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Gillian Tett, a Financial Times reporter, has written the best-selling “Fools’ Gold”, an account of the financial history of the last decade. I just finished it and found it highly informative, easy to understand, and quite gripping.

One of the biggest lessons of the book is that we cannot blindly and exclusively rely on financial models because their assumptions are not always sound and because they do not necessarily capture all of the drivers of risk and return. Tett makes this point clearly in her narrative, without getting into the mathematical complexities, particularly in her description of the mortgage-backed securities meltdown.

The upshot is that valuation is always going to require appraiser judgment, even if it is subjective, because models alone cannot accurately describe reality. Simply put, there is no such thing as a (reliable) “valuation formula” because the future will not necessarily resemble the past, past data may be limited, and / or formulas cannot always capture all of the relevant factors.

Here’s an example. If you use the build-up method to estimate the cost of equity capital, the 2008 Ibbotson data (relative to 2007) have as components a lower risk-free rate and a lower equity risk premium for sure, and maybe even a lower industry risk premium. Those suggest LOWER costs of equity capital and HIGHER multiples, which makes no sense today! The build-up model is not capturing the increased risk in the marketplace. So our judgment has to come into play to override the model’s shortcomings.

I guess this means our jobs are secure for awhile!

I often reread Revenue Ruling 59-60 just to see if I can gain any new insights. In my latest reading, I was struck by its emphasis on valuing individual estate or gift assets and the fact that it says nothing about valuing a the assets as a collection or portfolio. This is because the valuation is at a point in time (date of death or gift) and at any point in time values are fixed, and their movements over time (correlation or covariance) are irrelevant. Even though a diversified portfolio might be less risky than a single-asset portfolio, this is not considered in fair market value.

Let’s start with a pair of conflicting realities:

1. Value is a range.

Maybe it is a probability distribution (a range in which each value has a certain probability). Every so often it is a single number (usually when it is zero). Sophisticated techniques like scenario analysis, Monte Carlo simulation, option models, and statistical regression provide logically sound ways to incorporate probabilities and are heavily used in academic research. The problem with these methods is that the probabilities are unknown, requiring subjective inputs or proxies. Moreover, there is usually no way to condense the range or probability distribution to a single number. A mean, median, or mode (the most probable value) by itself says nothing about the uncertainty of the range.

2. Most appraisal assignments require that value be expressed as a single number.

This is obvious in tax, ESOP, and financial reporting assignments in which value has to be reported on a form as one number. In transactional and litigation assignments, ranges are permitted. In transactions, the parties use the range to negotiate a deal. In litigation, judges and juries have the job of concluding a single value number.

I don’t have any great insight to share with you as to resolving this conflict, except to say that we should be intellectually honest in recognizing that probability-based methods, although logically sound, are subject to challenge as to the probability assumptions. And we should be equally honest, and humble, about the fact that point estimates of value do not reflect their associated uncertainties.

At last week’s IBA-NACVA Superconference, I attended noteworthy presentations on sophisticated and complex valuation models, including Butler-Pinkerton (for the company-specific equity risk premium), Finison-Dailey (same) and an overview of lack of marketability discount methodologies. [These presentations and more are available elsewhere on this website.]

After these presentations, several people asked me whether I use these models. I do!

I use every model that I can to check and double-check my conclusions about these two items, which are often the toughest parts of valuation analysis and reporting.

Upon reflection, I wish I had thought to say more (which is what follows).

I do very little litigation work. I am deposed perhaps once a year and testify maybe once every other year. My practice is heavy on tax work, with a good deal of ESOP, financial reporting, and transactional engagements. As such, my reports are audited or reviewed by the IRS, the Department of Labor, CPA auditors, and other valuation professionals. These folks are almost always more knowledgeable about valuation than judges and juries. In my experience (which may not be typical), they understand that value is a reasonable range and that valuations are accordingly uncertain. They appreciate my application of multiple methods to narrow the reasonable range and buttress my conclusions. If they do not understand a method, I am happy to explain it to them. (This has nothing whatsoever to do with the fact that I am paid by the hour during audits…) What they usually question are my assumptions: reasonable, competent, honest men and women should always do this. I have no problem with that. In fact, if someone disagrees with my value conclusion, I urge them to show me where their assumptions are different from mine, and why! I try as hard as I can to explicitly state and justify every assumption with facts. When I must be subjective, I try to be objective (seeking the middle ground). If there are weak or arguable assumptions, I so state in my reports (and provide sensitivity analyses showing the impact of alternate reasonable suppositions). I am an imperfect human being: when I goof or can be persuaded that an assumption of mine is unreasonable, I correct and / or revise my opinion. Although this is embarrassing, I have found that accepting responsibility defuses tension and leads to agreement without the threat of sanctions on me.

If I did more litigation work, I probably would NOT use all of these models because they are difficult to explain to unsophisticated individuals and also because they require many subjective inputs that could be cross-examined. In litigation, I try to keep things as simple and concise as I can to avoid these risks.

This year I have fielded perhaps a dozen inquiries about valuing life insurance policies. In previous years, these were very rare. After checking things out with several people, I realized that the causes of the increase in inquiries are the recession (some want to sell or cash in policies) and changed market conditions (which affect policy resale values).

I am always flattered when people call me for valuation help, but I am not qualified to value life insurance policies. I refer such people to:

1. The company that underwrote the policy, to quote cash value. Cash value is what the policy owner would receive to close out the contract and is determined by the policy. It is just like a private company shareholder selling their stock to a company that has a buy-sell agreement that specifies value.

2. Insurance brokers, to quote resale value. Resale value is what the owner would receive if the policy were sold to a third party and remained in force. The third party (the new owner of the policy) pays future premiums and receives the death benefit. Here the private company shareholder is trying to find a better deal on the open market, but that market is illiquid.

It seems to me that cash value is the minimum possible value. A willing seller would never accept less than that. Resale value, if available (there may be no market for some policies), may be higher. But, again, I do not value life insurance policies.

