The secret to successful investing is to figure out the value of something and then pay a lot less!

Valuing a company you are investing into.

For simplicity, we will assume that the business in question will earn $10,000 each year for the next thirty-plus years.

Intuitively, we know that collecting $10,000 each year for the next thirty years is not the same as receiving all $300,000 today.  

Let us analyse and see what thirty-plus years of earning $10,000 per year are really worth to us today, using a discount rate of 6%.

Present value 

=  Annual Cash Flow / Discount rate

= $10,000 / 0.06 

= $166,667

(In reality, we should look for how much cash we receive from the business over its lifetime.  For the purposes in this post, we will assume that earnings are a good approximation for cash received.)

So, earning $10,000 a year for the next thirty-plus years turns out to be worth about $166,667 today.   

We have just figured out something incredibly important.  

A business guaranteed to earn us $10,000 each year for the next thirty-plus years or so, is worth the same as having $166,667 cash in our pocket today!

If we could be guaranteed that all of our assumptions were correct and someone offered to sell us the company for $80,000, should we do it?  If someone offered to give us $166,667 right now in exchange for $80,000, should we do it?  

Given all of our assumptions, the answer is easy:  of course we should do it!  

This is an incredibly important concept.  

If we can really figure out the value of a business, investing becomes very simple!  

The secret to successful investing is to figure out the value of something and then - pay a lot less!  

In fact, it couldn't be simpler:  $166,667 is a lot more than $80,000.

In practice, predicting so far into the future is pretty hard to do.

Are you really going to trust my predictions about what earnings will be over the next thirty years?

But will earnings actually shrink over those years?

Will they grow?

Will the company even be around in another thirty years?

In practice, predicting so far into the future is pretty hard to do.  In addition, many businesses are actually more complicated.

In fact, forget thirty years - it turns out that Wall Street analysts are actually pretty bad at predicting earnings for even the next quarter or the next year.  

You will probably pay less for those estimated earnings than if they were guaranteed.

Since no one rally knows for sure what earnings will be over the next thirty-plus years, whatever we use for estimated earnings during that time is just going to be a guess.   Even if this guess is made by a very smart, informed "expert", it will still be a guess.  

In practice, investors discount the price they will pay for future earnings that are based only on estimates.  

If there is no guarantee that you will actually collect that $10,000 after the first year of owning the business, you will probably pay less for those earnings than if they were guaranteed.  

In the above example, where next year's earnings of $10,000 were guaranteed, we discounted that payment by 6%, reflecting the fact that we had to wait a year to collect our $10,000.  Now, with only an estimated $10,000 coming in at the end of the first year, we will pay less.

How much less?  

That's not exactly clear, but we would certainly discount that hoped-for $10,000 by more than the 6% we used when the $10,000 was guaranteed - maybe we'd use a discount of 8% or 10% or 12%, or even more. (the amount of our discount would reflect in part how confident we were in our earnings estimate).  

But when we apply that higher discount to the next thirty-plus years of earnings estimates, that's when things really start to get silly (yes, it's true, math can be hilarious).

Value of the Company

At 6% discount rate

$10,000 /0.06 = $166,667

At 8% discount rate

$10,000 / 0.08 = $125,000

At 12% discount rate

$10,000 / 0.12 = $ 83,333

As it turns out, using a 12% discount rate, the value of the company is only $83,000.  We are starting to get in trouble!  It is no longer so obvious that a purchase price of $80,000 is such a bargain!

Figuring out the right discount rate isn't our only problem, we also have to estimate earnings. 

What is crystal clear, however, is that using different discount rates for our estimated earnings can lead to wildly different results when we try to value a business.   But figuring out the right discount rate isn't our only problem.  For simplicity, we have made some other assumptions that don't really hold up in the real world.  

For instance, as you might intuitively guess, most companies don't earn the same amount each year for thirty straight years.  Also, many businesses grow their earnings over time, while others due to competition, a bad product, or a poor business plan, see their earnings shrink or even disappear over the years.  

Let us see how funny the math gets when we try to value a business using not only different estimates for discount rates but we throw on top of that some different guesses for future earnings growth rates!

