Profitability Ratios in the Early Stages of a Startup

Transcription

1 The Joural of Etrepreeurial Fiace Volume 19 Issue 2 Fall 2017 Article 3 November 2017 Profitability Ratios i the Early Stages of a Startup Erkki K. Laitie Uiversity of Vaasa Follow this ad additioal works at: Part of the Corporate Fiace Commos, Etrepreeurial ad Small Busiess Operatios Commos, ad the Fiace ad Fiacial Maagemet Commos Recommeded Citatio Laitie, Erkki K. (2017) "Profitability Ratios i the Early Stages of a Startup," The Joural of Etrepreeurial Fiace: Vol. 19: Iss. 2, pp Available at: This Article is brought to you for free ad ope access by the Graziadio School of Busiess ad Maagemet at Pepperdie Digital Commos. It has bee accepted for iclusio i The Joural of Etrepreeurial Fiace by a authorized editor of Pepperdie Digital Commos. For more iformatio, please cotact josias.bartram@pepperdie.edu.

2 Profitability Ratios i the Early Stages of a Startup Cover Page Footote * Correspodig author: Phoe: (+358) , ekla@uva.fi This article is available i The Joural of Etrepreeurial Fiace:

3 Profitability ratios i the early stages of a startup Erkki K. Laitie, D.Sc. (Eco.), Professor Emeritus * Uiversity of Vaasa, Vaasa, Filad ABSTRACT This study develops a mathematical framework to aalyze the time series of profitability ratios i the early stages of a startup. It is assumed that the expediture of the startup grows at a steady rate ad geerates a proportioally idetical flow of reveue i each period. The profitability i terms of the iteral rate of retur (IRR) ad the lag structure of reveue flows are assumed costat over time i describig the adjustmet process towards the steady state. The startup is assumed to expese i each period a costat part of periodic expediture ad begiig-of-the-period assets. The adjustmet processes of three kids of profitability ratios are ivestigated: retur o ivestmet ratio, profit margi (as percet of et sales), ad (traditioal) cash-flow margi (as percet of et sales). It is show that IRR, growth, expese rate, ad lag structure strogly affect the early time-series behavior of profitability ratios. Thus, i the early years, due to ustable adjustmet processes, profitability ratios are uable to reflect profitability (IRR) properly ad ca give distorted sigals of the performace of a startup. These fidigs are supported by umerical aalyses with the parameters estimated for a sample of 2608 Fiish startups classified ito five clusters. Keywords: Startup, profitability ratios, early time-series, steady state, Fiish firms JEL: M13, L26, C22, D21, D22, G33, M41 * Correspodig author: Phoe: (+358) , ekla@uva.fi 1

4 1. Itroductio The importace of startups is remarkable for ay ecoomy ivestig o iovatios ad growth. Thus, the early stages of startups are domiat themes of busiess research, literature, ad govermet policy debate (Davila, Foster, He & Shimizu, 2015). The death ad survival of startups are ofte associated with Schumpeter s creative destructio process as startups with ew ideas eter ad replace old ad stagat firms (Huyh, Petruia & Voia, 2012). Huyh et al. (2012) emphasize that a potetial hidrace to this process is that startups have isufficiet fiacial resources to carry out their plas. Startups typically fid raisig equity capital difficult ad rely heavily o iteral fiace ad borrowig to fiace iitial operatios. Thus, Zigales (1998) suggests iteral fiace as the mai source of fiacial capital for these firms. Sufficiecy of iteral fiace is directly related to the early-stage growth ad profitability of startups. Therefore, it is essetial to the ivestors, fiacers ad etrepreeurs that the early developmet of growth ad profitability of startups is well uderstood. Profitability is i practice measured by reported fiacial ratios, which have obvious pitfalls (Murphy, Trailer & Hill, 1996; Losbichler, Hofer, Eisl & Zauer, 2012). Therefore, uderstadig of early profitability developmet of startups is coected with the characteristics of fiacial reportig. This is of importace, sice oe of the objectives of fiacial reportig is to make maagers accoutable to ivestors so that there is efficiet allocatio of capital. The most efficiet firms should receive fiacig ad have higher valuatios tha worse firms (Ak, Dechow, Su & Wag, 2013). The efficiecy of firms is measured by fiacial statemet aalysis where the geeral approach is to calculate ratios that represet key uderlyig costructs, such as profitability. The user ca the aalyze time-series ad cross-sectioal treds i the ratios. However, i order to get a reliable view the user must uderstad the cotet ad the sigals of the ratios. If a firm lives i a steady state, fiacial ratios geerate predictable profitability ad ivestors ca geerally agree o its value (Ak et al., 2013). However, i the early stages of developmet startups typically suffer from a strog ostatioary adjustmet process towards a potetial steady state, which makes predictio of future profitability ad valuatio extremely challegig. The survival rate of startups i the first five years is oly about 45-55% i U.S. ad Europe (U.S. Bureau of Labor Statistics, 2016; Eurostat, 2016). Therefore, it is of importace to uderstad the sigals of potetial failure give by fiacial ratios i the early stages of startups. Failure predictio methods based o fiacial ratios may give reliable sigals also for startups (Laitie, 1992). However, the reliability of these models typically suffers from the occurrece of extreme ratio values ad ostatioary failure processes (Balcae & Ooghe, 2006; Moses & Liao, 1987). These models also suffer from the low quality of fiacial iformatio that is typical for small firms ad especially for startups (Balcae & Ooghe, 2006). Therefore, uderstadig of the ostatioary ature of the developmet of startups ad the quality of fiacial iformatio plays a cetral role i applyig failure predictio models to startups. The academic research of the statioarity of the time series of fiacial ratios is wide (McLeay & Steveso, 2009; Ioaides, Peel & Peel, 2003; Gallizo & Salvador, 2003). Typically, this research is cocetrated o testig statioarity assumptio for large ad older firms, ofte usig differet adjustmet models. The results are mixed. Whittigto ad Tippett (1999) foud that the compoets of fiacial ratios may exhibit ostatioarity whereas Ioaides et al. (2003) cocluded that ratios are globally statioary, but that the behaviour close to equilibrium may result from a oliear partial adjustmet process. There is however also a large umber of startup studies o the statioarity of geeral developmet i the early years (Garsey, Stam & Heffera, 2006; Reid, 2003; Coad, Frakish, Roberts & Storey, 2013; Davila et al., 2015). Typically, these studies do ot pay attetio to fiacial ratios but are geeral idicatig that the developmet of startups is o-liear ad proe to iterruptios ad setbacks, which are stochastic ad quite difficult to explai usig differet variables ad processes (Garsey et al., 2006). Noe of the time series or developmet studies cocetrates o fiacial ratios ad their itrisic properties i the early years of startups from the accoutig poit of view. 2

