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The Valuation Email Chronicles: Spring 2015


The emails for this class will be collected on this page, arranged chronologically. Have fun with them!

Email content

For those of you who were in my corporate finance class, the torture begins again (http://www.youtube.com/watch?v=7edeOEuXdMU). For those of you who are new to this experience, you will soon find out... 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: Is it time to buy or sell Twitter? Is Uber worth $40 billion? Is there a market bubble? What is the value added by the Kardashian sisters? Are the Dallas Cowboys really worth more than the New York Yankees? If you have not visited my blog, I put my thoughts down on these issues (though I am still working on the Kardashian valuation):

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 page:

2. Syllabus & Calendar: The syllabus for the class is available on the website for the class 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. Delivery choices: I hope to see you all in class for every session, but there are three supporting delivery mechanisms that I would like you to take advantage of:
a. Yellowdig: I don’t much care for NYU classes and use it sparingly. I am trying out a new service called Yellowdig that combines social media, content and commentary.
You should be getting an invite to join the class. Please accept the invite.
b. iTunes U: I will also be posting the material for the class on iTunes U. If you have never used iTunes U, you need an Apple device (iPad or iPhone) and have to download the iTunes U app (free). Once you have the app, use the link below:
I really like the set up and I think you may enjoy it too.
c. YouTube Channel: There is a final option, if your broadband connection is not that great and you are watching on a Tablet/smartphone. There is a YouTube playlist for this class, where all class sessions will be loaded.
When you get a chance, check it out.

5. Books for the class: The best book for the class is the Investment Valuation book - the third edition. (If you already have the second edition, don't waste your money. It should work...) You can get it at Amazon or wait and get it at the book store... If you are the law-abiding type, you can buy "Damodaran on Valuation" - make sure that you are getting the second edition. If you can get the Asian edition, even better. It is exactly the same book and costs about a third. 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". https://www.stern.nyu.edu/~adamodar/New_Home_Page/public.htm

6. Valuation apps: One final note. I worked with Anant Sundaram (at Dartmouth) isn developing a valuation app for the iPad or iPhone that you can download on the iTunes store: http://itunes.apple.com/us/app/uvalue/id440046276?mt=8
It comes with a money back guarantee... Sorry, no Android version yet... As for Blackberry, fuggedaboutit... Dead technology walking!!! I am looking forward to seeing you in a few days (The first day of class is February 2, 2015. I think we are going to have a lot of fun (at least, I am... ).


Just a few quick notes leading into next week's class.

1. Please make sure that you got my email from last week. If you joined the class this week or just don't read class related emails during your break, you can find the entire email by going to

2. Please do accept the invite to the class on Yellowdig that I sent you last week. (https://www.yellowdig.com/board/Valuation+Spring+2015 )

3. Visit the website for the class and check out the Google calendar to make sure that you don't have any quiz conflicts:

Finally, we don't have to wait until next week to start talking about valuation, right? So, what do you think about the chaos in the currency market and how it is affecting stocks? What about oil prices? Lots to think about before class on Monday. Look forward to seeing you in KMEC 2-60 from 1.30-2.50 on February 2. Until next time!

2/1/15 As we get ready for class tomorrow, I think you my find this post that I put on my blog today useful in giving you a sense of what this class is about and what it is not about.
I am going to post it on Yellowdig and you can add your own views (which can be different from mine). If you have not accepted your invite to Yellowdig and cannot find it, I will send out another invite tonight. I will see you tomorrow in KMEC 2-60 at 1.30 pm. Game on! (Superbowl, I mean!)

First, a quick note about today's class. During the session, I told you that that this was a class about valuation in all of its many forms – different approaches (intrinsic, relative & contingent claim), different forums (for acquisitions, value enhancement, investing) and across different types of businesses (private & public, small and large, developed & emerging market). After spending some time laying out the script for the class (quizzes, exams, weekly tortures), I started on the intro to valuation by giving you my reasons for doing valuation (to fight looming lemingitis) and starting on the discussion of widely held misconceptions about valuations.

With that out of the way, 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 points to make:
• Please do find a group to nurture your valuation creativity, and a company to value soon. If you are ostracized, please let me know...
• 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 2012) and then visit the SEC website (http://www.sec.gov) (for US listings) and download 10Q filings. (You can pick any publicly traded company anywhere in the world to value. The non-US company that you value can have ADRs (but does not have to have ADRs) listed in the US but you still have to value it in the local currency and local market. You can even analyze a private company, if you can take responsibility for collecting the information.)
• The web cast for the first class are up and running (or at least the streaming version). You can access it by going to:
The links to iTunes U and Yellowdig have not been posted yet, since I don't have the downloadable video file link yet.
• Post class test: To review what we did in class today, I prepared a very simple post-class test. I have attached it, with the solution. Give it your best shot.
If you did not get the syllabus, project description and the valuation intro in class this morning, they are all available to print off from this site.

Sorry about the length of this email, but there will be more to come (I promise!).

Attachments: Post-class test and solution.


I hope that the sun outside is cheering you up and I hope that this email is not a downer. Two very quick notes before I leave you to your own devices. First, the first valuation of the week is up and I hope that you get a chance to do it. Uber, as you undoubtedly know, is the superstar of the car-sharing/tech space, attracting venture capital money at an almost unstoppable clip, It's value estimate has surged from a billion to $17 billion to $41 billion in the span of a year, which raises a valuation question. Is it worth that much? In this weekly challenge, I argue that the value that you attach to Uber is very much a function of what you think its business is (a car service company, a logistics company or a transportation company?), what type of networking advantages it will have in this business and its competitive advantages. You can start the challenge with this blog post that I had last month:
Follow it up by taking a look at the spreadsheet that I created for the company, where you can choose your narrative points and come up with a value.
Feel free to make your choices and come up with your own estimate of value. Once you have it, please go to this Google shared spreadsheet and share your estimate.
Let's get this going!

Second, the webcasts links are all up and running. Even if you were in class yesterday, pick your preferred link and try it out. You never know when you may need it:
Webcast page for the class for Stream, downloadable video and downloadable audio: https://www.stern.nyu.edu/~adamodar/New_Home_Page/webcasteqspr15.htm
iTunes U: https://itunes.apple.com/us/course/id959944561
Yellowdig: https://www.yellowdig.com/board/Valuation+Spring+2015
YouTube: http://youtu.be/l4Vb6mJqURs

Second, please work on becoming part of a group and picking a company. They don’t have to be sequential. It is true that some of you (law students, EMBAs, Langone MBAs) may have trouble finding a group. I have created a Google shared spreadsheet of Valuation Orphans where you can meet.


As I mentioned in Monday’s class, we will start each class with a simple test, previewing what we will be covering during the class. While this may seem ass-backwards, it is meant to illustrate a simple fact. Most of the time, you will be able to reason your way to the right answer, even before we unveil it in class, and when you do not, it is useful to examine why. While I will usually not send you the start of the class ahead of time, I decided to do so today because I would like you to spend some time (say 5-10 minutes) thinking about it. So, please give the attached test a scan before class today. See you in class!

Attachments: biastests.pdf


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

Speaking about input fatigure, I am attaching the link to a New York Times piece on decision fatigue. It is a fun and interesting read. Please take a look at it, when you get a chance:
We ended the class today with the question of whether equity valued directly (by discounting cash flows to equity at the cost of equity) will yield the same value as equity valued indirectly (by valuing the firm and subtracting out debt). i know that we really have not delved into valuation in depth, but if you are up to it, try the first weekly challenge (which is attached). When you are done, go into NYU Classes (it is the only time I will use NYU classes) and submit your answer. I will give you mine on Sunday. I am also attaching the post class test and solution for the session.

Attachments: Post-class test and solution.


It is never too early to start nagging you about the project. So, let me get started with a checklist (which is short for this week but will get longer each week. Here is the list of things that would be nice to get behind you:
Find a group: If you have trouble finding one, try the orphan spreadsheet for the class. (https://docs.google.com/a/stern.nyu.edu/spreadsheets/d/1aRV7UVM1Nh-x4rurEA-92mN73BFhoypD9lnhHKnoNkY/edit?usp=sharing )
Pick a company: This will require some coordination across the group to make sure that you meet the minimum criteria (at least one money loser, high growth, emerging market, service company)
Find the most recent annual report for your company.
If your company has quarterly reports or filings pull them up as well.

In doing all of this, you will need data and Stern subscribes to one of the two industry standards: S&P Capital IQ (the other is Factset). It is truly a remarkable dataset with hundreds of items on tens of thousands of public companies listed globally, including corporate governance measures. However, to use Capital IQ, you have to enroll and this is an email I got earlier this week about enrolling. Please, please register now. You will not regret it and it will not only save you lots of time in the future but will give you another weapon you can use in analysis.

Professor Damodaran,

My office has sent the below message to your department for distribution, but I wanted to make sure that you have this information, since I know you have incorporated Capital IQ into your coursework in the past.

The enrollment period for spring semester Capital IQ accounts is currently underway. If you are planning to have your MBA students use Capital IQ this semester, please let your students know they have from now until February 25th to request spring semester accounts by filling out the Capital IQ form on their Career Account. Please note that even if students will need Capital IQ for projects later on in the semester, they will need to request access during this official enrollment period at the beginning of the semester.

For non-MBA Stern students, there are 10 Capital IQ-enabled terminals on campus that do not require a Capital IQ account. The undergraduate terminals are located in the computer bank near Stair Y on the LC level, and the graduate terminals are located on the 5th floor of KMC outside Suite 5-100. Capital IQ is accessed by clicking the Capital IQ bookmark in Firefox or a different browser.

