The Gordon Growth Model

Variations of the Gordon Growth model are used to estimate a value of the future earnings stream of a company. It is the basis of many calculations in the income methods. It is the direct basis for the capitalization of earnings model and in estimating terminal value under the discounted cash flow model. A brief explanation follows.

The Gordon Growth model, also known as the dividend discount model (DDM), calculates the intrinsic value of a company's stock price. The stock value is calculated as the present value of all of the stocks' future dividends.

Generalizing this to fit all business sales, the formula becomes

For small businesses usually (but not always) instead of the dividend or distribution amount being used, the theoretical amount available for distribution (the distributable amount) is used. This figure is usually either EBITDA or EBIT or after-tax cash flow (essentially after-tax earnings plus depreciation and amortization) or somewhat improperly SDE.

This raises the issue of: how is reinvestment reflected in the model? The model assumes all reinvestment is at the perpetuity rate. In reality, as money is distributed, it often is spent or placed in safer investments that do not produce the same rate. This is an issue with the model as all models have problems. Again, professional judgment involves selecting the most useful models for our situation.

The Gordon Growth model accounts for the value of free cash flows that continue growing at an assumed constant rate in perpetuity.

Also, the projected free cash flow in the first year beyond the historic data (N+1) is used. This value is divided by the discount rate minus the assumed perpetuity growth rate:

• T₀ Value of future cash flows (Price)
• D₀ Cash flows estimated for the next period of time
• k    Discount rate
• g    Growth rate

See

• The cash flow (CF) for the year after the historic data is adjusted to grow at the estimated growth rate.
• The discount rate for the last year of the discrete cash flows then has the growth rate subtracted from it to estimate the capitalization rate.
• CF is then divided by the capitalization rate to find the value in perpetuity

Using this formula as the basis for estimating a value requires determining a cash flow, a discount rate, and a growth rate. Details on these matters and determining forecast cash flows and related issues under the income method are covered in the rest of this chapter.

Tax Affecting

In theory, buildup methods use after-tax cash flows because they are based on public companies which post after-tax earnings. When valuing a pass-through entity, valuators “tax affect” or make tax rate-based adjustments to maintain an equivalent cash flow basis (taxable to taxable) for the comparison.

Therefore, most valuators tax affect when using the income method to value very small tax pass-through entities.⁹ They believe it is the best alignment of the subject company to comparable data. Many small businesses are pass-through entities avoiding the double taxation of C corporations. These pass-through entities historically had a lower total tax to the investor at the investor level than non-pass-through entities. There is some level of debate about the true extent of this pass-through tax advantage, particularly with the passage of the Tax Cuts and Jobs Act (TCJA). Even prior to the TCJA, the tax rate of public entities in different industries was rarely the posted 35% average rate stated for companies with $10 million and above of taxable income.

TCJA may have solved most of the big differences in taxes to the shareholder between C corporations and pass-through entities at the Federal level but in high tax states, there still appears to be advantages for pass-through entities (PTEs) overall. Finally, it is still unclear what Code Section 199A Qualified Business Income Deduction (QBI) really means in the application for taxation of pass-through entity owners.¹⁰ More important, since it can depend on other income streams to the owner, how can we really make valid determinations as to what a buyer's tax benefits will be in our estimates?

There is a great debate on these topics at the time of writing of this book. It is beyond this book to go down every rabbit hole. Instead a reasonable methodology for use with small and very small businesses is going to be provided. Certainly, other methodologies may be used and there will be cases where this methodology is inappropriate but this should serve as a guide to work through these issues.

Factors to consider:

• Is this a valuation for the Internal Revenue Service (IRS)?
• Is the valuation standard fair value, investment value, or fair market value?
• Should state taxes be considered and deducted before the IRS rate?
• Do we have a reasonably reliable disposition date of the interests being valued?

IRS

The Tax Court has consistently found that when using the fair market value standard for PTEs, the cash flows should not be tax affected.¹¹ However, two recent cases have to give the IRS pause. These are the Estate of Aaron Jones¹² and Kress vs. United States.¹³ The IRS lost in both of these cases. What we don't know as of the writing of this book is if the IRS will acquiesce (i.e., accept them as law) with them or not. From a practical perspective it is unclear how the IRS will respond.

The historic IRS position has been that the future taxes of a hypothetical buyer are unknown. They cannot be known because different buyers will have different internal tax consequences depending on state taxes, loss carryforwards, whether the entity will remain private or become part of a public entity, etc. While this fails to deal with the issue of using two different income streams on different sides of the valuation equation, when valuing PTEs, it has been the IRS and Tax Court position at least until the Estate of Aaron Jones¹⁴ case. For this reason, many advisors take heed to this and use non-tax-adjusted cash flows for estate or gift tax type purposes.¹⁵

Issues with Tax Affecting

Similar to past IRS arguments, under fair market value, it is hard to know exactly what a buyer's tax status will be and if tax benefits of the seller will accrue to a buyer.¹⁶ This is made even more complex under the TCJA where a 20% qualified business income (QBI) deduction may be applied to a pass-through taxed business in certain industries that meet other income/wage limitations of the company and shareholders.

Qualification for these tax benefits are so complex as to almost be beyond many small and very small business tax advisors' ability to estimate future taxes, much less our ability as valuators to fully comprehend or adjust.

