In Step 3 of Validating a Business Valuation, you’ll learn:
- The core formula used in business valuation
- The five key metrics that need validation
- How to interpret the economics implied by the five key metrics
- How to validate a seller’s asking price
Why this is important to you:
Math doesn’t lie. This section will help you test the overall value conclusion using simple math.
Now that you know how to discern a professionally-prepared valuation from a hack job; and you know how to validate an appraiser’s professional judgment; the next step is to validate the science behind a business valuation. But remember, as with Steps 1 and 2, this section will demonstrate how to test the validity of valuation science, not how to become a valuation scientist!
The Core Formula Used in Business Valuation
You’ll be glad to know that any business valuation can be validated with one simple math formula – used many different ways – but still only one formula. The Gordon Growth Formula (“GGF”) is the backbone of any business valuation of a mature company in a competitive market. The GGF still does apply to growth businesses and start-up businesses; but there’s a bit more professional judgment in those situations because of the variances in growth as discussed in the Step 2 section on Projecting Cash Flow.
Remember that the growth rate needs to be constant in the GGF. So, this discussion will first focus on validating business valuations of companies with constant growth, which are typically very mature companies. Once the principles are understood, the next section will address the more common situation of a company with ‘super growth’ over the discreet projection period. If the business valuation you are validating shows a ‘super-growth’ period during the projection, you’ll need to take this into account in order to properly validate the results.
From this equation comes an enormous amount of insight. The GGF is THE FORMULA for business valuations. The appraiser might use many different supporting calculations in preparing the business valuation; but the GGF underlies the final valuation conclusion. So, if you want to validate a business valuation, you’ll need to understand all of the variables in the GGF and test each one for validity. Even though the appraiser has likely already calculated the cash flow (CF), the discount rate (k), and the long-term growth rate (g) in the Income Approach, you want to understand these variables in the context of the other methods and the overall value conclusion. These next few pages will show you how to do this.
But first, Figure 2 below shows an example of how the GGF works.
This formula has two caveats: as mentioned before, the long-term growth rate (g) is a constant rate. To the extent that the company has a ‘super growth’ period in its cash flow projections (See Step 2 in the section on Projecting Cash Flow), the growth figure will need to be adjusted upward. The second caveat is that the cash flow, rate of return, and growth rate are all assumed to be after tax. ‘After tax’ means that:
- the cash flow figure is after-tax cash flow - Not that there’s any other kind of cash flow; but don’t be tempted to replace this figure with a profit figure like Earnings Before Interest Taxes Depreciation and Amortization (‘EBITDA’) or Earnings Before Interest and Taxes (‘EBIT’). These are, as clearly stated, before tax calculations.
- the rate of return is the after-tax rate of return – What? Is this a real thing?? Yes, the rate of return needs to be the rate of return an investor expects to receive after the company pays its taxes.
- the growth rate needs to be the growth assumed for after-tax cash flow - not revenue growth, not profit growth, not customer growth, not growth in units sold, etc., etc.
The example calculation above shows you how the math is derived from the GGF. But, instead of showing the algebra needed to solve for each variable, below are the calculations. Depending on which variables you know, you can always solve for the others. Remember, calculate what’s inside the parenthesis first, then move outside the parenthesis for the rest of the calculation. For example, when solving for growth (g) using the formula below, divide cash flow by the value first, then subtract the rate of return (k), and then multiply all of that by negative 1.
The 5 Key Metrics that Need Validation
Now, how do you apply all of these fancy formulas? Well, it’s a bit easier than you might think. The example in Figure 11 below shows the critical metrics from each valuation method and the overall value conclusion. Creating a similar grid is all you need to use science (or simple math) to validate your business valuation. Some of the metrics below are provided in the valuation report and some can be easily calculated.
To have the 5 Key Metrics calculated for you, click the link below to access a Microsoft Excel spreadsheet called “Business Valuation Conclusion Metrics.” You can simply input certain parameters from your valuation report and the calculations will be made for you automatically. The example used in this section is also shown in the spreadsheet. Click here: Business Valuation Conclusion Metrics
The five key metrics are the capitalization rate, the rate of return, the constant growth rate, Price-to-Revenue multiple, and Price-to-Earnings Multiple. After you’ve populated the grid shown below, the next step is to interpret each metric so you can validate the overall value conclusion.
