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best way to reverse engineer DCFs

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7:18 pm
December 1, 2010


john_allen

Member

posts 46

10

Wow. I was travelling on business the last couple of days so  I just checked back in. Thank you so much for the informative post – it's incredible!

 

Thank you again!

 

-John

12:08 pm
December 1, 2010


valueinvestortoday

Member

posts 80

9

Sounds good Jae.

11:53 am
December 1, 2010


Jae Jun

Admin

posts 1463

8

ok thanks for clarifying.

I'll send you a copy of the edited article for you to review before I publish it.

That way we can iron it out so that anyone can get it.

11:39 am
December 1, 2010


valueinvestortoday

Member

posts 80

7

"Isn't the risk premium 7.5 – 5.9= 1.6%?"

 

Yes, I did the article so quickly that I didn't use proper terminology although the concept itself is sound. The 5.9% AAA Corporate Bond Yield represents the "Risk Free Return". The 7.5% Yield represents the "Opportunity Cost" of what I'm giviing up by chosing an alternative investment as opposed to the one that has historically provided a 7.5% yield. Therefore, the risk premium is the difference between the two.

11:19 am
December 1, 2010


Jae Jun

Admin

posts 1463

6

Post edited 10:52 am – December 1, 2010 by Jae Jun


Question.

Isn't the risk premium 7.5 – 5.9= 1.6%?

So instead of doing 1/(7.5+5.9) you would really just do (1/7.5)*100=13.3

1:53 pm
November 30, 2010


valueinvestortoday

Member

posts 80

5

Jae, I'd be honored.

1:39 pm
November 30, 2010


Jae Jun

Admin

posts 1463

4

Post edited 1:16 pm – November 30, 2010 by Jae Jun


FANTASTIC

Do you mind if I edit it and post it as a guest post?

I certainly learnt someting from this and believe it will be a classic investment learning article.

1:05 pm
November 30, 2010


valueinvestortoday

Member

posts 80

3

Post edited 8:48 pm – November 30, 2010 by valueinvestortoday


One example of how it could be done is to start by assigning a proper multiple factor to the earnings. If you find, for example, that the average yield on Long Term AAA Corporate Bonds (30 years) has produced 5.9% on average over whatever time period you're using and you also find that the market has produced an average annual return of 7.5% over that same period, then the combination of the opportunity cost (5.9%) and the risk premium (7.5%) may be something you'd be comfortable with using as your factor. To turn it into a factor simply add the two percentiles, divide into 1, then multiply by 100; resulting in a multiple of 7.46 for this example. This is just one way to come to a multiple. There are other ways that may make more or less sense. I use an alternative method which uses a combination of the opportunity cost, described above, a risk premium such as the one above, and the actual interest the company is charged on their debt. In any event, this example will serve its purpose here.

Multiply the Trailing Twelve Months in earnings by our 7.46 factor. We'll use JNJ as an example. They currently have a TTM EPS of $4.87 per share, according to Google Finance (don't count on it :)). We now arrive at $36.33 per share based on earnings, assuming our multiple is correct. Incidentally, this multiple assumes no growth projections into the future. Now find the excess cash of the business. Excess Cash = Total Cash & Equivalents – MAX(0, Current Liabilities – Current Assets excluding Cash & Equivalents). In the case of JNJ, their current assets cover their current liabilities so Excess Cash is equal to the actual cash on hand; $22.13 B. From this, deduct all interest bearing debt (not total liabilities). For this, we need to dig into the 10-K &/or 10-Q. For simplicity sake, we'll assume that amount is $12.02 B for JNJ. We deduct the $12.02 B from the excess cash and arrive at an asset valuation of $10.11 B which results in $3.68 per share.

We add that $3.68 per share into our earnings valuation of $36.33 and arrive at a total market valuation, pre-margin of safety as well as no growth, of $40.01 per share for JNJ. The one portion of our valuation that remains constant is the asset portion ($3.68). This number is what it is and doesn't change. Therefore, we need to find what portion of this amount is represented in the overal valuation. Simple, ($3.68 / $40.01) * 100 = 9.20%. Therefore, 9.20% of our valuation must consist of our asset valuation that doesn't change and 90.80% of our valuation must come from earnings that do change.

Two different approaches can be used now that produce two opposing views but utilizes the same share price. Both have their flaws yet give interesting information to think about; which is the ultimate goal of the project.

Example #1: Currently, JNJ is trading for $61.69 per share, a premium to our valuation. In order to find what the market is valuing the earnings to be currently, because our original estimate was based on a no-growth formula, we simply remove the $3.68 per share asset valuation from the current market price and arrive at $58.01 per share attributable to earnings. Skipping back to the factor we originally came up with of 7.46, we divide that multiple into $58.01 and arrive at $7.78 per share which represents what the market currently values their earnings to be worth.