Below are some problems, not with the concept of tax adjusting, which conceptually is an easy “yes” we should, but by how much to adjust.

• When might the tax rates be changed again?
• The normalization process for calculating EBIT, EBITDA, and after-tax cash flows changes the tax status of many owner benefits. Namely, they were expenses by the company and in some cases not recognized by the beneficiary, i.e., some auto expenses. After being recast, they are now taxed. This can be a substantial portion of small business cash flows in some situations.
• The interaction of 199A of the tax code with pass-through entities is still being digested by the tax community, making it difficult to compare. With this provision it may always be difficult to create cross-industry models. In fact, some buyers may lose QBI deductions for buying certain types of businesses. (For instance, investment banking and valuation have often been performed by the same companies. Investment banking qualifies for QBI but business valuation does not and could theoretically cause a disqualification for the overall entity.)
• The 199A provisions sunset end of 2025 meaning the value of the tax benefit drops every year.
• These results under TCJA may also vary with the income of the owner and possibly the spouse, if married and filing joint taxes. This is a much more pertinent issue with very small businesses. How do we know or account for that?
• Strictly for very small businesses: The inability to amortize the purchase price of C corporations that tend to be stock sales raises the cash flow necessary to successfully buy a business. This is a barrier to sale. Most very small business sales are leveraged buy-outs using SBA loans. If the purchase price cannot be amortized, all of the principal payments have to be “after-tax” dollars. While a 10-year loan does not line up perfectly with 15-year amortization, it does make a big difference. (Plot the cash flows yourself.) This can be a 15% +/- “penalty” or gross up in terms of earnings required to really make the payments.
• In some cases, this is offset by personal goodwill. But there is still likely to be a large portion of un-amortizable corporate purchase price. Fortunately with small and very small businesses, personal goodwill does tend to exist.
• Most industries do not pay the “stated” tax rate. How do we really know (or how can we calculate) the tax rate being paid in the underlying public company data? Industry adjustment in the buildup methods is related to beta. Does that really mean we now have an implied industry tax rate in the buildup data?
• High state taxes vs. low state taxes can swing the analysis. Does the fact that the cash flow in Idaho with a 7.4% C corporation tax or Wyoming,¹⁷ the state next door with no corporate income tax, mean pretax earnings are really worth 6–8% more than the adjacent state? How is that passed through in value? How would we prove it even if it is true?
• According to Nancy Fannon,¹⁸ an expert on business valuation and taxation, research indicates that because a portion of the public company investor earnings stream is long-term capital gains and because much of the dividend-issuing stock is owned by investment companies that have different tax rates than individuals, the estimated implied tax rate on stock appreciation is 9% not the 20% capital gains rate. (I assume plus state taxes for high income earners.) Yet another big swing that an analyst may or may not agree with but could be difficult to explain.
• Daniel R. Van Fleet, ASA, another noted expert on taxation and business valuation, concludes because of TCJA, “that there are now three distinct types of business entities from a tax perspective: (1) C corps, (2) PTE service businesses, and (3) PTE nonservice businesses.” He further concludes that C corps experienced the greatest increase in value, non-service PTEs continue to have benefits above C corps, but service PTEs' benefits have largely disappeared¹⁹ as compared to C corporations.
• Using a tax effect calculator, the results vary dramatically with many plausible situations. How do we account for that? See Figure 8.5 on p. 174.

Something that is clear compared to larger companies:

• One thing that does simplify the analysis is that most small and very small companies are either purchased by pass-through entities or the buyer forms a new pass-through entity. It is very rare for a small or very small business to be purchased by a C corp. Therefore, the cash flows and perhaps tax benefits of buyers are likely to be similar to sellers. (Again, beware of service vs. non-service PTEs if that can be determined.)
• Prior to the TCJA, a study of data from Pratt's Stats (at the time, only small private company data was represented) found evidence of a PTE premium WHEN the buyer can take advantage of the pass-through benefits. This premium was estimated to be in the 15–24% range using varying methodologies.²⁰

Some analysts may have clear answers to many of the above questions. Much of it does not appear to be knowable. Therefore, apply reason. Another situation for asking yourself: “Does this make sense?”

Suggested Tax Affecting Method for Small and Very Small Businesses

Based on the situation today, below may be one methodology to use. It is logical and supportable assuming a typical fact pattern. This area is in flux and lacks agreement. Use tax affecting or not according to your best judgment.

The first step is to tax affect the cash flows to the estimated corporate rate:

• Tax affect the found normalized cash flows.
• For guidance to the tax affect amount, assuming you are using an industry adjustment, look at the IRS statistics on corporate taxes by sector.
• Tax affect for the state tax rate. Again, most small businesses' income stream is often derived from one state. If it is derived from multiple states, a composite rate may be used. The first step is to tax affect the cash flows to the estimated corporate rate:²¹

An example of tax affecting to the corporate rate is shown in Figure 8.4.