Revenue Ruling 59-60 and business valuation standards require that we consider economic trends in our appraisals. I rarely see a report that does not do this in some fashion: we get it. But our reports do not have to contain multi-page, detailed, quantitative recitations of economic statistics and forecasts for every sector of the economy at the international, national, regional, state and local levels. Rather, the really good ones identify up front the most important economic drivers (such as business investment in construction, wage levels, and labor market conditions) for a commercial contractor) and the economic level (perhaps regional for a smaller contractor) relevant to the business. When I read this type of incisive diagnosis, my confidence in the appraiser rises.

For many business valuations, however, a focus on pure economic trends might be incomplete. The pace of technological change is much more important for biotechnology and Internet businesses. Demographic trends – the aging of the population – are consequential for health and elder care businesses. The list of potential non-economic factors is potentially endless and unique to each assignment.

As an aside, if you have ever been part of a strategic planning exercise for a non-profit or community organization, you may have run into this challenge. These exercises often begin with a “SWOT” (Strengths, Weaknesses, Opportunities, Threats) analysis that considers the organization (S and W) and the environment (O and T). Badly facilitated sessions can easily get way off track discussing trends of questionable relevance, and people can easily get lost in that thicket. It can be hard to keep such sessions focused on trends of real consequence.

Bearing this in mind, no appraisal can address every possible trend that might affect a business. It’s impossible, and certainly not acceptable in terms of what it would cost a client to commission such a treatise. We need way to home in on the most important trends – the drivers. I have found that key questions to ask are: “What makes this business tick?” and “What could really hurt this business?” First, I think about them by myself, based on my general knowledge (or lack thereof, in some cases). Then I consult our standard industry information sources like First Research, which (particularly in the management questions section of its reports) often mention critical trends. Finally, I ask these questions during my management interviews. (By the way, try this in your next community service strategic plan exercise. You’ll be a superstar! You will also, however, be asked to chair the committee and write the report. You have been warned

One last hint: call your “Economic” section of your report your “Environment” section instead. This encompasses all relevant trends, and helps you broaden your thinking while at the same time sharpening your focus on what really drives or endangers a business and its value.

Something has been bothering me for a long time about business appraisal, but I could not figure it out until I recently read an article discussing how intelligence services present data obtained from various sources. I was interested to learn that they attach “reliability ratings” to their reports (using a 1 to 5 scale, 5 being the highest reliability). I quite naturally started thinking about what would happen if we did this in business valuation reports.

How would you feel about reporting that “The concluded fair market value of the subject business interest is X$, but this value opinion is of low reliability”.

Me, too.

A challenge of business appraisal is that value is a range (or a probability distribution with unknown parameters of central tendency and variability). In some cases, the range might be a single number (a point estimate) and be very reliable (e.g. the value of the equity of a long-term cash-flow negative business whose liabilities far exceed its assets). In others, the range might be relatively narrow and also be reliable (because multiple approaches and methods result in similar values). In others, the range might be very wide and reliable, and in still others it might be very wide and unreliable (as in those for early stage companies with no revenue or proof of concept).

In valuations for taxation and compliance, however, the rules require that we opine point estimates of – single numbers that represent - value. They do not require that we attach reliability estimates. In litigation, whether point estimates or ranges are permitted, we are always open to cross-examinations that attack reliability. (“Mr. Curtiss, could the value be lower than you opined?”) In transaction engagements, everything is subject to negotiation, which makes them the most flexible of all.

But let’s forget about the rules for the rest of this discussion and take an honest intellectual look at reliability. This will reveal a deep dark secret!

We start with an overarching principle that underlies every single appraisal approach and method. The principle is that we can estimate the whole (the value of a business interest) by dividing it into parts. The parts are return and risk, and each has many sub-parts. Returns are expressed in cash values (e.g. asset or liability amounts in the Asset Approach, earnings or cash flows in the Income Approach, and revenues or other benefit streams in the Market Approach). Risks are expressed as discount or capitalization rates or multiples.

Many of the parts are interrelated. This is an essential point to remember. For example, if we use the Income Approach and Multi-Period Discounting Method, we forecast cash flow to equity for a number of years (and a terminal value). If we increase revenue by a considerable amount, we have to consider whether this implies higher risk and a higher discount rate, because risk and return are related.

To analogize, every appraisal method is like the engine of a car. Engines have many parts: pistons, crankshafts and so forth. Something can go wrong with any one, leading to a breakdown. Moreover, many of the parts are interconnected. A broken piston could damage the crankshaft. (Full disclosure: I am NOT an auto mechanic, so please excuse any technical inaccuracies and grant me artistic license It could also lead to incomplete fuel combustion, excess exhaust gases, a failed emissions test, and to that highly annoying “Service Engine Soon” dashboard light being illuminated. Again, the point is that some parts are connected, and a defect in one affects others and the operation of the entire engine. A small problem could lead to a big one.

Out of the garage and back in the office, the parts of a business valuation – the returns and risks – are also connected. A mistake in the analysis of the economy, industry, company and its finances and prospects will cascade into errors in the estimates of return and risk, all of which degrade the reliability of the value estimate. Particularly when we are required to furnish point estimates of value, these errors can be highly and adversely consequential.

Value is really a range or, abstractly, a probability distribution with unknown parameters. For the sake of discussion, assume that value can be characterized by a bell curve, the “normal” probability distribution. Nobody knows whether this is true (I suspect it is not), but this allows us to explore “reliability” with mathematical rigor.

If value is normally distributed, then we estimate the most probable value (per Revenue Ruling 59-60). A normal distribution has many helpful properties, one of them being that the most probable value (the mode) is also the mean (average) of the distribution. A normal distribution has another helpful property in that its dispersion or variability around the mean is symmetric and can be characterized and calculated by the standard deviation. In a normally distributed population, 67% of the values will fall within ±1 standard deviation of the mean. If we take the square of the standard deviation, we get the variance of the probability distribution.

