Owner-manager replacement: a venture capitalist decision model

Cressy, Robert Article Owner-manager replacement: a venture capitalist decision model Journal of Global Entrepreneurship Research Provided in Cooperation with: Springer Nature Suggested Citation: Cressy, Robert (2014) : Owner-manager replacement: a venture capitalist decision model, Journal of Global Entrepreneurship Research, ISSN 2251-7316, Springer, Heidelberg, Vol. 2, Iss. 1, pp. 1-10, https://doi.org/10.1186/2251-7316-2-5 This Version is available at: https://hdl.handle.net/10419/161750 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/2.0/ RESEARCH Open Access Owner-manager replacement: a venture capitalist decision model Robert Cressy Correspondence: [email protected] Birmingham Business School, England, UK Abstract We develop a theory of managerial replacement in which a venture capitalist monitors an investee firm run by a manager of unknown quality (Good or Bad). An informative signal S t correlated with performance (value-added) is available to the VC at a cost in each period t. The problem is when to replace him if he underperforms. We derive a solution to this problem that takes the form of an optimal cutoff for each period t, namely, S tþ1, such that, given his track record, the manager will be replaced if and only if next period’s signal falls below S tþ1. The probability of manager replacement is lower for managers with good track records, higher incremental values and lower VC discount rates, and is higher the higher the return to professional replacement, the cost of investment and the costs of monitoring manager performance. Replacement is also predicted to enhance company value. JEL codes: G24, G32 Keywords: Venture capital; Manager; Replacement; Bayesian learning; Monitoring; Patent Background “Cometh the moment cometh the (wo)man”(Anon) Academics rarely make good managers of high tech businesses and even when they do their usefulness to the company is ephemeral, depending very much on the stage of development the business has reached: for example, a manager useful at startup in product development may have skills that become redundant when full-scale production and marketing is required (Hellmann and Puri 2002; Wright et al. 2005; Wright and Lockett 2005; Wright et al. 2007). The facts demonstrate that very few first-time entrepreneurs (owner-managers) last the course from inception to maturity; in the first 7 to 8 years of the business’life, a high proportion are replaced by professional managers (with extensive previous management experience) often at the behest of the venture capitalist or other financier. (Baron et al. 2001; Hellmann 1998; Hellmann and Puri 2002) a . Clearly the replacement decision is an important one both for the entrepreneur and the VC whose investment is tied up in the company. The VC needs someone who is good at managing people (optimising individual performance), who is in touch with the market, the technology and competition (Hellmann and Puri 2002). All these things will influence the business’performance and ultimately the VC’sreturns. © 2014 Cressy; licensee Springer. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Cressy Journal of Global Entrepreneurship Research 2014, 2:5 http://www.journal-jger.com/content/2/1/5 However, when a start-up is run by inexperienced individuals (e.g. academics spinning out from a university science department or other technically-oriented entrepreneurs with little management experience–see Wright et al. 2005, 2007) their quality as executives is (at least initially) unknown. The VC will learn about this quality over time as a result of frequent (or not so frequent) contact with the new company in the form of monitoring and advice (Cumming and Johan 2007). At some point the manager’s ability is sufficiently well known for the VC to be able to make a decision about replacement in favour of a professional manager. This process and its criteria have an inherent economic logic as we shall shortly see, but the theoretical literature provides little guidance on the matter. Hence the current paper. In this paper we model the VC learning process and the replacement decision in a Bayesian