Who knows? You may be an expert witness on the lawsuit that I am sure is likely to follow?
11/28/12 Hi!
The good news is the last quiz is now behind us. The bad news is that the end of the semester is almost here, with more stuff to do. After the quiz, in class today, we expanded on the discussion of real options by first looking at the option to expand. In particular, we noted that a company may be willing to take a "bad" investment, if it believes that this investment could open the door for new markets or products. This is, in fact, what decision makers are (or should be) thinking about when they talk about "strategic" considerations. While the option to expand is an alluring one, it can also lead companies down the path of destruction, where bad investments in big markets are justified based on loose logic. To make the argument that the option to expand is worth a lot, you have to show evidence of exclusivity.. and that is where many of the arguments break down. We then looked at the option to abandon, i.e., the option to be able to walk away from bad decisions/investments. We used it to examine why building in escape hatches in long term, expensive projects may allow a company to overlook a negative NPV up front. If there are life lessons to be learned from the discussion of options, it is that they are valuable and that we should strive to hold on to them not just in business but in life.

Your quizzes are ready. I am leaving on a flight to Frankfurt in a couple of hours and managed to get them done just in time. They can be picked up in the usual spot. The solution and the distribution is attached.

Attachments: Third quiz, solution as well as the distribution of grades for the class.

11/29/12 Hi!
The good news is the last quiz is now behind us. The bad news is that the end of the semester is almost here, with more stuff to do. After the quiz, in class today, we expanded on the discussion of real options by first looking at the option to expand. In particular, we noted that a company may be willing to take a "bad" investment, if it believes that this investment could open the door for new markets or products. This is, in fact, what decision makers are (or should be) thinking about when they talk about "strategic" considerations. While the option to expand is an alluring one, it can also lead companies down the path of destruction, where bad investments in big markets are justified based on loose logic. To make the argument that the option to expand is worth a lot, you have to show evidence of exclusivity.. and that is where many of the arguments break down. We then looked at the option to abandon, i.e., the option to be able to walk away from bad decisions/investments. We used it to examine why building in escape hatches in long term, expensive projects may allow a company to overlook a negative NPV up front. If there are life lessons to be learned from the discussion of options, it is that they are valuable and that we should strive to hold on to them not just in business but in life.

I hope that you have had a chance to pick up your quiz. If you have a question about the grading, I should be back on Monday. In the meantime, I have attached the weekly newsletter... I will also leave you alone this weekend to catch up on your other classes. On Monday, though, I will send you a list of remaining-to-dos on the big project and will nag you through the end of the semester. So, enjoy your respite..

Attachments: Newsletter #11


I hope your weekend is going well. Tomorrow, we will complete the discussion of distressed equities as options. We will also begin with a discussion of acquisition valuation. I think that most egregious valuation mistakes are made in M&A, and some by the smartest people in the room. To understand the most common errors made in acquisition valuation, we will go through a series of tests. The tests are simple but failing them can have profound consequences. If you want to get a jump on the test questions, I have attached them to this email. Just browse through them and take the test before class. (It should take only a few minutes...) See you in class tomorrow! Until next time!

Attachments: Acquisition tests

12/3/12 Hi!
I hope your weekend is going well. Tomorrow, we will complete the discussion of distressed equities as options. We will also begin with a discussion of acquisition valuation. I think that most egregious valuation mistakes are made in M&A, and some by the smartest people in the room. To understand the most common errors made in acquisition valuation, we will go through a series of tests. The tests are simple but failing them can have profound consequences. If you want to get a jump on the test questions, I have attached them to this email. Just browse through them and take the test before class. (It should take only a few minutes...) See you in class tomorrow! Until next time!

As promised, here is your to-do list on the rest of the project. It is a long email but I hope it helps.

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
1.4. Review your final valuation for consistency

2. Relative valuation
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.

3. Option valuation (Wednesday'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: Go to updated data on my website and check towards the bottom of the page for the industry average standard deviations, Use the standard deviation in firm value (not equity value) as the standard deviation in the option pricing model.
3.2.5: The value of equity that you get from this model is your option pricing estimate of value for equity.
I have attached an excel spreadsheet that should help in this effort.

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 now (not in January 2012 or some earlier date)
4.3: Make your recommendation (buy, sell or hold)

5. Numbers to me!!!!
Fill in the attached excel spreadsheet when you have all the numbers for all of the people in your group and please get it to me by the evening of December 11, 2012 (If you have someone who is holding up the group, just send me the rest of the numbers). Please do not modify the spreadsheet in any way.

6. Final Project write up
Write up your findings in a group report. 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 Wednesday, December 12, 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.

And no.. you don't have to do everything that these groups did (So, don't spend the next five days converting your DCF valuations into pictures). 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.

