In Step 2 of Validating a Business Valuation, you’ll learn:

  • The art of selecting valuation methods
  • The art of implementing valuation methods
  • The art of reconciling valuation methods to determine the overall value conclusion

Why this is important to you: Professional judgment, or ‘art,’ is quite prevalent in business valuations. Validating the key areas of professional judgment can help you determine if the value conclusion is credible and reliable.


Now that you’ve been able to ‘dispel the magic’ from a business valuation, the next step is to understand how, when, and why professional judgment (aka, ‘art’) is applied in a business valuation. But, what is professional judgment? To be clear, professional judgment is the reasoning that extends from the underlying science; it’s not arbitrary or somehow separable from science. So, 'science' is the foundation and professional judgment stems from science. And, a professional opinion is the culmination of science and judgement, as shown in the hierarchy below:

Hopefully this description of professional judgment will help you identify it when you see it. What follows are the three areas of professional judgment that deserve the most scrutiny in a business valuation:

  • Selecting Valuation Methods
  • Implementing Valuation Methods
  • Reconciling Valuation Methods

The Art of Selecting Valuation Methods

Professional judgment plays a significant role in selecting which valuation methods to use. Simply knowing how certain valuation methods align with certain business characteristics can take you a long way toward testing the validity of a business valuation.

But before you can validate the selection criteria used by the appraiser, you need to understand the valuation standards that set the context for method selection.[1] A valuation standard, more commonly referred to as a ‘standard of value,’ is completely different from an approach or method. A standard of value sets forth the scenario or hypothetical sale conditions assumed in the valuation.

Common standards of value include fair market value, fair value, investment value, orderly liquidation value, forced liquidation value, and hypothetical value. All methods used in a business valuation must align with a standard of value that is: 1) consistent with the intended purpose of the business valuation, and 2) identified at the beginning of the engagement. Put simply, there can only be one standard of value per business valuation; the appraiser can’t assume a fair market value scenario in one method and then assume an orderly liquidation value in another.

1. Definitions of Valuation Approaches and Methods

So, what is a valuation method? You’ve probably heard the terms ‘valuation approach’ and ‘valuation method’ used interchangeably or indiscriminately. However, knowing what each of these mean and, most importantly, how they apply to different businesses is a critical step in testing the validity of a business valuation.

So, here’s what you need to know. There are only three valuation approaches; they are: the Income Approach, the Market Approach, and the Cost Approach. Inside each valuation approach, however, there are multiple valuation methods. What follows is a description of each Approach and the common Methods used for each.

 2. Correlation between Valuation Methods and the Business Life Cycle

Now that you know what the approaches and common methods are, you need to understand which ones apply to which types of businesses. The most basic determinate of valuation approach is the life cycle phase of the business. Every company can be characterized as being in one of four business life cycle phases: start-up, growth, maturity, and decline. As shown in Figure 3 below, the typical business life cycle consists of negative profitability during the start-up phase, rising to maximum profitability at the maturity phase, and then declining from there over time.

Thinking intuitively about the business life cycle should be helpful in understanding the correlation to different valuation methods. Figure 4 below identifies the relevance of certain methods at certain phases of company life cycle.

Relevance of Life Cycle on Valuation Method

(a) Start-up Phase Methods

There are generally two types of start-up companies: 1) A New Product Start-up Company, which is a start-up company that has a new product that the market has never before seen, and 2) An Imitation Start-up Company, which is a start-up company that’s new but offers products that are similar to other established companies, like the 10th restaurant in a chain of similar restaurants. It’s still a start-up; but its characteristics are more like a Growth Phase company that has known elements such as the timing of market adoption, the price customers are willing to pay, and the quantity they demand. So, the valuation methods used for Imitation Start-up Companies will resemble the methods used for Growth Phase companies as discussed in the next section.

Figure 4 above and this discussion here are focused on New Product Start-up Companies. During the start-up phase, these companies either have very low profit or no profit at all; so, projecting cash flow and determining a risk factor are extremely difficult. The appraiser’s judgment to use an Income Approach at all is largely dependent on his ability to benchmark the start-up to another similar company, which is what we discussed above as being similar to a Growth Phase company (where parameters such as price and quantity demanded can be known based on similarities with other companies). Otherwise, in its purest sense, an income approach applied to a start-up is where the proverbial hockey stick projection emerges: year one is projected to be flat (of course, it’s a start-up) and the following years are projected to have growth beyond your dreams - unicorns come out to play and rainbows cover the sky.

