VALUING PRIVATE COMPANIES AND DIVISIONS

PROCESS OF VALUING PRIVATE COMPANIES

• Choosing the right model
• Valuing the Firm versus Valuing Equity
• Steady State, Two-Stage or Three-Stage
• Estimating a Discount Rate
• Cost of Equity
• Estimating Betas
• Cost of Debt
• Estimating Default Risk
• Estimating an after-tax cost of debt
• Cost of Capital
• Estimating a Debt Ratio
• Estimating Cash Flows
• Analyzing the effects of lack of liquidity
• Effects of differential voting rights

ESTIMATING COST OF EQUITY FOR A PRIVATE FIRM

• Basic Problem: Most models of risk and return (including the CAPM and the APM) use past prices of an asset to estimate its risk parameters (beta(s)). Private firms and divisions of firms are not traded, and thus do not have past prices.

• Solution 1: Estimate the beta, based upon comparable firms, and after adjusting for risk.
• Step 1: Collect a group of publicly traded comparable firms, preferably in the same line of business, but more generally, affected by the same economic forces that affect the firm being valued.
• A Simple Test: To see if the group of comparable firms is truly comparable, estimate a correlation between the revenues or operating income of the comparable firms and the firm being valued. If it is high (and positive), of course, your have comparable firms.
• Step 2: Estimate the average beta for the publicly traded comparable firms.
• Step 3: Estimate the average market value debt-equity ratio of these comparable firms, and calculate the unlevered beta for the business.
• bunlevered = blevered / (1 + (1 - tax rate) (Debt/Equity))
• Step 4: Estimate a debt-equity ratio for the private firm. The basic problem, however, is that you have only book values for the private firms. This can be corrected in one of two ways ñ
• Assume that the private firm will move to the industry average debt ratio. The beta for the private firm will then also converge on the industry average beta. This might not happen immediately but over the long term.

Betaprivate firm = Betaunlevered (1 + (1 - tax rate) (Industry Average Debt/Equity))

• Estimate the optimal debt ratio for the private firm, based upon its operating income and cost of capital. Use this optimal debt ratio to calculate the beta. (Be consistent about then using the same debt ratio in your cash flow estimates)

Betaprivate firm = Betaunlevered (1 + (1 - tax rate) (Optimal Debt/Equity))

• Step 5: Estimate a cost of equity for the private firm, based upon this beta.
• Solution 2: Estimate an accounting beta
• Step 1: Collect accounting earnings for the private company for as long as there is a history.
• Step 2: Collect accounting earnings for the S&P 500 for the same time period.
• Step 3: Regress changes in earnings for the private company against changes in the S&P 500.
• Step 4: The slope of the regression is the accounting beta

There are two serious limitations - (a) The number of observations in the regression is small (b) Accountants smooth earnings.

ESTIMATING BETAS FOR PRIVATE FIRMS

 New World Coffee New York Yankees Wordperfect Corporation Comparable Firms Beta D/E Starbucks: 1.74 9.53% Au Bon Pain: 1.21 31.43% Sbarro: 1.12 0.00% Average 1.36 13.65% Beta D/E Topps 0.85 0.00% Beta D/E Adobe Systems 1.70 0.00% Borland Intl 1.35 6.00% Lotus 1.55 2.50% Microsoft 1.35 0.00% Average 1.49 2.12% Unlevered Beta for Comparable Firms 1.25 0.85 1.47 Debt/Equity Ratio for this firm 13.65% (Assumed move to industry average) 30.00% (Based upon management target) 10.00% (Target Debt Ratio) Estimated Beta for this firm 1.36 1.00 1.56 Estimated Cost of Equity 14.98% 13.00% 16.08%

ESTIMATING THE COST OF DEBT FOR A PRIVATE FIRM

• Basic Problem: Private firms generally do not access public debt markets, and are therefore not rated. Most debt on the books is bank debt, and the interest expense on this debt might not reflect the rate at which they can borrow (especially if the bank debt is old.)
• Solution 1: Assume that the private firm can borrow at the same rate as similar firms (in terms of size) in the industry.

Cost of Debt for Private firm = Cost of Debt for similar firms in the industry

• Solution 2: Estimate an appropriate bond rating for the company, based upon financial ratios, and use the interest rate estimated bond rating.

Cost of Debt for Private firm = Interest Rate based upon estimated bond rating for private firm

Note: If the beta is calculated based upon the assumption that the firm will move to its optimal debt ratio, use the corresponding bond rating.

• Solution 3: If the debt on the books of the company is long term and recent, the cost of debt can be calculated using the interest expense and the debt outstanding.

Cost of Debt for Private firm = Interest Expense / Outstanding Debt

Note: If the firm borrowed the money towards the end of the financial year, the interest expenses for the year will not reflect the interest rate on the debt.

