# How to Perform a Reverse Stock Valuation

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Written by

Jae Jun

Valuation Matters – Reverse Stock Valuation | Flickr: 401(K)2013

Many times, astounding and insightful information comes simply from asking and listening to the people around you.

A question was posed in the value investing forum regarding reverse DCF and how it was performed. I know of a simple way of how to calculate a reverse DCF, which I will discuss in the future, but this method uses both earnings and assets.

Essentially it’s more like a reverse Earnings Power Value (EPV) but definitely worth the time to dissect and analyze for yourself.

The original discussion can be found on our value investing forum but has been edited below for easier reading. I edited my comments in square brackets [ ].

This isn’t light material so take time to go through it and digest it.

As always if you have any questions, simply ask and you will be answered.

### Reverse Earnings Power Valuation Steps

2. Calculate Excess Cash of interest bearing debt into a per share price

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 feasible the proposition is based on the information at hand

### Reverse Earnings Power Valuation Example

One example of how [a reverse stock valuation] 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 risk free return (5.9%) and the opportunity cost (7.5%) may be something you’d be comfortable with using as your multiple.

To turn it into a multiple, simply add the two percentages, divide into 1, then multiply by 100 resulting in a multiple of 7.46.

• = 1/(5.9 + 7.5) x 100 = 7.46

[Jae Jun: the reason for the inverse fraction is that a yield is represented by a %. Earnings yield = E/P which too is a %. So if you have a yield and you flip it, you are getting 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 [TTM] in earnings by our 7.46 factor. We’ll use JNJ as an example. JNJ currently has a TTM EPS of \$4.87 per share.

• Multiply it by 7.46 and we now get [a share value of]\$36.33 based on earnings, assuming our multiple is correct.

Incidentally, this multiple assumes no growth projections into the future.

### 2. Calculate Excess Cash into a Per Share Price

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 which is \$22.13 billion.

From this, deduct all interest bearing debt (not total liabilities) and we need to dig into the 10-K &/or 10-Q.

For simplicity, we’ll assume that amount is \$12.02 billion for JNJ.

• We subtract 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.

[Jae Jun: when Jim talks about “asset valuation” it doesn’t refer to the entire assets of the company. Since we are looking at excess cash, the asset portion is really the excess assets that are not required to run the business.]

• Add \$3.68 per share to our earnings valuation of \$36.33 to arrive at a total market valuation for a no growth case of \$40.01 per share. This price does not include a margin of safety.

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.

We now need to find what portion of this amount is represented in the overall valuation.

• We find this by doing (\$3.68 / \$40.01) x 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.

### Reverse Stock Valuation Method #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

• remove the \$3.68 per share asset valuation from the current market price and arrive at \$58.01 per share.

This means that the current price of \$61.69 has \$58.01 attributable to earnings.

Skipping back to the multiple we originally came up with (7.46)

• divide that multiple into \$58.01 and arrive at \$7.78 [=58.01/7.46] per share

This represents what the market currently values their EPS to be worth.

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### Reverse Stock Valuation Method #2

Assuming that the relationship between Earnings and Assets always remains at 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.

• Amount attributable to assets is \$5.68 [=9.2% x 61.69]

and

• \$56.01 [=90.8% x 61.69] is attributable to the earnings.

Using our 7.46 multiple, this information translates into expected earnings of \$7.51 per share

• \$7.51 = 56.01/7.46

In method #1, the question becomes:

is the market over inflating the earnings?

In method #2, the quesiton becomes:

is the market over inflating the earnings and the assets?

If the current EPS is \$4.87 and the market is valuing that to be \$7.78 according to method #1, we need to find a proper earnings power to project how long it would take to arrive at the latter.

### 5. Determine an Earnings Growth Rate

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 10 years \$31.8 B.

This amount represents 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 numbers we arrived at produces an Earnings Power of 8.30%

• =0.2349 x 0.3532 x 100

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.

• CAGR formula = (4.45/1.73)^(1/9) -1 = 11.07%

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.

### 6. Find How Long it would take to Grow Shares to the Value from (4)

With JNJ’s TTM EPS of \$4.87, 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 scenario, assuming our 8.30% growth factor, it would take 5.88 years for JNJ to produce those earnings.