Please feel free to contact me if you have any questions about Capital IQ access,


I know that many of you still pondering your company choices and group dynamics, but if and when you pick a company, the first step is to get the raw material you need for your valuation. These include data on the company (annual reports, regulatory filings like the 10K/10Q), sector wide data (numbers for other companies in your sector) and macro economic data. I know that many of you already know exactly how to do this. However, if you feel uncertain, you can try this webcast out.
Incidentally, I do talk about using Capital IQ to get sector wide information in this webcast.

On a different note, a couple of reminders of notes that I have already sent out. First, the valuation of the week (Uber) and the shared google spreadsheet await you. You can find the full details on the webcast page for the class:
Give it a shot, when you get a chance. Second, the weekly challenge was posted (and emailed to you) a couple of days ago. I will post my solution on Sunday, but please try it out before then. To submit your answer on NYU classes, here is what you will need to do. Log into NYU classes and click on assignments. You will see the first weekly challenge up there. Come up with your answer and submit it here. You are off to the races.


Just a quick hit and run. Your first newsletter is attached. No real news to report, especially if you were in class, but no harm checking it out. Have a great weekend!

Attachments: Newsletter #1


First things first. This week, we will be delving into the mechanics of discount rates, starting with the risk free rate and then moving on to the equity risk premium. They are both central to valuation and we live in unusual times, where the former, in particular, is doing strange things. Additionally. I hope that you had a chance to try the first weekly challenge. If you did, you can check your solution against mine. Even if you did not, you can try the challenge now (or in the near future) and check out the solution.

Finally, we will be starting off tomorrow's class with the question of firm versus equity valuation. I am attaching the cash flow table that we will be using for the start-of-the-class test as well. If you get a chance, please take a look at it before you come into class.

Attachments: Weekly Challenge Solution, Start of the class test


Today's class started with a look at a major investment banking valuation of a target company in an acquisition and why having a big name on a valuation does not always mean that a valuation follows first principles. After setting the table for the key inputs that drive value - cash flows, growth, risk, we looked at the process for estimating the cost of equity in a valuation. The key concept is that of a "marginal" investor, who is diversified and looking at risk through that investor's eyes. We spent the rest of the session talking about what should be (but no longer is) the simplest input into the process: the risk free rate.
I hope that the discussion of riskfree rates a left you fairly clear about what to do next. In case, you are still confused, this is the next step in the process:
1. Pick a company (in case you have not already).
2. Determine a currency that you will value the company in. Once you have decided on the currency, find a riskfree rate in that currency. If your company is a US or European company, you just got lucky. Either take the easy way out and use the US T.Bond rate as the dollar riskfree rate and the German 10-year bond rate as the Euro riskfree rate, or adjust them for the default risk you see in each sovereign.
If you are valuing a company in an emerging market in the local currency (be brave), your job is a little more complicated.
2a. Get the longest term government bond rate you can get in the local currency. You can check out the Economist (look at the tables towards the end of the publication and at the long term interest rate). You can also try this site for long term local currency government bond rates:
2b. Get the local currency rating for the country by going to the moody's web site: http://www.moodys.com (Look under sovereign ratings). Estimate the default spread given the rating by downloading the country default spread spreadsheet that you can find at the link below
2c. If you prefer to get CDS spreads, use the current CDS spreads that I have as an attachment (I will post both under the webcast page fand on the coursekit page as well)
2d. Riskless Rate = Government bond rate - Default Spread given rating

I have a paper on riskfree rates that elaborates on the discussion in class today. It is really not a painful read, if you can spare the time. You can get to it by going to:
I also have a follow-up paper on the "What if" series.. what if nothing is riskfree
Finally, I did a post on my blog specifically on the question of the risk free rate being low and the implications for valuaton:

The topic seems to have acquired some followers among appraisers/analysts. This article provides a reasonable synopsis of where they stand:
The post class test and solution are also attached.

Attachments: Post-class test and solution.


This week’s valuation is of a very different company from last week’s, from the pinnacles of hope (Uber) to the valley of despair (Petrobras). It is a fascinating case study in how to destroy a company quickly, a perverse exercise in doing everything that you can do wrong in corporate finance. Start with the blog post:
Once you have read it, try the excel spreadsheet that contains the valuation:
When you have tried your hand at it, then go to the shared Google spreadsheet and give me your views;

Hope you get a chance to try it.

Attachment: Petrobras Valuation


We are little more than halfway through the discussion of equity risk premiums but the contours of the discussion should be clear.
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
Click on current data, and look to 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. Try the Bloomberg terminal. Find the equity index for the country in question (Bovespa for Brazil, Merval for Argentina etc.) and type in HVT. This should give you the annualized standard deviation in the index - change the default to weekly and use the 100-week standard deviation. Do the same for the country bond in question. The two standard deviations should yield the relative volatility. 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. The direct link is below:
On the same theme, the weekly challenge for this week will let you work your way through the country risk premium numbers on your own.

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 know that we barely touched this concept in class today, but its is not rocket science and I am sure that you can work with it. 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 February to come up with an equity risk premium of 6.01%.


Please try to update the implied premium, using today's numbers for the S&P 500 (easy) and the 10-year T.Bond rate (easy). Leave everything else untouched including growth rate in earnings for next five years & 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 a week from today (since there is no class on Monday).

The post class test and solution are attached.

Attachments: Post-class test and solution.


I hope the week was a good (and productive one). Next week is a short week, since we have no 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 after Monday's class 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 will be a good way to test your understanding. It is online in the usual spots (webcast page and iTunes U) and is attached to this email. As with the first weekly challenge, you should be able to submit it on NYU classes. By the way, if you do have a chance, give the Petrobras valuation (on webcast page) a few minutes of your time as well....

Once you have a risk free rate, here are your next few steps:
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...
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.
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. 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).

Attachments: Weekly Challenge #2


As you get ready for the long weekend, a couple of quick notes:
1. Implied ERP: In case you have a chance to try out the implied ERP spreadsheet (attached again to this email), I put together a short webcast (20 minutes) on both the mechanics of the implied ERP (using the February 2014 version of the spreadsheet) and how I get the numbers for the spreadsheet. I hope you get a chance to look at the webcast (and any feedback on making these webcasts more useful will be appreciated):
Webcast: https://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/ImpliedERP.mp4
Presentation: https://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/ERP/ImpliedERP.ppt
Spreadsheet: https://www.stern.nyu.edu/~adamodar/pc/implprem/ERPFeb14.xls
I have also put the links up on my webcast page(and Yellowdig & iTunes U) for the data on buybacks and earnings growth.

2. Musk’s narrative: In spite of my bearish views on Tesla, I have always liked Elon Musk for his charisma and vision. In fact, he has often been much more reasonable about Tesla’s growth prospects that some of his more rabid fans (who also happen to be Tesla stockholders). Thus, I was surprised to read this:
I especially focused on his rationale for why Tesla could be worth as much as Apple in 10 years. Quoting Musk, “If you take this year’s revenue, around $6 billion or thereabout, and if we’re able to maintain a 50% growth rate for 10 years and achieve 10% profitability number and have a 20 (price-to-earnings ratio), our market cap would be basically the same as Apple’s is today”. Remember we talked about narratives and how they can spill out of control, if you are not disciplined. This is about as absurd a set of presumptions that I have seen strung together in one sentence. Food for thought!

3. Review Sessions: If you are having trouble keeping up with the class or working through the concepts, the TAs will be running review sessions every week on Wednesdays from 4.30-5.30 in 2-90. To attend these sessions, please sign up in the shared Google spreadsheet that has been set up for the purpose.


Last week, we put the basics of valuation behind us and started on the nuts and bolts. In particular, we spent Monday talking about how to estimate risk free rates in different currencies and why they may be different. On Wednesday, we looked at equity risk premiums, talked about why historical risk premiums may be flawed and how to estimate equity risk premiums in other markets. Next week, we will have only one session and will examine a different way of thinking about equity risk premiums and also talk about alternatives to measuring the relative risk in a stock. I know that this is a long weekend and I hope you have fun. However, please do find a group, pick a company, estimate a risk free rate in the currency of your choice and start thinking about the ERP for your company. ( What a fun sucker? I know.. I know.. That is what my kids call me too…)

Attachments: Newsletter #2


I will keep this short. The solution to the second weekly challenge is attached, with the challenge. If you did not get a chance to do it, you can still try it. Next week is going to be a short one, since we have no class tomorrow. On Tuesday, I will still put up my valuation of the week and on Wednesday, we will look at how to estimate implied equity risk premiums and estimating the relative risk of a company. If you have picked a company, try to find a beta for your company from a service and bring it to class with you. Other than that, not much more to do. Have a wonderful rest of the weekend.