dynamic programming framework b . Briefly, a venture capitalist monitors a start-up run by a manager of unknown quality over a finite horizon. The problem is when to replace him should he underperform. The VC knows that his unobservable quality as a manager affects the likelihood of an increment to firm value next period, which will ultimately enhance the VC’s return. The VC can however observe an informative signal (e.g. ‘people skills’), c St,ofthemanager’s ability in periodtatcostc.Thisenableshertoupdateherprioronthemanager’sability and on the expected profits from retaining him for one more period rather than replacing him with a professional manager. The latter yields a known present discounted value to the VC of Πm. In each of the periods we derive an optimal cutoff S tfor the signal that results in a rule showing when to replace the manager. The chances of adding to firm value in any period are predicted to be positively related to past managerial performance (mean value of the signal). The probability of manager replacement is thus lower for managers with good track records (S 1 ). We find that it is also lower for managers with higher incremental values (π 3 (γ 2 )) and is higher for lower VC discount rates (r). Finally it is higher the higher the return to professional replacement (Πm), the cost of investment (I 2 ) and the costs of monitoring manager performance (c). Basics A VC does not know the quality of the manager he employs in his investee company. However, she has a prior distribution on manager quality and judges that the manager is of Good or Bad quality with probability p(G) and p(B) = 1–p(G). Only if the manager is Good is the return to the firm’s project in a period positive. The value of the project at t, if successful, π t , will in general itself depend on the manager’s track record, consisting of a set of observable past signals, Sτ;τ¼1;2;…;t−1:Thus we write πt¼π S1;S2;…St−1 ðÞ(see Figure 1). Thus the expected value of the project conditional on the information set to date is positive if and only if the manager’s quality is Good. The VC learning process Consider first a discrete quality two-period model. We begin by showing that under the Monotone Likelihood Property (Milgrom 1981) the posterior probability of the manager incrementing firm value is increasing in his track record defined as his period 1 Cressy Journal of Global Entrepreneurship Research 2014, 2:5 Page 2 of 10 http://www.journal-jger.com/content/2/1/5 signal value, S 1 . In the next section we develop the optimal value function in terms of these posterior probabilities and the optimal cutoffs associated with them. The VC can observe a costly signal of the manager’s quality which is either High (H) or Low (L). She thus starts off with a prior on the manager’s quality and then updates this estimate as monitoring occurs. The probability that a manager is Good given a signal S 1 is by Bayes rule: pG jS1 ðÞ¼ pS 1jGðÞpGðÞ pS 1GÞpGðÞþpS 1BÞpBðÞ j ð j ðð1Þ where S1∈H;L fg . This can be rewritten as pðGjS1Þ¼ 1 1þpS 1jBðÞpBðÞ pS 1GÞpGðÞ j ð ð2Þ showing more explicitly the dependence of the posterior on the likelihood ratio pS 1jBðÞpBðÞ pS 1GÞpGðÞ j ðð3Þ We shall without loss of generality assume in what follows that pBðÞ¼pGðÞ¼1=2 and that the ratio (3) satisfies the following inequalities: Assumption 1: pH jBðÞ pH jGðÞ <1<pL jBðÞ pLGÞ j ðð4Þ This is equivalent to assuming that the likelihood ratio is increasing in the signal S or that the distribution function for quality Q conditional on H first order stochastically Figure 1 The payoff function. Cressy Journal of Global Entrepreneurship Research 2014, 2:5 Page 3 of 10 http://www.journal-jger.com/content/2/1/5 dominates that of Q conditional on L (see Milgrom (1981) for details d ). We define for future use the terms x and y: Definition 1: x≡pH jBðÞ pH jGðÞ ;y≡pL jBðÞ pLGÞ j ðð5Þ Using Assumption 1 we can conclude that x<1;y>1 and therefore that pG jLðÞ<1 2<pGHÞ j ðð6Þ Thus the probability of success (of the manager being Good) in any period, given the signal, is increasing in the value of the signal S 2 (management performance). A second observation of the quality signal, S 2 , results in an updating of the