Example #2: Assuming that the relationship between Earnings and Assets always remains 9.20% / 90.80%, and that relationship could easily be improved on by calculating the various growth of assets and earnings, we can seperate the current $61.69 share price by the two factors resulting in $5.68 attributable to the assets and $56.01 attributable to the earnings. Using our 7.46 factor, this information translates into expected earnings of $7.51 per share.

In example #1, the question becomes: is the market over inflating the earnings?

In example #2, the quesiton becomes: is the market over inflating the earnigns and the assets?

If the current EPS is $4.87 and the market is valuing that to be, using example #1, $7.78 – we need to find a proper earnings power to project how long it would take to arrive at the latter. I'll present a calculation, disregarding detail for presentation purposes, that will help determine a proper earnings growth rate (earnings power). We'll use the last 10 years of data for JNJ.

in 2000, JNJ had a book value of $18.8 Billion. In 2009, their book value grew to $50.6 Bilion. Therefore, they increased their book value in the last 9 years $31.8 B. This amount represents the how much money the company has allocated back into the business (assets above obligations). There are many variables to consider in deciding this amount – far too detailed for this example. During the same period, JNJ grew its net income $7.47 B. The return on investment therefore is ($7.47 B / $31.8 B) * 100 = 23.49%. During this period, 2000-2009, JNJ produced aggregate earnings of $90.03 B. Therefore, the rate of reinvestment they produced is the amount of invested capital divided by the aggregate profits they produced: ($31.8 B / $90.03 B) * 100 = 35.32%. Multiplying the two percentiles we arived at, 23.49% & 35.32%, produces an Earnings Power of 8.30%.

To backtest the accuracy, JNJ produced $1.73 per share in earnings for 2000 and $4.45 per share in 2009. That equals an 11.07% averaged annual growth rate. Of course for accuracy, its best to go through the earnings to account for non-cash and one time events on the income statement and do accordingly in respect to intangibles and "other items" on the balance statement. Nonetheless, our 8.30% Earnings Power when compared to the past produces a very reliable assumption for JNJ.

Currently, JNJ's TTM EPS is $4.87. According to our previous assumptions in regards to value, we've found that the market (example #1) has valued JNJ's earnings at $7.78 per share. In this scenerio, assuming our 8.30% growth factor, it would take 5.88 years for JNJ to produce those earnings. These scenerios way heavily on how one arrives at his growth factor. Each individual has his own way of doing that and when in doubt, it's best to be conservative. I've found that a good rule of thumb is to start with the obvious opportunity cost. That, in my opinion, is what it is and shouldn't be tinkered with. Currently, 30-Y AAA Bonds yield 4.68%. Historically, they've produced 5.9%. Therefore, the beginning structure to your multiple will always start off with either the current rate of 4.68% or the average of 5.9% which produce a multiple of 21.37 and 16.95 respectively. Then, it would be wise to judge this multiple against the current PE of the market, say the S&P 500, as well as the historical average of the market. Currently it's around 21.5 and historically it's been 16.6. If your starting multiple, thus far, is greater or equal to the current PE of the market – I would advise caution that your multiple is too high. Also, if it is significantly higher than the historical average, I would caution that it "could be" too high as well.

That was the long answer, here's the short answer:

1. Create your multiple – as explained above.

2. Calculate Excess Cash of interest bearing debt into a per share price – as explained above.

3. Deduct Excess Cash per share price from the current market price of the stock.

4. Divide remaining amount by the multiple in step 1.

5. Determine a proper earnings growth rate or use an analysts assumption to draw ideas on (don't rely on the analysts information – just use it to see what information you can derive from it).

6. Find how long it would take to grow shares from what they are currently to what Step 4 produced using the assumed growth rate.

7. Determine in your own mind using logic and rationality how feasable the proposition is based on the information at hand.

In closing, the S&P 500 currently has a multiple of approximately 21.5. 1/21.5 = 4.65%. Essentially, the market is saying it expects to produce a 4.65% annual return. 30 Year AAA Corporate Bonds are 4.68% (last I checked). There's some information to contemplate in that.

 

All the best,

Jim

11:54 pm
November 29, 2010


Jae Jun

Admin

posts 1463

2

Yes you can use the spreadsheet.

A crude method I use is to simply keep the discount rate and FCF the same but play around with the growth rate until you get the intrinsic value equal to the share price. Then you know what the growth rate for the past 5 or 10 years has been.

The chart will help with visualizing it as well. Match the chart to the historical stock price and you'll get the reverse DCF growth.

7:25 pm
November 29, 2010


john_allen

Member

posts 46

1

Hi jae-

 

I was wondering what you think the best way to reverse engineer DCF valuations is, so that we  can see what is currently embedded in a stock's price. would you use the spreadsheet for this?

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