If you’re going to use the Microsoft Excel spreadsheet from Business Valuation Conclusion Metrics, you can skip to the next section below. Otherwise, what follows are the details for each calculation.
Calculating the Metrics in the Gordon Growth Formula (GGF) Grid
All of the metrics listed in the above grid with a ‘p’ should be provided in the valuation report. Those highlighted in gray and marked with a ‘c’ need to be calculated. So, the first step is to hunt through the valuation report and populate all of the metrics that are provided and then calculate the rest.
The long-term growth (g) is the only tricky metric. This example assumes that year-over-year cash flow growth is constant because the business is mature and growth is stable. In other words, this example assumes that the expected rate of growth is constant each year from the effective date of the valuation into perpetuity. Creating this table when there is a ‘super-growth’ projection period is a bit more complicated and will be explained later in this section. So, for now, assume that the long-term growth rate is constant and is the same as the long-term growth rate used in the Discounted Cash Flow Method. In this example, a typical 3% long-term growth rate is used.
Calculations for the Discounted Cash Flow Method
The three calculations needed for the Discounted Cash Flow method are very straight-forward. For the capitalization rate (k-g), simply subtract the long-term growth (g) provided in the report from the Rate of Return (k) provided in the report (13% - 3% = 10%). For the Price-to-Revenue and Price-to-Earnings Multiples, simply divide the value (V0) by the prior year revenue and earnings, respectively. ‘Earnings’ is typically a profit figure called Earnings Before Interest Taxes Depreciation and Amortization (aka, ‘EBITDA’). The Price-to-Revenue multiple is $3,000,000 value / $1,200,000 revenue = 2.5X. The multiple is always written as the number with an ‘X’ next to it, which stands for ‘times,’ as in “the value is 2.5 times revenue.” The Price-to Earnings multiple is $3,000,000 Value / $500,000 Earnings = 6.0X.
Calculations for both Market Approach Methods
First, calculate the capitalization rate, which is simply the year 1 cash flow divided by the value. In the Comparable Transactions Method example, the calculation is $300,000 divided by $5,000,000, which results in a cap rate of 6.0%. For the Comparable Publicly-Traded Companies Method, the result is $300,000 divided by $5,500,000, which equals a cap rate of 5.5%
Once you have the cap rate, you can easily figure out the rate of return. Cap rate = rate of return minus growth; so, using a little algebra, the Cap Rate + growth = the rate of return. For the Comparable Transactions Method, the rate of return is 6% + 3% = 9%; and for the Comparable Publicly-Traded Companies Method, the rate of return is 5.5% + 3% = 8.5%.
Calculations for the Overall Value Conclusion
The calculations for the Overall Value Conclusion are just as easy. First, calculate the capitalization rate, which is simply the Year 1 Cash Flow divided by the Value. The Year 1 Cash Flow is the same at $300,000; so, divide $300,000 by the overall value conclusion of $4,800,000, which results in an overall cap rate of 6.3%.
And once you have the cap rate, you can easily figure out the rate of return. Cap rate = rate of return minus growth; so, Cap Rate + growth = the rate of return. Assuming growth of 3%, the rate of return implied in the overall value conclusion is 6.3% + 3% = 9.3%.
For the Price-to-Revenue and Price-to-Earnings Multiples, simply divide the value (V0) by the prior year revenue and earnings, respectively. In this case, the ‘price’ is the Value (V0), so $4,800,000 divided by revenue of $1,200,000 equals 4.0X and $4,800,000 divided by earnings of $500,000 equals 9.6X.
Interpret the Economics Implied by the 5 Key Metrics
Now that you’ve populated all of the metrics provided in the valuation report and calculated all of the others, you have probably figured out that validating the overall conclusion will be centered on the rate of return. The growth rate is significant as well; but for purposes of simplicity, this section assumes the constant and typical long-term growth rate of 3%. The next section will discuss how to handle companies projected to have ‘super-growth,’ which is growth during the year-by-year discreet projection period that’s greater than the long-term constant growth.