Attachments: Weekly Challenge #2 Solution


I hope that you had a productive weekend (or at least a fun one). Well, it is time to get back to work and to celebrate. I usually don’t repeat valuations of the week, but I decided to make an exception this week, since this merger is one that we have all heard about (and have opinions about). A year ago, almost to the day, I posted my assessment of the Comcast/TWC deal. You can begin by reading the news story of the deal as it happened in February 2014:
I posted this on my blog on February 18, 2014:
You get the summary data, as of February 2014, for the two companies at the link below:
Comcast Summary data: https://www.stern.nyu.edu/~adamodar/pc/blog/ComcastSummary.pdf
TWC Summary data: https://www.stern.nyu.edu/~adamodar/pc/blog/TWCSummary.pdf
The spreadsheet containing my valuation of synergy is at the link below:

It is a year later and the merger that looked like a sure thing a year ago is faltering:
I know that the numbers have changed for the two companies, as have the risk free rate and equity risk premium. I updated all of the numbers in this spreadsheet:
If you get a chance, give the synergy spreadsheet a shot and when you are done, go into this shared Google spreadsheet and give me your assessments on what you think of this merger (that now may not go through):


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 stock prices, higher cash flows and higher expected growth all push up the ERP, whereas 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. (The 2015 edition should be out in the next two weeks)
As for betas, the key thing to recognize is that it is a means to an end: a way of adjusting for relative risk. So, keep your eyes on the prize and don't let your disdain for modern portfolio theory get in the way of adjusting for risk and estimating value. The post class test and solution are attached.

Attachments: Post class test and solution


We spent much of today’s sessions talking about equity risk premiums, how they have moved over time, both on their own and in relation to other variables such as the risk free rate, the corporate bond default spread and real estate cap rates. The best way to see the relationship is for you to look at the data yourself. So, when you get a chance try the weekly challenge for this week that comes accompanied with an excel spreadsheet containing historical data on equity risk premiums, interest rates and corporate bond default spreads.

Attachment: Implied premium challenge, data


If you have picked a company and collected the basic data (see last week's webcast), you probably more data in front of you then you want. In particular, those of you who have picked US companies have a 10K to read, in all of its bulk. Today's valuation tools webcast is about reading a 10K, with the intent of valuing a company. You can get the webcast by going to:
Webcast: https://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/Reading10Knew.mp4
The webcast is accompanied by some supporting material, which you can get below:
Presentation: https://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/PG/Reading10KPG.pdf
P&G 10K: https://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/PG/ProcterGamble10K.pdf
P&G valuation: https://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/PG/P&Gvaluationfixed.xls
This is a longer webcast than I would have preferred it to be.

Two final quick notes. First, if you are having troubles with this class, please do come in and see me. If you are too intimidated to do so (Why? Am I that scary?), you should draw on the TAs for the class and even try their review sessions next week.
Second, I don't mean to scare you but the first quiz is a week from next Wednesday (March 4). If you are interested in starting your preparation for the quiz, you can find every quiz 1 I have ever given in this class and there are a lot of them at the links below:
Past Quiz 1s: https://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz1.pdf
Past Quiz 2 solutions: https://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz1sol.xls


I hope that you are enjoying your “cold” weekend. I am attaching the newsletter for the week, in case you get really, really bored and have absolutely nothing else to do.

Attachment: Newsletter #3


I hope you had a chance to try the weekly challenge. If you did, you probably found it more an exercise in statistics than valuation and that is good. Statistics is a vastly under used tool in valuation. On a different note, we will complete our discussion of bottom up betas and discount rates this week. If you can find a beta page for your company (on Bloomberg or elsewhere) and the business breakdown for your company, you can see the contrast between the regression and bottom up betas for yourself.

Attachment: Weekly Challenge 2a solution


Today's class represented the final pieces of the discount rate puzzle. We began with a continued discussion of bottom up betas, focusing on defining comparable firms and expanding the sample. I did make a big deal about bottom up betas, but may have still not convinced you or left you hazy about some of the details. If so, I thought it might be simpler to just send you a document that I put together on the top ten questions that you may have or get asked about bottom up betas. I think it covers pretty much all of the mechanics of the estimation process, but I am sure that I have missed a few things.
We continued with the cost of debt, starting with a definition of the cost of debt as a long term, current cost of borrowing and laying out a procedure for estimating this cost, even for firms that don't have traded bonds/ bond ratings. We also took a detour into estimating the cost of debt for firms that may receive subsidized debt from the government/ other entities. I am attaching the post class test and solution for today's class.

Attachments: Post class test and solution


This week’s valuation is a fun one to do, since the company was started in New York and some of you may have eaten at it. The place to start your valuation is with my overview:
Follow up with the prospectus:

Get a sense of what the revenues and margins look like by restaurant:

Then create a narrative for Shake Shack. Is is going to be the Chipotle of the next decade? Cheesecake Factory? Ruby Tuesday? My valuation is in this spreadsheet:

I made it Ruby Tuesday-like in terms of revenues, gave it the margins of the 75th percentile restaurant and get a value per share of about $20, about the offering price but well below the current price. Have a go at it and once you have your values, visit the google shared spreadsheet:

Have fun with it.


Today's class looked at the getting the base year's earnings right and explored several issues:
1. To get updated numbers, you should be using either trailing 12 month numbers or complete the current year with forecasted numbers. In either case, your objective should be to get the most updated numbers you can for each input rather than be consistent about timing.
2. To clean up earnings, you have to correct accounting two biggest problems: the treatment of operating leases as operating (instead of financial) expenses and the categorization of R&D as operating (instead of capital) expenses. The biggest reason for making these corrections is to get a better sense of how much capital has been invested in the business and how much return this capital is generating.
3. While truly extraordinary items are easy to deal with, accounting ploys to move expenses into the extraordinary column may require some detective work. For those interested in forensic accounting, here are a couple of references:
Finally, this is an FT article on Amazon from last week that is illustrative of the games that companies play:

If you are really interested in nailing down the basics of cash flows (and preparing for the quiz next week), please try the post-class test (with solution) that is attached but really do try the weekly challenge for this week. It is a great exercise in tying up loose ends.

Attachments: Post class test and solution


With the quiz coming up next Wednesday (March 4), you have probably put the project on the back burner. But just in case you are working on it (and it is great preparation for your quiz), here is where you should be. You should obviously have a company picked and been able to estimate the different pieces that go into the cost of equity: a risk free rate in the currency of your choice, an equity risk premium reflecting where the company operates and a beta, reflecting the businesses it is in. For your debt, you should have a pre-tax cost of debt, based upon an actual or synthetic rating and converted this pre-tax cost of debt into an after-tax cost with a marginal tax rate. Finally, you should be able to use this pre-tax cost of debt, in conjunction with the book value of debt, interest expenses and the "weighted" maturity of the debt to convert the interest bearing debt into a market value.

If you find yourself struggling with the lease and R&D adjustments that we talked about yesterday, do try the weekly challenge, which I have attached to this spreadsheet. Also, if you want to get a start on prepping for the quizzes, you can find every quiz that I have given in the valuation class for the 17 years in the links below, with the solutions.
Past quizzes: https://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz1.pdf
Past quiz solutions: https://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz1sol.xls
The earlier you get started, the more problems you can work through, and the more you work through, the more comfortable you will get. Remember that you perfect a craft by doing.

Attachments: Weekly challenge #3


I know you are busy doing other stuff, but as the discussion shifts from discount rates to cash flows, the details start mounting and it is easy to get lost in abstractions. If you are interested in getting past abstractions, I have put together three webcasts for this week:
How to compute trailing 12 month earnings: https://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/Trailing12month.mp4 (Uses Apple from late 2012)
How to convert leases to debt: https://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/Leases.mp4 (Uses Disney in 2012)
How to capitalize R&D: https://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/R&D.mp4 (Uses Microsoft annual reports from 2012 & 2011)

They are all about 10-15 minutes each... and you can download the spreadsheets and supporting material by going to
I hope you get a chance (at least after the quiz) to watch one or more of these webcasts.


I hope that I have not ruined your weekend with the impending quiz, but if I have, so be it. I am attaching the newsletter for the week. I also posted a couple of items on my blog that you may find interesting. The first is a listing of what I term twisted DCFs, which have a D and a CF but don’t really result in a DCF:
The second is a post on why I think it is a mistake to keep talking about tech companies as if they shared common characteristics:

Attachment: Newsletter #4


Next week brings the quiz, with all the angst and stress that quizzes usually bring. Note that the quiz will be in the first 30 minutes (1.30-2) of Wednesday's class and will cover everything through cashflows (about page 145 in the packet). We will not cover growth on this quiz. So ignore them on the past quizzes. What past quizzes, you ask? Here are the links:
Past quizzes: https://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz1.pdf
Past quiz solutions: https://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz1sol.xls
It is open book, open notes and open iPad but not open laptops. (Sorry!) If you are going to miss the quiz, you need to let me know before Wednesday at 1.30.

We will spend tomorrow finishing the discussion of cash flows and then start on growth rates, by first looking at the usefulness (or lack thereof) of historical (past) growth. We will then move to both analyst estimates and what I like to term intrinsic or fundamental estimates of growth, which we probably will turn to after the quiz on Wednesday. Yes, there is class after the quiz. Finally, the weekly challenge #3, which I have been nagging you to do, has a solution. I have attached it (with the rating spreadsheet that I needed to get the solution).

Attachment: 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. 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. Also, if you see an equity risk premium of 5.5% being used when none is given in the problem, that reflects a time period when I used to let people look up the ERP in their lecture notes and that was the historical ERP at the point in time that these quizzes were written.

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 1.30 ON WEDNESDAY AFTERNOON. If you are, it is open-book, open-notes but no laptops. You can use your iPads but no connectivity... I have attached the post-class test and solution.

Attachments: Post class test and solution

3/3/15 have views on: Apple. As you may know, I have been posting on Apple a long time on my blog and rather than point you to every post, I will point you to a long post from April of last year, where I referenced all my earlier posts and valuations of Apple:
Once you have read this post, where I argued that Apple was approaching a full valuation in April, fast forward to the most updated numbers for Apple in this link:
Finally, here is my latest valuation of Apple:
Play with it and make your own judgments on growth, margins, trapped cash and risk. Once you have a number, go in and add it to the shared Google spreadsheet:
You may want to do this after the quiz but it will give you some talking points when you are sitting at the beach on Caribbean resort trying to impress someone with your investment acumen.