5 The puzzle related to the profitability ratios of startups is clearly empirically observable. Table 1 presets exemplary time series of profitability ratios for a set of radomly selected Fiish startups (source: the ORBIS database of Bureau Va Dijk). I the three paels of the table, the three first cases describe time series of survivig startups ad the two last colums those of failed oes. These time series are i lie of early startup developmet as described above by Garsey et al. (2006). I some cases, profitability ratios are almost costat but geerally, they are ostatioary icreasig or decreasig rapidly as a result of a adjustmet process. For a fiacial aalyst it is difficult or eve impossible to idetify what kids of sigals these time series are givig about the future ad the value of a startup or eve what kid of profitability these time series are reflectig upo. These time series are a result of startup growth process ad fiacial reportig. Therefore, the edogeous properties of these time series ca oly be explaied by a coceptual model based o growth ad accoutig cocepts. This puzzle forms the startig poit for the preset study. Table 1. Examples of profitability ratios of startups i early years. Pael 1. Cash flow to et sales ratio (%) Status of the startup after te years: Period Active Active Active Bakruptcy Bakruptcy 1-3,13 5,00-51,00 4,13 23,17 2 1,30 4,79-11,58 3,45 16,53 3 3,20 4,40 12,72 0,87 3,25 4 5,14 6,59 13,19-3,40-17,00 5 5,78 4,37 16,04 5,32 24,91 Pael 2. Profit margi to et sales ratio (%) Status of the startup after te years: Period Active Active Active Bakruptcy Bakruptcy 1 2,00-52,77-22,70 21,44 4,75 2 1,75-12,62-3,71 18,21 3,72 3 2,82 12,51-3,39 3,11 0,36 4 2,09 17,23 3,33 3,35-4,01 5 0,12 21,27 3,12 3,82 4,89 Pael 3. Retur o ivestmet ratio (%) Status of the startup after te years: Period Active Active Active Bakruptcy Bakruptcy 1 25,68-91,61-10,20-32,26 76, ,23-91,50 5,40-85,96 35, ,78 82,10 13,03 33,59 9, ,10 65,48 9,61-8,43 8, ,69 67,23 6,65-0,72 7,13 This study attempts to fulfill the gap i startup research outlied above. Thus, the objective is to develop a mathematical growth model of a startup based o accoutig cocepts i order to aalyze the time series of profitability ratios i the early stages of startup. This objective is importat sice the study of ew 3