### 7. Determine Using Logic and Rationale the Feasibility

These scenarios weigh 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 risk free rate. That, in my opinion, is what it is and shouldn’t be tinkered with.

Currently, 30 year 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 produces a multiple of 21.37 [=1/0.0468] and 16.95 [=1/0.059] 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.

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

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### 11 responses to “How to Perform a Reverse Stock Valuation”

1. C.T. Wu says:

Dear Jae,

It is not an apple-to-apple type of comparion between the corporate bond rate vs. S&P 500 earning yield derived from the PE ratio for the following reasons:

1. The bond rate will stay constant during the period of the contract.

2. Company’s instrinsic value tends to increase as its EPS grows, over the longer term a company’s stock prices track its EPS growth rates. Chuck Carnevale has excellent historical stock prices vs. EPS Growths charts published on seekingalpha.com for this.

Regards,
CT

2. valueinvestortoday says:

C.T.,

You’re exactly right and that’s why I left it up to the user to determine what the correct PE multiple would be for him. Deriving a PE was not the point of discussion. The question was, “how do you reverse engineer a valuation mechanic”. If we want to get technical, which is often foolish to do in the “art” section of value investing, Buffett has stated in his annual shareholder meetings that he doesn’t discount at 10 or 15%, but rather what the U.S. Treasury Bond rate is…and that’s it. Well, the U.S. Treasury Bond is about 1/2 of a point off from our AAA Corporate Bond rates and always has been – ever since 1919. Therefore, it’s not as far off from reality as you think. I’ve done extensive research in the, and I hate to say this word, “correlation” between AAA bonds and the S&P 500 – and the information is quite interesting…nearly identical to be honest.

3. valueinvestortoday says:

“1. The bond rate will stay constant during the period of the contract.”

I completely forgot to respond to your point #1. AAA Bond Rates, as in the sense I’m representing their use of, fluctuate on a daily basis. You certainly wouldn’t use what the AAA Bond Rate for 20 years ago was on a stock valuation for today. There’s always a Risk Premium that should be employed when coming up with your multiple. Whether you want to use AAA Bonds or U.S. Treasury Bonds is up to you but a Risk Free Rate should be used. Graham’s Formula that he made available in The Intelligent Investor used an 8.5 multiple. At that time, the AAA Corporate Bonds, which Graham exclusively used, was producing 4.4% in 1962. The market had been averaging approximately 7% at that time. I’m convinced from my research that is how Graham derived his multiple.

4. Jae Jun says:

@ Jim,
What do you think is a reasonable risk premium? I know it’s usually the difference between the stock market average performance and the risk free rate, but don’t you think that difference is too low?
Especially when it comes to small caps.

In the example of JNJ, I’m perfectly fine with the numbers you got, but what about something that is much smaller and not as stable in terms of operations?

5. valueinvestortoday says:

6. valueinvestortoday says:

Jae, what Warren says here is important I believe. “We don’t discount the future cash flows at 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.” – Warren Buffett.

Ben Graham used AAA Corporate Bond Yield.

7. valueinvestortoday says:

“In the example of JNJ, I’m perfectly fine with the numbers you got, but what about something that is much smaller and not as stable in terms of operations?”

Sorry I had to make 3 posts. For me, when dealing with small companies which is my main study, I’m more interested in the balance sheet than the future of the business. If there’s a business that has \$5 worth of tangible assets after all liabilities, and if cash flows are sufficient to operate the business, such as in the case of CNTY (one of my holdings), and that business isn’t burning through cash, then that is all the information I need in order to make an investment decision. When I purchased CNTY, I never did a DCF or an EPV of any kind. The business has to be a rather large and stable enterprise with a long history of operation and a strong moat in order for me to even think about predicting its future. If it isn’t, I’m more interested in what the balance sheet has to say.

8. valueinvestortoday says:

“Going off of recollection, in the last 10 years that average is approximately 4%”

I apologize, I meant to say the last 20 years.

9. fred oaks says:

When you refer to JNJ’s book value growing to \$50.6 billion in ten years, under caption 5, might you be thinking of net worth instead?