The Proper Discount Rate

9 04 2010

Once you understand the discounted cash flow models, valuing a business is pretty straight-forward (but not necessarily easy). The only factor that is seemingly subjective is the discount rate. When a 5% discount rate gives a value about 4 times higher than a 15% discount rate, you know that selecting the correct rate is highly important. But what is the correct rate? Let’s look at a few different perspectives on the issue.

Of course, I’ll start with good ole Mr. Buffett:

“Don’t worry about risk the way it is taught at Wharton. Risk is a go/no go signal for us—if it has risk, we just don’t go ahead. We don’t discount the future cash flows a 9% or 10%; we use the U.S. treasury rate. We try to deal with things about which we are quite certain. You can’t compensate for risk by using a high discount rate.”

Basically, Buffett uses the risk free rate to see what the company would be worth if the investment carried no possibility of loss. To compensate for the risk, he uses a margin of safety between his valuation and the current market price. When Buffett says that “you can’t compensate for risk by using a high discount rate,” he doesn’t mean it’s physically impossible to do. Rather, he means that it’s much easier to see and understand the difference between the intrinsic value and market price by looking at the margin of safety instead of the difference in discount rates. However, If Buffett was merely using the margin of safety to compensate for risk, he would not produce a return above the risk free rate. Buffett must also be using the margin of safety to create a higher than risk free rate of return (and a higher than market rate of return too!).

There are also other issues that I have with using the risk free rate. What happens when the treasury rate becomes ridiculously low? The 30 year treasury rate reached 4% again recently. Using that as a discount rate, one would see Johnson and Johnson to be at a 73% discount from its intrinsic value. Obviously that’s ridiculous. Now, you’re stuck guessing what margin of safety would actually supply you with a decent return. Turns out, Buffett has addressed this concern:

“For our discount rate, we basically think in terms of the long-term government rate. We don’t think we’re any good at predicting interest rates. But in times of what seem like very low rates, we might use a little higher rate.”

This seems like the most logical position to take on the issue. Take note that when the risk free interest rate rises above you’re discount rate, your intrinsic value becomes less.

How about Joe Ponzio of

“Personally, I use 15% [discount rate] and require a 25% margin of safety on large, stable companies and a 50% margin of safety on less-than-sure companies.”

“Why did I use 15%? That is the minimum return I expect when I buy a stock.”

This is another logical position to take. The main difference between this strategy and Buffett’s strategy is that Joe has essentially placed his desired return into the discount rate instead of the margin of safety. Joe is using the margin of safety mostly for risk, not return whereas Buffett is using it for both risk and return.

Which method is the correct one? I don’t think there is necessarily a correct method. It’s a matter of preference. I doubt either Buffett or Joe would miss an opportunity because of their rates. Buffett uses a lower rate and a higher margin of safety. Joe uses a higher rate and a lower margin of safety. The real message to take away from this post is to NOT use the long-term treasury rate no matter what it is. People have interpreted Buffett’s first quote as a ticket to use the long-term treasury rate when it is very low. That is a recipe for disaster.

For our discount rate, we basically think in terms of the long-term government rate. We don’t think we’re any good at predicting interest rates. But in times of what seem like very low rates, we might use a little higher rate.


It May Not be Too Late for JNJ.

6 04 2010

Up 35% from its lows a little over a year ago, JNJ has already had quite a run. Yet, there may still be some value in this stock.

As Warren Buffett has explained before, the proper way to arrive at a company’s intrinsic value is by discounting its future cash flows back to the present. In the 1986 Berkshire letter to shareholders, Buffett defined his cash flows (or “owner earnings”) as “(a) reported earnings plus (b) depreciation, depletion, amortization, and certain other non-cash charges…less ( c) the average annual amount of capitalized expenditures for plant and equipment, etc. that the business requires to fully maintain its long-term competitive position and its unit volume.” Thus, owner earnings are nearly the same as free cash flows; the only difference is that owner earnings subtract an average maintenance capital expenditure rather than the capital expenditure of each specific year.