Okay, back to reality. Applying a market approach in the start-up phase is similarly difficult, as there are usually too few benchmark companies to compare to a New Product Start-up Company. Any market multiple or correlation drawn between an established company and the New Product Start-up would be a weak benchmark and the method would likely be invalid.

So, assuming a lack of company bench-marking data, the New Product Start-up company is generally valued using the Cost Approach. The idea here is that a buyer would be willing to pay no more for a start-up company than the costs incurred to date to start the company. So, if the cost of new product research since inception of the company was $1 million, then the value to any buyer would be the $1 million they don’t have to spend to get the product in its current phase of development.

(b) Growth Phase Methods

As discussed above, Growth Phase companies already have a basic understanding of the market adoption rate and the path to profitability for their product. And presumably, the Growth Phase company has already started to see competing or substitute products enter the market. These products and the company’s own data give the appraiser benchmarks from which an Income Approach can be assembled. For this reason, the Income Approach in Figure 4 is shown to be relevant in the Growth Phase.

Similarly, the Market Approach also begins to become relevant in the Growth Phase, assuming that other similar companies have been sold or similar companies are being traded on a public exchange.

The Cost Approach, however, begins to lose relevance in the Growth Phase. A likely seller of a Growth Phase business would be interested in receiving consideration for the new product’s market adoption and prospects for profitability rather than just the cost of the investment made since inception.

(c) Maturity Phase Methods

While selecting valuation methods for Start-up and Growth Phase companies requires significant professional judgment, selecting valuation methods in the Maturity Phase does not. A mature company should have plenty of benchmark companies to compare sale prices, supply and demand, growth projections, and required rates of return. So, the professional judgment involved in valuing a company in the Mature Phase has much more to do with the judgment used to implement the methods rather than in the selection of the methods themselves. Very clearly, Mature Phase companies are valued using the Income Approach and the Market Approach. The professional judgment used inside these approaches will be addressed in Section 2.2: Implementing Valuation Methods.

(d) Decline Phase Methods

Many companies never enter a Decline Phase. As shown in Figure 5 below, these companies continuously innovate so that when one product begins to decline, other innovative products are emerging to continue the perpetual Growth and Maturity Phases of the company.

Business Life Cycle of a Continuous Innovator

Usually companies only enter the Decline Phase because they’ve failed to innovate at the rate of speed demanded by the competitive marketplace. Identifying when a company is actually in a Decline Phase can be contentious for an appraiser. These are the ‘emperor has no clothes on’ kind of moments. Nobody wants to say it, but the company’s chances of a turnaround are becoming more remote by the day.

This determination, of course, takes significant professional judgment on the part of the appraiser. The Income Approach and the Market Approach are still relevant; but the availability of benchmark data from companies in similar situations is limited. And, once comparable companies in decline start to go out of business, benchmark data becomes even more scarce. If the appraiser attempts to apply a Market Approach by using sale prices of innovative companies, or attempts to apply an Income Approach by assuming similar market risk as the innovative companies, then the results of such a method can be invalid.

But the Decline Phase opens the door to the Cost Approach once again. At some point, the value of the assets will exceed the ‘going concern’ value of the company. When this happens, break out the calculator and start adding up the sale prices you might get for each asset in an orderly liquidation.

The Art of Implementing Valuation Methods

Now that you understand the professional judgment used in determining which valuation methods are most appropriate for different kinds of businesses, this section will discuss the professional judgment that occurs inside the various methods. But please remember, this book is a ‘how to validate business valuations’ book; it’s not a ‘how to do business valuations’ book. So, this section will demonstrate how to test the validity of an appraiser’s professional judgment, not how to develop your own professional judgment.

1. Income Approach Methods

Recall the definition of the Income Approach: a perspective of value that considers the income-generating ability of an asset or business and the risk of receiving that income. The key areas of professional judgment used in the Income Approach are in projecting cash flow and assessing the investment risk of the company.

(a) Projecting Cash Flow

Projecting cash flow is an area of significant professional judgment; after all, the future is being predicted, right? Well, not exactly. The first step in testing the validity of a cash flow projection is to remember that nobody has a crystal ball and nobody can predict the future. So, don’t hold an appraiser to that standard; but, in the same vein, don’t accept a projection from an appraiser who implies that he or she has a crystal ball either!!

