Chapter 10

Analysis and Valuation of Privately Held Companies

Maier's Law: If the facts do not conform to the theory, they must be disposed of.

Inside M&A: cashing out of a privately held enterprise

When he had reached his early sixties, Anthony Carnevale starting reducing the amount of time he spent managing Sentinel Benefits Group Inc., a firm he had founded. He planned to retire from the benefits and money management consulting firm in which he was a 26% owner. Mr. Carnevale, his two sons, and two nonfamily partners had built the firm to a company of more than 160 employees with $2.5 billion under management.

Selling the family business was not what the family expected to happen when Mr. Carnevale retired. He believed that his sons and partners were quite capable of continuing to manage the firm after he left. However, like many small businesses, Sentinel found itself with a succession of planning challenges. If the sons and the company's two other nonfamily partners bought out Mr. Carnevale, the firm would have little cash left over for future growth. The firm was unable to get a loan, given the lack of assets for collateral and the somewhat unpredictable cash flow of the business. Even if a loan could have been obtained, the firm would have been burdened with interest and principal repayment for years to come.

Over the years, Mr. Carnevale had rejected buyout proposals from competitors as inadequate. However, he contacted a former suitor, Focus Financial Partners LLC (a partnership that buys small money management firms and lets them operate largely independently). After several months of negotiation, Focus acquired 100% of Sentinel. Each of the five partners—Mr. Carnevale, his two sons, and two nonfamily partners—received an undisclosed amount of cash and Focus stock. A four-person Sentinel management team is now paid based on the company's revenue and growth.

The major challenges prior to the sale dealt with the many meetings held to resolve issues such as compensation, treatment of employees, how the firm would be managed subsequent to the sale, how client pricing would be determined, and who would make decisions about staff changes. Once the deal was complete, the Carnivales found it difficult to tell employees, particularly those who had been with the firm for years. Since most employees were not directly affected, only one left as a direct result of the sale.1

Chapter overview

A privately owned corporation is a firm whose securities are not registered with state or federal authorities. Consequently, they are prohibited from being traded in the public securities markets. The lack of such markets makes valuing private businesses particularly challenging. Nevertheless, the need to value such businesses may arise for a variety of reasons. Investors and small business owners may need a valuation as part of a merger or acquisition, for settling an estate, or because employees wish to exercise their stock options. Employee stock ownership plans (ESOPs) also may require periodic valuations. In other instances, shareholder disputes, court cases, divorce, or the payment of gift or estate taxes may necessitate a valuation of the business.

Other significant differences between publicly traded and privately owned companies include the availability and reliability of data, which for public companies tend to be much greater than for small private firms. Moreover, in large publicly traded corporations and large privately owned companies, managers are often well versed in contemporary management practices, accounting, and financial valuation techniques. This is frequently not the case for small privately owned businesses. Finally, managers in large public companies are less likely to have the same level of emotional attachment to the business frequently found in family-owned businesses.

This chapter discusses how the analyst deals with these problems. Issues concerning making initial contact and negotiating with the owners of privately owned businesses were addressed in Chapter 5. Consequently, this chapter focuses on the challenges of valuing private firms. Following a brief discussion of such businesses, this chapter discusses in detail the hazards of dealing with both limited and often unreliable data associated with private firms. The chapter then focuses on how to properly adjust questionable data, as well as how to select the appropriate valuation methodology and discount or capitalization rate. Considerable time is spent discussing how to apply control premiums, minority discounts, and liquidity discounts in valuing businesses. This chapter also includes a discussion of how corporate shells, created through reverse mergers, and leveraged ESOPs are used to acquire privately owned companies and how PIPE financing may be used to fund their ongoing operations.

A review of this chapter (including practice questions) is available in the file folder entitled “Student Study Guide” on the companion site to this book (www.elsevierdirect.com/companions/9780123854858). The companion site also contains a Learning Interactions Library, which gives students the opportunity to test their knowledge of this chapter in a “real-time” environment.

Demographics of privately held businesses

More than 99% of all businesses in the United States are small. They contribute about 75% of net new jobs added to the U.S. economy annually. Furthermore, such businesses employ about one-half of the U.S. nongovernment-related workforce and account for about 41% of nongovernment sales.²

Privately owned businesses are often referred to as closely held, since they are usually characterized by a small group of shareholders controlling the operating and managerial policies of the firm. Most closely held firms are family-owned businesses. All closely held firms are not small, since families control the operating policies at many large, publicly traded companies. In many of these firms, family influence is exercised by family members holding senior management positions, seats on the board of directors, and through holding supervoting stock (i.e., stock with multiple voting rights). The last factor enables control, even though the family's shareholdings often are less than 50%. Examples of large, publicly traded family businesses include Wal-Mart, Ford Motor, American International Group, Motorola, Loew's, and Bechtel Group. Each of these firms has annual revenues of more than $18 billion.

Key Characteristics

The number of firms in the United States in 2009 (the last year for which detailed data are available) totaled 32.7 million, with about 8.2 million, or one-fourth, having payrolls. The total number of firms and the number of firms with payrolls have grown at compound annual average growth rates of 2.8% and 1.6%, respectively, between 1990 and 2009. Of the firms without a payroll, most are self-employed persons operating unincorporated businesses, and they may or may not be the owner's primary source of income. Of the total number of firms in 2009, about 19%, 9%, and 72% were corporations, partnerships, and single proprietorships, respectively. These percentages have been relatively constant since the early 1990s. The M&A market for employer firms tends to be concentrated among firms with 99 or fewer employees, which account for about 98% of all firms with employees.³

Family-Owned Firms

Family-owned businesses account for about 89% of all businesses in the United States.⁴ In such businesses, the family has effective control over the strategic direction of the business. Moreover, the business contributes significantly to the family's income, wealth, and identity. While confronted with the same business challenges as all firms, family-owned firms are beset by more severe internal issues than publicly traded firms. These issues include management succession, lack of corporate governance, informal management structure, less-skilled lower-level management, and a preference for ownership over growth.

Firms that are family owned but not managed by family members are often well managed, since family shareholders with large equity stakes carefully monitor those who are charged with managing the business.⁵ However, management by one of the founders' children typically adversely affects firm value.⁶ This may result from the limited pool of family members available for taking control of the business.

Succession is one of the most difficult challenges to resolve, with family-owned firms viewing succession as the transfer of ownership more than as a transfer of management. Problems arise from inadequate preparation of the younger generation of family members and the limited pool of potential successors who might not even have the talent or the interest to take over. Mid-level management expertise often resides among nonfamily members, who often leave due to perceived inequity in pay scales with family members and limited promotion opportunities. While some firms display an ability to overcome the challenges of succession, others look to sell the business.

Governance issues in privately held and family-owned firms

The approach taken to promote good governance in the Sarbanes-Oxley Act (SOX) of 2002 (see Chapter 2) and under the market model of corporate governance (see Chapter 3) is to identify and apply “best practices.” The focus on “best practices” has led to the development of generalized laundry lists, rather than specific actions leading to measurable results.⁷ Moreover, what works for publicly traded companies may not be readily applicable to privately held or family-owed firms.

The market model relies on a large dispersed class of investors in which ownership and corporate control are largely separate. Moreover, the market model overlooks the fact that family-owned firms often have different interests, time horizons, and strategies from investors in publicly owned firms. In many countries, family-owned firms have been successful because of their shared interests and because investors place a higher value on the long-term health of the business rather than on short-term performance.⁸ Consequently, the control model of corporate governance discussed in Chapter 3 may be more applicable where ownership tends to be concentrated and the right to control the business is not fully separate from ownership.

There is some empirical evidence that the control model (or some variation) is more applicable to family-owned firms than the market model.⁹ Director independence appears to be less important for family-owned firms, since outside directors often can be swayed by various forms of compensation. A board consisting of owners focused on the long-term growth of the business for future generations of the family may be far more committed to the firm than outsiders. While the owners are ultimately responsible for strategic direction, the board must ensure that the strategy formulated by management is consistent with the owners' desires.

Nevertheless, other studies find that private businesses are adopting many of the Sarbanes-Oxley procedures as part of their own internal governance practices. A 2004 survey conducted by Foley and Lardner found that more than 40% of the private firms surveyed voluntarily adopted the following SOX provisions: (1) executive certification of financial statements, (2) whistleblower initiatives, (3) board approval of nonaudit services provided by external auditors, and (4) adoption of corporate governance policy guidelines.¹⁰

Challenges of valuing privately held companies

The anonymity of many privately held firms, the potential for manipulation of information, problems specific to small firms, and the tendency of owners of private firms to manage in a way to minimize tax liabilities create a number of significant valuation issues. The challenges of valuation are compounded by the emotional attachments private business owners often have to their businesses. These issues are addressed in the next sections of this chapter.

Lack of Externally Generated Information

There is generally a lack of analyses of private firms generated by sources outside of the company. Private firms provide little incentive for outside analysts to cover them because of the absence of a public market for their securities. Consequently, there are few forecasts of their performance other than those provided by the firm's management. Press coverage is usually quite limited, and what is available is often based on information provided by the firm's management. Even highly regarded companies (e.g., Dun & Bradstreet) purporting to offer demographic and financial information on small privately held firms use largely superficial and infrequent telephone interviews with the management of such firms as their primary source of such information.

Lack of Internal Controls and Inadequate Reporting Systems

Private companies are generally not subject to the same level of rigorous controls and reporting systems as public firms. Public companies are required to prepare audited financial statements for their annual reports.¹¹ The SEC enforces the accuracy of these statements under the authority provided by the Securities and Exchange Act of 1934.

Although reporting systems in small firms are generally poor or nonexistent, the lack of formal controls, such as systems to monitor how money is spent and an approval process to ensure that funds are spent appropriately, invites fraud and misuse of company resources. Documentation is another formidable problem. Intellectual property is a substantial portion of the value of many private firms. Examples of such property include system software, chemical formulas, and recipes. Often only one or two individuals within the firm know how to reproduce these valuable intangible assets. The lack of documentation can destroy a firm if such an individual leaves or dies. Moreover, customer lists and the terms and conditions associated with key customer relationships also may be largely undocumented, creating the basis for customer disputes when a change in ownership occurs.

Firm-Specific Problems

Private firms may lack product, industry, and geographic diversification. There may be insufficient management talent to allow the firm to develop new products for its current markets or expand into new markets. The company may be highly sensitive to fluctuations in demand because of significant fixed expenses. Its small size may limit its influence with regulators and unions. The company's size also may limit its ability to gain access to efficient distribution channels and leverage with suppliers and customers. Finally, the company may have an excellent product but very little brand recognition.

Common Forms of Manipulating Reported Income

Revenue and operating expenses are most commonly misstated. How this may occur is explained next.

Misstating Revenue

Revenue may be over- or understated, depending on the owner's objectives. If the intent is tax minimization, businesses operating on a cash basis may opt to report less revenue because of the difficulty outside parties have in tracking transactions. Private business owners intending to sell a business may be inclined to inflate revenue if the firm is to be sold. Common examples include manufacturers, which rely on others to distribute their products. These manufacturers can inflate revenue in the current accounting period by booking as revenue products shipped to resellers without adequately adjusting for probable returns. Membership or subscription businesses, such as health clubs and magazine publishers, may inflate revenue by booking the full value of multiyear contracts in the current period rather than prorating the payment received at the beginning of the contract period over the life of the contract.¹²

Manipulation of Operating Expenses

Owners of private businesses attempting to minimize taxes may overstate their contribution to the firm by giving themselves or family members unusually high salaries, bonuses, and benefits. The most common distortion of costs comes in the form of higher than normal salary and benefits provided to family members and key employees. Other examples of cost manipulation include extraordinary expenses that are really other forms of compensation for the owner, his or her family, and key employees, which may include the rent on the owner's summer home or hunting lodge and salaries for the pilot and captain for the owner's airplane and yacht. Current or potential customers sometimes are allowed to use these assets. Owners frequently argue that these expenses are necessary to maintain customer relationships or close large contracts and are therefore legitimate business expenses. One way to determine if these are appropriate business expenses is to ascertain how often these assets are used for the purpose for which the owner claims they were intended. Other areas commonly abused include travel and entertainment, personal insurance, and excessive payments to vendors supplying services to the firm. Due diligence frequently uncovers situations in which the owner or a family member is either an investor in or an owner of the vendor supplying the products or services.