So what is JNJ’s maintenance capital expenditure? Over the last ten years, the capital expenditures have fluctuated from $1,646 million in 2000 to $3,310 million in 2007. I believe that maintenance cap ex is about $3,000. This may be a little high, but it’s better to be safe than sorry (especially when investing). Using this capital expenditures estimate, owner earnings were $11,510 million in 2006, $11,939 million in 2007, $11,907 million in 2008, and $14,206 million in 2009. For the base cash flow of our estimated intrinsic value, let’s use $12,000 million rather than $14,000 million just to be conservative. During the previous ten years, JNJ has averaged a 28-29% cash return on equity: one sign of a wonderful company. JNJ has also grown owner earnings at a rate of 14.8% of the last ten years. If we use a 9% discount rate and assume a growth rate of 8% for the next ten years, a growth rate of 3% for the next ten, and then a 0% growth rate for the company’s remaining life, we arrive at an intrinsic value of $250.6 billion dollars, or $91.00 per share. Is it possible that this intrinsic value is mistaken? Of course! Perhaps our growth rate is wrong. Perhaps disaster will strike the company. Perhaps the United States will sink into the ocean. But that’s exactly why value investors rely on a margin of safety! Selling at $65.50 today, JNJ is selling at a 28% discount from our estimated value. Since the valuation used conservative estimates too, 28% is a large enough discount for my tastes. $65.00 is also about the price that Buffett paid when he started acquiring JNJ back in 2007.

As a side note, I think it’s interesting to look at the chart of JNJ.

When the market price of a security remains flat for several years, there are three possible scenarios taking place:

1.) The company’s intrinsic value hasn’t changed in several years and isn’t expected to change.

2.) The company’s intrinsic value is catching up to an over inflated stock price.

3.) The company’s intrinsic value is rising and the price is not following.

JNJ first reached the $60 dollar range in early 2002, about 8 years ago. I believe JNJ was overvalued then, but the price hasn’t risen along with the underlying value of the company–possibly giving investors a great opportunity!

Disclaimer: This article should not be construed as investment advice. Investment decisions should be made according to an investor’s own evaluation and personal circumstances.

Disclosure: Author hasn’t purchased JNJ-but may soon!

Buffett and Coca-Cola, 1988.

5 04 2010

In his post here, Joe Ponzio trys to understand Buffett+Coke in terms of the F Wall Street model. He attaches the PDF of his analysis, showing that if Buffett had assumed a 21.8% growth rate for the first 10 years, the F Wall Street model shows a value of $22.3 billion. However, when I do the same analysis, I get a value of $18.7 billion. I can’t see his spreadsheet, so I really don’t know why there is a difference between our numbers. When I do the same analysis using my own model, I get a final value of $17.4 billion. Not a big difference, however, let’s look at what happens when we use a different discount rate- say 9%.

Because the final stage of my model is based on cash flows rather than equity, my model accurately reflects a change in the discount rate across all three stages. Joe’s, however, is only affected in the first two stages. Using the same growth rates and a 9% discount rate, my model shows a value of $44 billion (2.5X more than the 15% discount rate!). With the 9% discount rate, Joe’s model shows only $34 billion, or 22% less than mine.

So which version did Buffett see when he looked at Coke in 1988? We know that Buffett uses the long-term treasury yield for his discount rate because it’s risk free (he compensates for risk by using a margin of safety). The average treasury yield for 1988 was 8.6% so we’ll use that. In my opinion, Joe’s 21.8% growth rate is pretty ridiculous. The nature of his model, along with his high discount rate, require that you assume an absurd growth rate to make the KO investment seem sensible. I think that Buffett probably used a more conservative 12%ish growth rate for the first ten years. Using these parameters, Joe’s model says KO is worth $19.7 billion–only a 23% discount from the average 1988 market price for KO. My model shows KO to be worth $23.3 billion–a 35% discount from the average market price of 1988 and well above the “25% margin of safety rule” for big companies.

Note that if Coca-Cola had less economic goodwill (ie. required more equity to produce the same cash flows), Joe’s model would actually add to the valuation. That is, a crappy company would have a higher valuation than a great company. My model, on the other hand, isn’t affected by the company’s return on equity.

To make a short story shorter, Joe’s model overvalues companies with low returns on equity and undervalues companies with high returns on equity. Since Joe is a great thinker and analyst, I’m sure that he can see through the relatively minor difference between his model and the real value of the company. However, why use a model that obfuscates the evaluation?

Why the F Wall Street Model is Wrong (but Nearly Right).

4 04 2010

First of all, I criticize the F Wall Street model not because it’s terrible, but because it’s so close to being correct. F Wall Street is by far the best resource for the intelligent investor. The book is not perfect either, but I think it’s the greatest investment book I’ve ever read (the arbitrage/workouts section is priceless).

