Methodology: The Analysis of Valuation

1. Methodology: The Analysis of Valuation Josh Lerner Empirical Methods in Corporate Finance

2. An alternative approach • Much of empirical corporate finance has examined changes in valuation: • Presumption of efficiency  short-run event studies. • Search for anomalies has relied on long-run studies, despite: • Lack of theoretical foundations. • Benchmarking issues. • Problematic statistical properties.

3. An alternative approach (2) • Look at level of valuation, typically around financing events: • Is price “right”? • What affects prices? • Can borrow from substantial economic literature: • “Hedonic” pricing. • Price indices.

4. Long history in finance literature • Tests of dividend discount and other valuation models. • Analyses of information content of accounting earnings. • But generally limited understanding of the econometric issues explored in economics literature.

5. Growing sophistication • Continuing work in economics since Waugh’s [1928] pioneering study. • Growing awareness of estimation issues, interpretative challenges. • Development of approaches to address these issues.

6. Key elements • Criteria for selecting observations. • “Market” valuation of firms. • Data that should be correlated with market value: • Profitability. • Sales. • Information on similar firms. • Econometric specification for estimation.

7. The Valuation of Cash Flow Forecasts: An Empirical Analysis Kaplan and Ruback [JF, 1995].

8. Motivation • Seeks to assess which broad valuation methodologies work best: • Adjusted present value vs. comparables. • Also seeks to choose best tactics: • Different betas. • Different equity premia. • Different terminal growth rates. • Different comparable sources.

9. Overview • Examines 51 buyouts and recapitalizations in 1980s with detailed projections at time of deal. • Compares actual transaction valuations with forecasted value. • Formally and informally tests accuracy of valuation forecasts with different methods.

10. The Sample • 124 MBOs and 12 recapitalizations, 1980-1989. • ~40% have at least four years of projections (some only on pre-tax basis): • From “fairness opinion” at time of transaction, which is often filed with SEC. • Data on comparable Compustat firms and other LBOs.

11. Computing Market Value • Assume market value=future cash flows + excess cash: • Value of common stock at closing. • Plus value of preferred stock at closing. • Plus book value of debt. • Plus transaction fees. • Less cash and marketable securities.

12. Computing Predicted Value • Compute sum of cash flows to all capital: • Net income. • Plus depreciation and amortization. • Less change in net working capital. • Less capital expenditures. • Plus interest. • Plus cash from asset sales (after tax).

13. Computing Predicted Value (2) • Compute terminal value: • Equate CapEx and D&A. • Assume profitability will continue indefinitely. • Grow at various rates. • Discount all at cost of unlevered equity: • Using CAPM and firm data. • Using CAPM value-weighted portfolio of NYSE/AMEX firms in same industry. • Using beta of market as a whole.

14. Computing Predicted Value (3) • APV argues should discount tax shield from interest at lower rate (cost of debt): • It is significantly less risky! • For comparables, look at ratio of value to EBITDA for: • All firms in same four-digit SIC & >$40 million market capitalization. • All LBOs within same year. • All LBOs in same year and two-digit industry.

15. Comparing Market and Predicted Value • Compute logarithm of ratio of predicted to market values. • Examine extent within 15% and size of errors. • Best performance by: • APV-based methods. • Historical equity premium (7.4%). • 4% terminal growth rate.

16. Comparing Market and Predicted Value (2) • Hard to assess relative performance: • Tests are not nested. • Statistical properties of valuation ratio is not well-defined. • Compare to errors in the pricing of. other securities • But are the differences significant?

17. Regression Analyses • Regress log of market value on log of predicted value: • Hope to get coefficient of zero for constant, one for slope. • APV approaches give “better” answers. • Would like to see formal hypothesis testing. • Multiples analysis is less clean-cut. • When include multiple measures, both valuation approaches are significant.

18. Addressing Exogeneity • Are cash flows really unbiased expectations? • Could they be “reverse engineered” to generate predicted values? • Address by looking at ex post accuracy of predictions: • Some evidence of bias in cash flow numbers: • But U.S. entered recession in 1990. • No significant pattern in EBITDA/sales ratios.

19. Addressing Exogeneity (2) • Also segmented into where “gaming” may be more or less of a problem: • Little difference in highly levered and less levered transactions. • Argue that APV also provides good results in eight reverse LBOs, where projections are not public disseminated: • But “road show” presentations.

20. Other Issues • Do the market valuations capture everything? • Debt covenants. • Contingencies in purchase price. • Do other factors affect the price paid? • Kaplan-Stein [1993] on the rise of valuations in 1980s. • How endogenous is the filing of projections?

21. Take-Aways • Interesting effort to seriously address the determinants of firm value. • Great experimental setting for looking at these issues, despite remaining difficulties. • Refinements in testing are clearly possible.

22. Money Chasing Deals? The Impact of Fund Inflows on Private Equity Valuations Gompers and Lerner [JFE, 2000]

23. Growing Interest in Institutions and Asset Pricing • Earlier studies: • Why do valuations of a single company differ in two countries’ exchanges? • Why do valuations of closed-end funds differ from the securities that they hold? • How do trades by institutional investors affect stock prices? • How does long-run performance of IPOs relate to presence of institutional investors? • U.S. private equity is attractive arena.

24. Venture Capital Raised by Year

25. Implications of Fund Inflows • Accounts of capital inflows affecting prices, or “money chasing deals.” • Several periods of apparently severe over-valuation, followed by low returns. • May affect allocation of capital across firms and direction of innovation.

26. Few Earlier Examinations • Imbalance in amount of work on asset pricing in public and private markets. • Kaplan and Stein look at 124 leveraged buyouts of public firms in 1980s: • Increased pricing mirrored market moves. • But rising premiums. • Also work on impact of capital inflows into developing country markets.