Alternatively, if the business owner's objective is to maximize the selling price of the business, salaries, benefits, and other operating costs may be understated significantly. An examination of the historical trend in the firm's reported profitability may reveal that the firm's profits are being manipulated. For example, a sudden improvement in operating profits in the year in which the business is being offered for sale may suggest that expenses had been overstated, revenues understated, or both during the historical period.

Process for valuing privately held businesses

To address the challenges presented by privately owned firms, an analyst should adopt a four-step procedure. Step 1 requires adjustment of the target firm's financial data to reflect true profitability and cash flow in the current period. Determining what the business is actually capable of doing in terms of operating profit and cash flow in the current period is critical to the valuation, since all projections are biased if the estimate of current performance is skewed. Step 2 entails determining the appropriate valuation methodology. Step 3 requires the determination of the appropriate discount rate. Finally, the fourth step involves adjusting the estimated value of the private firm for a control premium (if appropriate), a liquidity discount, and a minority discount (if an investor takes a less than controlling ownership position in a firm).

Step 1: adjusting financial statements

The purpose of adjusting the income statement is to provide an accurate estimate of the current year's net or pretax income, earnings before interest and taxes (EBIT), or earnings before interest, taxes, depreciation, and amortization (EBITDA). The various measures of income should reflect accurately all costs actually incurred in generating the level of revenue, adjusted for doubtful accounts the firm booked in the current period. They also should reflect other expenditures (e.g., training and advertising) that must be incurred in the current period to sustain the anticipated growth in revenue.

The importance of establishing accurate current or base-year data is evident when we consider how businesses—particularly small, closely held businesses—are often valued. If the current year's profit data are incorrect, future projections of the dollar value would be inaccurate, even if the projected growth rate is accurate. Furthermore, valuations based on relative valuation methods such as price–to–current year earnings ratios would be biased to the extent estimates of the target's current income are inaccurate.

Earnings before interest and taxes, depreciation, and amortization has become an increasingly popular measure of value for privately held firms. The use of this measure facilitates the comparison of firms because it eliminates the potential distortion in earnings performance due to differences in depreciation methods and financial leverage among firms. Furthermore, this indicator is often more readily applicable in relative-valuation methods than other measures of profitability, since firms are more likely to display positive EBITDA than EBIT or net income figures. Despite its convenience, the analyst needs to be mindful that EBITDA is only one component of cash flow and ignores the impact on cash flow of changes in net working capital, investing, and financing activities. See Chapter 8 for a more detailed discussion of the use of EBITDA in relative valuation methods.

Making Informed Adjustments

While finding reliable current information on privately held firms is generally challenging, some information is available, albeit often fragmentary and inconsistent. The first step for the analyst is to search the Internet for references to the target firm. This search should unearth a number of sources of information on the target firm. Table 10.1 provides a partial list of websites containing information on private firms.

Table 10.1. Sources of Information on Private Firms

Source/Web Address	Content
RESEARCH FIRMS
Washington Researchers: www.washingtonresearchers.com Fuld & Company: www.fuld.com	Provide listing of sources such as local government officials, local chambers of commerce, state government regulatory bodies, credit reporting agencies, and local citizen groups
DATABASES
Dun & Bradstreet: smallbusiness.dnb.com Hoover: www.hoovers.com Integra: www.integrainfo.com Standard & Poor's NetAdvantage: www.netadvantage.standardandpoors.com InfoUSA: www.infousa.com Forbes: www.forbes.com/list Inc: www.inc.com/inc500	Information on firms' payments histories and limited financial data Data on 40,000 international and domestic firms, IPOs, not-for-profits, trade associations, and small businesses; limited data on 18 million other companies Provides industry benchmarking data Financial data and management and directors' bibliographies on 125,000 firms Industry benchmarking and company-specific data Provides list of top privately held firms annually Provides list of 500 of fastest-growing firms annually

Owners' and Officers' Salaries

Before drawing any conclusions, the analyst should determine the actual work performed by all key employees and the compensation received for performing a similar job in the same industry. Comparative salary information can be obtained by employing the services of a compensation consultant who is familiar with the industry or simply by scanning “employee wanted” advertisements in the industry trade press and magazines and the “help wanted” pages of the local newspaper.

Benefits

Depending on the industry, benefits can range from 14 to 50% of an employee's base salary. Certain employee benefits, such as Social Security and Medicare taxes, are mandated by law and, therefore, an uncontrollable cost of doing business. Other types of benefits may be more controllable. These include items such as pension contributions and life insurance coverage, which are calculated as a percentage of base salary. Consequently, efforts by the buyer to trim salaries that appear to be excessive also reduce these types of benefits. Efforts to reduce such benefits may contribute to higher overall operating costs in the short run. Operating costs may increase as a result of higher employee turnover and the need to retrain replacements, as well as the potential negative impact on the productivity of those that remain.

Travel and Entertainment

Travel and entertainment (T&E) expenditures tend to be one of the first cost categories cut when a potential buyer attempts to value a target company. What may look excessive to one who is relatively unfamiliar with the industry may in fact be necessary for retaining current customers and acquiring new customers. Establishing, building, and maintaining relationships is particularly important for personal and business services companies, such as consulting and law firms. Account management may require consultative selling at the customer's site. A complex product like software may require on-site training. Indiscriminant reduction in the T&E budget could lead to a loss of customers following a change in ownership.

Auto Expenses and Personal Life Insurance

Ask if such expenses represent a key component of the overall compensation required to attract and retain key employees. This can be determined by comparing total compensation paid to employees of the target firm with compensation packages offered to employees in similar positions in the same industry in the same region. A similar review should be undertaken with respect to the composition of benefits packages. Depending on the demographics and special needs of the target firm's workforce, an acquirer may choose to alter the composition of the benefits package by substituting other types of benefits for those eliminated or reduced.

Family Members

Similar questions need to be asked about family members on the payroll. Frequently, they perform real services and tend to be highly motivated because of their close affinity with the business. If the business has been in existence for many years, the loss of key family members who built relationships with customers over the years may result in a subsequent loss of key accounts. Moreover, family members may be those who possess proprietary knowledge necessary for the ongoing operation of the business.

Rent or Lease Payments in Excess of Fair Market Value

Check who owns the buildings housing the business or the equipment used by the business. This is a frequent method used to transfer company funds to the business owner, who also owns the bulding, in excess of his or her stated salary and benefits. However, rents may not be too high if the building is a “special-purpose” structure retrofitted to serve the specific needs of the tenant.

Professional Services Fees

Professional services could include legal, accounting, personnel, and actuarial services. This area is frequently subject to abuse. Once again, check for any nonbusiness relationship between the business owner and the firm providing the service. Always consider any special circumstances that may justify unusually high fees. An industry that is subject to continuing regulation and review may incur what appear to be abnormally high legal and accounting expenses.

Depreciation Expense

Accelerated depreciation methodologies may make sense for tax purposes, but they may seriously understate current earnings. For financial reporting purposes, it may be appropriate to convert depreciation schedules from accelerated to straight-line depreciation if this results in a better matching of when expenses actually are incurred and revenue actually is received.

Reserves

Current reserves may be inadequate to reflect future events. An increase in reserves lowers taxable income, whereas a decrease in reserves raises taxable income. Collection problems may be uncovered following an analysis of accounts receivable. It may be necessary to add to reserves for doubtful accounts. Similarly, the target firm may not have adequate reserves for future obligations to employees under existing pension and healthcare plans. Reserves also may have to be increased to reflect known environmental and litigation exposures.

Accounting for Inventory

During periods of inflation, businesses frequently use the last-in, first-out (LIFO) method to account for inventories. This approach results in an increase in the cost of sales that reflects the most recent and presumably highest-cost inventory; therefore, it reduces gross profit and taxable income. During periods of inflation, the use of LIFO also tends to lower the value of inventory on the balance sheet because the items in inventory are valued at the lower cost of production associated with earlier time periods. In contrast, the use of first-in, first-out (FIFO) accounting for inventory assumes that inventory is sold in the chronological order in which it was purchased. During periods of inflation, the FIFO method produces a higher ending inventory, a lower cost of goods sold, and higher gross profit. Although it may make sense for tax purposes to use LIFO, the buyer's objective for valuation purposes should be to obtain as realistic an estimate of actual earnings as possible in the current period. FIFO accounting appears to be most logical for products that are perishable or subject to rapid obsolescence and, therefore, are most likely to be sold in chronological order. In an environment in which inflation is expected to remain high for an extended time period, LIFO accounting may make more sense.

Areas That Are Commonly Understated

Projected increases in sales normally require more aggressive marketing efforts, more effective customer service support, and better employee training. Nonetheless, it is common to see the ratio of annual advertising and training expenses to annual sales decline during the period of highest projected growth in forecasts developed by either the seller or the buyer. The seller has an incentive to minimize such expenses during the forecast period to provide the most sanguine outlook possible. The buyer simply may be overly optimistic about how much more effectively the business can be managed as a result of a change in ownership; the buyer may also be excessively optimistic in an effort to induce lenders to finance the transaction. Other areas that are commonly understated in projections but that can never really be escaped include the expense associated with environmental cleanup, employee safety, and pending litigation.

Areas That Are Commonly Overlooked

In many cases, the value of the business is more in its intangible assets than in its tangible assets. The best examples include the high valuations placed on many Internet-related and biotechnology companies. The target's intangible assets may include customer lists, patents, licenses, distributorship agreements, leases, regulatory approvals (e.g., U.S. Food and Drug Administration approval of a new drug), noncompete agreements, and employment contracts. Note that for these items to represent sources of incremental value, they must represent sources of revenue or cost reduction not already reflected in the target's cash flows.

Explaining Adjustments to Financial Statements

Table 10.2 illustrates how historical and projected financial statements received from the target as part of the due diligence process could be restated to reflect what the buyer believes to be a more accurate characterization of revenue and costs. Adjusting the historical financials provides insight into what the firm could have done had it been managed differently. Similarly, adjusting the projected financials enables the analyst to use what he or she considers more realistic assumptions. Note that the cost of sales is divided into direct and indirect expenses.

Table 10.2. Adjusting the Target Firm's Financial Statements^a

^a The reader may simulate alternative assumptions by accessing a file entitled Excel Spreadsheet for Adjusting Target Firm Financials available on the companion site.

Direct cost of sales relates to costs incurred directly in the production process. Indirect costs are those incurred as a result of the various functions (e.g., senior management, human resources, sales, accounting) supporting the production process. The actual historical costs are displayed above the “explanation of adjustments” line. Some adjustments represent “add backs” to profit while others reduce profit. The adjusted EBITDA numbers at the bottom of the table represent what the buyer believes to be the most realistic estimate of the profitability of the business. Finally, by displaying the data historically, the buyer can see trends that may be useful in projecting the firm's profitability.