6 firm developmet suffers from a absece of coceptual models (Garsey et al., 2006). The developmet of a startup is a very complicated process. Therefore, it is strogly simplified i this framework assumig that the expediture of the startup is growig at a steady rate ad geeratig a proportioally idetical flow of reveue i each period. The profitability i terms of the iteral rate of retur (IRR) ad the lag structure of reveue flows geerated by periodic expediture are assumed costat. Furthermore, the startup is assumed to expese i each period a costat part of periodic expediture ad begiig-of-the-period assets. I spite of the steady assumptios, profitability ratios i the first years may suffer from ostatioary ad follow a strog adjustmet process towards a steady state. It is show that IRR, growth rate, expese rate, ad reveue lag structure strogly affect this adjustmet process. Thus, it is argued that i the early years profitability ratios are uable to reflect profitability (IRR) properly ad ca give wrog sigals of the performace of a startup. The iterpretatio of mathematical results is empirically supported by aalyzig umerical adjustmet processes for steady state estimates of a large sample of Fiish startups. I all, the parameters of the steady model are estimated for ie-year time series from fiacial statemets of 2608 startups. The cotet of the paper is orgaized as follows. Firstly, the itroductory sectio preseted the motivatio, objective, ad cotributio of the study. Secodly, the aalytical model of the time series of three profitability ratios (cash flow ratio, profit margi ratio, ad retur o ivestmet ratio) is draw up ad aalyzed i the secod sectio i detail. The mai poit is to explai how the model variables edogeously affect the adjustmet process of the profitability ratios towards a steady state. The theoretical iterpretatio of the results is supported by illustrative umerical examples. Thirdly, the mathematical results are demostrated by empirical time series data from a sample of Fiish startups i the third sectio. The purpose is to show how differet combiatios of model variable estimates i practice ca lead to differet adjustmet processes geeratig differet sigals of the profitability of a startup. Fially, the last sectio discusses ad cocludes the mai fidigs of the study. 2. Theoretical aalysis of profitability ratios 2.1. Growth ad profitability The early developmet of time series for a startup is a complicated ad stochastic process (Garsey et al., 2006). Therefore, Reid (2003) applied a dyamic theory to predict trajectories for key fiacial variables of a startup whereas Coad et al. (2013) used Gambler's Rui framework by arguig that startup performace is best modelled as a radom walk process. However, the preset framework is based o a set of simplified assumptios about behavior of profitability ratios uder certaity. These kids of accoutig-orieted frameworks have earlier bee applied to aalyzig the steady state associatio betwee the accoutig rate of retur (ARR, ROI) ad the iteral rate of retur (IRR) (Feestra & Fag, 2000; Laitie, 2006; 2012; Brief, 2013). I these frameworks, growth plays a importat role. For a startup, growth is critical for survival i the early stages, sice ew firms that do ot grow are more likely to fail or close (Garsey et al., 2006; Coad et al., 2013). I the preset framework, it is assumed that the etrepreeur periodically ivests o the startup a expediture growig at a steady rate i order to stregthe the early developmet of the firm. Thus, the time series of periodic expediture ca be described as follows: M M 0 (1 g) i0 i where M t refers to expediture spet i period t ad g is the steady rate of growth. For simplicity, radom elemets (Coad et al., 2013) are eglected i this framework. It is importat for the survival of the startup that the busiess starts to geerate reveue as quickly as possible after foudatio. I this way, the startup stregthes iteral fiace ad esures a successful etry to the market. Gilbert, McDougall & Audretsch (2006) review 48 empirical studies o ew firm growth cocludig that growth of sales reveue is oe of the most importat measures of growth. The preset model (1) 4

7 assumes that the busiess process of the startup is proportioally fixed ad repetitive so that periodic expediture geerates a similar but steadily growig flow of reveue already begiig i the ivestmet period. It is assumed that the lagged flow of reveue geerated by periodic expediture follows a geometric distributio, which leads to the followig expressio: R KM i i i i 0 ( 1 g) q KM q (1 g) q (2) i0 i0 1 1 (1 g) q KM (1 g) (1 g q) where K is the level parameter of the lagged reveue distributio whereas q is the lag parameter describig the geometric lag structure. Equatio (2) shows that the time series of total reveue (geerated by the past ad preset expediture) is a ostatioary process where the growth path is largely determied by the differece betwee g ad q. I the adjustmet process, the growth rate of reveue is covergig towards g faster, the lower is q. Whe approaches the ifiity, the growth rates of expediture ad reveue are equal ad the startup lives i a steady state. Whe it is assumed that the lag distributio is ifiite, IRR or r as the pricipal measure of startup profitability ca be icorporated i the model i the followig way: i i 1 r q M M K q (1 r) K (3) 1 r i0 which leads to the followig steady relatio betwee periodic expediture ad reveue R M (1 r q)(1 g) (1 r)(1 g q) (4) Equatio (4) idicates that i a steady state the reveue-expediture ratio is symmetric with respect to g ad r. It is also depedet o the lag parameter q. This lag parameter tells how quickly ivested expediture geerates reveue to the startup. The reveue lag is icreasig i q with the average lag defied as q/(1-q) =: L Expeses ad assets Whe the startup is fouded, it must periodically prepare the icome statemet ad the balace sheet accordig to the accoutig covetios ad doctrie. The goig cocer covetio is based o cotiuity of activity assumig that the busiess will be operatig idefiitely. The doctrie of cosistecy requires that fiacial statemets for differet accoutig periods are based o the same accoutig priciples makig fiacial results comparable. These geeral rules justify us to assume that certai accoutig parameters are fixed over time. Therefore, it is assumed that the startup periodically expeses a fixed proportio C of expediture ad o-expesed expediture i the balace sheet. This systematic accoutig procedure leads to the followig time series of expese: D CM CM i i i i 0 1 g) (1 C) C(1 C) M 0(1 g) (1 C) i0 i0 ( (5) 1 (1 g) (1 C) (1 g) ( g C) 1 which coverges towards the followig steady state: 5