So, the focus of this discussion is on expected rates of return when annual growth is projected to be constant from day 1 of the projection into perpetuity. Assuming a 3% constant growth rate in the Figure 11 example equates to an overall rate of return (k) of 9.3% (6.3% Cap Rate + 3% Growth Rate = 9.3% Rate of Return). But what does this mean? Is that good or bad? Valid or invalid? This requires an understanding of basic finance and economics to be able to validate your findings.
What follows in Figure 5 is a helpful guide. Figure 5 is not based on an in-depth research study; but it is a generally accurate rule of thumb for the spectrum of investment returns that a reasonable investor would expect given the associated risk. Keep in mind that these rules of thumb are for comparing the RESULTS of the valuation; they do not DETERMINE the valuation. If you need a formal research report to corroborate the guidelines shown below, you can do some quick internet searches and likely find more than you’d care to read.
Also, keep in mind that rates of return used in business valuations are ‘expected returns,’ meaning that they are forward-looking. They are not 5-year or 10-year historical returns. So, if a ‘blue chip’ stock like IBM has returned 12% over the past 10 years and negative 7% over the past 5 years, the ‘blue chip’ stock return that’s expected over a long- term investment horizon, which is the investment horizon assumed for the company being valued, is still roughly 10%.
In the example case from Figure 4, the rate of return used in the Discounted Cash Flow method was 13% yet the overall value conclusion implies a rate of return of 9.3%. Based on the rules of thumb shown in Figure 5 above, this is a significant gap. The 13% rate of return used in the Discounted Cash Flow method was likely derived from research studies and from rates of return of the comparable benchmark companies. So, to conclude an implied overall rate of return of 9.3% says that the appraiser: 1) did not have confidence in the rate of return calculation used in the Discounted Cash Flow Method, 2) did a poor job of bench-marking the comparable transactions and publicly-traded companies, or 3) was able to identify an extraordinary factor or factors that indicate that a higher value and lower overall rate of return is reasonable.
After all, the 9.3% implied overall rate of return puts the company in the category of ‘blue chip’ stocks. There are very few companies that can be called ‘blue chip.’ To say that a company deemed to have a 13% discount rate in the Income Approach has an overall value that implies a rate of return at the low-end of the blue-chip spectrum (9.3% compared to 9-11% range for blue chip stocks) would require significant explanation.
So, what’s the impact? The lower the rate of return, the higher the value; and the corollary is the higher the rate of return, the lower the value. In this case, the lower-than-expected overall rate of return implies that the overall value conclusion is possibly overstated. But by how much? Well, this situation just points out an area that needs further validation: Is the discount rate calculation in the DCF unreliable or was the bench-marking analysis of the comparable transactions and public companies inconclusive? You don’t really know. You have to pose these questions to the appraiser as part of your validation exercise.
However, you can’t conclude that the valuation is invalid just because these numbers fall into a less-than-perfect range; you just need to dig deeper to understand the appraiser’s judgment. One plausible explanation is that the appraiser has identified actual sales of company stock, like a private equity investment, where the price paid was consistent with the overall value conclusion. If there is a good reason to believe that a second private equity investor would pay the same price, then the higher value and corresponding lower rate of return should be considered. Technically, the price contemplated by the second private equity firm implies that the firm would project greater growth for the company than the appraiser did.
Keep in mind also that each method stands on its own merits (as discussed in Step 1: Dispel the Magic). The appraiser should never steer a valuation method toward the conclusion of another method. In the absence of an extraordinary factor like the private equity firm stock purchase, the appraiser simply needs to perform a deeper analysis of the discount rate. This means possibly preparing a second analysis that could corroborate the first one, or dig deeper into the nuanced differences between the company being valued and the benchmark comparable companies. But under no circumstances should the appraiser just tweak an analysis until all methods converge and these disparities disappear. Doing so would bring your validation exercise back to Step 1 of this book: Dispel the Magic!
Growth Rates (g) that are NOT Constant
The more likely scenario when validating a business valuation is that the Income Approach will show ‘super-growth’ during the year-by-year discreet projection period and then a long-term constant growth rate into perpetuity, as illustrated below in Figure 6. When this is the case, you cannot simply rely on the long-term growth rate to perform the calculations above!