In this illustration, the buyer believes that because of the nature of the business, inventories are more accurately valued on a FIFO rather than a LIFO basis. This change in inventory cost accounting results in a sizeable boost to the firm's profitability. Furthermore, due diligence revealed that the firm was overstaffed and it could be operated adequately by eliminating the full-time position held by the former owner (including fees received as a member of the firm's board of directors) and a number of part-time positions held by the owner's family members.

Although some cost items are reduced, others are increased. For example, office space is reduced, thereby lowering rental expense as a result of the elimination of out-of-state sales offices. However, the sales- and marketing-related portion of the travel and entertainment budget is increased to accommodate the increased travel necessary to service out-of-state customer accounts due to the closure of the regional offices. Furthermore, it is likely that advertising expenses will have to be increased to promote the firm's products in those regions. The new buyer also believes the firm's historical training budget to be inadequate to sustain the growth of the business and more than doubles spending in this category. The reader may simulate alternative assumptions by accessing the file entitled “Excel-Based Spreadsheet of How to Adjust Target Firm's Financial Statements” on the companion site.

Step 2: applying valuation methodologies to privately held companies

The methodologies employed to value privately held firms are very similar to those discussed elsewhere in this book. However, they are often subject to adjustments not commonly applied to publicly traded firms.

Defining Value

The most common generic definition of “value” used by valuation professionals is fair market value. Hypothetically, fair market value is the cash or cash-equivalent price that a willing buyer would propose and a willing seller would accept for a business if both parties had access to all relevant information. Furthermore, fair market value assumes that neither the seller nor the buyer is under any obligation to buy or sell.

It is easier to obtain the fair market value for a public company because of the existence of public markets in which stock in the company is actively traded. The concept may be applied to privately held firms if similar publicly traded companies exist. However, because finding substantially similar companies is difficult, valuation professionals have developed a related concept called fair value. Fair value is applied when no strong market exists for a business, or it is not possible to identify the value of substantially similar firms. Fair value is, by necessity, more subjective because it represents the dollar value of a business based on an appraisal of its tangible and intangible assets.¹³

Selecting the Appropriate Valuation Methodology

As noted in Chapters 7 and 8, appraisers, brokers, and investment bankers generally classify valuation methodologies into four distinct approaches: income (discounted cash flow), relative or market based, replacement cost, and asset oriented.

The Income or Discounted-Cash-Flow Approach

The validity of this method depends heavily on the particular definition of income or cash flow, the timing of cash flows, and the selection of an appropriate discount or capitalization rate. The terms discount rate and capitalization rate often are used interchangeably. Whenever the growth rate of a firm's cash flows is projected to vary over time, discount rate generally refers to the factor used to convert the projected cash flows to present values. In contrast, if the cash flows of the firm are not expected to grow or are expected to grow at a constant rate indefinitely, the discount rate used by practitioners often is referred to as the capitalization rate.

The conversion of a future income stream into a present value also is referred to as the capitalization process. It often applies when future income or cash flows are not expected to grow or are expected to grow at a constant rate. When no growth in future income or cash flows is expected, the capitalization rate is defined as the perpetuity growth model. When future cash flow or income is expected to grow at a constant rate, the capitalization rate commonly is defined as the difference between the discount rate and the expected growth rate (i.e., the constant growth model). Present values calculated in this manner are sometimes referred to as capitalized values.

Capitalization rates are commonly converted to multiples by dividing 1 by the discount rate or the discount rate less the anticipated constant growth rate in cash flows. These capitalization multiples can be multiplied by the current period's cash flow (i.e., if applying the perpetuity model) or the subsequent period's anticipated cash flow (i.e., if applying the constant-growth model) to estimate the market value of a firm. For example, if the discount rate is assumed to be 8% and the current level of a firm's cash flow is $1.5 million, which is expected to remain at that level in perpetuity, the implied valuation is $18.75 million—that is, (1/0.08) × $1.5 million. Alternatively, if the current level of cash flow is expected to grow at 4% annually in perpetuity, the implied valuation is $39 million—that is, [(1.04)/(0.08 – 0.04)] × $1.5 million. The capitalization multiples in the perpetuity and constant-growth cases are 1/0.08 and 1.04/(0.08 – 0.04), respectively.

Several alternative definitions of income or cash flow can be used in either the discounting or capitalization process. These include free cash flow to equity holders or the firm; earnings before interest and taxes; earnings before interest, taxes, and depreciation; earnings before taxes (EBT); and earnings after taxes (EAT or NI).

Capitalization multiples and capitalization rates often are used in valuing small businesses because of their inherent simplicity. Many small business owners lack sophistication in financial matters. Consequently, a valuation concept, which is easy to calculate, understand, and communicate to the parties involved, may significantly facilitate completion of the transaction. Finally, there is little empirical evidence that more complex valuation methods necessarily result in more accurate valuation estimates.

The Relative-Value or Market-Based Approach

This approach is used widely in valuing private firms by business brokers or appraisers to establish a purchase price. The Internal Revenue Service and the U.S. tax courts have encouraged the use of market-based valuation techniques. Therefore, in valuing private companies, it is always important to keep in mind what factors the IRS thinks are relevant to the process, because the IRS may contest any sale requiring the payment of estate, capital gains, or unearned income taxes. The IRS's positions on specific tax issues can be determined by reviewing revenue rulings. A revenue ruling is an official interpretation by the IRS of the Internal Revenue Code, related statutes, tax treaties, and regulations.

Revenue Ruling 59-60 describes the general factors that the IRS and tax courts consider relevant in valuing private businesses. These factors include general economic conditions, the specific conditions in the industry, the type of business, historical trends in the industry, the firm's performance, and the firm's book value. In addition, the IRS and tax courts consider the ability of the company to generate earnings and pay dividends, the amount of intangibles such as goodwill, recent sales of stock, and the stock prices of companies engaged in the “same or similar” line of business.

The Replacement-Cost Approach

This approach states that the assets of a business are worth what it costs to replace them and is most applicable to businesses that have substantial amounts of tangible assets for which the actual cost to replace them can be determined easily. This method is often not useful in valuing a business whose assets are primarily intangible. Moreover, the replacement-cost approach ignores the value created in excess of the cost of replacing each asset by operating the assets as a going concern. For example, an assembly line may consist of a number of different machines, each performing a specific task in the production of certain products. The value of the total production coming off the assembly line over the useful lives of the individual machines is likely to far exceed the sum of the costs to replace each machine. Consequently, the business should be valued as a going concern rather than as the sum of the costs to replace its individual assets.¹⁴

The Asset-Oriented Approach

Like the replacement-cost approach, the accuracy of asset-oriented approaches depends on the overall proficiency of the appraiser hired to establish value and the availability of adequate information. Book value is an accounting concept and generally is not considered a good measure of market value because book values usually reflect historical rather than current market values. However, as noted in Chapter 8, tangible book value (i.e., book value less intangible assets) may be a good proxy for the current market value for both financial services and product distribution companies. Breakup value is an estimate of what the value of a business would be if each of its primary assets were sold independently. This approach may not be practical if there are few public markets for the firm's assets. Liquidation value is a reflection of the firm under duress. A firm in liquidation normally must sell its assets within a specific time period. Consequently, the cash value of the assets realized is likely to be much less than their actual replacement value or value if the firm were to continue as a viable operation. Liquidation value is a reasonable proxy for the minimum value of the firm. For a listing of when to use the various valuation methodologies, see Table 8.4 in Chapter 8.

Step 3: developing discount (capitalization) rates

While the discount or capitalization rate can be derived using a variety of methods, the focus in this chapter is on the weighted-average cost of capital or the cost of equity. The capital asset pricing model (CAPM) provides an estimate of the acquiring firm's cost of equity, which may be used as the discount or capitalization rate when the firm is debt-free.

Estimating a Private Firm's Beta and Cost of Equity

Like public firms, private firms are subject to nondiversifiable risk, such as changes in interest rates, inflation, war, and terrorism. However, to estimate the firm's beta, it is necessary to have sufficient historical data. Private firms and divisions of companies are not publicly traded and, therefore, have no past stock price information. The common solution is to estimate the firm's beta based on comparable publicly listed firms.

Assuming that the private firm is leveraged, the process commonly employed for constructing the private firm's leveraged beta is to assume that it can be estimated based on the unlevered beta for comparable firms adjusted for the private firm's target debt-to-equity ratio. The process involves the following steps. First, calculate the average beta for publicly traded comparable firms. If the comparable firms are leveraged, the resulting average is a leveraged beta for the comparable firms. Second, estimate the average debt-to-equity ratio in terms of the market values of the comparable firms. Third, estimate the average unlevered beta for the comparable firms based on information determined in the first two steps. Fourth, compute the levered beta for the private firm based on the firm's target debt–to–equity ratio set by management and the unlevered beta for comparable firms determined in the third step. Alternatively, the industry average leveraged beta could be used by assuming the private firm's current debt-to-equity ratio will eventually match the industry average.

Once estimated using the CAPM, the cost of equity may have to be adjusted to reflect risk specific to the target when it is applied to valuing a private company. The CAPM may understate significantly the specific business risk associated with acquiring the target firm. Recall from Chapter 7 that risk premiums for public companies often are determined by examining the historical premiums earned by stocks over some measure of risk-free returns, such as ten-year Treasury bonds. This same logic may be applied to calculating specific business risk premiums for small private firms. The specific business risk premium can be measured by the difference between the junk bond and risk-free rate or the return on comparable small stocks and the risk-free rate. Note that comparable small companies are more likely to be found on the NASDAQ, OTC, or regional stock exchanges than on the New York Stock Exchange. Other adjustments for the risks associated with firm size are given by Ibbotson Associates in Table 7.1 in Chapter 7.

For example, consider an acquiring firm attempting to value a small, privately owned software company. If the risk-free return is 6%, the historical return on all stocks minus the risk-free return is 5.5%, the firm's financial returns are highly correlated with the overall stock market (i.e., the firm's β is approximately 1), and the historical return on OTC software stocks minus the risk-free return is 9%, the cost of equity (k_e ) can be calculated as follows:¹⁵

Estimating the Cost of Private Firm Debt

Private firms seldom can access public debt markets and are therefore usually not rated by the credit rating agencies. Most debt is bank debt, and the interest expense on loans on the firm's books that are more than a year old may not reflect what it actually would cost the firm to borrow currently. The common solution is to assume that private firms can borrow at the same rate as comparable publicly listed firms or estimate an appropriate bond rating for the company based on financial ratios and use the interest rate that public firms with similar ratings would pay.

For example, an analyst can easily identify publicly traded company bond ratings by going to any of the various Internet bond screening services (e.g., finance.yahoo.com/bonds) and searching for bonds using various credit ratings. Royal Caribbean Cruise Lines LTD had a BBB rating and a 2.7 interest coverage ratio (i.e., EBIT/interest expense) in 2009 and would have to pay 7.0 to 7.5% for bonds maturing in seven to ten years. Consequently, firms with similar interest coverage ratios could have similar credit ratings. If the private firm to be valued had a similar interest coverage ratio and wanted to borrow for a similar time period, it is likely that it would have had to pay a comparable rate of interest. Other sources of information about the interest rates that firms of a certain credit rating pay often are available in major financial newspapers such as the Wall Street Journal, Investors' Business Daily, and Barron's. Unlike the estimation of the cost of equity for small privately held firms, it is unnecessary to adjust the cost of debt for specific business risk, since such risk should already be reflected in the interest rate charged to firms of similar risk.

Estimating the Cost of Capital

In the presence of debt, the cost of capital method should be used to estimate the discount or capitalization rate. This method involves the calculation of a weighted average of the cost of equity and the after-tax cost of debt. The weights should reflect market values rather than book values. Private firms represent a greater challenge than public firms in that the market value of their equity and debt is not readily available in public markets. Calculating the cost of capital requires the use of the market rather than the book value of debt-to-total capital ratios. Private firms provide such ratios only in book terms. A common solution is to use what the firm's management has set as its target debt-to-equity ratio in determining the weights to be used or assume that the private firms will eventually adopt the industry average debt-to-equity ratio.