VCs prior to pG jS1;S2 ðÞ¼ 1 1þpS 1;S2jBðÞ pS 1;S2GÞjð ð7Þ If observations of the signal are independent this simplifies to pðGjS1;S2Þ¼ 1 1þpS 1jBðÞpS 2jBðÞ pS 1GÞpS 2GÞ j ð j ð ð8Þ It follows that the four possible posterior probabilities are related as follows: pGjH;HðÞ¼1=1þx2  ð9Þ pG jH;LðÞ¼pGL;HÞ¼1=1þxyðÞ j ðð10Þ pG jL;LðÞ¼1=1þy2  ð11Þ And, using 5: pG jH;HðÞ>pG jL;HðÞ¼pGH;LÞ>pGL;LÞ j ð j ðð12Þ Thus a superior ‘track record’(sequence of signals) of the manager results in a higher Bayesian estimate of his chances of producing an increment to firm value next period. Using 5, 9-11 we have 1=1þx2  >1=1þxðÞ>1=1þyðÞ>1=1þy2  ð13Þ so that the dispersion of conditional probabilities of success (value increment) is predicted to increase over time (rounds). The 2-period optimal value function Consider again the discrete quality two-period model. We begin by showing that under the Monotone Likelihood Ratio property (henceforth MLR) e and the posterior probability of the manager in adding value is increasing in his track record defined as his period 1 signal value, S 1 . We then develop the optimal value function in terms of these posterior probabilities and the optimal cutoffs associated with them. Cressy Journal of Global Entrepreneurship Research 2014, 2:5 Page 4 of 10 http://www.journal-jger.com/content/2/1/5 The VC has some initial belief about the manager’s quality and updates this measure, St;t¼1;2;…in period t, at a cost. A superior ‘track record’(sequence of past signals) of the manager results in a higher Bayesian estimate of his chances of incrementing value (i.e. generating a positive payoff) next period. Consider now the value function of the VC in period 2. Figure 2 shows the decision tree structure. Since we have just two periods, the optimal value function will be zero in period 3 and thereafter: EV 3¼EV 4¼…¼0. We can therefore write the period 2 VC value function as V2ðS2 e;S1;Þ¼ max−I2ðS2Þ eþδ½p3ðS2; eS1;Þπ3−c;Πmð14Þ where I2ðS2Þ e= signal-dependent investment in period 2, I20ðS2Þ e≥0. δ= discount factor (=1/(1 + r), where r = the risk-adjusted interest rate). p3ðS2;S1Þ≡pðGjS2;S1Þ= probability manager adds value (is Good) in period 3 given an observed signal about his ability from last period, S 1 , and the random variable representing his period 2 signal, S2 e. π 3 = period 3 value increment of the manager under success f . c = costs of monitoring managerial performance g . Πm=present discounted value (p.d.v.) of the VC’s return from the firm under professional management h . The second period value function V2then shows the present discounted value (p.d. v.) to the VC of either investing and continuing one more period with the existing manager of uncertain quality (yielding p.d.v. −I2ðS2Þ eþδ½p3ðS2; eS1;Þπ3−c) or investing and Figure 2 The VC’s decision tree. Cressy Journal of Global Entrepreneurship Research 2014, 2:5 Page 5 of 10 http://www.journal-jger.com/content/2/1/5 replacing her with an outsider of known quality (yielding p.d.v. Πm) i . Note that the continuous signal version of the MLRP guarantees that the first term in the max{.} expression in Equation 14 is increasing in the first period signal S 1 , since it implies ∂p3ðS2 e;S1Þ=∂S1>0. The expected value of this function with respect to (w.r.t.) S 2 for an arbitrary cutoff signal S2 ^is given by ES2V2ðS2 e;S1jS ^ 2Þ¼ES2maxn−I2ðS2Þ eþδ½p3ðS2 e;S1Þπ3−c;Πmo ¼ΠmZ0 S2 ^ dFðS2jS1ÞþZS2 ^ ∞−I2S2 ðÞþδp3S2;S1 ðÞπ3−c½ dF S2S1Þ j ð ð15Þ Choosing the cutoff optimally requires maximising (15) w.r.t. this cutoff and yields the first order condition −I2S 2  þδp3S 2;S1  π3−c  ¼Πmð16Þ (see Figure 3). The second order condition requires −I20S 2  þδπ3∂p3S 2;S1  =∂S 2>0ð17Þ We shall assume henceforth that this condition holds j . Combining this result with the second order condition for a maximum Equation 3 shows that the VC will at the beginning of period 2 choose to keep the manager if and only if the expected value to the company if he is retained, given his track record (S 1 ), is greater than the value of his replacement. More precisely we have the replacement rule: Replace the manager in period 2 if and only if δp3S2;S1 ðÞπ3−c½−I2S2 ðÞ<Πmð18Þ Figure 3 A better track record in