8 D CM 1 g g C (6) Equatio (5) shows that the relatio of periodic expese to periodic expediture depeds o g ad C. This relatio i the steady state (6) is decreasig i g whereas the margial effect of C is positive for g > 0 ad egative for g < 0. I (5) ad (6), C is ot specified. It is possible to cosider differet expese methods specifyig C i differet ways. For example, it ca be assumed that the expiratio of expediture as expeses i time follows the lag structure of reveue so that C = 1-q. This kid of expese method is cosistet with accoutig stadards (such as IASB Framework: paragraph 94). Appedix 1 presets the time series ad the steady state of expese for C = 1-q. The assets of the startup directly follow from the defiitio of the expese cocept, sice they are draw up from the uexpired expediture. This systematic procedure leads to the followig expressio for the time series of assets: A i i 1 i i 0 (1 g) (1 C) (1 C) M 0(1 g) (1 C) i0 i0 ( 1 C) M (7) (1 C) M 1 (1 g) (1 C) (1 g) ( g C) 1 which gives the followig steady state solutio: A i i (1 C) M (1 g) (1 C) 0 (8) i0 1 g ( 1 C) M g C The compariso of equatio (7) with (5) shows that the relatio betwee the time series of expese D ad assets A is simply C/(1-C). Appedix 2 shows the time series ad steady state for A i a special case of expese method whe C = 1-q Profitability ratios Cash flow ratio (CFR) The cash flow refers to the sufficiecy of iteral fiace beig therefore a importat idicator of a startup facig fiacial costraits. Startups with strog cash flows cotiue to operate ad grow, while startups with weak cash flows close ad evetually die (Huah et al., 2012). Usually it is suggested that highly cash-flow sesitive firms are those facig the least costraits (Almeida, Campello & Weisbach, 2004). Some researchers further argue that cash flows reveal iformatio about ivestmet quality (Alti, 2003). I this framework, the cash flow ratio (CFR) is defied with the aid of the differece betwee periodic reveue ad expediture as follows: CFR R M R (1 r) (1 g) (1 g q) 1 1 (1 r q) (1 g) q 1 6

9 (1 r) 1 g q 1 (9) (1 r q) 1 g ( q /(1 g)) q based o equatios (2) ad (3). Equatio (9) shows that the level of CFR is determied by r, q, ad g. However, the adjustmet process towards a steady state is based o the differece betwee 1+g ad q. The speed of adjustmet is determied by q/(1+g) =: S. The iitial level of CFR is reduced to CFR 0 = 1-1/K that is idepedet of g but icreasig i r ad decreasig i q. Equatio (9) idicates that the speed of covergece towards the steady state is higher, the lower is q ad the higher is g. The steady state of CFR ca be preseted i the followig way: CFR R M q( r g) (10) R (1 g)(1 r q) which shows that i the steady state CFR is positive if r > g ad zero if r = g. The level of steady CFR is decreasig i g but iflueced positively by q for r > g ad egatively for g > r. Table 2 presets umerical examples of CFR for differet values of r, g, q, ad C. The examples are classified i three groups accordig to the relatioship betwee r ad g (r > g, r = g, ad r < g). I each group, oe of the examples is draw for the special case that C = 1-q. The height of C ot arbitrary i practice but regulated by accoutig regulatios ad covetios. The rage betwee miimum C ad maximum C ca be called the expese maagemet flexibility limits (Choy, 2012). However, CFR is based o the cash flow ad is thus ivariat to C. This is also idicated by the figures i Table 2 where cases that differ oly with respect to C are idetical. Table 2 also idicates that CFR is sesitive to g. Whe g > r, the adjustmet process of CFR is i the first years similar tha for g < r but CFR coverges towards a egative steady state. Whe g = r, the steady value is 0. The effect of q o CFR is strog: the higher q, the more egative is CFP i the first years of a startup, ceteris paribus Profit margi ratio (PMR) Cash flow is ot based o the profit cocept ad is therefore idepedet of the expese method used by a startup. However, for the survival of a startup, profit is of importace (Davidsso, Steffes & Fitzsimmos, 2009). Profitability is usually theoretically associated with IRR (Feestra & Wag, 2000). IRR is also a widely used method i capital budgetig assessig ivestmet projects (Graham & Harvey, 2001). However, i practice the profitability at the level of the firm is typically measured by fiacial ratios, maily by the profit margi ratio ad the retur o ivestmet ratio (Murphy et al., 1996; Losbichler et al., 2012). These measures are the mai types of profitability ratios that ca aid a i-depth uderstadig of the busiess of a startup. I this framework profit margi ratio (PMR) is calculated as the ratio of profit to reveue. Usig equatios (2) ad (5), PMR ca be preseted i the followig form: 1 1 R D C(1 r) ((1 g) (1 C) )(1 g q) PMR (11) R (1 r q) ( g C)((1 g) q ) 1 C(1 r) ((1 ((1 C) /(1 g)) )(1 g q) (1 r q) ( g C)((1 ( q /(1 g)) ) 1 1 Equatio (11) shows that the iitial level of PMR is largely determied by r, C, ad q but that the adjustmet process towards a steady state is complicated. 7