ESTIMATING THE COST OF DEBT

 New World Coffee New York Yankees Wordperfect Corporation Comparable Firms kd D/E Starbucks: 9.00% 9.53% Au Bon Pain: 8.50% 31.43% Sbarro: NA 0.00% kd D/E Topps NA 0.00% kd D/E Adobe Systems NA 0.00% Borland Intl 9.00% 6.00% Lotus 8.25% 2.50% Microsoft NA 0.00% Median Cost of Debt 8.75% NA 8.60% Interest Coverage Ratio for this firm Not used 2.95 Not used Rating based upon this coverage ratio Not used BBB Not used Interest Rate paid on Recent Borrowing Not used Not used 8.80% Estimated Cost of Debt 8.75% (Assumed to borrow at industry rate) 9.50% (Based upon bond rating) 8.80%

ESTIMATING THE COST OF CAPITAL

• Basic problem: The debt ratios for private firms are stated in book value terms, rather than market value. Furthermore, the debt ratio for a private firm that plans to go public might change as a consequence of that action.

• Solution 1: Assume that the private firm will move towards the industry average debt ratio.

Debt Ratio for Private firm = Industry Average Debt Ratio

• Solution 2: Assume that the private firm will move towards its optimal debt ratio.

Debt Ratio for Private firm = Optimal Debt Ratio

Consistency in assumptions: The debt ratio assumptions used to calculate the beta, the debt rating and the cost of capital weights should be consistent. In other words, if the assumption is that the firm will move to the industry average debt ratio, the beta should be calculated using the industry average debt/equity ratio, the bond rating should be estimated by looking at similar firms in the industry, and the cost of capital should be calculated using the same debt ratio.

ESTIMATING COSTS OF CAPITAL FOR PRIVATE FIRMS

 New World Coffee New York Yankees Wordperfect Corporation Cost of Equity 14.98% 13.00% 16.08% E/ (D+E) 87.99% 76.92% 90.91% Cost of Debt 8.75% 9.50% 8.80% AT Cost of Debt 5.25% 5.70% 5.28% D/(D+E) 12.01% 23.08% 9.09% Cost of Capital 13.81% 11.32% 15.10%

ESTIMATING CASH FLOWS FOR A PRIVATE FIRM

• Special Problems associated with estimating cash flows for a private firm
• Shorter history: Private firms often have been around for much shorter time periods than most publicly traded firms. There is therefore less historical information available on them.
• Different Accounting Standards: The accounting statements for private firms are often based upon different accounting standards than public firms, which operate under much tighter constraints on what to report and when to report.
• Intermingling of personal and business expenses: In the case of private firms, some personal expenses may be reported as business expenses.
• Separating ìSalariesî from ìDividendsî: It is difficult to tell where salaries end and dividends begin in a private firm, since they both end up with the owner.
• Dealing with Special Problems
• Restate earnings, if necessary, using consistent accounting standards.
• If any of the expenses are personal, estimate the income without these expenses.
• Estimate a ìreasonableî salary based upon the services the owner provides the firm.

ESTIMATING VALUE OF PRIVATE FIRMS

 New World Coffee New York Yankees Wordperfect Corporation EBIT \$ 10.50 million \$27.50 million \$ 125 million EBIT Restated \$ 9.50 million (Owners did not charge themselves salaries in the firm. The combined salaries are assumed to be \$1 mil) \$32.50 million (Both salaries and operating expenses were high relative to other teams. The ìexcessí expenditure of \$ 5 million is stripped from EBIT) \$ 125 million EBIT Restated (1-t) \$ 5.70 million \$ 19.50 million \$ 75 million (CEx-Depr) \$ 3 million \$ 0.00 million \$ 15 million Working Capital as % of Revenues 10 % of Revenues: \$ 2 million No Working Capital 30% of Revenues: \$ 12 million Growth Rates High Growth Stable Growth 40% for 5 yrs; Transition is 5 yrs; 5% a year No high growth 5 % a year 15% a year for 10 years 5% a year Cost of Capital 13.81% 11.32% 15.10% Firm Value - Outstanding Debt = Equity Value \$ 254.32 million - \$ 30.55 million = \$ 223.77 million \$ 324.00 million - \$ 75.00 million = 249.00 million \$ 1269 million - 115 million = \$ 1154 million

ANALYZING THE EFFECT OF ILLIQUIDITY ON VALUE

Investments which are less liquid should trade for less than otherwise similar investments which are more liquid.