Value of the Business

At 4% growth rate, 8% discount rate

$10,000 / (0.08 - 0.04) = $250,000

At 4% growth rate, 12% discount rate

$10,000 / (0.12 - 0.04) = $125,000

At 6% growth rate, 8% discount rate

$10,000 / (0.08 - 0.06) = $500,000.

Annual Cash Flow / (Discount Rate - Growth Rate) = Present Value

According to finance theory and logic, the value of a business should equal the sum of all of the earnings that we expect to collect from that business over its lifetime (discounted back to a value in today's dollars based upon how long it will take us to collect those earnings and how risky we believe our estimates of future earnings to be).  

Will earnings grow at 2%, 4%, 6% or not at all?  Is the right discount rate 8%, 105, 12%, or some other number?   

The math says that small changes in estimated growth rates or discount rates or both can end up making huge differences in what value we come up with!

At 2% growth rate, 12% discount rate

$10,000 / (0.12 - 0.02) = $100,000

At 5% growth rate, 8% discount rate

$10,000 / (0.08 - 0.05) = $333,333

Annual Cash Flow / (Discount Rate - Growth Rate) = Present Value

Which numbers are right?

It is incredibly hard to know.  Whose estimates of earnings over the next thirty-plus years should we trust?  What discount rate is the right one to use?

The secret to successful investing is to figure out the value of something and then - pay a lot less.  

How are we going to figure out value?  How can anyone?  Do we have the answer yet?  Hopefully, we have learned some very valuable lessons even if we cannot answer them yet.

Summary:

1.  The secret to successful investing is to figure out the value of something and then pay a lot less!

2.  The value of a business is equal to the sum of all of the earnings we expect to collect from that business over its lifetime (discounted back to a value in today's dollars).  Earnings over the next twenty or thirty years are where most of this value comes from.  Earnings from next quarter or next year represent only a tiny portion of this value.

3.  The calculation of value in #2 above is based on guesses.  Small changes in our guesses about future earnings over the next thirty-plus years will result in wildly different estimates of value for our business.  Small changes in our guesses about the proper rate to discount those earnings back into today's dollars will also result in wildly different estimates of value for our business.  Small changes in both will drive us crazy.

4.  If our estimate of value can change dramatically with even small changes in our guesses about the proper earnings growth rate to use or the proper discount rate, how meaningful can the estimates of value made by "experts" really be?

5.  The answer to #4 above is - "not very."

Additional notes:

These concepts involve a discussion of the time value of money and discounted cash flow.  

In reality, we should look for how much cash we receive from the business over its lifetime.  For the above purposes, we will assume that earnings are a good approximation for cash received.

Be sceptical about expert advice

Experts will probably give you good advice, but do not overlook the possibility that they may be mistaken.

• For centuries, experts said that the world was flat, but Christopher Columbus proved them wrong.
• Experts (who were paid a lot of money) or some of them at least, failed to foresee and plan for the economic mess that has plaqued much of the world in 2008/2009.

You may not be a financial expert but you are probably an expert at your particular job.  If the advice feels wrong, perhaps it is wrong.

Some Valuation Models are conservative, some are aggressive.

Friday, March 12, 2010

Valuation Models

A private equity player of my acquaintance once confessed that he had a basic rule of thumb about investments: double estimated expenses and halve projected future profits!


There are more systematic methods of valuation. Some valuation methods are themselves optimistic, others conservative. The multiples assigned to the valuation may also be conservative or optimistic. For example, the price to book value (PBV) ratio is a conservative valuation method. The underlying assumption: in bankruptcy, the investor will receive some portion of the original investment back. A cut-off PBV of 1 or less would be a conservative multiple.


But in an emerging market such as India with its high growth rates, a more optimistic PBV multiple can be assigned. In fact, if one examines average index PBV since 1991, the PBV has never dropped below 1.5.

A dividend yield-based valuation method is also conservative. It assumes no capital appreciation and treats the original investment like debt. Again, a high or low cut-off yield could be set depending on the risk-appetite.

Earnings growth-based valuations such as the PEG (Price-earnings to projected Earnings Growth) ratio are optimistic. A PEG valuation implies that a reliable projection of forward earnings and forward earnings growth is possible. A PEG multiple of less than 1 is conservative but the valuation method itself is optimistic.