• More details to think about when applying the above suggested adjustment are shown in https://www.treasury.gov/resource-center/tax-policy/tax-analysis/Documents/Average-Effective-Tax-Rates-2016.pdf
• Here is average tax rates for individuals prior to TCJA: https://www.irs.gov/pub/irs-soi/14insprbultaxrateshares.pdf
• If they are not available or do not appear reasonable for your industry, use 21% for the corporate rate.²²
• State taxes can be difficult, as they vary. (Forty-four states levy a corporate income tax from 2.5% in North Carolina to 12% in Iowa. Four states have a gross receipts tax instead of an income tax. Two states have no corporate income tax or gross receipts tax.)²³ Small and very small businesses tend to be in one state and pay that state's tax. In addition, some larger cities have their own taxes so if that is material, they should be added. If multiple state taxes are paid, use a figure based on a reasonable weighting as most taxes are based on profits derived from earnings in the state.²⁴
• This should provide a reasonable adjustment to account for the corporate tax rate used in the buildup methods. Now the valuator must still adjust for differences between the buildup tax level and the pass-through entity tax level.

Adjust the discount rate or capitalization rate for the pass-through tax benefit (if any)

• Use the tax affect calculator below to develop a sense or range of options.
• Understand if the PTE is a service or non-service entity. This may require a detailed look-up. Many of the broad titles are misleading. For instance, it is widely stated that brokerage is under the service category. But real estate brokerage and business brokerage count as non-service. Architecture and engineering are in non-service but accounting is service.
• Non-service entities are likely to justify a reduction in discount or capitalization rate by 2% or 3% (example: 16% – 2% tax benefit = 14% cost of capital), a range based on Van Fleet's and Eric Barr and Peter L. Lohrey's findings.
• Use common sense and judgment.
• For small and very small businesses this may be like trying to perform surgery with a hatchet.

I find this simpler than trying to create a comprehensive formula. We are simply creating apples to apples with the cash flows, then adjusting for assumed advantages due to tax treatments where it appears they exist. This should also be much easier to explain to less sophisticated users and produce a reasonable result.

Use a tax affect calculator, such as the one in Figure 8.5, to approximately estimate the difference in after-tax cash flows between public C corporations and pass-through entities. Be sure to factor in both state and Federal taxes. In addition, remember the research that indicates a 9% paid tax rate on distributed cash flows from the public company earnings.²⁵ Use this with various scenarios to develop a sense of how your situation may play out. (A functional Excel file is on the related website.) Two scenarios are shown using a very simple tax affect converter table in Figure 8.5. Then use your best judgment.

This analysis may change as the current law is better understood, technology allows better tax estimates, and the tax law changes.

Adjusting Cash Flows for Working Capital, Capital Expenditures, and Debt under Capitalization of Earnings

The theory behind the income methods is that we are calculating the distributed cash flow to owners adjusted to compare to a public company and therefore after-tax data. In practice, particularly with the capitalization of earnings method for small businesses, distributable after-tax cash flow is often used. This can be justified because the undistributed cash flow is usually used in the business for expansion. This expansion, assuming it is profitable, increases future earnings power and often produces a higher growth rate than when the company distributes frequently. Remember, small and very small businesses have much less access to affordable capital. Because of their volatility, debt is often much more risky for them. So, retaining a portion of the distributable capital is usually neutral to a positive.

In some cases, if the cash needs during growth are high for two or three years, then phase out, it may be worth preparing a rough forecast as opposed to “jamming” that situation into the capitalization of earnings model. Again, this model works best with fairly consistent cash flows into the future.

Yet, in some circumstances, the best application of the model does include further adjustments to the distributable cash flow. These adjustments fall under the categories: increase or decrease in working capital, capital investment, and debt.

Because the method can only adjust all future cash flows (there is not a mechanism to change the cash flow year by year), the best that can be done when these factors are present is to estimate the current amount and then reasonably adjust the amount to a figure reasonable for use in perpetuity. This requires recognizing that early money and cash flow are much more valuable than later money. Because of the time value of money and the assumption of declining growth rates over time at typical capitalization rates for small and very small businesses, after about 40 years the present value contribution of earnings is near 0. See Figure 8.6.

Therefore, one factor in determining these adjustments for cash flow is how long the use of cash is likely to continue. Principal to pay off a new 10-year note might be shown at 50%, as it is to be allocated out over a reasonably long time early in the life of the projection. Perhaps a few larger mid-term equipment purchases would be allocated at 10% of the payment figure, if they are going to be reduced significantly after two or three years. Of course, if reinvestment is continuous, then the whole amount might be deducted from the cash flow. Again, this is an area for judgment and the capitalization of earnings model is used in these situations on a “best we can do” basis (Figure 8.7).

Increase or Decrease in Working Capital

A simple and usually sufficient formula for estimating working capital is provided in the balance sheet adjustments section in Chapter 11, Accounting Issues with Small and Very Small Businesses. If additional (or less) working capital is going to be required in the future, the question becomes how much working capital change is really required to tie into the assumption of perpetual growth at a fairly low but persistent rate. That figure can be tied to a rate of revenue growth and adjusted for perpetuity.

Finally, if the balance sheet shows excess assets on the valuation date, including excess working capital, this should be added to the final value found.

Capital Investment or Cap X

Some industries require constant capital investment in order to grow or even maintain operations. Trucking, excavation, some manufacturing lines that wear out equipment, and the like. Most small and very small businesses are using computer-based technology to enhance productivity and certainly many industrial machines have computer enhancements. But the cost and complexity of large-scale automated equipment have prevented large-scale implementation in small and very small businesses. Therefore, generally, most small and very small businesses, even in manufacturing, tend to do repairs, refurbishing, or assembly as opposed to heavy manufacturing. These businesses, similar to service providers, tend to have lesser capital investment compared to revenues and other cash flows.