7. Celebrate, but remember that your final exam is two days later.

Attachments: Equity as an option, Summary sheet


We began today's class by looking at the HP/Autonomy deal, looking at how the deal was marked up and then assigning blame for the write down. We then used that discussion and especially HP's then CEO's pronouncements about DCF and accretion to return to our discussion of acquisition valuation. We started with a discussion of how to value synergy in its different forms and noted again the tendency to leave this item blurry not value it. If you are interested in a reformed strategist's view of synergy, try this book by Mark Sirower (who used to teach at Stern):
We then looked at the use of transaction multiples, emphasizing the sampling bias in using other target companies in acquisitions. We finished the discussion by looking at where your value creating odds are highest in acquisitions: small as opposed to large companies, private companies/divisions instead of public companies and a focus on cost synergies as opposed to growth synergies.

Towards the end of the class, we began the discussion of value enhancement by noting the contrast to price enhancement. We then laid out the potential paths to value enhancement and spent the last part of the class talking about how to enhance cash flows from existing assets. We will continue this discussion next class.


As you work through the relative valuation section, a few questions that seem to be recurring:
1. Sample size: There is a trade off between sample size and finding companies that look more like yours. If you are doing a subjective comparison - comparing your company's PE with the PE ratio of comparables, controlling for differences with a story, you want a small sample of companies that look like yours. If you are doing a regression, you should try to get a larger sample, even if it means bringing in firms that may not look like yours. You can control for differences in the regression. And one more thing. Don't fight the data. If a regression does not work, it does not. Remember that you get to make the ultimate judgment and you can decide that given your company and its peers, the best estimate of relative value is just the average PE for the sector.

2. Market regressions: The updated market regressions from the start of 2012 are on my website under updated data. Look to the bottom of the page (and at the first link in the first column, not the archives). Here is the direct link
Unfortunately,  I don't have an update from right now (which is what you would want). So,take the market predictions with a grain of salt, since they are 11 months old and markets have gone up.

3. Option valuation
If you are one of those unlucky people who has been saddled with the money-losing company, here is one more cross to bear. If your firm owes a lot (my rule of thumb is a market debt to capital ratio that exceeds 50%), you can value the equity in your firm as an option... Before you jump out of the window, let me hasten to add that it is not as bad as it sounds. Here are the inputs you need to the option pricing model:
1. S = Value that you attached to your firm (not equity) in your DCF valuation. I would make this a conservative estimate (use low or no growth) to reflect the fact this is liquidation value.
2. K = Face value of all of the outstanding interest- bearing debt in your firm. If you can, add the expected coupon or interest payments to this number. Thus, if you have a 10 year, 8% loan for $ 100 million, your face value would be 100 + 10 * (.08*100) = 180 million
3. t = Weighted average duration of the debt ( I know... I know.. Duration is a pain in the neck to estimate... You can use maturity) There should be a table in your financial statements telling you how much debt comes due by year (there will be a thereafter... just make that a year beyond your last year) Take a face-value weighted average of when the debt comes due.
4. Standard deviation in firm value = Use the bottom up estimate for the sector that you can download off my site. Go to updated data and look towards the bottom of the page.
5. Riskfree rate - Find the treasury bond rate that corresponds to your option life
If you want to download a spreadsheet that does the calculation for you, you can find one under spreadsheets on my site....If you do not have a money losing, indebted firm, you do not have to do option pricing....

One final link. We spent this week talking about money losing acquisitions and conflicts of interest. Cleve Rueckert drew my attention to the Freeport McMoran fiasco that is playing out right now. You can read about it here:
Given the wall of disapproval of this merger, you would think managers would pull back, but it does not seem to be happening.

Until next time!


I hope that you are wrapping up your project number crunching, if not the report itself. Please do not forget to fill out the summary sheet (attached). The very last newsletter is also attached. See you in class on Monday!

Attachment: Newsletter #12


Today was the final chapter in the value story and, in many ways, it brings together all of the functions of business from marketing to production to strategy. If your focus is value enhancement, you have to be able to move one or more of the four levers of value. First, you can try to manage your existing assets more efficiently, generating higher after-tax cash flows from those assets. Second, you can try to generate more value from growth, though to do so, you have to be able to continue to generate excess returns (over and above your cost of capital) on your growth investments. Third, you can build on your strategic advantages - competitive advantages such as brand name, switching costs, legal protection or cost advantages - to allow for more excess returns for a longer period. Finally, you can try to reduce your cost of capital by not only changing your financing mix but also your financing type and fixed costs.

There are two key messages to take away from this process. The first is that cookbook approaches almost never work, since each company is different and needs a different prescription for value enhancement. The second is that value enhancement happens on the shop floor, in the marketing department and not for the most part in finance departments of companies.