Make Reasonable Assumptions

Making projections is not about predicting the future; it’s about making reasonable assumptions about how a company might grow over time given what we know about the market environment and the company itself. For example, an appraiser might look at customer contracts to determine how much revenue is under contract in years 1 through 5; an appraiser might purchase research reports from industry experts; or an appraiser might look at the public filings of a company’s competitors to determine the outlook for revenue growth and profitability. The key is that there are nearly unlimited ways to benchmark and triangulate cash flow projections.

To validate a cash flow projection, you just need to assess the appraiser’s evidence and support for the projection made. If it all seems to make sense, then move on to the next area. If it doesn’t make sense, or worse, if you bring forth evidence that contradicts the logic of the projection used, then you know that the projection is not valid.

Project Cash Flow from Existing Assets Only

One extremely important note to make here is that the projection of cash flow needs to only capture the anticipated cash flow generated from the assets owned by the company on the effective date of the valuation. This sounds silly to even mention; but this is a real issue and any test of validity should look for this error in logic.

You cannot assume that the company will have an asset in the future that it doesn’t currently have (unless this hypothetical assumption is clearly stated in the valuation report). This issue is generally rampant in the valuation of start-up companies or growth companies. The owners are sometimes so convinced that they’ll have a particular asset or compete in a new market by a certain date that they insist on having the associated revenue captured in the projection. The way to handle such issues is to value the business ‘as is’ with the assets it has; and then possibly perform a second projection of the cash flow the new asset would bring and treat it like an alternative investment for the company. So, the business as it currently stands is worth X to a buyer of the business; and, the new asset is worth Y to a prospective investor.

An example would be the following: The owner of a start-up business has a state-of-the-art operations center in Dallas with several customer contracts for clients in Dallas. When making his projection of revenue, however, he shows the revenue for the Dallas operations center but he also includes the projected revenue in Year 2 of the Cleveland and Jacksonville operations center that he plans to open. As you can see, the value of the existing business, which is really only the Dallas operations, would be overstated.

This situation could be partially remedied if the cost of construction of the Cleveland and Jacksonville locations was included; but when hypothetical scenarios start building on top of hypothetical scenarios, the value conclusion becomes an amorphous number that really doesn’t mean anything.  So, be sure that the projected cash flow is the cash flow generated from the assets that the business currently owns.

The Projection Time Period

The last issue to look out for in a cash flow projection is the time period of the projection, or the ‘discreet projection period’ as it’s called in the business valuation community. This topic can really fit in the Dispel the Magic section or the Understand the Science sections of this book. Sometimes there’s a bit of ‘Magic’ involved when the appraiser says, “a 5-year projection is standard.” Yet, there is also a bit of ‘Science’ involved in determining the length of a projection period. The truth is that determining the length of the projection period requires the same professional judgment as making the projection itself. The projection period is simply the time period in which the company goes from having higher-than-normal annual cash flow growth to having a normal, constant rate of annual growth.

But to be clear, any Income Approach applied to a going concern business (defined as a business that is deemed to live on in perpetuity) has an infinite projection. In these cases, appraisers never assume a finite life for the business. So, the projection period shown in the valuation, whether it’s 3 years, 10 years, or any number in between, is simply the number of years until cash flow growth is projected to be constant year-over-year into perpetuity.

So, if you’re validating the valuation of a growth company, you might have a reasonable expectation of a 15% year-over-year growth for the first several years. It could be 3 years or 5 years or any number of years that are reasonably supportable. This period of abnormal growth, or ‘super growth’ as it’s called in Finance 101 class, is the time period of the individually-projected years. But after that, as the growth levels-off to a long term constant growth rate, it tends to mimic the projected growth of the US economy as a whole, similar to the US Gross Domestic Product or maybe even inflation. Constant growth assumed in all the years after the super growth period will be discussed further in the next section. In fact, this whole topic will be addressed again from a slightly different angle in the next section called ‘Step 3: Understand the Science.’

Assessing Long Term Growth

In Figure 6 below, the ‘super growth’ period turned out to be five years. ‘Turned out be’ means that the appraiser did a thorough assessment of the company’s products and the result was that she could only reasonably project ‘super growth’ for the next five years. After that, the company is expected to perform consistent with macroeconomic benchmarks for growth like US GDP or US inflation, which are typically expected to be around 3% over the long term.