10 Table 2. Examples of time series of the cash flow ratio (CFR). IRR > Growth rate IRR = Growth rate (Golde path) IRR < Growth rate Case r 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10 g 0,05 0,05 0,05 0,05 0,10 0,10 0,10 0,10 0,15 0,15 0,15 0,15 q 0,35 0,35 0,35 0,55 0,35 0,35 0,35 0,55 0,35 0,35 0,35 0,55 C 0,55 0,65 0,75 0,55 0,55 0,65 0,75 0,55 0,55 0,65 0,75 0,55 Period C = 1-q C = 1-q C = 1-q 0-0,4667-0,4667-0,4667-1,0000-0,4667-0,4667-0,4667-1,0000-0,4667-0,4667-0,4667-1, ,1000-0,1000-0,1000-0,3125-0,1126-0,1126-0,1126-0,3333-0,1244-0,1244-0,1244-0, ,0154-0,0154-0,0154-0,1122-0,0333-0,0333-0,0333-0,1429-0,0499-0,0499-0,0499-0, ,0100 0,0100 0,0100-0,0299-0,0104-0,0104-0,0104-0,0667-0,0291-0,0291-0,0291-0, ,0182 0,0182 0,0182 0,0085-0,0033-0,0033-0,0033-0,0323-0,0230-0,0230-0,0230-0, ,0209 0,0209 0,0209 0,0275-0,0010-0,0010-0,0010-0,0159-0,0211-0,0211-0,0211-0, ,0218 0,0218 0,0218 0,0372-0,0003-0,0003-0,0003-0,0079-0,0205-0,0205-0,0205-0, ,0221 0,0221 0,0221 0,0422-0,0001-0,0001-0,0001-0,0039-0,0204-0,0204-0,0204-0, ,0222 0,0222 0,0222 0,0448 0,0000 0,0000 0,0000-0,0020-0,0203-0,0203-0,0203-0, ,0222 0,0222 0,0222 0,0461 0,0000 0,0000 0,0000-0,0010-0,0203-0,0203-0,0203-0, ,0222 0,0222 0,0222 0,0468 0,0000 0,0000 0,0000-0,0005-0,0203-0,0203-0,0203-0,0438 Steady 0,0222 0,0222 0,0222 0,0476 0,0000 0,0000 0,0000 0,0000-0,0203-0,0203-0,0203-0,0435 8

11 The steady state of the profit margi ratio (11) is as follows: PMR R D C(1 r)(1 g q) 1 (12) R (1 r q)( g C) Equatio (11) shows that the covergece of the ratio towards the steady state (12) depeds o the relatio betwee g, C, ad q. However, whe the startup makes use of the expese method to set C equal to 1-q, the ratio (11) ca be preseted i the followig form: PMR R D R (1 r)(1 q) rq 1 C 1 q (13) (1 r q) 1 r q which shows that PMR is iitially costat (steady state) without ay adjustmet process. Thus, the use of a expese method strogly affects the statioarity of the time series of the ratio. The level of the costat ratio (13) is sigificatly affected by q i additio to r. Table 3 presets examples of PMR for the same parameter values as used i the previous table (Table 2). For the special case C = 1-q PMR is costat irrespective of g. I spite of positive r, PMR is i years 0 ad 1 egative whe q or C is high (C > 1-q). For the cases where C < 1-q the time series of PMR is of a similar form idepedetly of the relatio betwee r ad g. PMR is i the early years highly positive but coverges towards the steady state that is icreasig i g. This steady state is icreasig i q whe r > g ad decreasig whe r < g. Thus, the ifluece of both C ad q o the time-series behavior (adjustmet process) of PMR is strog Retur o ivestmet ratio (ROI) Profit margi ratio is oly based o profit ad reveue flows without payig attetio to the assets of the startup. These assets are take ito accout by the retur o ivestmet ratio (ROI) that is likely the most widely adopted measure of profitability (Losbichler et al., 2012). It is also ofte cosidered a proxy of IRR i theoretical aalyses (Feestra & Wag, 2000). Usig equatios (2), (5), ad (7) this profitability ratio ca be preseted as follows ROI R D A C((1 C) (1 g) ) (1 C)((1 C) (1 g) ) 1 1 (1 r q)( q (1 g) )( g C) (1 r)(1 g q)(1 C)((1 C) (1 g) ) (14) R D A 1 1 (1 r q)(( q /(1 g)) 1)( g C)(1 g) (1 r)(1 g q)(1 C)(((1 C) /(1 g)) 1) 1 C(((1 C) /(1 g)) 1)(1 g) (1 C)(((1 C) /(1 g)) 1) Equatio (14) idicates that the adjustmet process of ROI is a complicated fuctio of the four model parameters. Its speed of covergece towards the steady state depeds o the relatioship betwee C, q, ad g. 9