If capital investment is a material factor and a requirement for the company's cash flow to continue, then it should be estimated and put into the cash flow calculation. Note that depreciation, whether accelerated or not, is often not a reasonable assumption for long-term capital investment in most cases. Some businesses have major investments from time to time. These are not always predictable. Estimating the timing of these investments may be difficult.

Increases and Decreases of Debt

Debt can be used for growth capital or to get “cash out” of an investment. If the debt is undertaken with the intent to get cash out of an investment, the discounted cash flow method will be superior, as this is almost always a one-time event, at least in the foreseeable future.

When a company carries material amounts of debt, it is important to align the cash flows with the discount/capitalization rate. Cash flow to equity (after the payment of all debt in the capital structure) can vary dramatically from cash flow to total invested capital. This is magnified by the fact that these are cash flows to perpetuity.

Most small businesses do not carry significant debt indefinitely into the future. When they do, it is often in the form of lines of credit against invoices or inventory, or equipment debt where the equipment is regularly replaced. Some small and very small companies do carry receivables lines and while they are short-term debt in name, the small companies often treat the line as long-term debt. These callable lines are not reduced but a long-term feature of the capital structure and should be treated as long-term debt.

Long-term debt may also be handled by not adjusting the cash flow (assuming EBITDA cash flow is being used) and reducing the value found by the debt similar to the treatment under the market method. This is often a reasonable treatment if the purpose is to determine equity value in a sale. In instances where the standard is more a value to the holder and the debt is continuing, a cash flow adjustment for principal payments may be the best solution to address the debt. Note these variations in treatment can result in large fluctuations in value if not performed thoughtfully.

Next we will review estimating cash flows under the discounted cash flow method. If you wish to continue reviewing the capitalization of earnings method, skip down to “Calculating a Discount or Cap. Rate”.

Review of Forecasts

Below is a checklist that should be used to review projections and forecasts. Clearly the more complex the company and the forecast, the more time and attention that will need to be applied.

• Look at historic data: three to five years.
  • Understand revenue, expense, and profit trends.
  • Understand management structure and product or services.
  • Look for bottlenecks and weaknesses in the soft side of business that could improve or worsen financial results.
  • Has something changed significantly with management, products, production, etc. (for instance, a transportation company went from using their own trucks to subcontracted trucks) during the historic period or going into the projection period?
• If the business is a start-up or if major changes are projected from the past, review all assumptions and the facts or basis for those assumptions.
  • What is the support for the changes?
• Carefully review the future forecasts.
  • Who prepared the forecast?
  • Why was the forecast created?
  • What date was it created?
  • Where did the key facts and assumptions come from?
  • If based on contracts or other existing back-up, can you review the back-up?
  • Is there a history of forecasts?
  • If so, compare forecasts vs. results. Are they reasonably consistent or is the variance consistent?
• Overall forecast review
  • Does it reasonably transition from historic data to forecast?
  • If there is a “hockey stick” effect, do the assumptions and facts and other support make sense? Unfortunately there often is an unsupportable jump or a jump that happens far faster than is likely to do so in real implementation. (Due to the time value of money moving up cash flows a year in the early years can greatly swing value.)
  • Harder to evaluate is a growth rate which is reasonable in one year but not over many years.
    • High growth over five or ten years is difficult for most companies even if the rate is reasonable for one or two years.
• Detailed forecast review. Look at cost of goods sold (COGS) and gross margins, expenses, and profits.
  • If gross margins and profits are increasing, is the increase supportable?
  • If gross margins and profits are falling, where does growth become unprofitable or unsupportable by cash flow or borrowing ability?
  • Where are breakpoints for the fixed costs, such as rent?
  • Are there other major capital investments required?
  • If so, what are the volume or dollar break points?
  • Are those being adequately addressed?
• Again, with long-term growth, can the soft side expenses such as the management team appropriately expand?
  • A $10 million revenue company may get by with a controller-level person but a $20 million revenue company might need both a controller and a true CFO. Is this addressed?
• Many small businesses are primarily labor or skilled labor providers (including many “service” businesses) or perform light assembly with similar types of people. Management is critical particularly if work is performed in multiple, possibly changing, locations.
  • What is the timing of and what is a realistic rate for adding quality managers and skilled employees?
    • This is often the true limiting factor and too often overlooked.
  • What systems, training, and checks are in place to manage the managers as necessary?
    • Many fast-growing service companies in cyclical businesses lose control of work quality and profitability in spurts of growth. Often this shows up in lower margins and warranty costs a year or two later. An example, a demolition contractor tore out two office bathrooms in an office building so they could be remodeled. Only they were on the wrong floor. A very expensive mistake due to quick recent growth and inexperienced middle management. This is not as unusual as you may think.
• While a generality, for smaller companies, less professional-looking forecasts prepared by the owner or key manager often are more likely to be supportable than fancy forecasts prepared by financial consultants who better understand how to “make the numbers look right” and sometimes use industry standard numbers that poorly tie into past financials.
  • Often valuation-adjusting entries will need to be made to the forecast. Document your work.
• Write down all questions and concerns.
  • If possible, have a conversation with the person who produced the forecast to make sure you fully understand assumptions, calculations, and the like.
  • Review with the owner or appropriate manager (or both) all your questions.
  • “Why” is a powerful question. Ask “why” and “how” often. Ask “why” three times in a row. You will be amazed at what you learn.
  • If you cannot have a direct conversation, get questions answered via email.
• Take notes and think about what was said. Write down key thoughts on why it works and/or why it does not work. Review Chapter 13, Assisting the Small Business Buyer or Seller, the section on How to Ask Questions Effectively.
• If the forecast is simple and needs adjustment in some circumstances, the analyst might make the adjustments. Be sure to document the assumptions and adjustments. You likely will want to show the original and the adjusted version in the report.
• If the forecast is complex, adjust either the discount rate (if using very long holding periods) or a likelihood adjustment prior to calculating a discount.
• At some point, the forecast may not be meaningful enough to use at all. This is quite common with small and very small businesses.