The quizzes are done and you can pick them on the ninth floor of KMEC. As you come of the elevators, head towards the main doors and before you get to the doors, look to your right and you should see a table. You will see two (neat) piles in alphabetical order, face down. Please pick up only your quiz. I have attached the solution (with the grading template) and the distribution. If you have any issues with the grading of your quiz, please come an see me and don’t go to the TAs. I will be in some of tomorrow and day after.

Attachments: First quiz , the solution and the distribution of grades.


I won't ask you how the first quiz went because that may evoke the wrong response. The good news is that it is over. If you were able to hang in there mentally and physically, we did complete our discussion of growth by looking at the fundamentals that drive growth. Starting with a very simple algebraic proof that growth in earnings has to come either from new investments or improved efficiency, we looked at how best to estimate growth in three measures of earnings: earnings per share, net income and operating income. With each measure of earnings, the estimation of growth boiled down to answering three questions: (1) How much is this company reinvesting to generating for future growth? (2) How well is it reinvesting? (3) How much growth is added or lost by changes in returns on existing investments? The weekly challenge for this week revolves around fundamental growth. Try it, if you get a chance. I have also attached the post class test and solution for today's class. Hope you get a chance!

Harking back to the quiz again, I am truly sorry for not sending you the review session. I know that it is too late for this quiz, but if you did badly, you may still find it useful (albeit frustrating).
The supporting presentation for the quiz is at the link listed below:

Attachments: Post class test and solution


I hope that most of you have picked up your quizzes. I will leave them out until Monday but please do pick them up, if you have not already. You are probably in no mood for more valuation, but if you are, I would spend some time estimating the "secret number" in valuation: the return on invested capital and/or return on equity. Here are the steps:
1. Start by getting the current year's operating income and net income. Do all of the things we talked about last week including
- removing any one time charges or income
- update the numbers to make them current
- see if you can find out the interest income earned on cash and multiply by (1-tax rate). If you cannot find it, just multiply last year's cash balance by the treasury bill rate during the year.
Your preliminary estimate of income will be:
After-tax operating income = Operating income (1- Effective tax rate)
Net Income from non-cash assets = Net Income - Interest income from cash (1- tax rate)

2. Go to the balance sheet for the prior year (if you are doing trailing 12 months, go to the same quarter of the previous year)
- Get the shareholders' equity (this can be negative for some firms)
- Add up the interest bearing debt on the balance sheet (short term and long term debt)
- Get the cash balance
Your preliminary estimate of invested capital
Invested capital = Shareholders equity + Total Debt - Cash
Your preliminary estimate of book value of equity in non-cash assets will be
Book equity from non-cash assets = Book equity - Cash

3. Adjust for leases & R&D
- Adjust the operating income and net income for leases & R&D
- Adjust the book debt for the PV of operating leases
- Adjust the book equity for unamortized R&D
Recompute your invested capital

4. Compute your ROE, non-cash ROE and ROIC
ROE = Net Income/ BV of equity
Non-cash ROE = Net Income from non-cash assets/ Book equity from non-cash assets
ROIC or ROC = After-tax operating income/ Invested Capital

You may get strange looking numbers. For instance, for some firms with large cash balances, your ROIC can be astronomical or negative. For young, growth firms, the ROIC and ROE can be negative. Don't freak out. You still have the power to override these numbers, when you make your forecasts for the future. In other words, what you really care about is ROE and ROIC on future new investments and you are not bound to use last year's numbers. If you are looking at industry averages for these numbers, they are on my website under updated data.

We also talked about items like goodwill and restructuring charges that can throw you off. If you are interested, here is the sleep-provoking paper of mine on ROE and ROIC that you will find absolutely engrossing (NOT!!!):


This week, we focused on estimating growth from fundamentals and built growth rates from accounting returns - return on equity and return on invested capital. Accounting returns can be messy and misleading. In this webcast (that some of you may remember from the corporate finance class), I look at the process of estimating accounting returns, using Walmart as my example:
Webcast: https://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/ROIC.mp4
Walmart 10K (2013): https://www.stern.nyu.edu/~adamodar/pdfiles/cfovhds/webcasts/ROIC/walmart10K.pdf
Walmart 10K (2012): https://www.stern.nyu.edu/~adamodar/pdfiles/cfovhds/webcasts/ROIC/walmart10Klastyear.pdf
Spreadsheet: https://www.stern.nyu.edu/~adamodar/pdfiles/cfovhds/webcasts/ROIC/walmartreturncalculator.xls
I hope you get a chance to take a look at it.

I have also attached this week’s challenge, though you are probably burnt out after the quiz. If you do get a chance, give it a shot. It is also centered around estimating fundamental growth for a company.


Finally, it looks like we have a weekend that we can actually be outside and I hope you get a chance. Two very quick notes. First, the newsletter for the week is attached. Second, the second and third packets are ready to download online.
Look to the top of the page. The bookstore should also have a combined packet that includes packets 2 and 3 on their shelves right now, if you want to skip downloading and printing on your own.

Attachment: Newsletter #5


I hope that you had a chance to try the weekly challenge (I know.. I know.. No chance.. but no harm trying).... I have attached thes solution to this email. Just a heads up that this week, we will turn our attention to that big number in every DCF valuation, the terminal value, as well as how best to pick the right DCF model to value your company. If you want to get started on the DCF valuation for your company, it is a good week to get started or moving.

Attachment: Solution to 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).
I have attached the post class test & solution for today's class.

Attachments: Post class test and solution

3/10/15 Given that you just got your quiz back and probably want to get to work on your DCF valuation. So, I decided to go off on a tangent and reuse an offbeat assessment that I did on Bitcoin about a year ago. Like me, you have probably been watching Bitcoin go from $13 to $1000 and back down to $280 and wondered not only what was driving the price but what exactly it was. In my post a year ago, when Bitcoin was at $640, I pondered whether Bitcoin had a future and what its value was:
The numbers in the post may be dated but try to make your own judgments on four issues:
1. Do you think Bitcoin is a currency?
2. If no, what is it? (An equity instrument, a credit card, a scam)
3. Would you buy Bitcoin for a transaction? (I have a list of vendors who accept Bitcoin, in my post, and lay out the process for acquiring Bitcoin)
4. Would you trade in Bitcoin at today's price?
Finally, I looked at five currencies: the US $, the Chinese Yuan, the Argentine Peso, Gold and Bitcoin as competing currencies and given my priors, I ranked them as follows from best to worst as a currency that I would like to be paid in or in my pocket in any part of the world: US dollar, Gold, Chinese Yuan, Bitcoin, Argentine Peso. Please make your own rankings. Once you have them, go to this shared google spreadsheet and give me your views:

Today's class was about the loose ends in valuation, items we often pay little heed to or attach arbitrary premiums/discounts for. We began by looking at cash and whether it should command a premium at some companies (if they have a good track record and have restrictions on raising capital) and a discount at others (if investors don't trust you with the cash). We then looked at cross holdings in other companies and the numerous barriers to valuing them. Third, we looked at other assets and argued that you should never double count assets. I have attached the post class test and solution.

On a different note, please do get a jump on the DCF valuation of your firm. The valuation is due on April 3 but only for feedback, not grading. So, don't feel the pressure to get it right. Just get it done. I have also attached the weekly challenge for this week, though this is little chance that you will be able to do it, on spring break. I will give a longer window than usual for submissions, and not send you the solution until March 23. Just one more email later today with the to do list for the valuation and I will then leave you to your own devices (I promise).

Attachments: Post class test and solution


s you take for different parts of the world, I know that the last thing you want to think about is your 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: if you are doing a FCFF valuation for a money losing firm or a high growth firm or want to allow your margins to change over time. (This is the most general model of the four.)
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 April 4, 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...

Finally, if you are one of those people who likes checklists, I have attached one of those as well. Hope you find it useful.

Attachments: Dividend Discount Model, FCFE Discount Model, FCFF Discount Model, General FCFF Model, Valuation Checklist


I hope that your spring break was great but the bad news is that it is almost over. I don't mean to be the skunk at your party, but it is my duty to remind you that your DCF valuation is due for feedback by April 3. If you are working on it or plan to work on it, you will undoubtedly find that errors you make on your terminal value can drown out all of the good work that you do in estimating your inputs. I have a webcast that you may find useful in checking your terminal value (or someone else's estimate of terminal value). I hope you get a chance to check it out.

Webcast: https://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/terminalvalue.mp4
Terminal value DCF (for use with the webcast): https://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/webcasts/TermValueCheck/termvalueDCF.xls
Terminal value analyzer: https://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/webcasts/TermValueCheck/termvaluecheck.xls

Finally, if you want to see how this works in practice, take a look at the attached equity research report on Tesla from Morgan Stanley. Skip through the first 40 pages (they are impressive but a distraction) and go to page 41 to the DCF valuation. Put the terminal value to the test (using both the EBITDA multiple and the perpetual growth model used by the analyst). I am also attaching the newsletter for this week.