27. Contrasts Two Views of Price Movements • Hypothesis 1: Rational asset pricing • Prices should reflect expected discounted future cash flows of firms. • Sufficient substitutes exist for each firm, so shifts in supply of funds should not matter. • Correlations with public market values in same industry, firm characteristics, etc.

28. Contrasts Two Views of Price Movements (2) • Hypothesis 2: Market frictions • May be relatively limited number of attractive firms or entrepreneurs. • Inflows of funds may lead to more competition between VCs and higher prices. • May have disproportionate effects on certain market segments.

29. The Data Set • VentureOne: • Established in 1987. • Collects profiles on venture-backed firms from firms and VCs on monthly basis. • Collects data on firms (e.g., industry, employment, sales), and financings (investors, amount, valuation). • Incentives for cooperation. • Valuation data in 55% of 7375 rounds, 1987-1995, or 4069 transactions.

30. Data Supplements • Missing start dates and industries. • Older employment and sales data. • Inflation-adjusted flow into venture and buyout funds by quarter. • Public market returns and accounting data from CRSP and Compustat for all firms in each of 35 three-digit industries.

31. Measures of Market Value • For each of 35 three-digit industries: • Equal- and value-weighted monthly indexes from 1987 to 1995 with monthly rebalancing. • Unweighted and weighted ratio of net income in previous four quarters to equity market value at quarter’s beginning (E/P). • Unweighted and weighted ratio of equity book value to equity market value at quarter’s beginning (B/M).

32. Econometric Methodology • “Pre-money” valuations. • “Log-log” specifications. • Independent variables: firm’s industry, stage, location, and age; industry market value; and VC inflows in past four quarters. • Employment, sales, or full sample. • Controls for small-cap stocks, later rounds, etc.

33. Econometric Methodology (2) • Many firms have multiple financings from VCs. • Dependent variable: difference in logarithm of valuations. • Independent variable: differences in the same variables used before.

34. Econometric Methodology (3) • Will the sensitivity of pricing to VC fund inflows or public market movements vary with: • stage of investment? • location of investment? • inflows into particular sector?

35. Econometric Methodology (4) • Ultimate outcomes: • Do shifts in inflows and pricing reflect changes in deal quality? • If inflows change in response to deal quality, and rate of investment adjusts more slowly, then quality will vary. • Look at probability of successful exit.

36. Take-Aways • Apparent evidence of impact of inflows on valuations: • Doubling of inflows into VC funds leads to 7% to 22% increase in valuations. • Address causation concerns in a variety of ways. • Remaining interpretative issues.

37. “Empirical Testing of Real Option-Pricing Models” Quigg JF, 1993

38. Attempts to seriously test “real options” • Focuses on real estate. • Seek to understand how much option to wait to develop adds to property value. • Compares with large sample of actual transaction prices.

39. Formal model • Building prices follow an observable, stochastic process. • Developer can choose to continue to hold undeveloped land, or construct project: • Based on Titman [1985] and Williams [1991].

40. The sample • 3200 transactions involving developed parcels, 1976-1979: • Will use to estimate ultimate potential for each parcel. • Estimates on cost of development of buildings of different types. • 2700 transactions involving unimproved parcels. • Urban setting biases against results.

41. First step • Estimate hedonic regression using developed parcels: • Separate regressions by year and zoning class. • Regress logarithm of price on: • Log of square footage. • Log of lot size. • Log of height. • Log of age. • Dummies for region and quarter.

42. Second step • Generated predicted building values for undeveloped sites: • Use coefficients from hedonic regression. • Predict height using average height. • Choose size that maximizes revenues, conditional on attributes. • Potential biases from underestimating newness, expected supply shifts, or not controlling for properties that don’t sell.

43. Third step • Generate expected values using option pricing model: • Sensitivity to pay-out rate from undeveloped property. • Sensitivity to economies of scale with size: • Will impact how large buildings developed. • Compute “intrinsic value” (case when =0, or immediate development).

44. Testing the results • Compare predicted variance of developed properties to published estimates: • Range of 19% to 28%. • Studies of repeat housing sales imply valuations of 15%. • Compare valuation implied by option pricing to immediate development: • Difference averages 6%: • Greatest in industrial. • May reflect data issues. • Even without industrial properties, about 5% premium.

45. Testing the results (2) • Regress market price (per square foot) on predicted value: • Neither model stands out. • Reject joint hypothesis that slope 1 and intercept 0 (errors in variables?). • Then use both intrinsic price and option premium as independent variables: • Constant falls. • Both coefficients closer to one. • But added explanatory power low.

46. Wrap-up • Serious attempt to test these ideas. • Choosing a study site where: • Tractable theoretical framework. • Sufficient data availability. • Hedonic analysis critical input into the process.

47. More General Methodological Issues • Heteroskedasticity: • Variance of estimates may differ due to differ to: • Volatility of market conditions. • Complexity of transactions. • Number of observations. • To address concern, may: • Weight by estimate of variance (as in event study approach). • Allow variance to vary across groups [White, 1980].

48. More General Methodological Issues (2) • Choice of specification: • Log, semi-log, and level are three common representations. • More complex structures also seen. • To address concern, may: • Choose one approach [Gompers-Lerner]. • Try alternative methods [Kaplan-Ruback]. • Formally test through a Box-Cox [1964] specification.

49. More General Methodological Issues (3) • Omitted variable bias: • Variables may be highly significant because correlated with other (missing) measures: • Weight in automobile pricing. • May lead to problematic interpretations: • May conclude that variable itself is important, when actually correlated measure is.

50. Addressing omitted variable bias • Add wide variety of control variables to limit possibility. • Use instrumental variable for key variables to reduce correlation. • Look at ex post outcome to limit assure that no correlation.