Once the forecast is understood, then adjustments need to be made to develop the cash flow that is going to be used in the discounted cash flow calculation.

Often EBITDA or after-tax cash flow is used to show cash flow for small businesses. Because, in theory, this is return to investors (in practice with small businesses, it tends to be potential return to investors), some decisions need to be made to determine what investors could receive. These areas include necessary increases or decreases in working capital, necessary capital investments, and obtaining additional credit and/or paying credit.

If the forecast is well built, it will include these factors. Yet, with small businesses, balance sheets are usually not provided (maybe never provided) and matters related to balance sheets are not considered. Therefore, the valuator may need to add them or, at a minimum, check if it is reasonable that the business could expand at the projected rate with the internal cash flow for working capital and capital investment.

Forecasts and Balance Sheet Accounts

Because balance sheets and other financial checks are often missing, important limitations on growth, or restrictions on distributions while growth is occurring, may be missed.

If possible, a balance sheet should be prepared each year as part of the annual forecasts. Since that possibility is unlikely with small and very small companies, the analyst should perform some level of analysis and, if necessary, make adjustments to the forecast or the discount or cap. rate when necessary. These should be factored into the forecasts each year in the discounted cash flow method.

Working Capital

In many industries where the small company is providing materials or labor to large companies, the subject company will be expected to extend short-term credit in the form of accounts receivable to their client base. The credit collection time term is often 45–60 days with some extending to 90 days. Many engineering firms, industrial manufacturers, construction subcontractors and the like can fall into this category.

Therefore, the first concern is, can the company generate enough cash to support growth? If not, what is a realistic growth rate or can the company borrow the cash, perhaps on a line secured by receivables? Just remember, receivables financing at reasonable rates tends to vanish in many industries during recessions.

A fairly detailed analysis on estimating working capital is shown in the “Working Capital” section of Chapter 11, Accounting Issues with Small and Very Small Businesses. If possible, adjust the forecast (even if a simplified model for your work papers) to understand the growth limits based on working capital needs.

Do finally note, excess assets, including excess working capital, on the balance sheet as of the valuation date should be added to the value found under this method.

Capital Expenditures

Certain industries require heavy capital equipment spending, e.g., excavation and some other construction trades, equipment rental companies, certain manufacturers, even distributors or retailers experiencing rapid growth. Rapid or high investment reduces otherwise distributable cash. With high levels of accelerated depreciation for small companies, a review of tax implications should also be performed if using an after-tax cash flow.

So carefully review the necessary level of capital investment to grow at the rates projected in the forecast. Is a proper cash flow set aside for these purposes? If not, adjust.

Increase or Decrease in Debt

Increasing debt provides cash to use for investment in working capital and capital goods. While somewhat rare with small and very small businesses, increasing debt can also provide cash for distributions.

Small company debt is likely to include personal guarantees, so the credit worthiness of the owner and potential collateral outside the business also may be factors that need to be reviewed, if valuing a high growth company. But, if increasing debt is a viable solution, make sure interest and, where applicable, principal payments are factored into the ongoing cash flows.

One issue with discounted cash flow models that is more pronounced with very short forecasting periods is the effect of working capital, capital investment, and debt that may not have properly stabilized when the forecast ends and the terminal value is calculated.

Generally, debt is not subtracted from the value found when using the discounted cash flow. With small businesses where debt tends to be called and required to be paid at conveyance (again, what is the purpose of the valuation?), there may be times when subtracting the debt from the value found is appropriate.

All valuators can do is use or adjust to reasonable forecasts. It will be very rare when they actually look like the future. But, they can be a reasonable model of a likely outcome.

Sources of Data for Discount and Capitalization Rates

The income method appears simple and when there only was the Ibbotson data available, it was. One needed to simply pull data from one page in a book and maybe look up the industry adjustment in another table that was maybe six pages long. It was simple to apply. Of course, very few people ever read the thick book where the one page was located.

The income method is often used by valuation professionals in litigation because of this apparent simplicity. This simplifies the understanding by a judge and jury and reduces the risk of cross-examination. In addition, since it is the most commonly used method, it clearly meets the judicial test of being a proven method.

The income method was never simple. Read the Valuation Handbook: Guide to Cost of Capital book by Duff & Phelps to begin to understand the complexities and assumptions made in the method. (This book can be downloaded, by chapter, from the Cost of Capital Navigator website at www.dpcostofcapital.com.) Another really curious issue that is rarely raised is the lack of clarity or connection between the history back to 1926 for the Center for Research in Security Prices (CRSP) data used in the Ibbotson calculations by Duff & Phelps and what that really tells us about tomorrow. Duff & Phelps' own methodology is calculated from 1963 onwards.