Note the importance of keeping assumptions used for the management's target debt-to-equity ratio (D/E) in computing the firm's cost of equity consistent with the weights used in calculating the weighted-average cost of capital. For example, the firm's target D/E should be consistent with the debt–to–total capital and equity–to–total capital weights used in the weighted-average cost of capital. This consistency can be achieved simply by dividing the target D/E (or the industry D/E if that is what is used) by (1 + D/E) to estimate the implied debt–to–total capital ratio. Subtracting this ratio from 1 provides the implied equity–to–total capital ratio.

When the growth period for the firm's cash flow is expected to vary, the cost of capital estimated for the high-growth period can be expected to decline when the firm begins to grow at a more sustainable rate. This rate often is the industry average rate of growth. At that point, the firm presumably begins to take on the risk and growth characteristics of the typical firm in the industry. Thus, the discount rate may be assumed to be the industry average cost of capital during the sustainable- or terminal-growth period. Exhibit 10.1 illustrates how to calculate a private firm's beta, cost of equity, and cost of capital.

Exhibit 10.1 Valuing Private Firms

Acuity Lighting, a regional manufacturer and distributor of custom lighting fixtures, has revenues of $10 million and an EBIT of $2 million in the current year (i.e., year 0). The book value of the firm's debt is $5 million. The firm's debt matures at the end of five years and has annual interest expense of $400,000. The firm's marginal tax rate is 40%, the same as the industry average. Capital spending equals depreciation in year 0, and both are expected to grow at the same rate. As a result of excellent working capital management, the future change in working capital is expected to be essentially zero. The firm's revenue is expected to grow 15% annually for the next five years and 5% per year thereafter. The firm's current operating profit margin is expected to remain constant throughout the forecast period. As a result of the deceleration of its growth rate to a more sustainable rate, Acuity Lighting is expected to assume the risk and growth characteristics of the average firm in the industry during the terminal growth period. Consequently, its discount rate during this period is expected to decline to the industry average cost of capital of 11%.

The industry average beta and debt-to-equity ratio are 2 and 0.4, respectively. The ten-year U.S. Treasury bond rate is 4.5%, and the historical equity premium on all stocks is 5.5%. The specific business risk premium as measured by the difference between the junk bond and risk-free rate or the return on comparable small stocks and the risk-free rate is estimated to be 9%.

Acuity Lighting's interest coverage ratio is 2.89, which is equivalent to a BBB rating by the major credit rating agencies. BBB-rated firms are currently paying a pretax cost of debt of 7.5%. Acuity Lighting's management has established the firm's target debt-to-equity ratio at 0.5 based on the firm's profitability and growth characteristics. Estimate the equity value of the firm.

Calculate Accuity's cost of equity and weighted average cost of capital:

1. Unlevered beta for publicly traded firms in the same industry = 2/(1 + 0.6 × 0.4) = 1.61, where 2 is the industry's average levered beta, 0.6 is (1 – tax rate), and 0.4 is the average debt-to-equity ratio for firms in this industry.

2. Acuity's levered beta = 1.61 × (1 + 0.6 × 0.5) = 2.09, where 0.5 is the target debt-to-equity ratio established by Acuity's management.

3. Acuity's cost of equity = 4.5 + 2.09 × 5.5 + 9 = 25, where 4.5 is the risk-free rate and 9 is the firm size or firm specific business risk premium.

4. Acuity's after-tax cost of debt = 7.5 × (1 – 0.4) = 4.5, where 7.5 is the pretax cost of debt.

5. Acuity's WACC = (25 × 0.67) + (4.5 × 0.33) = 18.24, where the firm's debt–to–total capital ratio (D/TC) is determined by dividing Acuity's debt-to-equity target (D/E) by 1 + D/E. Therefore,

Value Acuity using the FCFF DCF model using the data provided in Table 10.3.

Table 10.3. FCFF Model

^a EBIT grows at 15% annually for the first five years and at 5% thereafter.

^b Capital spending equals depreciation in year 0, and both are expected to grow at the same rate. Moreover, the change in working capital is zero. Therefore, free cash flow equals after-tax EBIT.

Step 4: applying control premiums, liquidity, and minority discounts

In Exhibit 9.2 in Chapter 9, the maximum purchase price of a target firm (PV_MAX ) is defined as its current market or stand-alone value (i.e., the minimum price or PV_MIN) plus the value of anticipated net synergies (i.e., PV_NS):

(10.1)

This is a reasonable representation of the maximum offer price for firms whose shares are traded in liquid markets and where no single shareholder (i.e., block shareholder) can direct the activities of the business. Examples of such firms could include Microsoft, IBM, and General Electric. However, when markets are illiquid and there are block shareholders with the ability to influence strategic decisions made by the firm, the maximum offer price for the firm needs to be adjusted for liquidity risk and the value of control. These concepts are explained next.

Liquidity Discounts

Liquidity is the ease with which investors can sell their stock without a serious loss in the value of their investment. An investor in a private company may find it difficult to quickly sell his or her shares because of limited interest in the company. As such, the investor may find it necessary to sell at a significant discount from what was paid for the shares. Liquidity or marketability risk may be expressed as a liquidity or marketability discount. This discount equals the reduction in the offer price for the target firm by an amount equal to the potential loss of value when sold due to the lack of liquidity in the market.

Empirical Studies of the Liquidity Discount

Liquidity discounts have been estimated using a variety of methodologies. The most popular involves so-called restricted stocks. Other studies have involved analyzing conditions prior to initial public offerings (IPOs), the cost of IPOs, option pricing models, and the value of subsidiaries of parent firms.

Restricted stock (letter stock) studies

Issued by public companies, such shares are identical to the firm's equities that are freely traded except for the restriction that they not be sold for a specific period of time.¹⁶ The restriction on trading results in a lack of marketability of the security. Registration (with the SEC) exemptions on restricted stocks are granted under Rule 144A of Section 4(2) of the 1933 Securities Act. Restricted stock may be sold in limited amounts through private placements to investors, usually at a significant discount. However, it cannot be sold to the public, except under provisions of the SEC's Rule 144.

Prior to 1990, a holder of restricted stock had to register the securities with the SEC or qualify for exemption under Rule 144 to sell stock in the public markets. This made trading letter stock a time-consuming, costly process, as buyers had to perform appropriate due diligence. In 1990, the SEC adopted Rule 144A, allowing institutional investors to trade unregistered securities among themselves without filing registration statements. This change created a limited market for letter stocks and reduced discounts. In 1997, this rule was again amended to reduce the holding period for letter stocks before they could be sold from two years to one.

Empirical studies of restricted equities examine the difference in the price at which the restricted shares trade versus the price at which the same unrestricted equities trade in the public markets on the same date. Table 10.4 provides the results of 17 restricted stock studies. A comprehensive study undertaken by the SEC in 1971 examined restricted stock for 398 publicly traded companies and found that the median discount involving the restricted stock sales was about 26%.¹⁷ Size effects appeared to be important, with firms having the highest sales volumes exhibiting the lowest discounts and the smallest firms having the largest discounts. An analysis completed on a smaller sample of 146 publicly traded firms found that restricted shares traded at a discount of 33%.¹⁸ Other studies estimated the discount to be in the 33 to 35% range.¹⁹ The size of liquidity discounts tends to decrease for firms with larger revenues and profitability and for smaller block sales of stock.²⁰ The magnitude of these estimates from the pre-1990 studies is problematic in view of the types of investors in unregistered equities. These include insurance companies and pension funds, which have long-term investment horizons and well-diversified portfolios. Such investors are unlikely to be deterred by a one- or two-year restriction on selling their investments.

Table 10.4. Empirical Studies of Liquidity Discounts

Study	Time Period (Sample Size)	Median Discount (%)
Restricted Stock Studies
Institutional Investor Study Report	1966–1969 (398)	25.8
Gelman (1972)	1968–1970 (89)	33.0
Trout (1977)	1968–1972 (NA)	33.5
Morony (1973)	1969–1972 (146)	35.6
Maher (1976)	1969–1973 (NA)	35.4
Standard Research Consultants (1983)	1978–1982 (NA)	45.0
Wruck (1989)	1979–1985 (99)	13.5
Hertzel and Smith (1993)	1980–1987 (106)	20.1
Oliver and Meyers (2000)	1980–1996 (53)	27.0
Willamette Management Associates Inc. (Pratt and Niculita, 2008)	1981–1984 (NA)	31.2
Silber (1991)	1981–1988 (69)	33.8
Management Planning, Inc. (Pratt and Niculita, 2008)	1980–1995 (NA)	28.9
Hall and Polacek (1994)	1979–1992 (NA)	23.0
Johnson (1999)	1991–1995 (72)	20.0
Aschwald (2000)	1996–1997 (23)	21.0
Aschwald (2000)	1997–1998 (15)	13.0
Finnerty (2002)	1991–1997 (101)	20.1
Pre-IPO Studies
Willamette Management Associates Inc. (Pratt and Niculita, 2008)	1981–1984 (NA)	45.0
Emory (2001)	1981–2000 (631)	45.9
IPO Cost Studies
Loughran and Ritter (2002)a	1990–2000 (NA)	22.0
Option Studies
Longstaff (1995)	NA	25–35
Parent Subsidiaries Studies
Officer (2007)	1997–2004 (122)	15–30

NA = Not available.

^a Measures maximum discount.

Certain factors that have been found to be reliable indicators of liquidity discounts include the following: revenues, earnings, market price per share, price stability, and earnings stability.²¹ Firms that were the most profitable showed 11% discounts,²² while firms with the highest sales volumes showed discounts of 13%.²³ Firms showing the greatest earnings stability had a median discount of 16.4%.

More recent studies of restricted stock sales since 1990 indicate a median discount of about 20%.²⁴ Moreover, following the holding period change under Rule 144 from two years to one after 1997, the median discount declined to 13%.²⁵

Pre-IPO studies

An alternative to estimating liquidity discounts is to compare the value of a firm's stock sold before an IPO, usually through private placements, with the actual IPO offering price. Firms undertaking IPOs are required to disclose all transactions in their stocks for a period of three years before the IPO. Because the liquidity available is substantially less before the IPO, this difference is believed to be an estimate of the liquidity discount. Ten separate studies of 631 firms between 1980 and 2000 found a median discount of 45.9% between the pre-IPO transaction prices and the actual post-IPO prices.²⁶ The magnitude of the estimate remained relatively unchanged in each study. Such studies are subject to selection bias because only initial public offerings that were completed are evaluated. IPOs that were withdrawn because of unattractive market conditions may have received valuations more in line with pre-IPO private placements and therefore exhibited smaller discounts.