We used the discussion of value enhancement to set up the debate about the expected value of control, which is a function of two variables - the probability that you can change the way a company is run and the value change that you can accomplish with a management of change. The expected value of control is a key component in hostile acquisitions, but the market price of every publicly traded company reflects an expected value of control as does the premium for voting over non-voting shares.

Finally, consulting firms have often made it their calling card to come up with "new" and "improved" measures of value creation. The bottom line is that the mechanics of intrinsic value are the same in all these so called revolutionary new measures. Value is value, and driven by the same determinants, no matter how you slice it.

Don't forget to send your project numbers to me in the summary sheet, attached again to this email, by tomorrow. And do come to class on Wednesday, even if you have preferred the virtual classes so far. Until next time!

12/11/12 Hi!
As your project summaries and reports come in, it is getting a little messy in my mailbox. Could you please do the following to help me out? If you are sending in just a summary, put "THE END IS NEAR" as the subject. If you are sending in your final project, please put "THE GRAND FINALE" in the subject. If you have already sent your project in, don't worry. I have it. Thank you...

Today's session was a wrap-up of the class and I used Dante's layers of hell to illustrate the types of mistakes we make in valuation. Starting with the base year fixation, moving through taxes, growth and discount rates and ending with the investment bankers' deepest layer of hell, we looked at how easy it is to trip up and make valuation mistakes. We then looked at the results of your valuations, and I have attached the file with the summaries to this email. I have also put the presentation for the class online and you can get it at the top of the webcast page. You can browse through it, looking for your own best deals. As for me, I will buy one of the top 10 most under valued companies but only if you are too (with you being the person who did this valuation). After all, if I am not comfortable with your valuations of the companies, I am standing behind my own class.
The project report is due by 5 pm today (with the subject "THE GRAND FINALE") and the final is scheduled for Friday from 10-12 in KMEC 2-60. It will be comprehensive and cover the entire class but 60% of the final will cover the three topics that we examined after the third quiz - acquisition valuation, value enhancement and real options. See you on Friday! Until next time!

Attachments: Summary of project findings


You probably know the routine by now. When a class ends, you have to complete a course evaluation for the class. In addition to providing me with feedback in the class, there is another much more critical reason why you should get this done as soon as you can (preferably today, even better, right now...). I also have a completely selfish reason to nag you to get this done. If you do not fill out the CFE, you cannot check your grades online. If you cannot check your grades online, you will email me and I will feel the responsibility to look up your grade and email you back. That will delay your looking up your grade and create pain/ suffering for me. So, please, please, please do your CFE right now. It should take more than three minutes:

Student Instructions for Completing Online CFEs

1. Login to https://ais.stern.nyu.edu and provide your password. Use the same login and password that you use for accessing email. If you have not activated your Stern account yet, please visit http://start.stern.nyu.edu to activate your Stern account and password.
2. Select the "Submit CFEs" link (select correct term) under "Course Evaluation".
3. In the dialog box, highlight the course you wish to evaluate and follow the instructions.

Until next time!


As you get ready for the final exam, three questions seems to be coming up on the real options problems and m afraid 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.

How do I get N(d)?
I will give you a cumulative normal distribution table, though it will be in 0.05 increments. If you can, I would like you to interpolate. Thus, if N(d1) = 0.48, you should interpolate between the 0.45 and the 0.50 numbers, weighting the latter 60% and the former 40%. If you cannot, just use the closest number on the table.

See you tomorrow, and don't forget to do your CFEs. Until next time!


Your final exams are ready to pick up in the usual spot. The usual rules also apply - do not mess with the alphabetical order and please don't mess up the sequence. I have attached the solution to the final exam to this email. You can check your exam against the solution. There is no distribution attached because the final grades should be up very soon (they may be up already, since I have submitted them). Until next time!

Attachment: Solution to final exam


I hope you are done and are out celebrating. However, just in case you still care about grades, yours should be online. This will be my last email to you as Stern MBAs, unless you want to repeat the class again next semester. I want to to wish you the very best with whatever you plan to do with your lives. I hope whatever it is brings you as much joy as my choices have. As I tell my kids repeatedly (and they roll their eyes every time I do), if you enjoy what you are doing, you will never have to work a day in your life...

I know that this email does not end with the three (corny) words that every one of my prior emails to you has, i.e., "until next time" but you have my email address for life and 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"). It has been a pleasure having you in my class for the last semester or two. Have a joyous holiday season and a wonderful break, no matter what you are planning to do. Thank you!

Aswath Damodaran

P.S: I know that you will have this nagging question (which some of you will feel the need to ask me) of how close you were to the next highest grade. At the risk of exposing yourself (and myself) to some severe angst, you can use this spreadsheet to enter your scores and check your grade.

Attachment: Grade Checker for class

  The end is here!!!!