• Determinants of the Liquidity Discount
• Type of Assets owned by the Firm: The more liquid the assets owned by the firm, the lower should be the liquidity discount for securities issued by the firm.
• Size of the Firm: The larger the firm, the smaller should be size of the liquidity discount.
• Health of the Firm: Stock in healthier firms should sell for a smaller discount than stock in troubled firms.
• Cash Flow Generating Capacity: Securities in firms which are generating large amounts of cash from operations should sell for a smaller discounts than securities in firms which do not generate large cash flows.
• Size of the Block: The liquidity discount should increase with the size of the block.
• Empirical Evidence

Restricted Stock: Restricted securities are securities issued by a company, but not registered with the SEC, that can be sold through private placements to investors, but cannot be resold in the open market, except under provisions of SECís rule 144. Restricted securities are defined in SEC 144 as ìsecurities that are acquired directly or indirectly from the issuer... that are subject to resale limitationsî. SEC 144 goes on to add that ìa minimum of two years must elapse between the later of the date of the acquisition of the securities from the issuer.. and any resale of such securitiesî. They cannot be sold for a two-year holding period, and limited amounts can be sold after that.

• In studies of these securities going back to 1966, there have been several consistent findings ñ
• Restricted securities trade at significant discounts on publicly traded shares in the same company.
• Maher examined restricted stock purchases made by four mutual funds in the period 1969-73 and concluded that they traded an average discount of 35.43% on publicly traded stock in the same companies.
• Moroney reported a mean discount of 35% for acquisitions of 146 restricted stock issues by 10 investment companies, using data from 1970.
• In a recent study of this phenomenon, Silber finds that the median discount for restricted stock is 33.75%.
• Silber reports that the discounts tend to be smaller for larger and more diversified companies, and larger for companies in trouble. Silber (1991) develops the following relationship between the size of the discount and the characteristics of the firm issuing the registered stock ñ

LN(RPRS) = 4.33 +0.036 LN(REV) - 0.142 LN(RBRT) + 0.174 DERN + 0.332 DCUST

where,

RPRS = Relative price of restricted stock (to publicly traded stock)

REV = Revenues of the private firm (in millions of dollars)

RBRT = Restricted Block relative to Total Common Stock in %

DERN = 1 if earnings are positive; 0 if earnings are negative;

DCUST = 1 if there is a customer relationship with the investor; 0 otherwise;

• Interestingly, Silber finds no effect of introducing a control dummy - set equal to one if there is board representation for the investor and zero otherwise.

From Concept to Practice

• Approach 1: Use the average liquidity discount, based upon past studies, of 20% for private firms. Adjust subjectively for size - make the discount smaller for larger firms.
• Approach 2: Using registered shares, estimate the discount as a function of the determinants - the size of the firm, the stability of cash flows, the type of assets and cash flow generating capacity. (Do a regression, like Silber) Plug in the values for your company into the regression to estimate the liquidity discount.

Application: Estimating the Liquidity Discount on the New York Yankees

REV : Revenues in 1993 (last full year of baseball) = \$ 120 million

Liquidity Discount for small firm - with negligible revenues = 30%

Liquidity Discount for the New York Yankees = 30% - 6% = 24%

[The 6% comes from the graph above, as the reduction in liquidity discount as a function of the revenues]

Estimated value for the Yankees in a private transaction = \$324 million ( 1 - 0.24) = \$246.24 million

ANALYZING THE VALUE OF CONTROL

If one class of shares have no voting rights while the other class of shares do, the difference in voting rights, other things being equal, might make the latter more valuable.

A General Framework for estimating the value of control

• The value of the control premium that will be paid to acquire a block of equity will depend upon two factors -

1. Probability that control of firm will change: This refers to the probability that incumbent management will be replaced. this can be either through acquisition or through existing stockholders exercising their muscle.

• In the more general case, this probability of control changing will depend upon the following factors ñ
• Legal Restrictions on Takeovers: Other things remaining equal, the greater the legal restrictions on takeovers the smaller the probability of control changing.
• Anti-takeover and Pro-incumbent restrictions in corporate charter: The greater the restrictions on takeovers and on changes in incumbent management (staggered elections, restrictions on proxies...), the lower the probability of control changing.
• Market Attitudes towards Control Changes: The probability of control changing will be much greater is markets accept and welcome challenges to incumbent managementís authority. (Are shareholders willing to listen to those challenging incumbent managers? Are bankers willing to finance their acquisitions? Will institutional stockholders stand and fight?)
• Size of stock holding controlled by incumbent management: The greater the proportion of the voting stock controlled by the incumbent management, the lower the probability of control changing.
• Diffusion of Holdings: While 51% is often viewed as the magic number for gaining control, one might be able to exert control with less than 51% if the holdings are widely held. Thus an investor with 35% of the stock in a company may be able to exert control over the company, if the remaining 65% is held widely. The greater the diffusion in holdings, the lower will be the threshold for gaining control of the company.
• Relative numbers of voting and non-voting shares: The value of control is distributed among all of the voting shares. The greater the number of voting shares, relative to non-voting shares, the smaller is the control premium per share.

2. Value of Gaining Control of the Company = Present Value (Value of Company with change in control - Value of company without change in control) + Side Benefits of Control.

• The value of gaining control of a company arises from two sources - the increase in value that can be wrought by changes in the way the company is managed and run, and the side benefits and perquisites of being in control. In the most gener