Another, more conservative valuation method using earnings, is comparing earnings yield with the yield from a risk-free instrument. If the earnings yield is higher than the risk-free yield, the stock is worth investment. Again, conservative investors will keep greater margins of safety.

In a bull market, people give maximum weight to PEG ratios. In bear markets, more conservative methods come to the fore. At the peak of a business cycle, businesses will tend to be optimistically valued at high multiples. At the bottom, the same businesses will be available at low multiples.

In fact, historically, peaks and troughs in the same economy tend to be associated with similar levels of valuation. In India, bear market bottoms tend to be associated with conservative average multiples.  

• Usually the Nifty will be available at an earnings yield that is higher than the 364-day T-Bill yield. 
• The PEG will be well below 1. 
• The Price-book-value ratio will be down to less than 2.5 and 
• the Nifty's dividend yield will be over 2 per cent.

At the top of a bull market on the other hand, these multiples are all optimistic. 

• The PEG will be 1 or higher. 
• The earnings yield will be below the T-Bill yield. 
• The PBV will be higher than 4 and 
• the dividend yield will be below 1 per cent. 

Usually the PEG ratio is the last to go into the red zone by rising above 1. This is because the PEG is subjective and growth estimates tend to be optimistic during bull markets. There are minor variations but these average multiples have held good through the cycles of the last 15 years. This means that a conservative value-investor can buy when the multiples are in the bear-market range. And, it is time to sell when the multiples are in the range of a bull-market top.


Since January 2006, most of the valuation multiples have been high. However until late 2007, the PEG was below 1. It was only in early 2008 that the PEG rose beyond 1 and gave the final sell signal. By then, the market had already peaked.


The crash in October has pulled all the valuation multiples back close to the levels that would be expected at a bear market bottom. Right now, at a Nifty level of 2900, the PBV is at 2.42, while the dividend yield is 1.96 per cent and the PE ratio is 12.57, with an earnings yield of 7.9 per cent in comparison to the T-Bill yield of 7.4 per cent.


At the 2550 levels that prevailed for a while in late October, these multiples were even more attractive. The PEG ratio incidentally is close to 1. While the current PE ratios have dropped, so have the forward earnings growth estimates for 2008-09. But given the turmoil, there could be further EPS downgrades.


Is it worth buying into this market? Yes, it looks that way. Certainly systematic accumulation at these prices should work over the long-term.


This column appeared in the November 2008 Issue of Wealth Insight.

http://stockmakers.blogspot.com/2010/03/valuation-models.html

Difference in Expert Opinion on Valuation of a closely held firm

Valuation of Closely Held Firm:  Difference in Expert Opinion


http://www.nafe.net/JFE/j02_1_03.pdf

The paper reviews four basic approaches to the valuation of the equity of a closely-helf firm:  net asset value, discounted cash flow, earnings multiples, and captialized earnings.  Financial and narrative information on an anonymous closely-held firm were evaluated by 18 valutaion experts.

Findings:

1.  All respondents reported valuation methods; 15 recommended values ranging from $6.0 million to $17.5 million. 

2.  The dispersion of values was not consistent with our expectation of convergence of value estimates.

3.  The professional training and background of the experts proved significant in the valuation methodology and estimate.  The 8 experts who are investors fvoured, by 7 to 1, a non-DCF approach, such as an earnings multiple or capitalized earnings.  The 10 consultants/appraisers expressed a slight preference, 6 to 4, for the DCF approach.

4.  The greatest disparity between investor experts and consultants was in the recommended value of the firm.  The average value recommende by the consultants was $14.7 million, almost 50 percent higher than the investors' average estimate of $9.87 million.


Conclusions:

Three implications of the study.

1.  The substantial variation in valuation opinions suggests that courts cannot expect convergence of expert valuation of a firm even from a large number of experts.

2.  The variation in opinion may be related to the professional training and background of the experts.  Consultants, those who are not investors or risk bearers, offered significantly higher valutaion opinions than investor experts. 

3.  The valuation expert who are interested in economically sound valuation opinons would be well-advised to use more than one valuation approach, if circumstances permit, cross verify valuation estimates.  The dispersion of values provided by the sample of experts suggests that the expert who can demonstrate the soundness of an opinion by the independent application of two or more methods is likely to have more credibility.