Now, assume we are appraising the fair market value for tax purposes of 100% of the equity of a business that has no liabilities and owns just two assets, a parcel of land and a building on it. A respected real estate appraiser valued the land and building at $40,000 and $30,000 on the valuation date. Their total value, the fair market value of the equity, was $70,000.

If we had to attach a reliability estimate to this value, it would be a 5. We had good real estate appraisals – point estimates of value - and everything else was simple.

Consider this assignment in a HYPOTHETICAL probabilistic world. In it, the real estate appraiser’s values were the means of the probability distributions of the values of the land and building. He also told us that the standard deviation of each probability distribution was $5,000. In other words, 67% of the time, the actual values of each piece of real estate would be within $5,000 of the mean. If we calculated the coefficient of variation (the standard deviation divided by the mean) of each estimate, they would be .13 for the land and .17 for the building. Not bad. Maybe the real estate appraiser would rate the reliability of his appraisals as “4”? And he told us something else: that the values of the land and building are closely related (the building sits on the land). If the land value goes up, the building value goes up. What he said was that they have a “covariance” of $120,000,000. Covariance measures the extent to which two variables’ values are related. If two variables move completely randomly relative to each other, they have a covariance of zero. (The covariance is related to the correlation between the variables.)

Now in this hypothetical world, the value of the combined real estate and of the equity is still $70,000. That did not change. What about the reliability of that estimate?

The following formula relates the variance of the total to the variances of the parts (the squares of their standard deviations) and their covariance:

Variance of business = Variance of land + Variance of building + covariance

Variance of business = ($5,000) x ($5,000) plus ($5,000) x ($5,000) + $120,000,000
= 25,000,000 + 25,000,000 + 120,000,000
= 170,000,000

The standard deviation of the business value is $11,402, the square root of $170,000,000, and the coefficient of variation of the business value is 0.19.

Look what happened to variability! The land and building values had standard deviations of $5,000, but because of their interrelationship (correlation / covariance), the standard deviation of the total value estimate ($70,000) rises to $11,402. The coefficient of variation of the land and building value (0.19) is bigger than that for the land and building considered individually.

Now at last, the problem that was bothering me can be summarized: when we break values into pieces and estimate the values of the pieces, the fact that those pieces are interrelated significantly increases the uncertainty associated with the sum of the values of those pieces. We are not required to report this (or possibly even to defend it), but it is true.

Moreover the example above understates the problem. Consider the build-up of the equity cash flow discount rate. There are five parts: risk free rate, equity risk premium, industry premium, size premium, and company-specific premium. Each has uncertainty associated and each may co-vary with the other parts. With five variables co-varying (not two as in the simple example above), there are 10, not one additional covariance additions in the formula, and the variance of the total could soar!

Even worse, small sample sizes (particularly with some industry risk premiums) lead to very high variances!

This is the deep dark secret: by dividing business values into parts, we significantly increase the uncertainty of our value estimates because the parts are interrelated. We may never have to defend this directly, but we should be aware of it.

The key point about an asset sale is that the selling company’s equity (stock) does not change hands. The selling company’s shareholders retain their equity interests. They still own the company, but the company now owns different assets – whatever it received in exchange for selling its original assets, and it may owe different liabilities if some or all were transferred as part of the asset sale.

Most business sales are set up as asset sales because asset sales give the buyers tax advantages (the ability to write up and depreciate or amortize purchased assets) and also allow them to negotiate which, if any, liabilities they will assume. In a stock sale, the buyer of the stock gets all the assets and assumes all the liabilities as well.

Selling a home is a perfect analogy. If the house sells for $100,000 and there is a $40,000 mortgage on it, the selling homeowner has $60,000 of equity in their house. They might just sell the house (an asset sale) for $100,000, pay off the mortgage from the sale proceeds, and net $60,000 before taxes. Alternatively, if the mortgage can be transferred, they might sell the house and transfer the mortgage in exchange for receiving $60,000 before taxes. Either way, they end up in the same place.

Some business owners are unaware of, forget, or choose to ignore the difference between asset and stock sales. This can cause confusion when discussing the “value of their business”. Yes, they might be able to sell their assets for $10 million, but if they have $4 million in debt, they will net $6 million before taxes. Alternatively, they might sell their assets and transfer the debt to the buyer, who would pay their company $6 million, which would be their pretax, pre-liquidation proceeds. In an equity sale, they would sell their stock outright for $6 million (before taxes). As in the house example, the end results are the same.

Most owners would probably like to give themselves credit for the asset sale value. After all, it is more impressive to say “I sold my business for $10 million” than it is to say “I sold my business for $6 million”. On the above facts, both statements are true, but the higher value ignores the retained liabilities. Also, this can lead to confusion about multiples. If the business was earning $1 million, the asset sale would be at a multiple of 10 times earnings and the stock sale (and the net proceeds of the asset sale) would be at 6 times.

Make sure to clarify whether an asset sale or stock sale value is being discussed, both to yourself and to your clients and their advisors. Most of the time, we appraisers end up having to value equity (stock-sale) based interests, but because most transactions are asset sales, it is easy for confusion to arise.

A recent Tax Court case, The Estate of Jorgensen v. Commissioner, shows why appraisers have to be cautious when considering court cases. If you Google the case, you will find many explanations of what happened. To summarize them, the Tax Court voided the transfers of assets to two FLP’s, disallowing their existence. As a result, the assets were included in the decedent’s taxable estate. This cost the estate a lot of money.

The reason for the Tax Court’s verdict was what is called “bad facts”. These, in this case, were rather egregious errors that the taxpayer and the attorney made in planning and administering the FLP’s. In other words, they messed up and this cost them.

What is the significance of this case for appraisers? In my opinion, none! When there are bad facts (not relating in any way to what the taxpayer’s appraiser did), the game is lost before it starts. The Tax Court did NOT find that the appraised valuation discounts were wrong. They DID find that they were invalidated by the other errors. In other words, they were irrelevant because of the bad facts.