12 Table 3. Examples of time series of the profit margi ratio (PMR). IRR > Growth rate IRR = Growth rate (Golde path) IRR < Growth rate Case r 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10 g 0,05 0,05 0,05 0,05 0,10 0,10 0,10 0,10 0,15 0,15 0,15 0,15 q 0,35 0,35 0,35 0,55 0,35 0,35 0,35 0,55 0,35 0,35 0,35 0,55 C 0,55 0,65 0,75 0,55 0,55 0,65 0,75 0,55 0,55 0,65 0,75 0,55 Period C = 1-q C = 1-q C = 1-q 0 0,1933 0,0467-0,1000-0,1000 0,1933 0,0467-0,1000-0,1000 0,1933 0,0467-0,1000-0, ,1357 0,0467-0,0214-0,0313 0,1377 0,0467-0,0241-0,0333 0,1396 0,0467-0,0267-0, ,0996 0,0467 0,0140 0,0137 0,1041 0,0467 0,0089 0,0091 0,1082 0,0467 0,0042 0, ,0793 0,0467 0,0286 0,0421 0,0859 0,0467 0,0220 0,0350 0,0919 0,0467 0,0160 0, ,0687 0,0467 0,0343 0,0595 0,0769 0,0467 0,0268 0,0502 0,0842 0,0467 0,0201 0, ,0634 0,0467 0,0364 0,0698 0,0726 0,0467 0,0285 0,0589 0,0807 0,0467 0,0215 0, ,0610 0,0467 0,0371 0,0758 0,0707 0,0467 0,0291 0,0637 0,0792 0,0467 0,0220 0, ,0598 0,0467 0,0374 0,0792 0,0699 0,0467 0,0293 0,0663 0,0785 0,0467 0,0222 0, ,0593 0,0467 0,0375 0,0811 0,0695 0,0467 0,0294 0,0677 0,0783 0,0467 0,0222 0, ,0591 0,0467 0,0375 0,0821 0,0693 0,0467 0,0294 0,0684 0,0782 0,0467 0,0222 0, ,0590 0,0467 0,0375 0,0827 0,0693 0,0467 0,0294 0,0688 0,0781 0,0467 0,0222 0,0569 Steady 0,0589 0,0467 0,0375 0,0833 0,0692 0,0467 0,0294 0,0692 0,0781 0,0467 0,0222 0,

13 If the startup is usig a expese method to make C equal to 1-q, equatio (14) ca be simplified as follows: R D ROI A 1 (1 q)(( q /(1 g)) q(( q /(1 g)) 1 (1 r q)(( q /(1 g)) 1)(1 g) (1 r) q((( q /(1 g)) 1) 1 1)(1 g) 1) C 1 q (15) where the adjustmet process of ROI towards its steady value is depedet o the relatio betwee q ad g. The complexity of equatio (15) largely depeds o the fact that periodic profit is i ROI divided by A -1 (assets defied o the begiig-of-the-period basis). If ROI is calculated for A, a costat ratio is resulted as ROI = r/(1+r) givig also a reasoable but slightly biased proxy of IRR. I practice, assets are ofte defied as average of the begiig- ad ed-of-the-period bases, which leads to a time-series of ROI with dimiished o-statioarity i compariso to (15). The steady state of ROI is the followig: ROI R D A (1 r q)(1 g)( g C) C(1 g) (1 r)(1 g q)(1 C) C 1 1 (16) which is strogly affected by r but also by g, q ad C. If the startup systematically uses the expese method makig C equal to 1-q, the steady state ratio ca be preseted i the followig form: ROI R D A r(1 g) (1 ) 1 r & C 1 q (17) which is icreasig i r ad g. Equatios (16) ad (17) idicate that ROI i the steady state correctly reflects IRR oly whe r = g (golde path) which is a well-kow result i theoretical aalyses of IRR (Feestra & Wag, 2000). Table 4 presets exemplary figures of ROI for the previous sets of the model parameters. If C < 1-q, the values of ROI are i the first years very high clearly overestimatig r. If C = 1-q, this overestimatio is ot strog ad the time series coverges quickly towards to the steady state. Whe g = r, this steady state ROI equals r accordig to the golde path rule. Whe q or C is high (C > 1-q), ROI is i the first year egative ad icreases after that towards the steady state. Thus, i the first years of a startup, ROI does ot give a reliable sigal of the true level of IRR due to the adjustmet process. 11