That being said, commonly used or referenced sources at the time of publication include:

• Duff & Phelps/Ibbotson (Duff & Phelps continue to publish the Ibbotson methodology)
• Duff & Phelps
• BV Data
• Aswath Damodaran
• Pepperdine Cost of Capital

Sources appear to be multiplying, so more likely do exist.

Duff & Phelps Products. Under Duff & Phelps model, a calculated risk-free rate is used to smooth out fluctuations that are thought to come from quantitative easing and other sources. Yet as time passes, low risk-free rates are looking more and more the norm.²⁸ How does this really affect small and very small businesses? Certainly small and very small business interest rates have not dropped commensurate with large company rates. (The typical SBA rate at the date of writing in August, 2019 is prime at 5.25% plus 2.5% or 7.75% while Grade A Corporate bonds are at 3.21%.)²⁹

Duff & Phelps calculate both the forward-looking and the backward-looking cost of capital figures. Again, valuation theory is forward-looking. Historic data is backward-looking, supply side is forward-looking. Forward looking requires more assumptions. Assumptions about the future vs. using the past (which is not the future, yet we rely on the past for trend analysis). We are looking to predict the near-term future. This is a constant tension in business valuation.

Duff & Phelps also calculate the buildup data using the same formulas as the Ibbotson data. This may be the most commonly used set of indicators as it has the advantage of long-term use and familiarity. This data includes the breakdown of Decile 10 which is very important for valuing small and very small businesses.

The Cost of Capital Navigator is a complex product. There are complaints of it being a “black box”; however, Duff & Phelps have now included supplementary data that clarifies how the results are estimated. Yet the buildup method was always this complex. At least now we can look at different components individually and intelligently select the components that most affect the subject company, and, using professional judgment, select the correct discount rate. This judgment will improve as valuators work with the product.

Duff & Phelps products (https://www.duffandphelps.com/learn/cost-of-capital) are still the most widely accepted and used for most cost of capital purposes.

Aswath Damodaran. He calculates forward-looking cost of capital data that is based on current financial market results.³⁰ Dr. Damodaran tends to work with very large capitalization companies and therefore the data may not be as useful for small and very small companies. He also calculates and publishes industry beta information and debt to equity relationships. Very useful for the Cap-M buildup method and the weighted average cost of capital iteration. Every business valuator should visit his website, which has a humble appearance, but is filled with information (http://pages.stern.nyu.edu/∼adamodar/).

BV Resources. BV Resources' product, “Cost of Capital Pro” (https://www.bvresources.com/products/cost-of-capital-professional) allows valuators to select the start year for data instead of assuming 1926. It uses the CRSP data just as Duff & Phelps does. It does not break down Decile 10. This is unfortunate when valuing small and very small businesses as Decile 10 businesses (even the small end of them) are still huge compared to small and very small businesses. The product is claimed to be simpler and transparent but it is based on the CRSP data, which is quite complex when fully researched.

Different start dates produce radically different results. This leads to a host of questions that did not exist when valuators presumed one start date for all data. At this point there does not appear to be an answer to the questions of which year do we choose as a start date and why?

The BV data originally referred the valuator to the Damodaran Beta charts. They now have the charts as part of their tool. Again, these products are changing rapidly as adaptation from books to databases is opening up more options and ways to compare data. Overall, this is a very good product and has gained market share quite rapidly since its release.

Pepperdine Private Capital Markets Report. This is an unscientific survey of what investors and banks are requesting, which can be quite different from what they receive. (As many investors told me when I was raising capital, “We want 25–35% internal rate of return (IRR)³¹ on the forecast but if you really get us 12–15% over three to five years, we will invest again.” I will also note that statement was given at a time (1995) when there were much higher treasury bill rates.) The study is based on asking participants, such as owners, private equity groups, bankers, business brokers, investment bankers, and other groups questions about the cost of capital and the state of the sales and finance market.

The 2018 Pepperdine Survey also revealed that 48% of small and very small business owners think that their cost of equity is less than 10%. That is a very questionable assumption to assert, at least for third party money. For years, these reports were free, but now are available for purchase on Amazon. The Pepperdine Survey is a wonderful reasonableness/sanity test but use with caution.³²

Partnership Profiles. Partnership Profiles' model³³ is used to calculate a cost of capital for holding companies and family limited partnerships, particularly non-marketable minority interests. With the higher estate tax limits, valuations of these interests (particularly small and very small holdings) have become less common and will not be discussed in this book.³⁴

There are other sources of discount rates for various valuations in specialized circumstances. These will rarely be encountered or necessary when valuing small and very small businesses.

Estimating the Growth Rate

The capitalization of earnings method uses past data to estimate a cash flow. In this regard, the cash flow is adjusted and weighted and an estimate selected in a process similar to the market method, plus a few additional steps.

Note there is the real growth rate, that is growth before inflation, and the nominal growth rate is that underlying real growth plus inflation. Valuators should be using the nominal growth rate. Over time, broad economic measures have grown by about 5–6%. Most valuators view this nominal growth rate as the maximum growth rate to use in most situations. Economic and industry growth data along with the specific company data should be reviewed when selecting a growth rate. Again, if possible, check whether the industry growth data is real or nominal growth.