IPO cost studies

The total cost of an IPO includes both direct costs of flotation and indirect under-pricing costs. The direct costs entail management fees, underwriting fees, and selling concession (i.e., difference between gross and net proceeds of the issue) as a percentage of the amount of the issue. Indirect costs are measured by the frequent under-pricing of the securities by underwriters interested in selling the entire issue quickly. Direct costs run about 7% and indirect costs about 15%, implying that firms seeking to achieve liquidity incur an average cost of 22%.²⁷

Option pricing studies

Such studies suggest that uncertainty and time are important determinants of liquidity discounts. With respect to uncertainty, the greater the volatility of the shares, the greater the magnitude of the discount. The longer the length of time the shareholder is restricted from selling the shares, the greater the discount. If a shareholder holds restricted stock and purchases a put option to sell the stock at the market price, the investor has effectively secured access to liquidity. The liquidity discount is the cost of the put option with an exercise price equal to the share price at the date of issue as a percent of the exercise price.²⁸ Maximum liquidity discounts were found to be in the 2 to 35% range for two-year holding periods and 15 to 25% for one-year holding periods.²⁹

Studies of parent subsidiaries

Sales of subsidiaries of other firms and privately owned firms often sell at discounts of 15% to 30% below acquisition multiples for comparable publicly traded firms. This discount may reflect the price paid by such firms for the liquidity provided by the acquiring firm. Discounts tend to be greater when debt is relatively expensive to obtain and when the parent's stock returns tend to underperform the market in the 12 months prior to the sale. This is consistent with the findings of several restricted stock studies, which identify profitability as a reliable indicator of the size of a firm's liquidity discount.³⁰

In summary, empirical studies of liquidity discounts demonstrate that they exist, but there is substantial disagreement over their magnitude. Most empirical studies conducted prior to 1992 indicated that liquidity discounts ranged from 33 to 50% when compared to publicly traded securities of the same company.³¹ More recent studies indicate that such securities trade at more modest discounts, ranging from 13 to 35%.³² This range excludes the results of the pre-IPO studies that, for reasons discussed previously, are believed to be outliers. Four recent studies show a clustering of the discount around 20%. The decline in the liquidity discount since 1990 reflects a reduction in the required holding period for Rule 144 security issues and improved overall market liquidity during the periods covered by these studies. The latter is due to enhanced business governance practices, lower transaction costs, and greater accessibility to information via the Internet and other sources about private firms and the industries in which they compete. Note that the 2008–2009 capital market meltdowns are likely an aberration and, as such, should not affect the magnitude of the liquidity discount in the long term.

Purchase Price Premiums, Control Premiums, and Minority Discounts

For many transactions, the purchase price premium, which represents the amount a buyer pays the seller in excess of the seller's current share price, includes both a premium for anticipated synergy and a premium for control. The value of control is distinctly different from the value of synergy. The value of synergy represents revenue increases and cost savings that result from combining two firms, usually in the same line of business. In contrast, the value of control provides the right to direct the activities of the target firm on an ongoing basis.

While control is often assumed to require a greater than 50% ownership stake, effective control can be achieved at less than 50% ownership if other shareholders own relatively smaller stakes and do not band together to offset the votes cast by the largest shareholder. Consequently, an investor may be willing to pay a significant premium to purchase a less than 50% stake if they believe that effective control over key decisions can be achieved.

Control can include the ability to select management, determine compensation, set policy and change the course of the business, acquire and liquidate assets, award contracts, make acquisitions, sell or recapitalize the company, and register the company's stock for a public offering. Control also involves the ability to declare and pay dividends, change the articles of incorporation or bylaws, or block any of the aforementioned actions. Owners of controlling blocks of voting stock may use this influence to extract special privileges or benefits not available to other shareholders, such as directing the firm to sell to companies owned by the controlling shareholder at a discount to the market price and to buy from suppliers owned by the controlling shareholder at premium prices. Furthermore, controlling shareholders may agree to pay unusually high salaries to selected senior managers, who may be family members. For these reasons, the more control a block investor has, the less influence a minority investor has and the less valuable is that person's stock. Therefore, a control premium is the amount an investor is willing to pay to direct the activities of the firm. Conversely, a minority discount is the reduction in the value of the investment because the minority owners have little control over the firm's operations.

Purchase price premiums may reflect only control premiums, when a buyer acquires a target firm and manages it as a largely independent operating subsidiary. The pure control premium is the value the acquirer believes can be created by replacing incompetent management, changing the strategic direction of the firm, gaining a foothold in a market not currently served, or achieving unrelated diversification.³³

Empirical Studies of the Pure Control Premium

While many empirical studies estimate the magnitude of the liquidity risk discount, the empirical evidence available to measure the control premium is limited. As is true of the liquidity discount, empirical studies confirm the existence of a pure control premium. However, considerable disagreement continues over their size. Empirical studies to date focus on block transaction premiums, dual-class ownership, and M&A transactions.

Evidence from block transaction premiums

An estimate of the magnitude of the pure control premium can be obtained by examining the difference between prices paid for privately negotiated sales of blocks of voting stock (defined as greater than 10,000 shares) constituting more than 5% of a firm's equity with the posttransaction share price. In an analysis of 63 block trades between 1980 and 1982, the median premium paid for these private blocks of voting stock compared to the publicly traded price was found to be about 20%.³⁴

In a more recent study involving a cross-country comparison of 412 block transactions in 39 countries from 1990 to 2000, the median control was about 14%. However, estimates of the control premium ranged from –4 to 65%.³⁵ Negative results occur whenever the price paid for the block is less than the market price. This could occur whenever a firm is facing bankruptcy, management is widely viewed as incompetent, or the firm's products are obsolete. For example, Morgan Stanley's offer price for 40% of financially insolvent Bear Stearns voting shares in 2008 at $10 per share was $2 less than the market price on the day of the announcement.

In this same cross-country comparison, countries such as the United States, the United Kingdom, and the Netherlands exhibited median premiums of 2% compared to premiums in Brazil and the Czech Republic of 65 and 58%, respectively. The value of control appears to be less in countries with better accounting standards, better legal protection for minority shareholders, more competitive markets, an independent press, and high tax compliance.³⁶

In a study of 27 control transactions in Italy between 1993 and 2003, block transaction (tender) premiums equaled about 12 to 14%, depending on the size of the block of shares to be acquired.³⁷ A 2008 study of block transaction premiums in China estimated median control premiums in China of 18.5%.³⁸ The wide variation in results across countries may reflect the small samples used in evaluating transactions in each country as well as significantly different circumstances in each country.

Evidence from dual-class ownership

Dual-class ownership structures involve classes of stock that differ in voting rights. Those shares having more voting rights than other shares typically trade at much higher prices, with control premiums for most countries falling within a range of 10 to 20% of the firm's current share price. However, the dispersion of control premiums is substantial, with the United States, Sweden, and the United Kingdom displaying premiums of 5.4, 6.5, and 12.8%, respectively, compared to Israel and Italy at 45.5 and 82%, respectively.³⁹ In an 18-country study in 1997, the estimated median control premium was 13%. However, the results varied widely across countries, with the United States and Sweden at 2% and Italy and Mexico at 29.4% and 36.4%, respectively. Two-thirds of the cross-country variance could be explained by a nation's legal environment, law enforcement, investor protection, and corporate charter provisions that tend to concentrate power (e.g., supermajority voting).⁴⁰

Evidence from mergers and acquisition transactions

The premium paid to target company shareholders in part reflects what must be paid to get the firm's shareholders to relinquish control. In a study examining 9,566 transactions between 1990 and 2000 in the United States, Japan, Germany, France, Italy, the United Kingdom, and Canada, two samples were analyzed: one in which buyers acquired a minority position and one where buyers acquired a controlling position. The study found that a controlling position commanded a premium 20 to 30% higher than the price paid for minority positions in U.S. transactions. Similar premiums were found in other market-oriented nations, such as the United Kingdom and Canada. However, premiums were much smaller in those nations (i.e., Japan, Germany, France, and Italy) in which banks routinely make equity investments in publicly traded firms.⁴¹

In summary, country comparison studies indicate a huge variation in median control premiums from as little as 2 to 5% in countries where corporate ownership often is widely dispersed and investor protections are relatively effective (e.g., United States and United Kingdom) to as much as 60 to 65% in countries where ownership tends to be concentrated and governance practices are relatively poor (e.g., Brazil and the Czech Republic). Median estimates across countries are 10 to 12%.

The Relationship between Liquidity Discounts and Control Premiums

Market liquidity and the value of control tend to move in opposite directions—that is, whenever it is easy for shareholders to sell their shares, the benefits of control diminish. Why? Because shareholders who are dissatisfied with the decisions made by controlling shareholders may choose to sell their shares, thereby reducing the value of the controlling shareholder's interest. Conversely, when it is difficult for shareholders to sell without incurring significant losses (i.e., the market is illiquid), investors place a greater value on control. Minority shareholders have no way to easily dispose of their investment, since they cannot force the sale of the firm and the controlling shareholder has little incentive to acquire their shares, except at a steep discount. The controlling shareholder can continue to make decisions that may not be in the best interests of the minority shareholders with minimal consequences. Therefore, the sizes of control premiums and liquidity discounts tend to be positively correlated, since the value of control increases as market liquidity decreases (i.e., liquidity discounts increase).

Equation (10.1) can be rewritten to reflect the interdependent relationship between the control premium (CP) and the liquidity discount (LD) as follows:

(10.2)

where

CP% = control premium expressed as a percentage of the maximum purchase price

LD% = liquidity discount expressed as a percentage of the maximum purchase price

The multiplicative form of Eq. (10.2) results in a term (i.e., LD% × CP%) that serves as an estimate of the interaction between the control premium and the liquidity discount.⁴² Note that while CP% can be positive if it is a premium or negative if it is a minority discount, the value of LD% always is negative.

Estimating Liquidity Discounts, Control Premiums, and Minority Discounts

Given the wide variability of estimates, it should be evident that premiums and discounts must be applied to the value of the target firm with great care. The implication is that there is no such thing as a standard liquidity discount or control premium. In general, the size of the discount or premium should reflect factors specific to the firm.

Factors Affecting the Liquidity Discount

The median discount for empirical studies since 1992 is about 20%, with about 90% of the individual studies' estimated median discounts falling within a range of 13 to 35%. Table 10.5 suggests a subjective methodology for adjusting a private firm for liquidity risk, in which the analyst starts with the median liquidity discount of 20% and adjusts for factors specific to the firm to be valued. Such factors include firm size, liquid assets as a percent of total assets, financial returns, and cash-flow growth and leverage compared to the industry. While this is not intended to be an exhaustive list, these factors were selected based on the findings of empirical studies of restricted stocks.

Table 10.5. Estimating the Size of the Liquidity Discount

Factor	Guideline	Adjust 20% Median Discount as Follows
Firm size	• Large • Small	• Reduce discount • Increase discount
Liquid assets as % of total assets	• >50% • <50%	• Reduce discount • Increase discount
Financial returns	• 2 × industry mediana • ½ × industry median	• Reduce discount • Increase discount
Cash-flow growth rate	• 2 × industry median • ½ × industry median	• Reduce discount • Increase discount
Leverage	• ½ × industry median • 2 × industry median	• Reduce discount • Increase discount
Estimated firm-specific liquidity discount	???

^a Industry median financial information often is available from industry trade associations, conference presentations, Wall Street analysts' reports, Yahoo! Finance, Barron's, Investors Business Daily, The Wall Street Journal, and similar publications and websites.

The logic underlying the adjustments to the median liquidity discount in Table 10.5 is explained next. The liquidity discount should be smaller for more highly liquid firms, since liquid assets generally can be converted quickly to cash with minimal loss of value. Furthermore, firms whose financial returns exceed significantly the industry average have an easier time attracting investors and should be subject to a smaller liquidity discount than firms that are underperforming the industry. Likewise, firms with relatively low leverage and high cash-flow growth should be subject to a smaller liquidity discount than more leveraged firms with slower cash-flow growth because they have a lower breakeven point and are less likely to default or become insolvent.