When I first started to do tax valuations twenty years ago, I panicked when a verdict like this was announced, thinking that it was the end of valuation discounts. Nothing could be further from the truth. Cases like this – with bad facts – show only that non-appraisal related mistakes can make appraisals irrelevant. Because the appraisals are irrelevant, nothing can logically be concluded about them. Moreover, appraisers are not qualified to advise clients on how to avoid (non-appraisal related) mistakes, as that would be practicing law without a license.

We do have to think carefully about some cases. These arise when verdicts concern what appraisers did (or did not do). They might involve big issues (like whether to tax-effect “S” corporation earnings, an ongoing controversy). They might suggest things we ought to consider (such as the Mandelbaum discount for lack of marketability factors). They might be more technical (e.g., the weight to be accorded to pre-IPO or restricted stock studies as proxies for marketability discounts).

The reason we have to think carefully about these cases is that sometimes good appraisal practice may differ from what the courts decide. Sometimes, “good appraisal practice” may be unclear. (Do you think there are marketability discounts for controlling interests We have to consider these issues, take positions, and defend them as best we can, recognizing that our opinions may not prevail in the end.

Courts can also issue conflicting opinions on similar cases. Moreover, we do not always know why they decided what they did, or how they arrived at their conclusions. Perhaps the litigators did not do a great job. For these reasons, court cases are not probative (constituting evidence) for appraisers.

You may have read the challenge to the Butler-Pinkerton Model of the cost of equity capital published in the current issue of ASA’s Business Valuation Review and the authors’ rebuttal posted on the Business Valuation Resources website. Both are tough sledding to read since they are highly technical, based on the rigorous mathematics of the Capital Asset Pricing Model. Because of this, it is easy to lose sight of the fundamental purpose of the CAPM (or build-up method) and the Butler-Pinkerton Model, both of which ESTIMATE the cost of equity capital based on analysis of HISTORICAL data.

You might find it helpful, as I did, to reread Pratt’s Cost of Capital (Second Edition) which was published back in 2002. Although the numerical data are obviously outdated by subsequent results, I found three passages particularly worthwhile:

1. On page 5, that the “Cost of Capital is Forward Looking”, representing investors’ expectations of the future and to be used with expected cash flows. Historical data are backward looking, and to use them blindly with future cash flows could be highly inaccurate.

2. On page 78, that “Recent Research on the Equity Risk Premium” indicates that there is considerable error associated with the arithmetic average equity risk premium (of course, the magnitude of the estimate has changed due to subsequent years’ results, but the error remains today). In other words, the average historical rate of return has uncertainty associated with it.

3. On page 185, to avoid “Mistaking Historical Rates of Return for Expected Rates of Return”, since the future will not necessarily be like the past.

As professionals, our job is to help our clients identify and solve problems. Nobody knows everything; we all have gaps in our knowledge and expertise that limit our problem-solving abilities.

Here is a list of the kinds of experts I am glad to have in my personal network:

Actuaries help with the cash values of life insurance policies, pension plan interests, pension plan funding liabilities, and ESOP stock repurchase liabilities.

Fixed asset appraisers help with real estate (including special purpose assets like hotels and hospitals), equipment, personal property, and vehicles (cars, trucks, airplanes and boats).

Industry specialists (including other appraisers) are essential in highly regulated industries such as health care, and in rapidly changing industries like high tech.

Executive recruiters help with salary surveys for industries not adequately covered by published sources.

Other financial services specialists such as venture capitalists, commercial bankers, merger and acquisition intermediaries and brokers, investment bankers, investment managers, financial planners, and insurance agents are also very insightful, particularly in real-transaction engagements.

It is not just what we know, but who we know – our networks - that help us help our clients.

Some businesses are nearly or completely dependent on specific assets, which can make it very hard to separate the value of the “business operations” from that of the underlying assets. Some recent engagements of mine – all for estate or gift taxation – highlight some of the challenges.

A deceased bowling alley owner’s business owned the land (parking lot and building), bowling lanes and pin spotting equipment, and a bar and restaurant on the premises. The estate had commissioned a real estate appraisal. It was based on sales of bowling alleys that included the land, equipment, and that had bars and restaurants on the premises. The appraiser did not, however, develop an Income Approach value indication. The question arose as to whether the real estate appraisal reflected the value of the “bowling alley, bar and restaurant businesses”. I concluded that it did, because the comparable sales all included such operations and also because the subject company was operating at or below equity cash flow breakeven (net of reasonable owner-manager compensation.)

A cavern tour operator that leased its real estate (caverns and surface parking lots) from a state authority for a very long term. This was easy because the real estate was leased. I used the Income Approach.

A hotel including the real estate. I referred this to an industry specialist. I do this for (privately owned) hospitals, nursing homes and other specialized use buildings.

An antiques dealership. This was complicated by the fact that the owner was over 90 years old and had no succession plan. His inventory was huge compared to sales. Fortunately, he is an ASA-certified personal property appraiser specializing in antiques and was very comfortable taking responsibility for appraising his own inventory. I valued the business assuming that he would not purchase any new inventory, and liquidate what he owned over the next 5 years. This was a combination of the Income and Asset Approaches.

I received a call today from two very competent appraisers who were struggling. They were valuing a non-marketable minority interest and had nailed down everything except for the possibility of future dividends. They wanted to quantify them and consider their effect on the discount for lack of marketability, but were unable to do so because:

1. The entity was only one year old, and had no track record.
2. Despite their best (and very extensive) efforts, the client would or could not disclose financial projections or a business plan, so there was no reasonable basis for forecasting whether the business would be cash flow positive (able to make dividend payments), when, to what extent, or for how long.
3. The entity operating agreement was vague with respect to when dividends might be paid, how much, and under what circumstances. As of the valuation date (December 31, 200, the entity’s directors had not met to determine whether dividends would be paid, and still have not done so.
4. The interest would be held for a long (almost ten-year) period, and it was expected to grow rapidly (rate undisclosed), both of which implied a high marketability discount in the absence of dividends.