The historic growth rate should be assessed. Of course, with many small and very small businesses, this is going to be erratic. Also it may not be indicative of future growth. A typical small business growth chart is shown in Figure 8.9. For many companies, this cycle extends 20–25 years. Sometimes new management or ownership restarts the cycle.

Part of the assessment of the growth rate is determining where the business is in its lifecycle.⁴² A business in early growth stages will have a very different growth rate than one that is mature or even in decline. Also consider if there is a reason the business will be reinvigorated and, in effect, move down the business lifecycle by things like new ownership or new management. In those cases (depending on the standard and purpose), those circumstances should be factored into growth.

While in theory the growth rate is in perpetuity due to the nature of present value discounting for small and very small businesses, a 5% or 6% growth rate will NOT produce a company that is larger than GE. As was shown in Figure 8.6, after about 40 years, at most growth rates that would be selected by analysts, the present valuing effect will offset any potential growth.⁴³

Certainly, valuators should be judicious with the selected growth rate but when forecasts are not possible, and a company clearly has 5 or 10 years of rapid growth, a higher growth rate may be the best solution. The growth rate is only the growth rate of the earnings or distributable cash flow being used in the valuation. Other measures of growth are not part of this estimate.

Finally, high levels of growth require checking that the working capital, capital investment, and debt adjustments in the cash flow formula are consistent with the growth rate. Growth is often expensive.

Adjusting for Next Period Cash Flow

The capitalization rate is applied to the next year's estimated cash flow. So either the cash flow is grossed up by the growth rate to equal the next year's rate, or the capitalization rate is adjusted by next year's growth rate. The formula to adjust the capitalization rate to this year's cash flow is:

   16% is the capitalization rate

   4% is the estimated growth rate

Mid-Year Capitalization Rate

The assumption in the capitalization of earnings method is that the company's cash flows are valued at year end. For many businesses, an assumption that the cash flows are received evenly over the course of the year may justify using a mid-year convention capitalization rate. This is a matter for professional judgment.

This often applied to professional service businesses. Outside of seasonal businesses due to weather and perhaps Christmas, it would seem many businesses receive their cash flow evenly over the course of the year. For small and very small businesses, the adjustment will result in an increase of value but materially may be small. The formula for the mid-year convention capitalization rate formula is shown in Figure 8.10.

Issues with Weighted Average Cost of Capital

Many small and very small businesses are started with some family money (maybe) and a lot of sweat equity. They often have comparably little long-term debt. However, due to the success of the SBA loan programs, when small businesses sell, they often are very highly leveraged and have high debt. But, operating debt is theoretically what is being measured, not purchase price debt. The ability to separate the two types of long-term debt is not common as they are not identifiable in small business data.

Because debt coverage can vary so much, average debt data is likely almost meaningless. (The average of $100,000.00 and $0.00 is $50,000.00 but it is not useful for predicting anything about the two data points.) Another issue is that credit for most small and very small businesses is extended based on personal guarantees in addition to the business credit. Namely, for most financing, the owner's assets are being relied on in addition to the businesses. This restricts the buyer pool and often restricts the ability of the company to expand using debt.

As mentioned, the weighted average cost of capital recalculates the cost of capital based on the full capital structure not just equity. But as debt increases, so does the risk of default. This increases investors' required rates of return. This risk adjustment is very hard to measure and estimate with small companies.

Another issue is how to handle the principal payments during the payment period since investors are in theory interested in what they can receive, and they cannot receive what is due to the note-holder. Further, at some point typically in five to ten years, the long-term debt will be paid, the capital structure will be all equity. Again, most small and very small businesses carry little debt “forever.” The model has no way to replicate this.

For smaller companies debt has tax advantages, as interest expense is deductible.

If valuation theory is correct, an equity discount rate buildup and a weighted average cost of capital buildup would produce nearly the same value. In practice, except with the most experienced valuators, the weighted average cost of capital tends to product a lower discount rate and higher valuation.

In most cases for smaller businesses, the weighted average cost of capital is likely a level of detail that will not produce more effective results because there are too many assumptions for which there is not effective data. But, there are always exceptions, so a limited presentation will be made. Figure 8.11 shows a typical weighted average cost of capital calculation.

Weighted Average Cost of Capital (WACC) Calculation

In the weighted average cost of capital calculation the valuator estimates the portion of the capital structure that will be represented by long-term debt. The estimate can be based on specific company and fact pattern factors, industry data, or a combination. In some cases, the subject company's current structure can be used. As mentioned above, while questionable in theory, the figure used is often an “average” estimated debt from recognized comparable data sources. This data is often obtained from RMA, or Integra or other data services.

The cost of the debt is then estimated. This can often be found by checking with banks. For small and very small businesses, it is often in the prime plus 2 to 3% range. Sometimes the bank rate includes a floor rate such as 7%. At times of very low interest rates, the valuator must check the floor value or run the risk of understating interest.

Interest payments on debt are tax deductible (that is still the case for small and very small businesses) so the estimated tax benefit is calculated by deducting the tax benefit on the interest payments. Then the portion of the capital structure represented by debt, perhaps 30%, is added to the portion of the capital structure represented by equity, in this case, 70%. The two figures are added and the cost of capital is calculated.

When estimating the equity value of the company being valued using WACC, remember that the interest-bearing debt (usually both short- and long-term) must be subtracted from the value found when estimating equity interests.

Again, common sense dictates that as the amount of debt rises, investors' cost of equity will increase due to the increased risk that they will not be paid their required return on investment. In fact, because debt is paid before equity, equity holders run a greater risk that they will lose their investment.