Attachments: Newsletter #6

3/22/15 Hope you are back and raring to go (Right... But no harm hoping...)! Anyway, ready or not, we are back to work tomorrow. After tying up a couple more loose ends (complexity, debt to net out of firm value to get to equity value and employee options/restricted stock), we will start on a series of valuations. We will begin easy, using a stable growth dividend discount model to value Con Ed, move up the difficulty ladder to value 3M with a FCFF model before and just after the 2008 market crisis and follow up with a valuation of the S&P 500 at the start of 2015. We will then move into what I call the dark side of valuation, looking at difficult to value companies across the life cycle (from start up to decline), across sectors (financial service, cyclical, commodity) and across markets. If you are having trouble with your DCF valuation, odds are that we will address that issue in the context of valuing some other company in the next few sessions. I am also attaching the solution to the weekly challenge for this week. While you probably did not get a chance to work through the challenge, please do take a look at it since it relates to DCF's biggest number, the terminal value.

Today, we put the last two loose ends to rest. First, wwe went back and looked at defining debt. While we used a narrow definition of debt, when computing cost of capital, we argued for using a broader definition of debt, when subtracting from firm value to get to equity value. Next, we talked about how best to deal with both currently outstanding employee options and potential options grants in the future. With the former, we argued for using an option pricing model to value the options and netting that value out of equity value, before dividing by the number of shares outstanding. With the latter, we suggested incorporating the expected cost into the operating expenses, thus lowering future earnings and cash flows.
We then started on our first valuation, Con Ed, using a stable growth dividend discount model. To qualify to be valued with this model, we argued that a company had to meet three criteria: have a high payout ratio, have a fundamental growth rate less than that of the economy (or the risk free rate) and a beta close to one. We will continue with more valuations in Wednesday’s session. If you are interested in downloading the excel spreadsheets with these valuations, you can get them here:
I have also attached the post class tests/solutions for today.

Attachments: Post class test and solution


I am sorry to get this to you so late in the day but I was otherwise occupied. The company that I valued this week is CRH, an Irish company. If you have never heard of it, I don’t blame you because I had not either. It is the third largest construction company in the world and you can start by reading the Bloomberg description of the company.
You can then check the financial history of the company and its current bond rating, again using Bloomberg summaries:
Financial Summary: https://www.stern.nyu.edu/~adamodar/pc/blog/CRHBloombergFA.pdf
Bond/Debt Rating: https://www.stern.nyu.edu/~adamodar/pc/blog/CRHBloombergDebt.pdf
Finally, take a look at the annual report for 2014 for the company, which contains information on geography and product segments:
My valuation of CRH from earlier today (fresh of the press) is at the link below.

You are probably wondering why I picked such a boring company to analyze and here is where it gets interesting. As part of a merger of Lafarge and Holcim, two European construction/engineering companies, those companies were required by the EU to shed assets and CRH was the acquirer.
Story on merger: http://www.wsj.com/articles/holcim-lafarge-confirm-asset-sale-talks-with-crh-1422859051
Story on asset purchase: http://www.wsj.com/articles/crh-confirms-6-5-billion-deal-to-buy-holcim-lafarge-assets-1422807500
We know that CRH paid 6.5 billion Euros for the assets and that the assets generate 6 billion Euros revenues in Asia, Latin America, UK and Canada. That is a big investment and if you are valuing CRH, you are probably at a loss on how to incorporate the effect of this asset acquisition into the value. Here is how I did it and you can take issue with it. I treated it like a capital budgeting project and estimated earnings and cash flows, based upon the average across construction companies globally for EBITDA margins and working capital. The present value of my cash flows came in at 6.27 billion Euros, about 230 million Euros less than what CRH paid for them.
It is true that my estimates are based upon very limited information but it illustrates a simple process for dealing with add on actions. Since this may happen with the firms that you are valuing, please take a look at what I have done. It may be helpful. Finally, if you do try your hand at the valuation, you can input your numbers into the shared Google spreadsheet:


In today's class, we started with two conventional valuations, one of 3M and the other of the S&P 500. We then talked about the valuaton of young, growth companies by emphasizing that you will be wrong 100% of the time and that it was okay, because the market is usually even more wrong. Next session, we will continue with the discussion by looking at mature companies. Overall, we are approaching the end of the DCF section of this class. If you have not printed off packet 2 of the lecture notes, please do so or buy the packet at the bookstore (you will get packets 2 & 3 consolidated). We will be getting to it next week. I have also attached the weekly challenge for this week (built around management options) and the post class test and solution.

Attachments: Post class test and solution


So, where are you in the DCF process? I hope that you have picked a company, collected the financials and actually tried to do a base case. A piece of advice. Get a base case valuation going with just minimal information (last annual report or 10K) and come back to it with more details. I have reattached the valuation checklist I sent you a couple of weeks ago, since you may find it more useful now. In case, you have forgotten which spreadsheets work best if you want to start with one of mine, you should stick with the ginzu versions:
a. fcffginzu.xls: For a firm with stable operating income and return on capital: https://www.stern.nyu.edu/~adamodar/pc/fcffginzu2015.xls
b. fcffsimpleginzu.xls: For a money losing firm or a high growth firm or want to allow your margins to change over time (This is the most general model and you can use it for almost any non-financial service firm): https://www.stern.nyu.edu/~adamodar/fcffsimpleginzu2015.xls
c. fcfeginzu.xls: For valuing a firm using the FCFE approach: https://www.stern.nyu.edu/~adamodar/pc/fcfeginzu2015.xls
d. divginzu.xls: for financial service firms and perhaps REITs/MLPs: https://www.stern.nyu.edu/~adamodar/pc/divginzu2015.xls

Finally, if yesterday’s session provoked or rekindled your interest in Amazon, you may find this blog post I had in October 2014 interesting (because it not only compares my forecasts from 2000 to the actual numbers at the company but also provides an updated valuation):

Attachments: Valuation Checklist

3/27/15 As you work on your perfect DCF valuations, employee options that your company has granted and continues to grant may be a source of imperfection. I know that we went through the mechanics in class. First, value the outstanding options, using an option pricing model. Second, subtract the value of the options from the equity value that you estimated in a DCF. Third, divide the remaining value by the number of shares outstanding (the actual number, not the diluted number). The mechanics of doing this can be tricky and that is why this week's weekly challenge is built around options. After you have tried the challenge, you may also want to watch this webcast that I put together on doing this in practice. I used Cisco, a monster option granter, to illustrate the mechanics. You can find the links below:
Webcast: https://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/Employeeoptions.mp4
Cisco 10K: https://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/webcasts/EmployeeOptions/cisco10K.pdf
Spreadsheet for options: https://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/webcasts/EmployeeOptions/ciscooptions.xls
I hope you get a chance to watch the webcast and that you find it useful.

If you have finished your DCF and sent it to me, thank you! You should be hearing from me soon. If you are working on your DCF right now, I am sorry for distracting you. Please get back to work. If your question is “what DCF”, I don’t know what to tell you. No matter what you are doing, the newsletter is attached.

Attachment: Newsletter # 7 (March 28)


News on two fronts. The first is that the solution to the option weekly challenge is attached. If you are at all confused about valuing employee options, I would check it out. The second is an update on the week to come. We will start tomorrow by looking at other companies on the dark side of valuation, including distressed companies, cyclical companies and emerging market companies. On Wednesday, we will (hopefully) finish our discussion of packet 1. If you can, please download, print or buy packets 2/3. They are both ready to download online:
Packet 2: https://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/packet2spr15.pdf
Packet 3: https://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/packet3spr15.pdf
You can also get the powerpoint versions on the website for the class:
Look to the top of the page.
Also, not to be a nag, but please do work on your DCFs and get them to me by Friday.

Attachments: Weekly Challenge #5: Solution & Option value


In today's session, we started with the depressing job of valuing declining and distressed companies, moved on to emerging market companies and ended with financial service companies. We are almost to the end of the DCF process now with only a couple of loose ends to tie up. Next session, we will look at the difference between value and price, what it tells us and what it does not. The post class test and solution are attached.

On a different note, please do work on your DCF valuations this week and try to get them to me by Friday. I could draw lines in the sand (by 5 pm Friday, or else) but I will not. So, do your best and I will do mine.

Attachments: Post class test and solution

3/31/15 In keeping with my exhortations to you to go where it is darkest, I decided to value Lukoil, a Russian oil company. You can start by reviewing the blog post that I had in November 2014 about Lukoil and Vale:
You can follow up with this updated summary of where Lukoil stands today (from Bloomberg):
You can back up the Bloomberg numbers and get more details by downloading the Lukoil annual report for 2014 (it is in English):
You can check out my valuation of Lukoil from March 2015:
Finally, you can tweak, modify or adjust the numbers to arrive at your own estimate of value for Lukoil and enter them in the shared Google spreadsheet:

In today's class, we finally put to rest DCF by having a discussion of the difference between value and price, why they might be different and when the gap will close. Before entering into that discussion by talking about the values of intangible asset companies and commodity/cyclical companies. With the latter, we noted the importance of keeping separate our macro views (about the economy or commodity) from our micro views, and the use of Monte Carlo simulations to deal with uncertainty. During that discussion, I talked about a paper that I have on statistical distributions and the link is below:

We ended the class by starting the discussion of multiples and comparable firms. We will continue that discussion after the second quiz. I have put the review session up online (on the webcast page for the class) with the presentation. The links are below:
Presentation: https://people.stern.nyu.edu/adamodar/pdfiles/eqnotes/valquiz2review.pdf
Webcast: https://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/valquiz2review.mp4

You can also find all past quizzes with the solutions in the following links:
All past quiz 2s: https://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz2.pdf
Quiz 2 solutions: https://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz2sol.xls
You will see relative valuation problems (multiples) popping up in the pre-2008 quizzes. You can ignore them!