There are two reasons that the long-term growth rate is significant: 1) The appraiser has determined that there is no reason to continue with a detailed year-by-year analysis of cash flow, and 2) The long-term growth rate can have a significant effect on the overall value conclusion of this method.

So, if the appraiser feels that a detailed year-by-year cash flow analysis is no longer necessary, then how does he or she determine what long-term growth rate to use? Well, you probably guessed it: Professional Judgment.

In this case, professional judgment is used to determine how much growth a company can sustain over the long term. The appraiser should take into account rates of inflation and Gross Domestic Product (“GDP”). Inflation is simply the rate at which prices for goods and services increase each year. So, unless the company being appraised cannot raise its prices, then the appraiser should assume that the company can grow by at least the anticipated rate of inflation.

GDP is also a good indicator. If GDP growth is anticipated to be 3% over the long term, then the appraiser should figure that half of the companies in the US will grow by less than 3% and the other half by more than 3%. If the company being appraised has shown an ability to continue reinventing itself, as shown in Figure 5, then maybe the company should be assumed to grow at a rate greater than 3%.

Keep in mind, however, that a significantly higher long term growth rate implies that either the company is still in super growth phase, which would require an extension of the year-by-year discreet projection period, or there’s an assumption that new assets will be added that are simply unknown today. In the latter case, the appraiser makes the error of projecting cash flow from assets that don’t yet exist.

(b) Assessing the Required Rate of Return

After projecting the cash flow, the next step is to determine the appropriate rate of return that an investor would require in order to invest in the company (or buy it). There will be more discussion on this in Step 3: Understand the Science; but for now, know that the basics of the Income Approach are to project cash flow, as described above, and then convert the projected cash flow into an investment amount (i.e., value) that a buyer would pay today to receive that cash flow over time.

The way to “convert” the projected cash flow into value is through a required rate of return, more commonly referred to as a ‘discount rate.’ There are essentially three ways to determine an appropriate discount rate for a company. These three ways depend on the type of company, whether it’s: 1) a start-up company, 2) a company that doesn’t have comparable publicly-traded benchmark companies (e.g., a dental practice or an accounting firm), and 3) a company that can be benchmarked to publicly traded companies (or is publicly traded itself).

Start-up companies, if the appraiser chooses to use an Income Approach at all, are very difficult to benchmark. So, appraisers will generally use evidence from venture capital investments made in similarly risky companies. There’s not much to this analysis; and the selection of a discount rate is nearly all professional judgment. This is why using an Income Approach for a start-up company without benchmark comparable companies is very difficult.

The second type of company is mature but doesn’t have any comparable publicly-traded companies. These companies are also difficult to benchmark; but there are tons of research reports done by PhD’s in Finance and Economics that help appraisers estimate a discount rate for these types of companies. Using these research reports to estimate a discount rate is referred to as “The Build-up Approach” because the discount rate consists of several components from the PhD research that “builds-up” on each other until you get an appropriate discount rate.

The third type of company, those that are comparable to other publicly-traded companies, has specific benchmark data that can be used to determine an appropriate discount rate. Though much of the analysis is science rather than professional judgment, the appraiser should at least use enough professional judgment to know to use publicly-traded comparable companies when available to determine a discount rate.

Now, whether the build-up approach or the publicly-traded comparable companies is used, there is one major area of professional judgment known as the company Specific Risk Premium (aka, the ‘SRP’ or ‘alpha’ in math-speak). The SRP is applied in the build-up approach and the publicly-traded companies approach because the appraiser believes that either the PhD research data or the comparable public company data was not a completely adequate benchmark. This determination is perfectly reasonable in many cases; but the adjustment made is nearly always subjective. Since the SRP can have a significant impact on the overall value conclusion, the appraiser should be prepared to explain the logic behind the SRP used in the discount rate.

2. Market Approach Methods

Recall the definition of the Market Approach: a perspective of value that considers the implied value of an asset or a business based on the prices paid for comparable assets or businesses. There are essentially two different market approach methods: the Comparable Transactions Method and the Comparable Publicly-Traded Companies Method. The key area of professional judgment used in these two methods is in drawing comparability between companies that have been sold and the company being appraised.