Rule of Thumb: Finance Method

The finance method is called a rule of thumb. Basically it is the reverse of the weighted average cost of capital. In the finance method, the valuator takes the cost of financing across the entire capital structure and divides it into the cash flow to come up with a value. This is a practical and easy rule of thumb to use as a check for any value found with small businesses, particularly where small business sales markets are driven by SBA loans or other debt that is easy to price. An example of the calculation is shown in Figure 8.12.

The finance method can be further enhanced to take equity investment into account also. That would generally raise the overall rate.

These estimated rates are drawn from reasonable approximations available by talking to local bankers and estimates from the Pepperdine Survey. They are estimates. While 35% was used, an analyst may be able to justify a 50% internal rate of return on a 20% equity investment with 80% leverage because of the increased risk of loss.

While this is viewed as a rule of thumb type sanity test, if thought is put into the inputs, the model will produce useful results.

Estimating Value Using the Discounted Cash Flow Method

The next step is to estimate the value for the discrete periods shown in the forecast. These will be added together along with the terminal value estimate that will be shown later to determine the full value.

The formula with a three-year forecast looks like this:

• NCF = Net Cash Flow
• k = Discount rate
• g = Growth

During the discrete periods (each year) the discount rate is geometric series to determine future cash flow. (The first year is the estimated rate, the second year is squared, the third year is cubed, and so on.) This adjusts the discount rate for present value. An example of the calculations to estimate each year's rate are shown in Figure 8.13. It may be easier to actually understand how this works by downloading the Excel version on the website and looking at the formulas.

We will address the final step, terminal value next.

Terminal Value

In most cases, business valuation relies on the assumption that businesses will exist into perpetuity. This assumption is poorly supported by facts even for very large organizations but any other assumption would likely be even more difficult to model.⁴⁴ Discounted cash flow forecasts are for discrete periods usually between three and ten years. With small and very small businesses it is rare that forecasts extend beyond five years and many may only be for two years. Therefore, the value derived from the cash flows for the years after the forecast period need to be calculated and added to find the full value.

One of the concerns of the discounted cash flow is that the terminal value often makes up far more than 50% of the total value found.⁴⁵ With very short forecast periods, this will be even more common. Still, it is likely to be more accurate than using the capitalization of earnings method, particularly where investment or cash flow change is forecast in the near term.

Two methods are used to determine terminal value. The most common used by valuators is a version of the capitalization of earnings model. This calculation assumes that growth will be a constant rate into perpetuity. An estimated growth rate into perpetuity must be selected. These are often between 2% and 6%. With inflation running between 2–3%, anything below that figure is actually losing value after inflation. Negative growth can be selected if the company is expected to contract but this is fairly rare in practice. Most valuators use between 2–4% most of the time, depending on real growth prospects.⁴⁶ Roger Grabowski and Ashok Abbott recently performed a detailed study and came up with “real” growth rates (above inflation) for most established (called “Long Term”) publicly traded companies in the 2% range counting acquisitions.⁴⁷

Calculating the Terminal Value

For simplification as in the capitalization of earnings method, a variation of the Gordon Growth model is used to account for the value of free cash flows that continue growing at an assumed constant rate in perpetuity.

The projected free cash flow in the first year beyond the forecast horizon (N+1) is used. This value is divided by the discount rate minus the assumed perpetuity growth rate:

• T₀ = Value of future cash flows (price).
• D₀ = Cash flows at a future point in time which is immediately prior to N+1, or at the end of period N, which is the final year in the forecast period.
• k = discount rate.
• g = growth rate.

• The cash flow (CF) for the first year past the forecast period is assumed to grow at the estimated long-term growth rate.
• The discount rate then has the long-term growth rate subtracted from it to estimate the capitalization rate.
• CF is then divided by the capitalization rate which is then multiplied by the present value factor of the last period in the projection to find the terminal value.

The terminal value is then added to the value found for the discounted years to find the total value. See Figure 8.15 on p. 213 for an example of a complete discounted cash flow calculation.

Exit Multiple Approach

The other method used to determine the terminal value is the exit multiple approach. Yes, it is a version of the market method. This method tends to be used by investment bankers and not valuation professionals but, remember, multipliers and capitalization rates are really just two ways to say the same thing.

In the exit multiple approach the analyst estimates the multiplier for the cash flow being used which is usually based on EBITDA. The multiple as selected is applied to the last year in the forecast's cash flow. This is applied against a present value factor and added to the discrete period's total. Again, this method is often used by investment bankers and does not have strong endorsement by the valuation community if for no other reason than it is combining two methods. See an example of this calculation in Figure 8.14.

Estimating the Value Using the Discounted Cash Flow Method

The final step is to add the discrete year calculations to the terminal year calculations to come up with the final enterprise value. Cheryl Hyder sent me the original version of this format and I have found it very useful over the years. See Figure 8.15 for the complete calculation. Note that the Excel file on the website also includes tabs for estimating the discount rate and estimating the present value factors.

This completes a basic discounted cash flow calculation. Please note this is a basic model suitable for small companies. Models can be adjusted to include debt and for partial years or for a mid-year discount rates. For very small businesses the effort is unlikely to materially change the results. But if necessary for your project, see Hitchner's Financial Valuation.⁴⁸