As you can see, the overall expected growth rate for the company shown in Figure 6 must be greater than 3%, as the first five years are all greater than 3%. Not incorporating the growth from the discreet projection period could greatly underestimate the expected growth of the business and make the Gordon Growth Formula variable calculations inaccurate. Without an accurate constant growth rate, you’ll end up with the capitalization rate (k-g) rather than just the rate of return (k) that you’ll need to validate the results. To use Figure 5: Meaning Behind the Expected Rate of Return, you’ll need to isolate the rate of return (k) from growth (g).
The easiest way to calculate the implied constant growth rate for companies with a ‘super growth’ discreet projection period is to use the Microsoft Excel spreadsheet discussed earlier. It has all the calculations from this section already created. You can just plug in the numbers you have from your valuation report into Tab 2: 5 Key Metrics to Validate and see the results and interpretations. Click here if you didn't before: Business Valuation Conclusion Metrics
If you’re more mathematically inclined, you can calculate it yourself using the formula below in Figure 7. This calculation results in an estimate of the implied constant growth rate that should suffice for the purpose of validation. Just work from the inside doing calculations inside each parenthesis first and you’ll get there. The ^ symbol signifies an exponent, which stands for “raised to the power of.” You don’t need to remember the “order of operations” from junior high math class; just calculate what’s in parenthesis from inside to outside and you’ll be fine. The sample inputs can be found in Figure 8.
Figure 7 shows the cash flow projected for the 5-year super growth period assuming super growth each year. Year 1 is consistent with the example in Figure 4 at $300,000. Each year thereafter grows by the rate shown for each year of the discreet projection period. The Cash Flow in Year 0 should be provided in your valuation report; but if it’s not, the calculation is simple: $300,000/(1+15%).
The implied constant growth rate, if the formula above is used correctly, should be 4.7%. Using this growth rate, the new Business Valuation Conclusion Metrics are as follows:
Note that the Value Conclusion (V0) for the Discounted Cash Flow Method is greater in Figure 9 than it was in Figure 4. Obviously, this company has much greater growth prospects than the example company in Figure 4 (4.7% growth assumed in Figure 9 versus the 3% growth assumed in Figure 4).
If all the other value conclusions were the same, including the overall conclusion, you can see that the metrics fall more in line. The 11% rate of return (k) implied by the overall value conclusion is much closer to the 13% rate of return calculated by the appraiser for the Discounted Cash Flow method. However, this should not be interpreted to mean that the appraiser should just tweak growth up or down to get the 5 Key Metrics to line up!
Growth Rate Metrics
An appraiser hearing your concerns about the low 9.3% rate of return implied by the overall value conclusion in Figure 4 could simply keep raising the projected growth until the rate of return looks reasonable. After all, growth is subjective, right? Well, not so much.
Just like there is a range of reasonableness for the expected rate of return (as shown in Figure 5), there is a similar range for the implied constant growth rate. See Figure 10: Meaning behind Implied Constant Growth Rates below.
Keep in mind, however, that start-up companies and growth stage companies are outliers here. Such companies might have extraordinarily-high growth prospects for quite some time, making the Income Approach more about professional judgment than science. For mature companies, however, the following growth spectrum adds support to the reasonable limits.
Validating a Seller’s Asking Price
A broker who’s been hired to sell a company will typically supply you with an asking price rather than a valuation. As an advocate for the seller, the broker will put together an ‘offering memorandum’ that will include the asking price and/or the Price-to-Revenue multiple the seller expects to receive. What follows is the information you’re likely to receive from the broker.
Below are the calculations you’ll need to analyze the asking price in the same way that you analyze the conclusion of a business valuation. However, this calculation is a bit more imprecise because the broker likely won’t provide you with a discounted cash flow analysis or a comparable transactions analysis.
The implied constant growth rate will likely be difficult to calculate. Review the offering memorandum carefully to find clues as to what the growth expectations are. As you might imagine, brokers might embellish a bit on the growth prospects of the company, which will make the implied rate of return seem reasonable. When this is the case, you should refer to Figure 10 above for the meaning behind Implied Constant Growth Rates.
But even if you find that the broker’s asking price is unreasonable or completely invalid, the broker is unlikely to make any changes. He isn’t interested in achieving a credible value; he’s only interested in finding a buyer that will pay as close to the asking price as possible. So, your best bet is to mitigate the high asking price by negotiating favorable terms or wait until the seller has no other offers and is willing to entertain yours.