Attachments: Post class test and solution

4/2/15 I know that it seems like I am piling on, with your DCF due tomorrow and your quiz on Monday and I am sorry. However, I will not harass you too much today.
1. DCF: Please remember to put "My Perfect DCF" in the subject, when you send your DCF to me. All you have to send is your spreadsheet, with questions and comments embedded in it (if you have any)
2. Quiz: The quiz review, presentation and links to past quizzes were in yesterday's email (which I just resent). In case you did not get it or my retry, you can also get them by going to

As I check my mailbox, I see that most of you have turned in your DCF valuations. I appreciate the effort and will get them back to you as soon as I can. I spent all day yesterday adn the day before grading corporate finance quizzes which came due on Wednesday and have not had a chance to look at the DCFs but I promise that I will get them back to you soon. There is no valuation tools webcast this week, as we take a break to get ready for the quiz. However, if you really miss the weekly challenges, I have attached the one for this week but it is on multiples (and hence not on your quiz). I will see you Monday at 1.30. Please don't be late and if you are going to miss the quiz, let me know ahead of 1.30

Attachments: Weekly challenge #6


Just in case you run out of things to do this weekend, the newsletter is attached. I am working my way through your valuations and will try to get them to you by Monday.

Attachment: Newsletter# 8 (April 4)


We have the quiz tomorrow in the first 30 minutes, followed by a continuation of the discussion of relative valuation. We will look at defining, describing and analyzing multiples. Please bring packet 2 to class tomorrow. Until next time! (I am also attaching the solution to weekly challenge #6 on the off chance that you tried it).

Attachment: Weekly Challenge #6 Solution


By now, all but a handful of you (I think I have about 8 DCFs left to do) should have received back your DCF valuation back. If you don’t hear back by tomorrow, 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 2% 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 0.2%, 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 5.7% (April 2015). If you are using a premium of 4%, 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 by the time you get to year 10, 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 (and there is a webcast that you can use as well from a few weeks ago)

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. Until next time!

Attachments: Growth Check, Terminal Value Check, Post Mortem


Your quizzes and are ready to be picked. Please take just your quiz, leave the pile in alphabetical order and don’t browse. I have attached the solution and the grading distribution. As always, if there is a screw up, it is my fault. Please bring your quizzes in and I will fix my mistake.

Attachments: Solution as well as the distribution of grades


I meant to send this yesterday but events got ahead of me. This week, I turn to pricing and to how the price you attach to a company (or any asset) will depend on the comparables that you use. I use Amgen and the healthcare sector to illustrate my point. I have attached spreadsheets containing (1) all health care firms, (2) only firms that are categorized as pharmaceuticals by Cap IQ and (3) only firms that are categorized as biotech by Cap IQ. The spreadsheets include about ten multiples computed for each firm, ranging from standard PE to EV/Sales. In a very simple exercise, I then pick PE to illustrate its weakness in this sector and also its distributional properties and price Amgen, relative to both pharma and biotech companies. It is the most sophisticated exercise in the world, but it indicates how different your conclusions can be. If you really want to explore multiples, try EV/Sales and see what you get as a comparison.

Attachments: The Healthcare Sector (US): Raw company data, The Pharmaceuticals: PE Ratio Distribution and Statistics, The Biotechnology firms: PE Ratio Distribution and Statistics, Pricing Amgen as a pharma company and then as a biotech company


In today's class, we extended our analysis of multiples by first looking at PE and PEG ratios, then moving on to PBV ratios and finally examining enterprise value multiples: EV/Invested Capital, EV/EBITDA and EV/Sales. In particular, we noted that the drivers for EV multiples are analogs of the equity multiples: growth in operating income replacing growth in net income, reinvestment rates replacing payout ratios, ROC replacing ROE and cost of capital replacing cost of equity. There is a simple way to find the companion variable (the key driver) for a multiple. With an equity multiple, you can get this variable by dividing the net income by the denominator of the multiple. With an enterprise value, you divide after-tax operating income by the denominator of the multiple. With the EV/Sales ratio, this yields the after-tax operating margin as the determining variable. We used that measure to evaluate the value of a brand name, by comparing the pricing of Coca Cola with its current operating margin with its value with a generic margin. Finally, I am attaching the post class test/solution for today as well as the weekly challenge for this week. Until next time!

Attachments: Post class test and solution


As promised (or threatened), the mystery project is ready for you. It is a group project, due two weeks from today (Wednesday, April 24, 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 iTunes U).

Attachments: The mystery project, Data for mystery project

4/10/15 One of the most confusing aspects of multiples is dealing with the variants of value out there: firm value, enterprise value and equity value. In this webcast, I look at what the differences are between these different numbers and how our assessments of leases & R&D can change these numbers. Start with this blog post:
Then watch the webcast:
You can download the presentation:

And the spreadsheet that goes through the calculations:

Just a quick note. Last week, we continued to explore the determinants of multiples, looking at PE ratios, PEG ratios and EV multiples. In the process, we uncovered the unsurprising reality that the determinants of multiples are cash flows, growth and risk, the same variables that determine intrinsic value. Next week, we will finish our discussion of relative valuation. In fact, you have all the tools you need to do your mystery project, if you are so inclined. The newsletter for the week is attached. Until next time!

Attachment: Issue 9 (April 11)


In the week to come, we will continue and complete our discussion of multiples, by looking at extending the comparable list to the entire market. On Wednesday, we will look at asset based valuation, including liquidation and sum of the parts valuation. I have attached the solution to this week's weekly challenge (that you may or may not have looked at). Until next time!

Attachment: Weekly challenge solution


In today’s session, we continued with our discussion of pricing companies based upon how similar companies are priced, by examining how the process can be extended to the entire market. We ran a market-wide regression of PE ratios against the intrinsic fundamentals (beta, growth and payout) and noted two issues:
1. The correlation between beta, growth and payout creates multicollinearity which can play out as coefficients whose signs don’t make sense on a stand alone basis.
2. The market regression can still be used to get predicted PEs for individual companies and make pricing judgments, relative to the market.
Earlier in the class, we looked at the challenge of pricing young companies in a young sector and suggested two alternatives. One is to use proxies for whatever investors are focusing on in pricing these companies. The other is to use forward (future) revenues or earnings, while recognizing that a big chunk of that value will be lost in the process of bringing it back to today. Until next time!

Attachment: Post class test and solution

4/14/15 A couple of weeks ago, I valued Lukoil, using an intrinsic valuation model, and found it to be over valued. Today, I price Lukoil and to price it, just like with any other stock, I had to make judgments about what companies (all oil or integrated oil, global/emerging/Russian oil companies) to use as comparable firms and what multiple (equity vs enterprise, earnings/revenues/book value) to use. I explain my choices and findings in this document:
The raw data with my analysis is in the spreadsheet at the link below:
If you do get a chance to price Lukoil (and it is good practice for your project, the third quiz and the mystery project), please enter your numbers in the Google shared spreadsheet:
4/15/15 In today's class, we closed the book on relative valuation by looking at how to pick the "right" multiple for a valuation, with the answers ranging from cynically picking one that best fits your agenda to picking one that reflects what managers in that business care about. It is amazing how widespread relative valuation is. I found this link recently on rules of thumb in valuation. Take a look at it.... especially the multiples mentioned
And the site below has valuation spreadsheets as well as a valuation blog.
Finally, here is a fun article on how relative valuation is used in hotel valuation (It can be based on how much a can of soda at the hotel costs... I am not kidding)
We then moved on to asset based valuation: liquidation valuation, accounting valuation and sum of the parts valuation, and closed the class by starting on the process of valuing private businesses. Finally, the third packet is available to be printed off online. (If you bought the second packet in the book store, it already includes packet 3... So, you are all set). Post class test and solution is attached, as is the weekly challenge for this week.

For the moment, I expect that you are working on the mystery project. I don't have much specific advice for you on the project, but remember that your mission is to do a relative valuation (not an intrinsic value). That gives you a lot more leeway in how you deal with items. For instance, if your were doing DCF valuations, you would have to value the employee options, using option pricing models, and subtract from the value of equity to get to value of common stock. With multiples, you may adjust for options much more casually (adjusting the number of shares for options outstanding, for instance). It will also mean that if you do not have the data to do something correctly, you may have to settle for an approximation. In case, the confusion about the due date is still persisting, the mystery project is due on April 24 at 5 pm.

I have also put up a webcast that is more statistics than finance about how to look at data and try to evaluate relationships between variables. I use the banking sector to illustrate my case but I hope that you find it useful for both your mystery project as well as for your overall project. If you are solid on your statistics, you can skip this webcast, since you already know everything that I am saying. If you need a quick review of the process, I think it will be useful.
Start with the webcast:
Download the slides:
Here is the raw data:
And the descriptive statistics:


I hope that you are getting a chance to enjoy the weather today, even if it means lugging your laptop to the park. Anyway, the newsletter for the week is attached. And keep plugging away at the mystery project. And one more thing, we will be starting on packet 3 on Monday. If you get a chance, please print it off. If you bought the packet at the book store, it should already be in the packet. Until next time!

Attachment: Issue 10 (April 18)


If you did try the weekly challenge, the solution is attached. Even if you did not, you can take a quick look at it. Tomorrow, we will continue our discussion of valuing private businesses by looking at illiquidity and key person discounts in a private-to-private transaction, how value changes when the buyer is a public company and close this section with a discussion of how valuation for an initial public offering and to a venture capitalist. We will be beginning on lecture note packet 3. If you have not downloaded it yet, please do so.
If you did buy packet 2 from the bookstore, it is a combinations of packets 2 and 3. So, you are all set.