(a) Analyzing Comparable Transactions

The Comparable Transactions Method looks at actual purchases of companies similar to the one being valued. This is no different than a home appraisal where the appraiser looks at ‘comparable sales,’ or ‘comps’ as they’re called, of homes in the neighborhood to determine what a particular home is worth. In the case of a business valuation, the appraiser looks at ‘comparable sales’ of companies to determine what a particular company is worth.

But, just like every home is different, every company is different too. A particular home that sold last month might have had a newly renovated kitchen; whereas the home being appraised has its original, 25-year-old kitchen. The appraiser would need to account for this. Likewise, a company being appraised might have higher profitability than the comps; or it might have spent $6 million to replace all of its manufacturing equipment last year. The appraiser needs to account for this difference as well.

This is where significant professional judgment plays a role in business valuations. For most companies, the appraiser should be able to collect enough data on actual sales to make a determination as to which sold companies are most comparable. Though data about new equipment or similar purchases is difficult to acquire, the appraiser should be able to perform basic statistical analysis (i.e., linear regression analysis) to determine any relevant correlations between profitability or other metrics.

For example, a typical correlation that is usually found is that Price-to-Revenue multiples are usually impacted by company profitability, meaning that the more profitable a particular company was when it was sold, the higher the Price-to-Revenue multiple it received. Figure 7 below illustrates this exact case. Each diamond in the grid represents a company that sold over the past five years. Each sold company’s diamond is placed on the grid where its profit margin on the X-axis meets its Price-to-Revenue multiple on the Y-axis.

The noticeable trend that you see in the graph below is as expected: the more profitable the company (moving from left to right on the X axis), the higher its Price-to-Revenue multiple (moving from low to high on the Y axis). So, the appraiser should select a Price-to-Revenue multiple based on the profit margin of the company being appraised.

This might seem to be a bit more science than professional judgment; but the key here is that professional judgment applies to which methods get used and how each method is ultimately applied. The analysis shown below in Figure 7 is one element of support for the appraiser’s judgment of which Price-to-Revenue multiple most appropriately applies to the subject company. So, when you’re validating a business valuation, you should look for this kind of support for the professional judgment used by the appraiser.

Figure 7: Profitability-Adjusted Price-to-Revenue Multiple Analysis

Profitability Adjustments for Price to Revenue Multiples in the Market Approach

(b) Analyzing Comparable Publicly-Traded Companies

While the Comparable Transactions Method looks at actual sales of companies, the Comparable Publicly-Traded Companies Method relies on stock prices of comparable publicly-traded companies to determine an implied value of the company being appraised. The professional judgment used in this method consists of selecting public companies that are comparable and then bench-marking those companies to the company being appraised.

The good news for the appraiser is there is a large amount of information available on publicly-traded companies due to their requirements to file annual reports with the US Securities and Exchange Commission. While an appraiser typically benefits from having lots of information, there still remains a bit of difficulty in drawing comparability between larger publicly-traded companies and the typically smaller, privately-owned company being appraised. The next two sections will address how to validate the appraiser’s judgment as it relates to analyzing comparable publicly-traded companies.

Assessing Comparability to Publicly-Traded Companies

Professional judgment abounds in selecting which publicly-traded companies are comparable to the company being appraised. Obviously, the appraiser will want to identify all companies in the same industry or even the same industry sector if possible. But, publicly-traded companies tend to be dynamic organizations that, while they might do roughly the same thing as the company being appraised, they often have other means of competing or are in more than one industry sector. For this reason, the appraiser might eliminate some companies from the analysis because their scope of products or services makes them not comparable. Other reasons to exclude a seemingly comparable company might be an overabundance of debt that weighs down a company’s stock price or a pending lawsuit that has investors leery of purchasing the company’s stock.

Typically, an appraiser should identify the full universe of comparable companies and then articulate the logic used to eliminate certain companies as benchmarks. Ultimately, the appraiser will need to identify a core group of companies that are most comparable and then rely more heavily on the stock prices of these companies in the analysis.