The appraisers were concerned about their liability concerning the dividend assumption and its impact on their valuation. In their view (and I agreed with them) they had provided a very strong basis for the valuation in all respects except for dividends and their valuation impact. Stated another way, if it had been justified to assume no dividends would be paid, they would have had no problem whatsoever with their valuation conclusion.

I counseled them as follows:

1. Present the valuation conclusion developed without consideration of dividends as a starting point. There was nothing to worry about here. They had all the facts,
2. Cite all of the above information limitations that made dividend projections highly speculative at best and impossible to forecast with confidence.
3. Subjectively reduce their discount for lack of marketability by a selected percentage to reflect the possibility that dividends might be paid. Admit that this judgment was necessitated by the limitations but also their attempt to give fair consideration to the possibility of dividends.
4. State that this was their informed judgment, based on their best efforts to obtain information, and that they reserved the right to update their opinion pending receipt of additional information that might mitigate the limitations.
5. State also that a willing buyer and seller would give some consideration to the possibility of dividends being paid, but discount their significance because of the surrounding uncertainties.
6. Do some calculations to see what rate of dividends were be implied by the subjective decrease in the discount (the QMDM is ideal for this purpose).
7. If challenged, do not be embarrassed by the subjectivity of the dividend assumption. Turn the challenge around and ask a skeptic to provide a better basis for an alternative judgment, i.e. to “prove it”. If they could prove it with information available as of the valuation date, agree with them. If not, stand by their judgment made at the time based on what information was available.

EVERY appraisal is uncertain, some more than others. All we can do is gather the requisite information, cite its limitations, base our assumptions and analyses on what we know, admit what we do not, and try if possible to analyze the impact of the latter. That is why appraisals are OPINIONS, not factual findings! As long as we do our best in all these areas, we have nothing to fear but fear itself.

I hope that this post stimulates you to learn more about option valuation methodology for several reasons. The demand for such valuations is rising due to the enactment of FAS 123R and IRC 409A which require such valuations for financial reporting and tax compliance purposes. The application of option valuation methodology – more generally, contingent claims analysis – is a major area for academic research, and much useful progress is being made. Moreover, option valuation methodology can help us with some of the more challenging appraisal assignments we encounter.

Financial options are a subset of real options, which are applicable to strategic business decisions such as capital investments and R&D. Although real options theory is interesting, I do not think that most of us will have occasion to use it in our business valuation practices.

Financial options grant their owners the right but not the obligation to acquire or dispose of specific assets at a predetermined price and for a specific time period. A European style option can only be exercised at the end of the period. An American style option can be exercised any time during the period. (Employee stock options for 123R and 409A are almost all American style options.) Call options give their owners the right to purchase, and put options give them the right to sell. Most of the options I have valued are calls.

The most important and unique aspect of financial options is the holder’s ability to defer the exercise decision and therefore limit their loss. A call option owner does not have to buy the asset if its market value is less than the exercise price of the option. If the option expires, their only loss is what they paid for the option. They cannot lose any more than that. But their upside is unlimited; as high as the price of the asset could rise. Because the loss is limited and the gain is unlimited, the returns are asymmetric, giving options their unique flavor.

Options are sort of like climbing a mountain using stakes (pitons) that the climber hammers into the cliff. Each stake gives them a secure foothold and prevents them from falling (limited downside). It also lets them climb as high as they want (unlimited upside). They are also like lottery tickets.

Because of the asymmetric returns, the option’s value increases as the variability of the asset price rises. The more the price moves up, the higher the potential value. Price declines are irrelevant because the option owner’s loss is limited.

Options are valued using many different models, but all of them work the same way. In the “lattice” or “binomial” model, you divide up the option’s maturity into discrete intervals. You assume that the stock price will move up or down a certain amount during each interval with some probability. You also assume that this period’s movement is independent of any previous movements. This is known as the “random walk” model of stock price behavior. All possible price paths (combinations of up or down movements in each period) are charted out, resulting in a distribution of possible stock price outcomes, from which the option value is calculated for each one. The resulting graphic looks like a decision tree. The probability weighted option value (based on how many times out of the total outcomes a given value results) is then calculated. Derivative Valuation Associates, LLC has made available a lattice model calculator through the BVR website. I use it regularly.

If you shrink the discrete time intervals to infinitely small periods, you end up with what is called a “continuous” option valuation model, which is known as Black-Scholes. Black-Scholes results in a calculus-based (parabolic partial differential) equation that can be solved for the option value. (I do not understand the math involved.) There are many free Black-Scholes calculators available on the Internet. I use the one developed by Economic Research Associates.

Both the lattice and continuous models have been widely validated and accepted. We need not understand their mathematical underpinnings in detail. They are black boxes we rely on. As always, it is all about the assumptions we put into them.

One of the key assumptions made by both models is that stock price movements follow some sort of normal (bell curve) probability distribution. This may be arguable at a high academic level. See my earlier post entitled “The Black Swan”.

Having put forth all of this, what makes option valuation methodology different from traditional valuation approaches – the Market, Income, and Asset Approach – is that option analysis builds uncertainty in the form of the volatility of the stock price and provides the owner with the flexibility to exercise or not. Yes, the volatility assumption is hard (what is the volatility of the price of the stock of a private business – it is not traded All of the traditional approaches are static in that we assume a fixed set of price multiples, asset and liability values, or financial forecast and discount rate. None of them incorporates uncertainty, unless we perform sensitivity analysis and / or make probability assessments about assumptions, which can be challenging.

It seems to me that option valuation methods can be very useful in engagements where uncertainty is very large, such as:

● Valuing minority interests in businesses whose liquidation values exceed going concern values, but the control owner will not liquidate. A minority equity interest is an option on liquidation value.
● Valuing convertible securities
● Valuing callable debt
● Valuing contingent claims such as lawsuits or environmental problems
● Valuing companies which might sell off some assets
● Early stage businesses
● Personal guarantees of corporate debt
● Valuing control (where control owners have prerogatives that are like options)
● Valuing lack of liquidity

I do not have all the answers as to how to apply option valuation methods to these cases, but I bet there are ways to do so.