Attachment: Solution


In today's class, we put the finishing touches on private company valuation by looking at key questions that arise in private company valuation (illiquidity, key person etc.) and then looked at valuing IPOs. In particular, the question of what happens to the proceeds from an offering can affect value per share, and the offering price itself is subject to the dynamics of the issuance process, with investment bankers more likely to under price than over price offerings. We will start on real options and packet 3 on Wednesday! So, please don’t forget to get packet 3 before class on Wednesday. The next quiz is a week from today and will cover all of packet 2, thus encompassing all of relative valuation, asset based valuation and private company valuation. While that seems like a lot, a great deal of it is old wine in new bottles. Here are the links to past quiz 3s and solutions. As you work through, please remember to ignore the option-based problems that you may find on the earlier quizzes:
Past Quiz 3s: https://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz3.pdf
Past Quiz 3 solutions: https://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz3sol.xls

Attachments: Post class test and solution


I was going to pick a new IPO and value it this week, but there is nothing big on the horizon. So, I decided to go back in time to last year and use my Alibaba IPO valuation. If you don't know much about Alibaba, start with this article from the Economist (which while dated captures the spirit of Alibaba):
Then, visit Alibaba's main merchandising site, Taobao.com. (http://www.taobao.com/market/global/index_new.php) You will see what I meant when I talked about chaos.

You can read my first blog post about Alibaba here:
You can read my follow up blog post, after the bankers priced the offering at $68/share here:

You can get the original prospectus filed by Alibaba in May 2014 and an updated one from the end of August 2014 here:
May 2014: https://www.stern.nyu.edu/~adamodar/pc/blog/AlibabaProspectus.pdf
August 2014: https://www.stern.nyu.edu/~adamodar/pc/blog/AlibabaProspectusAug14.pdf

My valuations for Alibaba in May 2014 and the updated one from September 3, 2014 are here:
May 2014: https://www.stern.nyu.edu/~adamodar/pc/blog/AlibabaIPO.xls
September 2014: https://www.stern.nyu.edu/~adamodar/pc/blog/AlibabaIPOSept14.xls

Download the latter, and change the numbers you don't like (The key three inputs are revenue growth, a target margin and a sales/capital ratio) Once you have your estimate of value, please go to the google shared spreadsheet and enter your value:
It will be fun to see how close you get to the offering price, which was $68/share and the price by the end of the first trading day (close to $93). The stock is trading at $82 today.


Lots to pack into one email. In today's session, we tried applying (with mixed results) option pricing to value a patent. We argued that the fact that a patent is not viable today does not imply that the patent is not valuable. Valued as an option, patents have values in excess of their discounted cash flow value, though the magnitude of the premium can be a function of how competitive the market place is. In general, you are on pretty weak ground in using option pricing to value viable patents but it may be more useful in valuing non-viable patents in risky businesses.I have attached an option valuation spreadsheet that you can use to value patents as well as the post class test & solution.

I hope that your mystery project is progressing. The deadline remains Friday at 5 pm. When you do submit your project, though, please follow these guidelines:
1. Electronic format: Please try to create a pdf file of your submission. It is easier for me to work with, comment on and grade.
2. Cover page: On the cover page, please include the names of everyone in your group (in alphabetical order) and the following information: the multiple or multiples you used, your five cheapest stocks, your five most expensive ones and your buyout target.
3. Format: Please keep your write up short and to the point. Explain why you picked the multiple that you used, how you used that multiple to find cheap and expensive stocks and what process you used to find your buyout target. Should not take more than 2-3 pages.
4. Excel spreadsheets: You don't have to add on all of your excel spreadsheets and worksheets.
5. Mail subject: In the subject, please enter "No mystery here", when you send your submission.

I know that you have neither the time nor the inclination to deal with a weekly challenge. However, when you get done with your mystery project, you may find this weekly challenge that deals with the issues that you face when valuing private businesses to be useful in preparing for the next quiz. I know that we have not dealt with the voting right and non-voting right shares in class yet (and it will not be on the quiz) but give it a shot. The solution will be posted on Sunday.

Attachments: Post class test and solution, Patent valuation spreadsheet

4/23/15 The review session for quiz 3 is up and running! You can get it on the webcast page for the class. The link to the webcast is below:
The slides for the presentation are at this link:
You can find the past quiz 3s and the solutions below:
Past quiz 3s: https://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz3.pdf
Solutions: https://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/quiz3sol.xls
Remember that the earlier quiz 3s included a big chunk of real options, which are not covered on this quiz. So, stick with the relative valuation and private company valuation questions. Until next time!
4/24/15 I know that you have absolutely no time for this, but just in case, I have a webcast on valuing patents as options:
Webcast: https://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/optiontodelay.mp4
Presentation: https://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/webcasts/optiontodelay/optiontodelay.pdf
Spreadsheet: https://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/webcasts/optiontodelay/productoption.xls

By now, you should have your mystery projects back. If you have not, please send it to me again. Looking over your analyses, here are some of the overall impressions I have:

1. Multiple used: The most widely used multiple, by far, was PE.

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 a few 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. Four 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. As I checked through the lists, I was struck by how little commonality there was across the lists. Each of you had your own idiosyncratic list, which tells me that there are no clearly under or over valued companies that stick out, across all approaches and multiples. Good to know, but perhaps not surprising. However, there were some companies that showed up more frequently than others.
Company Number of groups
Petrobras 9
Gilead Sciences 7
SAIC Motor 7
Twenty-First Century Fox 7
Gazprom 6
Orange 5
Taiwan Semi 5

The fact that Petrobras shows up on so many lists is a sign of the one of the weaknesses of PE ratios. If you don’t control for leverage, highly levered firms can sometimes look really cheap. It is also worth noting that Twenty-First Century Fox also showed on two of the most overvalued lists.

Most over valued firms
Company Number of groups
Regeneron 12
Enel 6
AstraZeneca 5
Kinder Morgan 5

Regeneron is the runaway winner, with a PE ratio in excess of 100. I am not going to sell short right away, but it would be worth pursuing further in terms of a full-fledged valuation.

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 a scattering of companies that were choses. Only three were picked by more than one group: Canon, Orange and Phillips 66. 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. If you get a chance, please browse through it.


Sure that you are sick and tired of valuation, but the end is near. Here is the second-to-last newsletter for the class. See you at the final quiz on Monday.

Attachment: Issue 11 (April 25)


I know that you are ready for the quiz. If you did try the weekly challenge, I have attached the solution. After the quiz, we will continue with our discussion of real options by looking at natural resource options and the option to expand. On Wednesday, we will complete the real options section.

Attachments: Weekly Challenge #9 solution


In today's class, we completed our discussion of the option to delay by looking at natural resource options, i.e., undeveloped reserves owned by natural resource companies. We argued that these reserves will be under valued using conventional DCF approaches, which ignore the optionality embedded in them, and that the option premium would increase with the uncertainty about natural resource prices. We also looked at the options to expand into new markets or products and how it derives its value from exclusivity. I am attaching the post-class test and solution.

Attachments: Post class test and solution


This is the time of the year that we see news stories about CEOs, like this one:
This, of course, triggers the standard responses from all sides. The populist camp is quick to note how much CEOs make and how this is symptomatic of the greed of the one percenters. At the other extreme are those who believe that CEO pay is set by the market, based upon demand and supply for CEOs and reflects the value added by these CEOs. I fall somewhere in the middle, and believe that the pricing of CEOs may not reflect the value added by them and also that the only group that is entitled to complain are stockholders in that CEO's company. Start with this pdf file of the blog post on the topic that I plan to post tomorrow:
Incidentally, if you find any typos in the post or have suggestions on how I can improve it, please let me know before tomorrow morning (when I plan to post it) and I will fix the problems before I post it on my blog.

In the post, I set up a framework for valuing a CEO and create a spreadsheet (based on my fcffsimpleginzu) to estimate that value. I apply it to Microsoft in this spreadsheet:
The raw data for this valuation comes from two files, Microsoft’s last 10K (from August 2014) and its historical data (which also has the trailing 12 month numbers)
Microsoft’s last 10K: https://www.stern.nyu.edu/~adamodar/pc/blog/MSFT10K.docx
Microsoft’s historical financials: https://www.stern.nyu.edu/~adamodar/pc/blog/MSFThistorical.xls
If you are up to it, take the MSFT CEO value spreadsheet for a spin and make your own judgment on how much Satya Nadella is worth and enter the numbers in this shared Google spreadsheet:


We started today's class by looking at valuing financial flexibility as an option, and argued that it was worth more to capital-constrained companies with unpredictable and high-value-added investments. We continued with our examination of equity in trouble, debt-laden companies. Given that the equity in these companies takes on the characteristics of an option, we teased out three implications:
The equity in these companies will be valued as out-of-the-money options are and not as conventional stocks. Thus, they will retain their value, even in the face of daunting debt, and will become more valuable as the risk in the business increases and with longer term debt.
Letting equity investors in deeply distressed companies make investment decision can lead to perverse consequences: risky, negative NPV projects may be attractive to these investors, because the transfer of wealth from lenders overcomes the drop in value from the negative NPV.
Acquisitions of companies in other businesses, if not funded with additional debt or accompanied by a renegotiation of interest rates on existing debt, can make equity investors in the acquiring company worse, even if the acquisition is at fair value.
The bottom line on options: they are everywhere, most of them are worth nothing or very little and only a few can be valued with option pricing models. I have attached the post class test and solution, and this week's weekly challenge, if you are so inclined.

