# Evidence on IPCPL theory from global mid-market M&A transaction data

**Implied Private Company Pricing Line** (IPCPL) theory was, to my knowledge, the first coherent theory of the relationship between public and private capital markets; developed originally by Robert Dohmeyer and Peter Butler in 2012. This is a particularly important theory because it essentially bridges a gap between asset pricing theory and transaction cost economic theory. Specifically, IPCPL theory explains and predicts that, under the fundamental no-arbitrage risk pricing principle, differences between public and private capital asset prices are caused by differences in transaction costs; e.g., brokerage commissions, legal costs, due diligence costs, transaction advisory fees, etc. Perhaps most interestingly, an analysis of IPCPL theory suggests that incremental private capital market transaction costs are most accurately interpreted as the shadow price of liquidity risk; a risk that is not to observably priced in private capital markets.*And yet IPCPL is not just a theory: The predictions of the theory have been repeatedly tested using fairly large data sets comprised of US private capital market transaction data, and the empirical tests consistently demonstrate that real world private capital market data is consistent with the theory.*

*But why are IPCPL theory and methods important from a practical perspective? They are, in short, important because they represent the only existing way to rationally estimate the fair market value (FMV) of assets traded in private capital markets from public capital market risk prices in the presence of significant private market transaction costs. And without a clear understanding of FMV, buyers and sellers do not know if there is any benefit in buying or selling an asset.*

*This article presents empirical estimates and tests of IPCPL functions for four international regions: the United States and Canada (USC), Brazil (BR), Australia and Asia (AA), and Europe, Middle East, and Africa (EMEA). The data used in developing the estimates and tests were obtained from a global survey of investment bankers and M&A advisors with respect to mid-market M&A transactions; sponsored by Firmex, a virtual data room services provider. The empirical results show, once again, that private capital market data is consistent with IPCPL theory. Please read on … *

#### 1. A brief review of IPCPL theory

I will not provide a detailed explanation of IPCPL theory here because my co-author, David Goodman, and I have already written several articles on IPCPL theory and empirical tests of the theory, which can be accessed online:

David H. Goodman and Malcolm McLelland (2016) The Implied Private Company Pricing Line (IPCPL): On the Nature, Scope, and Assumptions of IPCPL Theory. *Business Valuation Review*: Spring 2016, Vol. 35, No. 1, pp. 18-29.

David H. Goodman and Malcolm McLelland (2018) Private Market Equity Prices and Transactions Costs: Generalized IPCPL Theory and Private Market Empirical Tests. *Business Valuation Review*: Winter 2018, Vol. 37, No. 4, pp. 127-137.

Pre-published versions are also available, here and here.

The basic structure and empirical implications of IPCPL theory can be seen in the simplest case of the current *t* = 0 price of a single risky, expected future cash flow at *t* = 1:

The basic empirical implications of IPCPL theory can be seen most easily in the simplest case where there is a single future cash flow of 1:

The phrase *increasing convex function of transaction costs* means that (i) expected returns (discount rates) increase as transaction costs increase and (ii) there is positive curvature in this relationship (which will be seen clearly below). The following empirical model of the relationship between *observable transaction costs as a proportion of observable transaction price* (*tc*) conditional on *transaction price* (*P*) can be derived directly from IPCPL theory; where ln( . ) denotes a natural logarithm:

There are, of course, details of the derivation of the IPCPL theory and the related empirical model that I have omitted here, but the above expressions capture the essence of the theory.

#### 2. Global empirical tests of IPCPL theory* *

Using mid-market M&A transaction data obtained from a survey of investment bankers and M&A advisors (Firmex, 2020, “M&A Fee Guide, 2018-2019”), the proportional transaction cost function model shown above was estimated using the least absolute deviation method (because of the robustness of the estimation method to extreme observations) for the whole world and for each of four regions / countries:

Note that each of the estimated transaction cost functions are entirely consistent with the predictions of IPCPL theory: Transaction costs are a decreasing, convex function of transaction price; and it can be shown that this implies that risk-adjusted expected *private* market rate of return is an increasing, convex function of transaction costs. Along with the estimated functions, I have included *p*-values below each parameter estimate (shown in parentheses), the sample size for each estimate (*n*), and the *R*-squared statistic for each estimated function. Most importantly, all of the *p*-value statistics are small enough to suggest that the parameter estimates–subject to the Gauss-Markov theorem assumptions holding for each of the models–result in accurate, reliable estimates of median transaction costs conditional on transaction price.

It is helpful to see graphs of the estimated functions to better understand the implications of IPCPL theory:

(Note that the global median transaction cost function is shown as a dotted line.) In addition to seeing that the estimated transaction cost functions are decreasing, convex functions of transaction price–consistent with IPCPL theory–it can be seen that Brazil generally has the highest median mid-market M&A transaction costs; while transaction costs in other regions generally depend on transaction price (*P*), which ranges from USD $0 million to USD $150 million in the graph.

#### 3. Valuation implications of IPCPL methods

I suppose one reason why most valuation professionals have not yet begun implementing IPCPL theory and methods in valuation practices is that the simply don’t know how to apply IPCPL-derived, empirical functions (like those above) to their valuation estimates. Although I will not do so here, it can be shown (and I will show in future articles) that an IPCPL-derived estimated proportional transaction cost function implies that a private market transaction cost adjustment would be added to an appropriate risk-free rate and public market risk premiums to obtain a fair market risk-adjusted discount rate for use in valuation:

The one complication with respect to applying the IPCPL method is that proportional transaction costs, *tc*(*P*), depends on the gross transaction price, *P* (i.e., selling price before transaction costs); as shown. So, given (i) expected cash flows, (ii) risk-free rate, (iii) public market risk premiums, and (iv) the estimated IPCPL function, it is possible to solve for *P*, which then results in the total risk-adjusted discount rate shown above and estimated FMV of the capital asset in the private capital market.

The above basically settles three different and important aspects of IPCPL theory: (1) the basic structure and implications of IPCPL theory, (2) evidence from global mid-market M&A transactions consistent with IPCPL theory circa 2018-2019, and (3) a summary of the IPCPL method as it applies to determining risk-adjusted discount rates and estimates of FMV in private capital markets.

There seems, however, to be one remaining question: Now, 8 years after the introduction of IPCPL theory, evidence, and methods, why are IPCPL methods not being applied somewhat widely in valuation practice? But that’s a question for another time and perhaps another article … .

MMc

São Paulo

**Caveats.** Please note: (i) views presented above are my own and do not reflect those of others; (ii) like anyone, I’m not infallible and am responsible for any errors; (iii) I greatly appreciate being informed of any significant errors in facts, logic, or inferences and am happy to give credit to anyone doing so; (iv) the above article is subject to revision and correction; and, (v) the article cannot be construed as investment or financial advice and is intended merely for educational purposes. MMc