14 Table 4. Examples of time series of the retur o ivestmet ratio (ROI). IRR > Growth rate IRR = Growth rate (Golde path) IRR < Growth rate Case r 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10 g 0,05 0,05 0,05 0,05 0,10 0,10 0,10 0,10 0,15 0,15 0,15 0,15 q 0,35 0,35 0,35 0,55 0,35 0,35 0,35 0,55 0,35 0,35 0,35 0,55 C 0,55 0,65 0,75 0,55 0,55 0,65 0,75 0,55 0,55 0,65 0,75 0,55 Period C = 1-q C = 1-q C = 1-q 0 1 0,2879 0,1273-0,0818-0,0556 0,3025 0,1318-0,0955-0,0611 0,3172 0,1364-0,1091-0, ,1603 0,1034 0,0467 0,0202 0,1748 0,1077 0,0308 0,0138 0,1893 0,1120 0,0151 0, ,1159 0,0979 0,0937 0,0592 0,1319 0,1023 0,0748 0,0509 0,1478 0,1067 0,0564 0, ,0965 0,0963 0,1120 0,0828 0,1139 0,1007 0,0912 0,0723 0,1311 0,1052 0,0710 0, ,0877 0,0957 0,1189 0,0971 0,1060 0,1002 0,0970 0,0847 0,1240 0,1047 0,0760 0, ,0836 0,0955 0,1214 0,1056 0,1026 0,1001 0,0990 0,0917 0,1211 0,1046 0,0776 0, ,0818 0,0955 0,1223 0,1105 0,1011 0,1000 0,0997 0,0956 0,1199 0,1046 0,0782 0, ,0810 0,0955 0,1226 0,1133 0,1005 0,1000 0,0999 0,0977 0,1194 0,1046 0,0783 0, ,0806 0,0955 0,1227 0,1148 0,1002 0,1000 0,1000 0,0988 0,1192 0,1045 0,0784 0, ,0804 0,0955 0,1227 0,1157 0,1001 0,1000 0,1000 0,0994 0,1191 0,1045 0,0784 0,0848 Steady 0,0803 0,0955 0,1227 0,1167 0,1000 0,1000 0,1000 0,1000 0,1191 0,1045 0,0784 0,

15 3. Empirical aalysis of adjustmet processes 3.1. Sample of firms The objective of empirical experimets is to illustrate the adjustmet processes of early profitability ratios usig parameter values estimated for a large sample of real Fiish (SME) startups. The data for the experimets are extracted from the ORBIS database of Bureau Va Dijk (BvD). Estimatio of the steady parameters for a firm requires a log time-series of fiacial statemets. The selectio of the sample was therefore made uder restrictio that the selected startup must have successive fiacial statemets available for at least 10 years. Because the parameters are iteded to describe the adjustmet process of ratios i early years, it was required that the startup has published fiacial statemets begiig from 1-4 years after its foudatio (registratio) year. It was also required that the selected startup is fouded after year 2000, is idustrial, private limited compay, ad has less tha 50 employees i its first data year. Therefore, this aalysis excludes startups, which have failed durig the first te years of their active life. The sample also excludes large startups. The search uder these restrictios gave us fiacial statemets from 4000 active Fiish firms, 2 firms i isolvecy proceedigs, 29 bakrupt firms, 160 dissolved firms, ad 1 firm ivolved with merger or take-over, ad 15 firms beig i liquidatio. For the preset aalyses, 4000 active ad 29 bakrupt startups were selected due to their clear status. The fiacial status of the large group (160) of dissolved firms is ot determied ad therefore these firms were excluded from the sample. I Filad, limited liability compaies must submit their fiacial statemets to the Trade Register either with their tax retur or directly to the Fiish Patet ad Registratio Office (PRH). Practically, ORBIS icludes all Fiish firms, which have delivered their fiacial statemets to PRH (The Fiish Trade Register) as required by Fiish Accoutig Act. Therefore, the sample is cosidered statistically represetative for all Fiish small startups (limited compaies) survivig at least 10 years after foudatio Estimatio of parameters For all startups i the sample (4029), time-series data of fiacial statemets for 10 years were extracted from ORBIS. The estimatio of the parameters of the distributed lag model is oly based o the time series of total reveue R t ad total expediture M t. R t is here measured as et sales ad M t as the sum of short-term (curret) ad log-term (fixed) expediture. M t is calculated from fiacial statemets as the sum of total expeses (curret expeses ad depreciatios) D t ad chage i ivetories ad i fixed assets A t A t-1. Therefore, fially we have ie-year time series of R t ad M t available for statistical estimatio. The estimatio of the parameters g, q, ad r was made i several stages. Firstly, the steady rate of growth g was estimated from the ie time-series observatios applyig the ordiary least squares (OLS) method to the logarithmic time series of both M t ad R t as follows: M R t t M R 0 0 (1 g) (1 g) t t e e l M l R t t l M l R 0 0 t l(1 g) t l(1 g) (18) where is a radom residual. The fial estimate of firm-level steady growth rate was calculated as the weighted average of the estimates of (18) usig the sum of time-series of M t ad R t over the ie observatios as weights. Secodly, q ad r were estimated for the startups usig a distributed lag model specificatio. However, a reliable estimatio of these parameters is a exceptioally challegig task due to the sesitivity of estimates (Laitie, 1997; compare with Hall, 2007) ad to the time-series properties of startups (Garsey et al., 2006). They were estimated usig the Koyck trasformatio applied to the distributed reveue lag fuctio. Furthermore, liear restrictios were icorporated i the estimatio to make the estimates more stable 13