The F Wall Street model:

The model is a traditional two stage discounted cash flow model. The first stage is ten years long, and the growth rate is decided according to an analysis of the company. The second stage is another ten years at a five percent growth rate. Now, the point where this model diverges from my own is at the following instance: After discounting twenty years of cash flows, Joe adds the equity of the company to the final calculated value. In my model, instead of shareholder’s equity, I add the discounted value of the 20th year cash flow projected out to infinity at a zero percent growth rate.

Why Joe’s Model is a Little Screwy:

In a comment on his blog, I explained to Joe the following:

“Your valuation method produces strange results. For instance, a business with $1 million dollars in equity, earning a 1% rate of return is worth more than $1 million dollars [according to the F Wall Street model]. In reality, $1 million dollars worth of equity earning a below market rate of return is worth less than $1 million dollars. Similarly, a bond earning 1% on principle is going to decrease in value when interest rates rise to 5%.”

Joe responded with the following:

“The valuation method assumes that you are buying a good business and that you would skip the above business altogether. The equity is added as a “terminal value” instead of projecting cash flows out to infinity, and assumes that the equity would grow at a satisfactory rate over time. If the business has bad economics, the F Wall Street method of buying good businesses at cheap prices won’t work.”

While I see his point, why bother with a method that’s not consistent with the theory behind value investing? It’s merely a coincidence that the equity value is usually about equal to the discounted value of infinitely projected cash flows. Since Joe’s method diverges from theory, it necessarily has problems in practice. It over values companies earning a poor return on equity and undervalues companies earning a great return on equity. I’ve explained an instance of the former and I will explain an instance of the latter in the next post.

Consistent Cash Flow Earners

3 04 2010

Valuing a company that doesn’t create consistent cash flows is either difficult or impossible. So why isn’t there a screener that can search for companies with consistent cash flows? While I was looking around for one, I came across a guy who has already compiled such a list.

The list is kind of old, so I updated it and added P/FCF too. P/FCF is a good starting point, but it’s pretty much useless for a lot of these companies because most have high growth prospects.

Company:                                Ticker:         P/FCF:

j2 Global Communications, Inc.

Alcon, Inc.

Quest Diagnostics Incorporated

Danaher Corporation

USANA Health Sciences, Inc.

L-3 Communications Holdings, I International, Ltd.

VCA Antech, Inc.


Somanetics Corporation

Energen Corporation

Mettler-Toledo International

Coach, Inc.

Yum! Brands, Inc.

Digital River, Inc.

Portfolio Recovery Associates,

Boeing Company, The

Core Laboratories N.V.

Nordstrom, Inc.

MICROS Systems, Inc.

Amphenol Corporation

Paychex, Inc.

United Technologies Corporatio

Shuffle Master, Inc.

Meridian Bioscience, Inc.

Cisco Systems, Inc.

Euronet Worldwide, Inc.

Blackbaud, Inc.

Akamai Technologies, Inc.

Pfizer Inc.

Immucor, Inc.

Graco Inc.

Quality Systems, Inc.

General Dynamics Corporation

Healthways, Inc.

Meredith Corporation

Amerigon Incorporated

Zimmer Holdings, Inc.

Citrix Systems, Inc.

Continucare Corporation

Abbott Laboratories


Teva Pharmaceutical Industries

Oracle Corporation

Parker-Hannifin Corporation



























































































Trading Sucks

1 04 2010

Did you need more evidence that trading is not a profitable way to invest? No. But here it is anyways:

And that’s what they’re teaching at universities…

The Problem With Stock Screeners

28 03 2010

The greatest question of value investing: How do you find an undervalued stock?

I screen for companies with a low price/free cash flow and hope to find a hidden gem. Most of the companies returned by the screen have very negative future outlooks. Still, there are ones that are worthy of real attention. Also, these screens won’t include companies trading at mediocre multiples with high growth expectations (take Buffett’s famous investment in Coke).

So, how does Warren Buffett recommend that we look for stocks (more importantly, why does he recommend this)?

Here is a great blog post on the subject:

Basically, looking through every publicly traded company gives you a great bank of knowledge to increase your circle of competence, and consequently, your rate of return. That’s why I’m “starting with the A’s.”