period 1 reduces the chances of replacement in period 2. Cressy Journal of Global Entrepreneurship Research 2014, 2:5 Page 6 of 10 http://www.journal-jger.com/content/2/1/5 where S 2 is the realised value of S2 e. Equivalently, we can say that the manager will be replaced, given his initial performance, if and only if his second period performance falls below a certain threshold: Replace the manager in period 2 if and only if, given S 1, S2<S 2ð19Þ Plugging 3 into 2 the optimal period 2 value function now becomes ES2V 2ðS2 e;S1Þ¼Πmð20Þ where ES2V 2ðS2 e;S1Þ≡maxS2ES2V2ðS2 e;S1S2Þ . We now let the manager’s incremental value, π 3 (γ 2 ), be increasing in a market demand parameter γ 2 . Consider the continuous signal case. Using the MLR property of the distribution function we get ∂p2 ∂S1 >0ð21Þ Differentiating w.r.t. the various parameters we then get the following comparative static results: ∂S 2 ∂S1 ;∂S 2 ∂γ2 ;∂S 2 ∂δ<0ð22Þ ∂S 2 ∂Πm ;∂S 2 ∂η2 ;∂S 2 ∂c>0ð23Þ where ηis a shift parameter in the function I 2 (I2η>0Þ. Thus we have shown that in the second period the probability of manager replacement is lower for managers with good track records(S 1 ), higher incremental values (π 3 (γ 2 )) and lower VC discount rates (r), and that it is higher the higher the return to professional replacement (Πm), the cost of investment (I 2 ) and the costs of monitoring manager performance (c). Figure 3illus- trates the effects of better performance on the likelihood of manager replacement. We move back now to period one. The period 1 value function is given by V1ðS1 eÞ¼ max−I1ðS1Þ eþδ½p2ðS1 eÞπ2ðS1 eÞ−cþES2V2ðS1;S e2Þ;Πmð24Þ with expected value ES1V1ðS1 eÞ¼ES1max−I1ðS1Þ eþδ½p2ðS1 eÞπ2−cþES2V2ðS2 e;S1 eÞ;Πm ¼ΠmþZS1 ^ ∞−I1ðS1Þ eþδ½p2S1 ðÞπ2−cþES2V2ðS2 e;S1 eÞdF S1 ðÞ ð25Þ Choosing the period 1 cutoff optimally requires −I1ðS1 eÞþδ½p2S 1  π2þES2V2ðS2 e;S 1Þ ¼ Πmð26Þ Cressy Journal of Global Entrepreneurship Research 2014, 2:5 Page 7 of 10 http://www.journal-jger.com/content/2/1/5 Substituting back into Equation 11 the optimal period 1 value function now becomes ES1V 1ðS1 eÞ¼Πmð27Þ It is clear that whilst the optimal value function is a constant the optimal cutoffs will vary with the information available at the time. The comparative statics of the first period cutoff with respect to the relevant parameters, assuming symmetrically that π 2 =π 2 (γ 1 ) is increasing in the demand parameter, γ 1 , show that, as might be expected, the first period probability of manager replacement is lower for managers with good track records(S 1 ), higher incremental values (π 3 (γ 2 )) and lower VC discount rates (r); it is higher the higher the return to professional replacement (Πm), the cost of investment (I 2 ) and the costs of monitoring manager performance (c) k . The T-period model The generalisation of the model to T periods is straightforward and we present most of the results rather than proving them in the text. The obvious way to represent the manager’s track record in the multiperiod context is by the mean of the signals over the periods up to the present (t). For some distribution functions (e.g. the Normal) the mean of the signal history and the number of periods before the present, t-1, will be a sufficient statistic for the signal history l . Restricting ourselves to such distributions we can write the t th period value function as VtðSt e;  St−1Þ¼ max −ItðStÞ eþδ½ptðSt; e St−1Þπtþ1−cþEStþ1Vtþ1ðS etþ1;  St−1Þ;Πm ð28Þ where  St¼X t i¼1 Si=tis the mean signal from the manager up to time t m . Taking expectations with respect to the period t signal we get E˜ StVt ˜ St; St−1  ¼E˜ Stmax(−It ˜ St  þδptþ1  St−1 h πtþ1−cþE˜ Stþ1Vtþ1 ˜ Stþ1; St  ;Πm) ¼ΠmF ^ St  þZ∞ ^ St (−It ˜ St  þδ½ptþ1St; St−1  πttþ1−cþE˜ Stþ1Vtþ1 ˜ Stþ1; St i )dF St ðÞ ð29Þ Differentiating w.r.t. the t th period cutoff we get the optimality condition −ItS t  þδ½ptþ1S t;  St−1  πtþ1−cþEStþ1Vtþ1ðS etþ1;  S tÞ ¼ Πmð30Þ where we define  S t¼t−1S tþt−1ðÞ  St−1  ð31Þ We have using the MLR property that the probability of success increasing in the manager’s track record: ∂pt ∂  St−1 >0ð32Þ e Cressy Journal of Global Entrepreneurship Research 2014, 2:5 Page 8 of 10 http://www.journal-jger.com/content/2/1/5