How would you value (at fair market) control vs. minority interests in a business whose liquidation value far exceeds going concern value?

I think we all agree that the control interest should be valued at liquidation, consistent with highest and best use and exercise of the control prerogative to liquidate. Even if the control owner plans not to liquidate, that is an irrational decision, and fair market value implies rational parties. (The decision not to liquidate is an investment value decision based on the control owner’s personal situation. Maybe they think the company can grow profitably. Maybe they want to pass the business to the next generation. Whatever.)

The minority interest is another story. This owner cannot force liquidation short of filing an oppression suit – risky and costly. I would not disagree with those who value the minority interest at going concern value. In fact, that is how I did it for many years. I was never challenged or rebutted.

Now I am rethinking things. The minority owner of a business with high liquidation value and low going concern value may not be able to force liquidation, but if it happens, they effectively own a lottery ticket on the (higher) liquidation value. That value is not reflected in going concern value.

I can think of two general ways to capture the lottery ticket value:

1. Value the stock as an option on liquidation value. The minority stock is a deep in-the-money call option on liquidation value. Using Black Scholes comports with financial theory, but I have problems specifying the assumptions. Black-Scholes assumes that an option will be exercised if the asset price exceeds the strike price. But we already know that the majority owner controls the ability of the minority owner to exercise the option. So Black-Scholes will not work. Perhaps a binomial lattice model would work, but there would have to be some decision rule built in that would determine when the company would liquidate and at what price. Quite simply, this is beyond me.

2. Do a DCF analysis with (projected) liquidation value as the terminal value. I can se4e exactly how to do this. There would have to be sensitivity analysis about how long until liquidation and liquidation value, but this is very doable. Now, compare this to a baseline DCF with no liquidation (going concern value). Now, make a major assumption about the probability of liquidating or not. The weighting will give some probabilistic value to going concern and some to liquidation.

Having studied Roger Grabowski’s article cited in a previous post, reread the SBBI book, the Duff & Phelps publications, and other literature, I have some additional suggestions about the Rate of Return Paradox.

Above all, remember that we are trying to ESTIMATE the cost of equity capital for a subject private business. We CANNOT MEASURE it directly or precisely by observation or any other method, because it is forward looking. We are going to apply a discount rate (the cost of equity capital) to future cash flows, which are unknown, and the value of the subject business’s equity is also unknown.

We use HISTORICAL data from the public markets - stock prices, dividends, and computed rates of return - as data on which to form our estimates. (Duff & Phelps and SBBI use the same basic data, information from the Center for Research on Securities Prices or CRSP). This gives us one of the unknowns – stock price – but it comes with two costs.

First, we have the problem of assuming that the future will be like the past. It won’t be, but we hope that, by using very long-term time series (going back to the 1920’s), we capture enough historical trends and volatility to be comfortable. That is arguable, but the famous graph on page 22 of the 2008 SBBI book shows that stocks have historically earned greater long-term returns than other securities. From this we assume that, in the future, this relationship will continue to hold, so this data will be a reasonable proxy, or substitute, for the cost of equity capital that we are trying to estimate.

Second, we know our subject company is not the same as the stock market as a whole in terms of its risk / return characteristics. We thus assume that we can adjust for that with good analysis, which means we break up the long-term stock market return into a number of parts and try to understand how the parts relate to our subject company. The problem is that when we do so, we have to estimate the value of each of the parts. None of those estimates is perfect, each one is a source of potential error, they are all based on the same underlying data (with a great deal of sophisticated statistical processing and adjustments) and it is definitely illogical to assume that the errors will cancel out.

Current build-up methodology breaks the cost of equity capital into parts: the risk-free rate, the equity premium, the industry premium, the size premium, and the company-specific risk premium. Focusing just on the first two, note that the equity risk premium is the total return on stocks minus the risk-free rate. These three time series are as of the same date and based on the same historical time series. As of the end of 2008, the SBBI risk-free rate (20-year Treasurys) was 3.0% and the long-horizon equity risk premium (based on historical data) was 6.5%, As of the date of this post, 20-year Treasurys are yielding (call it) 4%. The stock market is also up for the year. In theory, if we are valuing a business as of today, you would use the 4% risk-free rate AND an equity risk premium updated through today. It would not be correct to use the current 4% risk-free rate and the 12/31/08 6.5% equity risk premium, because they are reflective of different dates and historical periods. Granted, this error might be small, but if interest rates continue to rise this year (and most people think they will), this error will become larger.

Likewise with the industry and size premium components and the company-specific risk premium (particularly if you use the Butler Pinkerton Model) – in theory they should be updated as of the valuation date. But most of us do not have access to this data, so we must be aware of the errors we are introducing by using out-of-date numbers. Remember, we are ESTIMATING the cost of capital. Our estimate will not be perfect. That does not allow us to make conscious estimation errors, in fact, it requires that we acknowledge them and try to compensate as best we can (which unfortunately creates even more error).

Do not get lost in the details of the parsed data. Remember, we are ESTIMATING a future cost of private equity capital from historical rates of return on public equity capital. All estimates are subject to uncertainty. The future will not be like the past, public and private capital markets are fundamentally different, and our dividing the data into parts and estimating them creates additional errors.

In the end, the only way to achieve more comfort with all of this is to go back to basic common sense. One way to do that is to put the CRSP-based data aside, and think of the problem of estimating the cost of equity capital in a different way. I do it along these lines. For a going concern private business, the cost of equity capital should be no lower than the cost of mezzanine money (subordinated debt with equity kickers like warrants), which is normally around 20%. It should be no higher than that for a startup – at least 40%. (The 20% and 40% are arguable.) Both of these numbers are after-tax to the company but pretax to the investor (that is, before income taxes on dividends and capital gains taxes on appreciation). This gives us a reasonable range for the cost of equity capital.