Attachments: Post class test and solution


There is good news and bad news in this email. The good news is that the end of the semester approaches. The bad news is that the end of the semester approaches. 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. You can find the regressions here:

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: Estimate the variance in firm value, using your own estimates or the industry averages that I have estimated and are built into the linked spreadsheet.
3.2.5: The value of equity that you get from this model is your option pricing estimate of value for equity.
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 2015 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 May 10, 2015 (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 and submit as a pdf file. The report should be brief and need not include the gory details of your DCF valuation. Just provide the basic conclusions, perhaps the key assumptions that you used in each phase of valuation. (There should be relatively little group work. So, you may not really need to get together for much more than basic organization of the report) The group report is due electronically by Monday, May 11, at 5 pm. A pdf format works best. You do not need to attach the raw data and excel spreadsheets). I am not a stickler for format but here are good examples of reports from previous semesters online.


The final weekly challenge is attached. It relates to valuing a patent. Give it a shot, using my patent-pricing spreadsheet, if you have a chance.

Attached: Weekly Challenge #10

5/1/15 If your company is the one that meets the equity-as-option test (losing money, lots of debt), you are probably not happy. However, it is really not an involved exercise. To assist you, I did put up my latest valuation tools webcast, on valuing distressed equity as an option. I used Jet India, an Indian airline with a history of losses and a mega debt load to illustrate the process. You can start with the webcast below:
The financials for Jet India are contained in this sheet:
The DCF valuation that you need to get your option model started is here:
The value of Jet India's equity as an option is contained in this spreadsheet:
It is pretty straight forward and may be useful.

A few quick notes on this absolutely stunning weekend (which I am sorry to be ruining). First, the last newsletter for the class is attached. Second, the early final option is for Tuesday from 6 pm to 8 pm on 3-110. I will need to have a sense of who is taking the early final soon and I will figure out a way that is more efficient that emailing me. (Perhaps a shared google spreadsheet). Third, I hope that you are working your way down the to-do list that I sent you last week.

Attachment: Issue 12 (May 2)


Next week, we will cover the last two pieces of valuation. Tomorrow, we will look at what is different and not different about valuing companies for acquisitions. We will start with the sorry track record of acquisitions and argue that at least some of the failures can be attributed to ignoring first principles in valuation. To set up for the class, I would like you to go through the attached pre-class test. Since the entire session will be built around these tests, both you and I will gain, if you can spend the 5-10 minutes it will take to review the questions and make your choices. On Wednesday, we will switch hats and move from estimating value (which is what we spent all semester doing) to ways of enhancing value. I think that this session will bring together corporate finance and valuation and be a foundation for those of you who are thinking about starting your own businesses, consulting or going into other disciplines.

Attachment: Acquisition tests


I am sorry if you found today's session to be a downer. Don't get me wrong. Acquisitions are exciting and fun to be part of but they are not great value creators and in today's sessions, I tried to look at some of the reasons. While the mechanical reasons, using the wrong discount rate or valuing synergy & control right, are relatively easy to fix, the underlying problems of hubris, ego and over confidence are much more difficult to navigate. There are ways to succeed, though, and that is to go where the odds are best: small targets, preferably privately held or subsidiaries of public companies, with cost cutting as your primary synergy benefit. If you get a chance, take a look at a big M&A deal and see if you can break it down into its components. Post class test and solution are attached. I am also including the solution to the weekly challenge for last week on patent valuation.

Attachments: Post class test and solution


First things first. As I mentioned in class yesterday, there will be two final exams: one on Tuesday from 6 pm to 8 pm in KMEC 3-110 and the other on Wednesday in KMEC 2-60 from 1.30-3.30. I would like to have some sense of how many of you will be taking the early final and I have a Google shared spreadsheet where you can let me know (by putting an X in the box):

Now, on to the project. 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 2015 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

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....


In yesterday's class, we started by drawing a contrast between price and value enhancement. With value enhancement, we broke down value change into its component parts: changing cash flows from existing assets, changing growth rates by either reinvesting more or better, lengthening your growth period by creating or augmenting competitive advantages and lowering your cost of capital. We then used this framework to compute an expected value of control as a the product of the probability of changing the way a company is run and the value increase from that change (optimal - status quo value). This expected value of control allows us to explain why market prices for stocks rise when corporate governance improves, why voting shares usually trade at a premium over non-voting shares (and why they sometimes don't) and why there is a minority discount in private company transactions. I have attached the post class test and solution.

I know that you are probably busy on your final projects, but just in case you are ready to turn your attention to the final exam, the webcast review for the final exam is now accessible:
Webcast: https://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/valfinalreview.mp4
Slides: https://www.stern.nyu.edu/~adamodar/pptfiles/val3E/valfinalreview.pptx
Past finals: https://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/finals.pdf
Past final solutions: https://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/finals.xls
Hope this helps.

Attachment: Post class test and solution

5/8/15 1. Final Exam: The final exam is scheduled for Wednesday (1.30-3.30) in KMEC 2-60 and the early final is on Tuesday from 6 pm- 8 pm in KMEC 3-110. Just in case you missed it, the Google shared spreadsheet for letting me know which exam you will be taking is here:
As I mentioned in yesterday’s email, I have a review session I put together focusing primarily on real options, acquisition valuation and value enhancement which will be 60% of the final exam. You can find it by going here:
Webcast: https://www.stern.nyu.edu/~adamodar/podcasts/Webcasts/valfinalreview.mp4
Slides: https://www.stern.nyu.edu/~adamodar/pptfiles/val3E/valfinalreview.pptx
Past finals: https://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/finals.pdf
Past final solutions: https://www.stern.nyu.edu/~adamodar/pdfiles/eqexams/finals.xls
2. Project: Not much that I can add to what I have already told you about the project, but please fill out the summary sheet as soon as you have the numbers and email it to me with the subject heading of "Valuation summary”. When you do have your final project report ready to send in, please convert it to a pdf file and sent it to me with the subject heading of “The Grand Finale”. I will nag you through the weekend for the summaries.
5/9/15 I know that you still have time as an ally and I promised that I would not nag. But in the interests of keeping you informed, I will post an update of summaries received through the weekend:
Summaries received so far: 1
Summaries yet to come: 120+ (though I am sure that you are really, really close)
If you are asking “what summary?”, I am attaching the summary sheet, just in case. By the way, if you are stuck on a detail or a valuation dead end, I will be checking my email through the weekend.
5/10/15 Hi!
Summaries in: 73
Yet to come: 50+
As for tomorrow, I will pull your numbers together and try to make copies of the presentation for class. Even if you have been skipping classes for the last few weeks, please do try to make it to class tomorrow. I don't want to make promises I cannot keep, but if you do show up, I will work on making it scintillating and memorable.

Thank you for being at the closing class. I have attached both the closing presentation and the summaries of your valuation findings (for the entire class). If you are on the list of the ten most undervalued companies and are buying your recommended stock, please let me know. I may very well join in. On a different note, the exam is scheduled for Wednesday (1.30 pm - 3.30 pm) in KMEC 2-60. If you are taking the earlier exam, it is on Tuesday from 6 pm - 8 pm in KMEC 3-110.

Finally, please remember to do your CFEs. If you don't get them done, you will not be able to check your grades. I have been told that they will be accessible after midnight tonight but the window is open only for a day (tomorrow all day). So, please do it tomorrow.
Student Instructions for Completing Online CFEs

Login to https://www.stern.nyu.edu/cfe. 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.
Select the CFE that you wish to complete.

Attachments: Closing presentation, Project summaries (for entire class)

5/12/15 Thank you for getting the final projects to me on time yesterday. They have all been graded and returned. You should have received your graded version already. If not, check with your group first. The final exam is scheduled for tomorrow from 1.30-3.30 in KMEC 2-60. There is an earlier version today from 6 pm to 8 pm in KMEC 3-110. I Finally, another reminder on the CFEs. They should be accessible now and the window is open only for 36 hours. So, please do them now and get them out of the way.

There are 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.

3. How am I going to estimate N(d1) and N(d2)?
I will give you the cumulative normal distribution. You still should be able to estimate d1 and d2 on your calculator. While the distribution may not give you a precise N(d), I will accept the nearest number. Thus, if d =0.48, I will take N(.50) as your estimate.


The final exams are ready and can be picked up in the usual spot. I am attaching the solution but have added no grades to the distribution, since the final grades will be up in a few hours.

Attachments: Final exam solution.


I hope you are done and are out celebrating. However, just in case you still care about grades, yours just went online. Since many of you are graduating, this will be my last email to many of you. I want to to wish you the very best with whatever you plan to do with your lives. I hope your "job" brings you as much joy as mine has to me. If you enjoy what you are doing, you will never have to work a day in your life. I mean it when I say that you have my email address for life and you can bounce off any questions, queries or issues that you have with corporate finance, valuation or the most valuable sports franchises in the world (the answer to the last is always the "Yankees"). I probably will not be at graduation and it has been a pleasure having you in my class for the last semester or two.

And just in case, you need a valuation fix... here are some links:
Website: http://www.damodaran.com
Blog: http://aswathdamodaran.blogspot.com/
Twitter feed: @AswathDamodaran (Do your part to advance me to Lady Gaga status…)

If you have any questions about your grade, use the attached spreadsheet to see where you ended up.

Attachments: Grade checker.