Benchmarking using size, growth, and profitability

Once the list of comparable companies is set, there still remains a challenge in drawing comparability between public companies and the company being appraised. There are three commonly-used adjustments when an appraiser does such benchmarking: adjustments for size, growth, and profitability. So, if benchmark Company A has a Price-to-Revenue multiple of 3.0X, that multiple needs be adjusted to account for differences in size, growth, and profitability between Company A and the company being appraised. So, if the company being appraised is smaller, has less growth prospects, and is less profitable, then a Price-to-Revenue multiple of 1.5X might be more reasonable.

Adjusting for these three factors makes sense. If you were analyzing two stocks and trying to decide which one to buy, you would probably want to buy the stock of the company that is larger, has greater growth prospects, and has higher profitability. The larger company, all things equal, is less risky. After all, it has likely been around longer; it has better customer relationships; and it has better economies of scale. Similarly, you would probably seek to buy the stock of the company with higher growth prospects and higher profitability because these both translate into higher investment returns for you.

So, common sense says that each of these are critical. The question now is how does an appraiser address these issues quantitatively? An appraiser can’t just conclude that Company X is better than Company Y. She needs to quantify the impact that these factors have on the value of the company being appraised. Not considering these three adjustments makes the whole method useless. It would be similar to a home appraiser ignoring the location or the square footage of a house!

The adjustments also need to be made in a logical pattern across all benchmark companies. In other words, the adjustments can’t be randomly applied; each adjustment needs to make sense relative to each other adjustment. For example, if two benchmark companies have a profit margin of 30% and the company being appraised has a profit margin of 15%, then the downward adjustment applied for profitability should be identical for both benchmark companies. Applying these adjustments randomly leads an appraiser to direct a valuation method toward a certain value conclusion.

The last area of validation is to look for quantification of the adjustments. Significant scientific data exists on size premiums for stock returns; so, the appraiser should be able to quantify a size adjustment. The same can be said for growth rates. They are used in developing capitalization rates, so they should be used to determine differences between a benchmark company and a company being appraised. Lastly, we’ve already discussed adjustments for profitability as shown in Figure 7. Assuming that there are plenty of comparable publicly-traded companies, a similar analysis can be used to quantify profitability adjustments.

3. Cost Approach Methods

Recall the definition of the Cost Approach: a perspective of value that considers the cost of reproducing an asset or business of similar characteristics. Start-up companies and companies in decline are typical candidates for the cost approach, as they might have a collection of assets but they don’t really have an ongoing business with significant customer contracts or goodwill.

But be careful; the valuation of such assets goes far beyond what you might be able to sell them for on e-bay. Or, in the case of intangible assets such as internally-developed software, the value considerations could go well beyond the cost of recreating them.

The valuation principle generally applied in the Cost Approach is called Replacement Cost New Less Depreciation (“RCNLD”). This essentially means that the value of individual assets is based on what you would spend to buy a new version of that asset. The price would then be adjusted downward to account for the fact that the asset being valued doesn’t have the new bells and whistles; it might not be as functional as it once was; and, it has a diminished useful life relative to the new version. These are all factors of “Depreciation” in the RCNLD calculation and they must be accounted for in order to have a credible valuation conclusion.

The other concept to consider is what’s called “standard of value” which represents the hypothetical sale conditions for the assets. As you might imagine, the sale scenario of a declining company might very well be different than the sale scenario of a start-up technology company. The sale of the technology company might assume that the business would continue operating and the sale of the declining company might assume a fire sale of assets or an orderly liquidation in bankruptcy. These scenarios matter; and the appraiser must identify which valuation standard is used and what elements of depreciation exist in order to produce a credible valuation opinion of the assets.

The Art of Reconciling Valuation Methods

Now that the professional judgment has been applied in determining which are the most appropriate valuation methods, the next step is to reconcile all of the individual valuation conclusions into one overall opinion of value. Simply taking the average of all methods is usually not done unless there is sound reason to believe that all methods have equal credibility and all assumptions are adequately supported.

But this would rarely happen. Just like there are reasons why some methods might apply and some may not, the appraiser will follow similar logic here to determine which methods are the best indicators of value of the company. Methods that have adequate bench-marking data would be weighted higher in establishing the overall value opinion. So, look for the appraiser to articulate the professional judgment and logic used to conclude the overall value opinion.

[1] There is another common use of the term ‘valuation standard.’ Valuation standards often refer to the Professional Code of Ethics and the Uniform Standards of Professional Appraisal Practice, which is more akin to quality control standards for valuation professionals to follow.

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