Factors Affecting the Control Premium

Factors affecting the size of the control premium include the perceived competence of the target's current management, the extent to which operating expenses are discretionary, the value of nonoperating assets, and the perceived net present value of currently unexploited business opportunities. The value in replacing incompetent management is difficult to quantify, since it reflects the potential for better future decision making. The value of nonoperating assets and discretionary expenses are quantified by estimating the after-tax sale value of redundant assets and the pretax profit improvement from eliminating noncritical operating activities or individual positions. While relatively easy to measure, such actions may be impossible to implement without having control of the business.⁴³

If the target business is to be run by the acquirer as it is currently, no control premium should be added to the purchase price. However, if the acquirer intends to take actions that are possible only if the acquirer owns enough of the voting stock to achieve control, the purchase price should include a control premium large enough to obtain a controlling interest. Table 10.6 provides a subjective methodology for adjusting a control premium to be applied to a specific business. Note that the 10% premium used in the table is for illustrative purposes only and is intended to provide a starting point. The actual premium selected should reflect the analyst's perception of what is appropriate given the country's legal system and propensity to enforce laws and the extent to which firm ownership tends to be concentrated or widely dispersed.

Table 10.6. Estimating the Size of the Control Premium to Reflect the Value of Changing the Target's Business Strategy and Operating Practices

Factor	Guideline	Adjust 10% Median Control Premium as Followsa
Target management	• Retain • Replace	• No change in premium • Increase premium
Discretionary expenses	• Cut if potential savings >5% of total expenses • Do not cut if potential savings <5% of total expenses	• Increase premium • No change in premium
Nonoperating assets	• Sell if potential after-tax gain >10% of purchase priceb • Defer decision if potential after-tax gain <10% of purchase price	• Increase premium • No change in premium
Alternative business opportunities	• Pursue if NPV >20% of target's stand-alone value • Do not pursue if NPV <20% of target's stand-alone value	• Increase premium • No change in premium
Estimated firm-specific control premium		???

^a The 10% premium represents the median estimate from the Nenova (2003) and Dyck and Zingales (2004) studies for countries perceived to have relatively stronger investor protection and law enforcement.

^b The purchase price refers to the price paid for the controlling interest in the target.

The percentages applied to the discretionary expenses' share of total expenses, nonoperating assets as a percent of total assets, and the NPV of alternative strategies are intended to reflect risks inherent in cutting costs, selling assets, and pursuing alternative investment opportunities. These risks include a decline in morale and productivity following layoffs, the management time involved in selling assets and the possible disruption of the business, and the potential for overestimating the NPV of alternative investments. In other words, the perceived benefits of these decisions should be large enough to offset the associated risks. Additional adjustments not shown in Table 10.6 may be necessary to reflect state statutes affecting the rights of controlling and minority shareholders.⁴⁴

As a practical matter, business appraisers frequently rely on the Control Premium Study, published annually by FactSet Mergerstat. Another source is Duff and Phelps. The use of these data is problematic, however, since the control premium estimates provided by these firms include the estimated value of synergy as well as the amount paid to gain control.⁴⁵

Factors Affecting the Minority Discount

Minority discounts reflect the loss of influence due to the power of a controlling block investor. Intuitively, the magnitude of the discount should relate to the size of the control premium. The larger the control premium, the greater the perceived value of being able to direct the activities of the business and the value of special privileges that come at the expense of the minority investor. Reflecting the relationship between control premium and minority discounts, FactSet Mergerstat estimates minority discounts by using the following formula:

(10.3)

Equation (10.3) implies that an investor would pay a higher price for control of a company and a lesser amount for a minority stake (i.e., larger control premiums are associated with larger minority discounts). While Eq. (10.3) is routinely used by practitioners to estimate minority discounts, there is little empirical support for this largely intuitive relationship.

Exhibit 10.2 illustrates what an investor should be willing to pay for a controlling interest and for a minority interest. Note that the example assumes that 50.1% ownership is required for a controlling interest. In practice, control may be achieved with less than a majority ownership position if there are numerous other minority investors or the investor is buying supervoting shares. The reader should note how the 20% median liquidity discount rate (based on recent empirical studies) is adjusted for the specific risk and return characteristics of the target firm. Furthermore, note that the control premium is equal to what the acquirer believes is the minimum increase in value created by achieving a controlling interest. Also, observe how the direct relationship between control premiums and minority discounts is used to estimate the size of the minority discount. Finally, see how median estimates of liquidity discounts and control premiums can serve as guidelines in valuation analyses.

Exhibit 10.2 Incorporating Liquidity Risk, Control Premiums, and Minority Discounts in Valuing a Private Business

Lighting Group Incorporated, a holding company, wants to acquire a controlling interest in Acuity Lighting, whose estimated stand-alone equity value equals $18,699,493 (see Exhibit 10.1). LGI believes that the present value of synergies due to cost savings is $2,250,000 (PV_SYN) due to the potential for bulk purchase discounts and cost savings related to eliminating duplicate overhead and combining warehousing operations. LGI believes that the value of Acuity, including synergy, can be increased by at least 10% by applying professional management methods (and implicitly by making better management decisions). To achieve these efficiencies, LGI must gain control of Acuity. LGI is willing to pay a control premium of as much as 10%. The minority discount is derived from Eq. (10.3). The factors used to adjust the 20% median liquidity discount are taken from Table 10.5. The magnitudes of the adjustments are the opinion of the analyst. LGI's analysts have used Yahoo! Finance to obtain the industry data in Table 10.7 for the home furniture and fixtures industry.

Table 10.7. Industry Data

NA = Not available or not applicable.

^a Median estimate of the liquidity discount of empirical studies (excluding pre-IPO studies) since 1992.

^b From Exhibit 10.1. $5,101,147/$18,699,493 = 0.27.

What is the maximum purchase price LGI should pay for a 50.1% controlling interest in the business? For a minority 20% interest in the business?

To adjust for presumed liquidity risk of the target firm due to lack of a liquid market, LGI discounts the amount it is willing to offer to purchase 50.1% of the firm's equity by 16%.

Using Eq. (10.2):

If LGI were to acquire only a 20% stake in Acuity, it is unlikely that there would be any synergy because LGL would lack the authority to implement potential cost saving measures without the approval of the controlling shareholders. Because it is a minority investment, there is no control premium, but a minority discount for lack of control should be estimated. The minority discount is estimated using Eq. (10.3)—that is, 1 – (1/(1 + 0.10)) = 9.1.

Reverse mergers

Many small businesses fail each year. In a number of cases, all that remains is a business with no significant assets or operations. Such companies are referred to as shell corporations. Shell corporations can be used as part of a deliberate business strategy in which a corporate legal structure is formed in anticipation of future financing, a merger, joint venture, spin-off, or some other infusion of operating assets. This may be accomplished in a transaction called a reverse merger, in which the acquirer (a private firm) merges with a publicly traded target (often a corporate shell) in a statutory merger in which the public firm survives. See Chapter 11 for more on reverse mergers.

The Value of Corporate Shells

Merging with an existing corporate shell of a publicly traded company may be a reasonable alternative for a firm wanting to go public that is unable to provide the two years of audited financial statements required by the SEC or is unwilling to incur the costs of going public. Thus, merging with a shell corporation may represent an effective alternative to an IPO for a small firm.

After the private company acquires a majority of the public shell corporation's stock and completes the reverse merger, it appoints new management and elects a new board of directors. The owners of the private firm receive most of the shares of the shell corporation (i.e., more than 50%) and control the shell's board of directors. The new firm must have a minimum of 300 shareholders to be listed on the NASDAQ Small Cap Market.

Shell corporations usually are of two types. The first is a failed public company whose shareholders want to sell what remains to recover some of their losses. The second type is a shell that has been created for the sole purpose of being sold as a shell in a reverse merger. The latter type typically carries less risk of having unknown liabilities.

Are Reverse Mergers Cheaper Than IPOs?

As noted previously, direct and indirect costs of an IPO can be as much as 22% of gross proceeds, or about $1.1 million for a $5 million IPO. Reverse mergers typically cost between $50,000 and $100,000, about one-quarter of the expense of an IPO, and can be completed in about 60 days, or one-third of the time to complete a typical IPO.⁴⁶

Despite these advantages, reverse takeovers may take as long as IPOs and are sometimes more complex. The acquiring company must still perform due diligence on the target and communicate information on the shell corporation to the exchange on which its stock will be traded and prepare a prospectus. It can often take months to settle outstanding claims against the shell corporation. Public exchanges often require the same level of information for companies going through reverse mergers as those undertaking IPOs. The principal concern is that the shell company may contain unseen liabilities, such as unpaid bills or pending litigation, which in some instances can make the reverse merger far more costly than an IPO.

Empirical studies show mixed results. One study completed in 2002 found that 32.6% of the sample of 121 reverse mergers between 1990 and 2000 were delisted from their exchanges within three years. The authors argue that reverse mergers may represent a means by which a private firm can achieve listing on a public stock exchange when it may not be fully able to satisfy the initial listing requirements if it were to undertake an IPO.⁴⁷ However, this claim is disputed in a larger and more recent study involving a sample of 286 reverse mergers and 2,860 IPOs between 1990 and 2002. The study found that private firms using the reverse merger technique to go public rather than the IPO method tend to be smaller, younger, and exhibit poorer financial performance than those that choose to go public using an IPO. Of those private firms listed on public exchanges either through a reverse merger or an IPO, 42% using reverse mergers are delisted within three years versus 27% of firms using IPOs. However, the study found that only 1.4% of their sample of reverse mergers were unable to satisfy the initial listing requirements of public exchanges. See Case Study 10.1 for an example of a company taken public via a reverse merger.⁴⁸

Financing Reverse Mergers

Private investment in public equities (PIPEs) is a commonly used method of financing reverse mergers. In a PIPE offering, a firm with publicly traded shares sells, usually at a discount, newly issued but unregistered securities, typically stock or debt convertible into stock, directly to investors in a private transaction. Hedge funds are common buyers of such issues. The issuing firm is required to file a shelf registration statement on Form S-3 with the SEC as quickly as possible (usually between 10 and 45 days after issuance) and to use its “best efforts” to complete registration within 30 days after filing.

PIPEs often are used in conjunction with a reverse merger to provide companies with not just an alternative way to go public but also financing once they are listed on the public exchange. For example, assume a private company is merged into a publicly traded firm through a reverse merger. As the surviving entity, the public company raises funds through a privately placed equity issue (i.e., PIPE financing). The private firm is now a publicly traded company with the funds to finance future working capital requirements and capital investments.⁴⁹

Using leveraged employee stock ownership plans to buy private companies

An ESOP is a means whereby a corporation can make tax-deductible contributions of cash or stock into a trust comprising up to 25% of its annual pre-tax payroll. The ESOP's assets are allocated to employees and are not taxed until withdrawn by employees. ESOPs generally must invest at least 50% of their assets in employer-chosen stock. Three types of ESOPs are recognized by the 1974 Employee Retirement Income Security Act: leveraged, where the ESOP borrows to purchase qualified employer securities; leverageable, where the ESOP is authorized but not required to borrow; and nonleveraged, where the ESOP may not borrow funds. As noted in Chapter 1, ESOPs offer substantial tax advantages to sponsoring firms, lenders, and participating employees.

Employees frequently use leveraged ESOPs to buy out owners of private companies who have most of their net worth in the firm. ESOPs are particularly popular for this purpose during periods of economic slowdowns when business owners wishing to sell their businesses have fewer options. ESOP valuations done by professional appraisers are often much lower than purchase prices that could be obtained in a more conventional acquisition or merger.