Now, I have been doing this for 25 years and I think I can distinguish whether a business is very low risk (20%), about average (30%), high risk (40%) based on my economic, industry, company and financial analyses. In other words, I can tell between white, gray and black. Maybe I can even distinguish a low-to-average (25%) or average-to-high (35%) risk level. That would be light or dark gray. I do not ever think I can do better than that. This exercise gives me a reasonability test of my build-up of the cost of equity capital. If the exercise and build-up are off by more than 5%, then I review all of my assumptions and analysis until they converge. When they do, I at least have some comfort that I am in the realm of what is reasonable.

When control owners of businesses decide to sell or gift partial interests, people (including us appraisers can get confused about what is supposed to be valued and on what basis.

Let’s take a simple example. Mr. Jones owns 100% of the stock (all of one class) and wants to gift 49% of it to his daughter. After the gift, he will retain control (51%) and his daughter will own a minority (49%) interest. The subject interest – what is being transferred - is the 49% interest, and it should be valued as such, definitely with a discount for lack of control and possibly with a discount for lack of marketability (if applicable). Mr. Jones will keep a 51% and controlling interest, and it should be valued as such, if need be (i.e. if he dies with 51%).

The key point is that Mr. Jones will retain control. No matter what else goes on – maybe the stock is recapitalized into voting and non-voting, or there are gifts to more than one person (still adding up to 49%) – control is maintained so the subject interest is valued on a minority basis.

What if Mr. Jones wants to gift 51% to his daughter and keep 49%? Now control is being transferred and preserved, in the form of the 51% interest, so it has to be valued as a controlling interest. Mr. Jones will end up with a 49% minority interest, valued as above.

What if he decides to gift 33 1/3% each to two daughters? Now control is being destroyed and not transferred. In the end there will be three equal 33 1/3% owners, the interests being transferred are each minority interests, and nobody will have control. All of the interests are minority, although some would argue that the lack of control discount is mitigated somewhat by “swing value” because any two shareholders acting together would have control.

I have found, and I make it a point in my appraisal reports, to address the issue of who currently and prospectively will own what, what is being transferred, and whether control is preserved, destroyed, or transferred at the very beginning of my appraisal report. In those instances where control is retained (as in the first example above), the value of the retained interest does NOT need to be addressed in the appraisal report, and may lead to confusion.

Not an hour after my previous post, the current issue of the ASA's Business Valuation Review arrived in the mail, and it contains a superb article by Roger Grabowski that is right on point and goes into much more depth on this very subject. I think it is a "must read"!

The Ibbotson rate of return data indicate that both the risk-free rate and the equity risk premium declined in 2008. If everything else – the other components of the built-up discount rate and the expected cash flows of a business – stays the same, then this leads us to conclude that the overall discount rate is lower, and discounted cash flow value is higher.

But market multiples are down, so we would expect business values to go down.

These statements are contradictory. How do we resolve this paradox?

I can think of three ways: one based on the assumption that historical rates of return are indicative of expected rates of return, one based on the fact that the build-up assumptions and cash flow forecast are somewhat interrelated, and one based on the definition of “market multiples”.

The equity risk premium is based on long-term historical average rates of return. If you use it in a build-up, you are assuming that the future will be like the past. The Ibbotson book has a good discussion of the implications of this assumption starting on page 60. The bottom line of this argument is that the 2008 market decline lowered the price of assuming risk, leading to a lower discount rate (the cost of taking risk).

Is it realistic to assume that “everything else stays the same” (other components of the discount rate and expected cash flows) today as opposed to a year ago? In a few words, maybe and maybe not. The industry risk premium may have changed for a given company’s industry, and the company-specific risk premium may also have changed, given what happened last year. The expected cash flows may also have changed. In other words, you have to look at every single piece of the puzzle, because they all may indeed change.

Finally, market multiples are based on historical (trailing twelve-month) results, rather than expected results. For companies that experienced declines last year, of course the values are down on a multiple of historical earnings basis, but expected earnings may be far higher.

Most of my clients have never prepared financial forecasts. This means I have to get the process started by presenting a preliminary one to educate them and give us a basis for discussion. On the other hand, some clients do prepare them, and I consider them in my analysis. This post compares and contrasts how I handle these two situations.

When I work for a client who does not forecast, I begin with the default assumptions in my financial model (discussed in other posts). This is a “things continue as is” forecast with extended historical growth, constant margins, and most assets and liabilities growing with revenue. I then blend in considerations from the economic and industry analyses. This first cut forecast does not (unless the client has mentioned them) get into things like fixed versus variable costs and major capital expenditures. The purpose of the first cut is only to be able to put something relatively simple in front of my client that helps them understand what assumptions are most important (sensitive) and how the numbers work. Once they get a feel for that, I can address the more sophisticated issues. This may take a few iterations, but the end result is a forecast that considers everything that I and the client believe to be important, provides good basis, and is plausible, supportable, and replicable.

When clients prepare their own forecasts, I usually find that they do a pretty good job with revenue and expenses, sometimes providing extensive detailed support. I will check these against my economic and industry outlooks to make sure we are on the same page. The challenge I usually run into is that clients forecast just income statements, not balance sheets. How can they project interest expense, pretax income, and net income? In this case, I put their revenue and expense projections into my model as a starting point and prepare a complete (income statements, balance sheets and cash flow statements) forecast for discussion with them. Again, we iterate some versions, but end up as above.

Regardless of whether the client provides a forecast, I am independent, since I have an objective, factual basis for each assumption: either I provided it and the client confirmed it or the client provided it and I confirmed its reasonability independently.