For firms having established ESOPs, the business owner sells at least 30% of their stock to the ESOP, which pays for the stock with borrowed funds. The owner may invest the proceeds and defer taxes if the investment is made within 12 months of the sale of the stock to the ESOP, the ESOP owns at least 30% of the firm, and neither the owner nor his or her family participates in the ESOP. The firm makes tax-deductible contributions to the ESOP in an amount sufficient to repay interest and principal. Shares held by the ESOP are distributed to employees as the loan is repaid. As the outstanding loan balance is reduced, the shares are allocated to employees, who eventually own the firm.⁵⁰

Empirical studies of shareholder returns

As noted in Chapter 1, target shareholders of both public and private firms routinely experience abnormal positive returns when a bid is announced for the firm. In contrast, acquirer shareholders often experience abnormal negative returns on the announcement date, particularly when using stock to purchase publicly traded firms. However, substantial empirical evidence shows that public acquirers using their stock to buy privately held firms experience significant abnormal positive returns around the transaction announcement date. Other studies suggest that acquirers of private firms often experience abnormal positive returns regardless of the form of payment. These studies are discussed next.

A study of the returns to public company shareholders when they acquire privately held firms found an average positive 2.6% abnormal return for shareholders of bidding firms for stock offers but not cash transactions.⁵¹ The finding of positive abnormal returns earned by buyers using stock to acquire private companies is in sharp contrast with the negative abnormal returns earned by U.S. bidders using stock to acquire publicly traded companies.

Ownership of privately held companies tends to be highly concentrated, so an exchange of stock tends to create a few very large block stockholders. Close monitoring of management and the acquired firm's performance may contribute to abnormal positive returns experienced by companies bidding for private firms. These findings are consistent with studies conducted in Canada, the United Kingdom, and Western Europe.⁵²

Firms acquiring private firms often earn excess returns regardless of the form of payment.⁵³ Acquirers can also earn excess returns of as much as 2.1% when buying private firms or 2.6% for subsidiaries of public companies.⁵⁴ The abnormal returns may reflect the tendency of acquirers to pay less for nonpublicly traded companies, due to the relative difficulty in buying private firms or subsidiaries of public companies. In both cases, shares are not publicly traded and access to information is limited. Moreover, there may be fewer bidders for nonpublicly traded companies. Consequently, these targets may be acquired at a discount from their actual economic value. As a consequence of this discount, bidder shareholders are able to realize a larger share of the anticipated synergies.

Other factors that may contribute to these positive abnormal returns for acquirers of private companies include the introduction of more professional management into the privately held firms and tax considerations. Public companies may introduce more professional management systems into the target firms, thereby enhancing the target's value. The acquirer's use of stock rather than cash may also induce the seller to accept a lower price since it allows sellers to defer taxes on any gains until they decide to sell their shares.⁵⁵

Some things to remember

Valuing private companies is more challenging than valuing public companies, due to the absence of published share price data and the unique problems they face due to their size. Owners considering the sale of their firms may overstate revenue and understate cost; however, during the normal course of business, private firms are more likely to overstate costs and understate revenues to minimize tax liabilities. As such, it is crucial to restate the firm's financial statements to determine the current period's true profitability.

When markets are illiquid and block shareholders exert substantial control over the firm's operations, the maximum offer price for the target must be adjusted for liquidity risk and the value of control. Given the wide variability of estimates, it should be evident that premiums and discounts must be applied to the value of the target firm with great care. In general, the size of the premium or discount should reflect factors specific to the firm. The median liquidity discount from empirical studies since 1992 is about 20%. While varying widely, recent studies indicate that median pure control premiums across countries are about 12 to 14%. However, such premiums in the United States fall in the 2 to 5% range. Increasing control premiums are associated with increasing minority discounts. The author suggests that factors specific to each circumstance need to be analyzed and used to adjust these medians to the realities of the situation.

In contrast to studies involving acquisitions of U.S. public firms, buyers of private firms in the United States and abroad often realize significant abnormal positive returns, particularly in share-for-share transactions. This result reflects the concentration of ownership in private firms and the resulting aggressive monitoring of management, a tendency of buyers to acquire private firms at a discount from their economic value, and tax considerations.

Discussion Questions

10.1 Why is it more difficult to value privately held companies than publicly traded firms?

10.2 What factors should be considered in adjusting target company data?

10.3 What is the capitalization rate, and how does it relate to the discount rate?

10.4 What are the common ways of estimating the capitalization rate?

10.5 What is the liquidity discount, and what are common ways of estimating this discount?

10.6 Give examples of private company costs that might be understated, and explain why.

10.7 How can an analyst determine if the target firm's costs and revenues are understated or overstated?

10.8 What is the difference between the concepts of fair market value and fair value?

10.9 What is the importance of IRS Revenue Ruling 59-60?

10.10 Why might shell corporations have value?

10.11 Why might succession planning be more challenging for a family firm?

10.12 How are governance issues between public and private firms the same and how are they different?

10.13 What are some of the reasons a family-owned or privately owned business may want to go public? What are some of the reasons that discourage such firms from going public?

10.14 Why are family-owned firms often attractive to private equity investors?

10.15 Rank from the highest to lowest the liquidity discount you would apply if you, as a business appraiser, had been asked to value the following businesses: (a) a local, profitable hardware store; (b) a money-losing laundry; (c) a large privately owned firm with significant excess cash balances and other liquid short-term investments; and (d) a pool-cleaning service whose primary tangible assets consist of a two-year-old truck and miscellaneous equipment. Explain your ranking.

Answers to these Discussion Questions are available in the Online Instructor's Manual for instructors using this book.

Practice Problems and Answers

10.16 It usually is appropriate to adjust the financials received from the target firm to reflect any changes that you, as the new owner, would make to create an adjusted EBITDA. Using the Excel-Based Spreadsheet on How to Adjust Target Firm's Financial Statements on the companion site, make at least three adjustments to the target's hypothetical financials to determine the impact on the adjusted EBITDA. (Note: The adjustments should be made in the section on the spreadsheet entitled “Adjustments to Target Firm's Financials.”) Explain your rationale for each adjustment.

10.17 Based on its growth prospects, a private investor values a local bakery at $750,000. She believes that cost savings having a present value of $50,000 can be achieved by changing staffing levels and store hours. Based on recent empirical studies, she believes the appropriate liquidity discount is 20%. A recent transaction in the same city required the buyer to pay a 5% premium to the average price for similar businesses to gain a controlling interest in a bakery. What is the most she should be willing to pay for a 50.1% stake in the bakery?

Answer: $336,672

10.18 You have been asked by an investor to value a local restaurant. In the most recent year, the restaurant earned pretax operating income of $300,000. Income has grown an average of 4% annually during the last five years, and it is expected to continue growing at that rate into the foreseeable future. By introducing modern management methods, you believe the pretax operating-income growth rate can be increased to 6% beyond the second year and sustained at that rate through the foreseeable future. The investor is willing to pay a 10% premium to reflect the value of control. The beta and debt-to-equity ratio for publicly traded firms in the restaurant industry are 2 and 1.5, respectively. The business's target debt-to-equity ratio is 1, and its pretax cost of borrowing, based on its recent borrowing activities, is 7%. The business-specific risk for firms of this size is estimated to be 6%. The investor concludes that the specific risk of this business is less than other firms in this industry due to its sustained profit growth, low leverage, and high return on assets compared to similar restaurants in this geographic area. Moreover, per capita income in this region is expected to grow more rapidly than elsewhere in the country, adding to the growth prospects of the restaurant business. At an estimated 15%, the liquidity risk premium is believed to be relatively low due to the excellent reputation of the restaurant. Since the current chef and the staff are expected to remain if the business is sold, the quality of the restaurant is expected to be maintained. The ten-year Treasury bond rate is 5%, the equity risk premium is 5.5%, and the federal, state, and local tax rate is 40%. The annual change in working capital is $20,000, and capital spending for maintenance exceeded depreciation in the prior year by $15,000. Both working capital and the excess of capital spending over depreciation are projected to grow at the same rate as operating income. What is the business worth?

Answer: $2,110,007

Answers to these practice exercises and problems are available in the Online Instructor's Manual for instructors using this book.

Chapter Business Cases

Case Study 10.1

Panda Ethanol Goes Public in a Shell Corporation

In early 2007, Panda Ethanol, owner of ethanol plants in west Texas, decided to explore the possibility of taking its ethanol production business public to take advantage of the high valuations placed on ethanol-related companies in the public market at that time. The firm was confronted with the choice of taking the company public through an initial public offering or by combining with a publicly traded shell corporation through a reverse merger.

After enlisting the services of a local investment banker, Grove Street Investors, Panda chose to “go public” through a reverse merger. This process entailed finding a shell corporation with relatively few shareholders who were interested in selling their stock. The investment banker identified Cirracor Inc. as a potential merger partner. Cirracor was formed on October 12, 2001, to provide website development services and was traded on the over-the-counter bulletin board market (i.e., a market for very low-priced stocks). The website business was not profitable, and the company had only ten shareholders. As of June 30, 2006, Cirracor listed $4,856 in assets and a negative shareholders' equity of $(259,976). Given the poor financial condition of Cirracor, the firm's shareholders were interested in either selling their shares for cash or owning even a relatively small portion of a financially viable company to recover their initial investments in Cirracor. Acting on behalf of Panda, Grove Street formed a limited liability company, called Grove Panda, and purchased 2.73 million Cirracor common shares, or 78% of the company, for about $475,000.

The merger proposal provided for one share of Cirracor common stock to be exchanged for each share of Panda Ethanol common outstanding stock and for Cirracor shareholders to own 4% of the newly issued and outstanding common stock of the surviving company. Panda Ethanol shareholders would own the remaining 96%. At the end of 2005, Panda had 13.8 million shares outstanding. On June 7, 2007, the merger agreement was amended in order to permit Panda Ethanol to issue 15 million new shares through a private placement to raise $90 million. This brought the total Panda shares outstanding to 28.8 million. Cirracor common shares outstanding at that time totaled 3.5 million. However, to achieve the agreed-on ownership distribution, the number of Cirracor shares outstanding had to be reduced. This would be accomplished by initiating an approximate three-for-one reverse stock split immediately prior to the completion of the reverse merger (i.e., each Cirracor common share would be converted into 0.340885 shares of Cirracor common stock). As a consequence of the merger, the previous shareholders of Panda Ethanol were issued 28.8 million new shares of Cirracor common stock. The combined firm now has 30 million shares outstanding, with the Cirracor shareholders owning 1.2 million shares. Table 10.8 illustrates the effect of the reverse stock split.

Table 10.8. Effects of Reverse Stock Split

^* In millions of dollars.

A special Cirracor shareholders' meeting was required by Nevada law (i.e., the state in which Cirracor was incorporated) in view of the substantial number of new shares that were to be issued as a result of the merger. The proxy statement filed with the SEC and distributed to Cirracor shareholders indicated that Grove Panda, a 78% owner of Cirracor common stock, had already indicated that it would vote its shares for the merger and the reverse stock split. Since Cirracor's articles of incorporation required only a simple majority to approve such matters, it was evident to all that approval was imminent.

On November 7, 2007, Panda completed its merger with Cirracor Inc. As a result of the merger, all shares of Panda Ethanol common stock (other than Panda Ethanol shareholders who had executed their dissenters' rights under Delaware law) would cease to have any rights as a shareholder except the right to receive one share of Cirracor common stock per share of Panda Ethanol common. Panda Ethanol shareholders choosing to exercise their right to dissent would receive a cash payment for the fair value of their stock on the day immediately before closing. Cirracor shareholders had similar dissenting rights under Nevada law. While Cirracor is the surviving corporation, Panda is viewed for accounting purposes as the acquirer. Accordingly, the financial statements shown for the surviving corporation are those of Panda Ethanol.

Discussion Questions

1. Who were Panda Ethanol, Grove Street Investors, Grove Panda, and Cirracor? What were their roles in the case study? Be specific.

2. Discuss the pros and the cons of a reverse merger versus that of an initial public offering for taking a company public. Be specific.

3. Why did Panda Ethanol undertake a private equity placement totaling $90 million shortly before implementing the reverse merger?

4. Why did Panda not directly approach Cirracor with an offer? How were the Panda Grove investment holdings used to influence the outcome of the proposed merger?

Answers to this case are provided in the Online Instructor's Manual available for instructors using this book.

Case Study 10.2

Determining Liquidity Discounts—The Taylor Devices and Tayco Development Merger

This discussion56 is a highly summarized version of how a business valuation firm evaluated the liquidity risk associated with Taylor Devices' unregistered common stock, registered common shares, and a minority investment in a business that it was planning to sell following its merger with Tayco Development. The estimated liquidity discounts were used in a joint proxy statement submitted to the SEC by the two firms to justify the value of the offer the boards of Taylor Devices and Tayco Development had negotiated.

Taylor Devices and Tayco Development agreed to merge in early 2008. Tayco would be merged into Taylor, with Taylor as the surviving entity. The merger would enable Tayco's patents and intellectual property to be fully integrated into Taylor's manufacturing operations, since intellectual property rights transfer with the Tayco stock. Each share of Tayco common would be converted into one share of Taylor common stock, according to the terms of the deal. Taylor's common stock is traded on the Nasdaq Small Cap Market under the symbol TAYD, and on January 8, 2009 (the last trading day before the date of the filing of the joint proxy statement with the SEC), the stock closed at $6.29 per share. Tayco common stock is traded over the counter on “Pink Sheets” (i.e., an informal trading network) under the trading symbol TYCO.PK, and it closed on January 8, 2009, at $5.11 per share.

A business appraisal firm was hired to value Taylor's unregistered (with the SEC) shares. The appraisal firm treated the shares as if they were restricted shares because there was no established market for trading in these shares. The appraiser reasoned that the risk of Taylor's unregistered shares is greater than for letter stocks, which have a stipulated period during which the shares cannot be sold, because the Taylor shares lacked a date indicating when they could be sold. Using this line of reasoning, the appraisal firm estimated a liquidity discount of 20%, which it believed approximated the potential loss that holders of these shares might incur in attempting to sell their shares.

The block of registered Taylor common stock differs from the unregistered shares in that they are not subject to Rule 144. Based on the trading volume of Taylor common stock over the preceding 12 months, the appraiser believed that it would likely take less than one year to convert the block of registered stock into cash and the appraisal firm estimated the discount at 13%, consistent with the Aschwald (2000) studies.

The appraisal firm also was asked to estimate the liquidity discount for the sale of Taylor's minority investment in a real estate development business. Due to the increase in liquidity of restricted stocks since 1990, the business appraiser argued that restricted stock studies conducted before that date may provide a better proxy for liquidity discounts for this type of investment. Interests in closely held firms are more like letter stock transactions occurring before the changes in SEC Rule 144 beginning in 1990 when the holding period was reduced from three to two years and later to one after 1997. Such firms have little ability to raise capital in public markets due to their small size, and they face high transaction costs.

Based on the SEC and other prior 1990 studies, the liquidity discount for this investment was expected to be between 30 and 35%. Pre-IPO studies could push it higher to a range of 40 to 45%. Consequently, the appraisal firm argued that the discount for most minority interest investments tended to fall in the range of 25 to 45%. Because the real estate development business is smaller than nearly all of the firms in the restricted stocks studies, the liquidity discount is believed by the appraisal firm to be at the higher end of the range.

Discussion Questions

1. Describe how the various historical restricted stock studies were used by the appraiser to estimate the liquidity discount.

2. What other factors could the appraiser have used to estimate the liquidity discount on the unregistered stock?

3. In view of your answer to question 2, how might these factors have changed the appraiser's conclusions? Be specific.

4. Based on the 13% liquidity discount that was estimated by the business appraiser, what was the actual purchase price premium paid to Tayco shareholders for each of their common shares?

Answers to these questions are available on the Online Instructor's Manual for instructors using this book.

¹ Adapted from Simona Covel, “Firm Sells Itself to Let Patriarch Cash Out,” Wall Street Journal, November 1, 2007, p. B8

² See U.S. Small Business Administration.

³ U.S. Census Bureau

⁴ Astrachan and Shanker, 2003

⁵ Bennedsen et al., 2006; Perez-Gonzalez, 2006; Villalonga and Amit, 2006

⁶ Claessens et al., 2002; Morck and Yeung, 2000

⁷ Robinson, 2002b

⁸ Habershon and Williams, 1999; de Visscher, Aronoff, and Ward, 1995

⁹ Astrachan and Shanker, 2003

¹⁰ The audit consists of a professional examination and verification of a company's accounting documents and supporting data for the purpose of rendering an opinion as to their fairness, consistency, and conformity with generally accepted accounting principles.

¹¹ Foley and Lardner, 2007

¹² Such booking activity results in a significant boost to current profitability because not all the costs associated with multiyear contracts, such as customer service, are incurred in the period in which the full amount of revenue is booked.

¹³ Unfortunately, the standard for fair value is ambiguous, since it is interpreted differently in the context of state statutes and financial reporting purposes. In most states, fair value is the statutory standard of value applicable in cases of dissenting stockholders' appraisal rights. Following a merger or corporate dissolution, shareholders in these states have the right to have their shares appraised and receive fair value in cash. In states adopting the Uniform Business Corporation Act, fair value refers to the value of the shares immediately before the corporate decision to which the shareholder objects, excluding any appreciation or depreciation in anticipation of the corporate decision. Fair value tends to be interpreted by judicial precedents or prior court rulings in each state. In contrast, according to the Financial Accounting Standards Board Statement 157 effective November 15, 2007, fair value is the price determined in an orderly transaction between market participants (Pratt and Niculita, 2008).

¹⁴ The replacement-cost approach sometimes is used to value intangible assets by examining the amount of historical investment associated with the asset. For example, the cumulative historical advertising spending targeted at developing a particular product brand or image may be a reasonable proxy for the intangible value of the brand name or image. However, because consumer tastes tend to change over time, applying historical experience to the future may be highly misleading.

¹⁵ Note that the rationale for this adjustment for specific business risk is similar to that discussed in Chapter 7 in adjusting the CAPM for firm size (i.e., small firms generally are less liquid and subject to higher default risk than larger firms).

¹⁶ “Letter” stock gets its name from the practice of requiring investors to provide an “investment letter” stipulating that the purchase is for investment and not for resale.

¹⁷ Institutional Investor, 1971

¹⁸ Gelman, 1972

¹⁹ Maher, 1976; Trout, 1977

²⁰ Silber, 1991

²¹ The Management Planning Study cited in Mercer (1997) reported a median 28.9% discount.

²² Hall and Polacek, 1994

²³ Johnson, 1999

²⁴ Johnson, 1999; Aschwald, 2000; Finnerty, 2002; Loughran and Ritter, 2002

²⁵ Aschwald, 2000

²⁶ Emory, 2001

²⁷ Chaplinsky and Ramchand, 2000; Loughran and Ritter, 2002

²⁸ Alli and Thompson, 1991

²⁹ Longstaff, 1995

³⁰ Officer, 2007

³¹ Gelman, 1972; Moroney, 1973; Maher, 1976; Silber, 1991

³² Hertzel and Smith, 1993; Hall and Polacek, 1994; Longstaff, 1995; Oliver and Meyers, 2000; Aschwald, 2000; Koeplin, Sarin, and Shapiro, 2000; Finnerty, 2002; Officer, 2007

³³ Another example of a pure control premium is that paid for a firm going private through a leveraged buyout, in that the target firm generally is merged into a shell corporation with no synergy being created and managed for cash after having been recapitalized. While the firm's management team may remain intact, the board of directors usually consists of representatives of the financial sponsor (i.e., equity or block investor).

³⁴ Barclay and Holderness, 1989

³⁵ Dyck and Zingales, 2004

³⁶ Dyck and Zingales, 2004

³⁷ Massari, Monge, and Zanetti, 2006

³⁸ Weifeng, Zhaoguo, and Shasa, 2008

³⁹ Zingales, 1995

⁴⁰ Nenova, 2003

⁴¹ Hanouna, Sarin, and Shapiro, 2001

⁴² If control premiums and minority discounts and control premiums and liquidity discounts are positively correlated, minority discounts and liquidity discounts must be positively correlated.

⁴³ This is true because such decisions could involve eliminating the positions of members of the family owning the business or selling an asset owned by the business but used primarily by the family owning the business.

⁴⁴ In more than one-half of the states, major corporate actions, such as a merger, sale, liquidation, or recapitalization of a firm, may be approved by a simple majority vote of the firm's shareholders. In contrast, other states require at least a two-thirds majority to approve such decisions. In these states, a minority of slightly more than one-third can block such actions. Furthermore, a majority of the states have dissolution statutes that make it possible for minority shareholders to force dissolution of a corporation if they can show there is a deadlock in their negotiations with the controlling shareholders or that their rights are being violated. If the suit is successful and the controlling shareholders do not want to dissolve the firm, the solution is to pay the minority shareholders fair value for their shares.

⁴⁵ Damodaran (2002) suggests that the way to estimate a control premium is to view it as equal to the difference between the present value of a firm if it were being operated optimally and its present value the way it is currently being managed. This approach presumes that the analyst is able to determine accurately the value-optimizing strategy for the target firm.

⁴⁶ Sweeney, 2005

⁴⁷ Arellano-Ostoa and Brusco, 2002

⁴⁸ Cyree and Walker, 2008

⁴⁹ To issuers, PIPEs offer the advantage of being able to be completed more quickly, cheaply, and confidentially than a public stock offering, which requires registration up front and a more elaborate investor “road show” to sell the securities to public investors. To investors, PIPEs provide an opportunity to identify stocks that overoptimistic public investors have overvalued. Such shares can be purchased as a private placement at a discount to compensate investors for the stock's underperformance following the issue. Once registered, such shares can be resold in the public markets, often before the extent of the overvaluation is recognized by public investors. As private placements, PIPEs are most suitable for raising small amounts of financing, typically in the $5 to $10 million range. Firms seeking hundreds of millions of dollars are more likely to be successful in going directly to the public financial markets in a public stock offering.

⁵⁰ Only C and Sub-Chapter S corporations generating pretax incomes of at least $100,000 annually are eligible to form ESOPs.

⁵¹ Chang, 1998

⁵² Draper and Padyal (2006), in an exhaustive study of 8,756 firms from 1981 to 2001, also found that acquirers of private firms in the United Kingdom paying with stock achieved the largest positive abnormal returns due to increased monitoring of the target firm's performance. These findings are consistent with the positive abnormal announcement returns of more than 2% for acquirers of private firms in Canadian and European studies, where ownership is often more highly concentrated than the highly dispersed ownership of publicly traded firms in the United States (Ben-Amar and Andre, 2006; Bigelli and Mengoli, 2004; Boehmer, 2000; Dumontier and Pecherot, 2001). This conclusion is consistent with studies of returns to companies that issue stock and convertible debt in private placements (Fields and Mais, 1991; Hertzel and Smith, 1993; Wruck, 1989). It generally is argued that, in private placements, large shareholders are effective monitors of managerial performance, thereby enhancing the prospects of the acquired firm (Demsetz and Lehn, 1996). Wruck and Wu (2009) argue that relationships such as board representation developed between investors and issuers contribute to improved firm performance due to increased monitoring of performance and improved corporate governance. Such relationships may be a result of the private placement of securities.

⁵³ Ang and Kohers, 2001

⁵⁴ Fuller, Netter, and Stegemoller, 2002

⁵⁵ Poulsen and Stegemoller, 2002

⁵⁶ Answers: SEC Form S4 filing of a joint proxy statement for Taylor Devices and Tayco Development, dated January 15, 2008.