A few years ago, a management team completed a seller-financed leveraged buyout. Last year the company had a very good year ( and the shareholders decided to contribute their annual bonuses back to the company. They invested the money in a certificate of deposit. They agreed in writing that the funds would be reserved for “(1) paying debt still owed to (the seller) or (2) emergency company use” and that none of them “could withdraw any money contributed”. They accounted for the transaction as an asset (the CD) and a (current) liability. When their accountant prepared their annual financial statements, and during my valuation, the question arose as to whether this transaction created debt (a liability of the Company) or equity (either paid-in surplus or more stock shares). After discussion, it was concluded that the transaction created additional equity due to the contributors’ inability to withdraw the funds, which eliminated the justification for it being a liability. It was also concluded that the transaction created new shares of stock, not paid-in surplus, because the seller (who retired once the buyout closed) retained an equity interest and did not contribute capital. It would have been unfair to the contributors not to receive benefit in the form of increased shares (and for the seller to get an increase in his book equity) as a result of the capital contribution. Fortunately, everybody agreed to this. This raised a bigger question for me: what is the definition of equity as opposed to debt? I am not an accountant, and have not been able to research what the regulatory authorities say about this. (Anyone who knows, please let me know, and I will publish the results.) I Googled the subject and found something at: http://pages.stern.nyu.edu/~igiddy/articles/moodys_hybrids.pdf Although dated 2003 and somewhat technical, this Moody’s publication contained (on page 2, under the “Background…” section) a clear and, at least to me, very useful definition of the characteristics of pure equity: 1. No maturity 2. No ongoing payments that could trigger a default if unpaid 3. Loss absorption for all creditors In other words, pure equity has no principal due date, no ongoing payments, and is paid only after all creditors are satisfied. I infer from this that anything that doesn’t meet these criteria has elements of debt. I checked it with the above problem, and it worked out perfectly, telling me that the subject money should be treated as equity. The rest of the Moody’s paper, which was interesting but not overly relevant to us, describes how they developed a continuum to classify “hybrid” securities that have elements of both debt and equity, and how they place them in different “baskets” with different percentages of debt and equity allocated for purposes of financial ratio analysis. This is subjective, and gets into issues such as how subordinated (to senior debt obligations) a hybrid security might be, whether dividends can be deferred, how much financial flexibility the security provides, the impact of call options and conversion features, liquidation preferences, and how they might evolve over time in terms of the issuer’s ability to pay dividends / interest and principal under different scenarios. This sounds a lot like business valuation to me, but from a debt rather than an equity perspective…and now I can tell the difference!

The Ibbotson data for 2008 are now available. As we knew but can now quantify definitively, the risk-free rate and the equity risk premium are both down. This means that other things (the industry risk premium and the specific company equity risk premium) being equal, equity cash flow discount rates are lower.

This has several important implications.

First, for businesses that expect to grow and earn higher cash flows, lower discount rates mean higher equity values.

Second, the specific company equity risk premium (if unchanged) will be a higher proportion of the total (lower) discount rate. This makes it even more important not to proclaim this premium without proof. We have to do the best we can, based on company analysis, to justify its magnitude. We also have to be honest about the uncertainty associated with estimating it.

Third, lower discount rates make them more sensitive valuation assumptions for a given set of forecast cash flows. Calculate this for yourself. Check the percentage differences between discounted cash flow values for rates of 15 versus 17% and 10 versus 12%, just to pick values at random. Both discount rate sets differ by 2%, but the valuation differential between 10 and 12% is a lot greater than that between 15 and 17%.

Nobody said business valuation is easy…recent market developments have made it even harder!

In the course of teaching, mentoring, consulting, and litigation support, I have reviewed reports prepared by many other appraisers. I usually reach an overall opinion of the quality of a report after reading it for the first time:

1. It is way off the mark (due to many fundamental errors and omissions).
2. I am not sure (so I need to read it again).
3. It is probably pretty good.

Here are ten things I look for in my first readings of reports, with explanatory examples of each, assuming the assignment is to determine non-marketable minority fair market value:

1. Did they identify the relevance of each Revenue Ruling 59-60 factor?

Earning capacity: Equity cash flow was the selected metric. It is the annual change in cash before dividends. It adjusts profits for non-cash items, capital outlays, asset sales, and changes in working capital, debt, and liabilities.

2. Did the economic analysis focus on company value and risk drivers?

The valuation of a local car dealership should consider things like the outlook for domestic automobile sales, the local economy, and consumer credit. Trends in other macroeconomic factors like business investment, balance of payments, etc. are irrelevant.

3. Did the industry analysis focus on company value and risk drivers?

For a car dealer, there’s a big difference between General Motors and Honda today!

4. Did the company analysis focus on value and risk drivers?

Key person risk is always at the top of my list.

5. Were financial statement adjustments identified and justified authoritatively?

Appraisers who ignore good sources like ERI (Economic Research Institute) and rely on Risk Management Association data are not sufficiently diligent,

6. Was their financial forecast complete (full statements) and were the assumptions clearly identified and justified?

Debt is repaid as scheduled per the Company’s financial statement footnotes.

7. Did the Market Approach development justify the price multiple chosen?

If you compare the subject company to industry norms (e.g. Risk Management Association ratios) you can build a strong case for its relative attractiveness.

8. Did the Income Approach development justify the company-specific equity risk premium?

Did they mention revenue and expense uncertainty, amount of debt, adequacy of equity capital, etc.?

9. Was enterprise value subjected to a justification of purchase test?

If someone bought the business for the indicated value, could they pay themselves or a manager a fair market salary, adequately service debt, and earn a satisfactory return on equity investment?

10. Was the discount for lack of marketability justified with multiple methods and based on company-specific facts?

Benchmarking and the QMDM can be used in tandem for this purpose.

I am sure there are more aspects of good reports that I have not mentioned here…as always, your input is appreciated! What I have found is that reports that hit all of the above points well are usually pretty good. If I have disagreements with them, they will be either judgment calls (should the growth rate be 5% or 6%) upon which there can be legitimate differences of opinion, or the errors are local in nature (e.g. a math error or inconsistent levels of value concluded with various methods) and easily corrected.