16 (Johsto, 1972: ; Fomby, Hill & Johso, 1984: 82-85). The Koyck trasformatio shows that the relatio betwee R t ad M t ca be preseted i the form of the followig equatio: R a K M q R (19) t t t1 where a is to be set equal to 0, K = (1+r-q)/(1+r), ad is a radom residual. The cetral liear restrictio is based o the assumed steady relatio (4) betwee reveue R ad expediture M. Because R/M = K (1+g)/(1+g-q), the followig steady relatio holds: ( 1 g) K ( R / M ) q ( R / M ) (1 g) (20) which leads to the followig matrices of restrictios: H 0 1 g R / M 0 h ( R / M ) (1 g) (21) These restrictios ca be preseted i the matrix form as h = H B where B is the 3 x 1 matrix of estimates. I these restrictios, the estimate of g ad R/M were used to stabilize the estimates of q ad r. R/M was estimated as the ratio of the cumulated sum of reveue ad the cumulated sum of expediture over the period of the ie time-series observatios. Because of the sesitivity of estimates for startups, the procedure provided us with a umber outliers (i the form of q < 0 or q > 1), which were excluded from the further aalyses. Thus, the fial sample oly icluded 2599 (66.0%) active firms ad 23 (79.3%) bakrupt firms. Fially, the (costat) rate of expese C was estimated (as the weighted average) for the last ie years of startups as the ratio of cumulated expeses to the cumulated sum of expediture M t ad assets A t-1 i the begiig of the year. The three estimatio stages gave us a set of estimates (for g, q, r, ad C) based o a steady state assumptio that rarely completely holds eve for larger firms durig their mature stages of life cycle. Therefore, the estimatio results should be cautiously iterpreted ad maily regarded as actig as demostrative purposes oly. It is expected that the reliability of the estimates is ot very high for sigle startups. Thus, oly statistical averages of estimates obtaied for large sub-groups (types) of startups are aalyzed i experimets to show the variatios i adjustmet processes of profitability ratios Cluster aalysis The purpose of further aalyses is to fid out represetative types of startups ad to demostrate adjustmet processes i these basic types. The search for the types was made by the TwoStep Cluster Aalysis of SPSS. This aalysis is a exploratory tool desiged to reveal atural groupigs (or clusters) withi a dataset that would otherwise ot be apparet. The algorithm employed by this procedure has several desirable features that differetiate it from traditioal clusterig techiques. It allows us to aalyze large data files ad it ca automatically determie the optimal umber of clusters. Here, the Bayesia Iformatio Criterio (BIC) was specified as the criterio to determie the umber of clusters. Bachler, Wezig & Vogler (2004) regard the method as promisig because it may solve some of the problems with traditioal methods such as k-meas ad hierarchical clusterig methods. They use simulatio to show that the TwoStep Cluster Aalysis performs well if the variables are cotiuous. I this aalysis, the four cotiuous parameter estimates of the steady model (r, g, q, ad C) were used as clusterig variables. 14

17 The TwoStep Cluster Aalysis method applied to the sample of active firms ( = 2599) provided us with five clusters. For techical reasos, the procedure dropped 14 startups (0.5%) from the fial solutio. The cluster quality (silhouette measure of cohesio ad separatio) was foud fair (0.4 whe refer to good value). Table 5 presets the distributio of the startups betwee the five clusters. Each cluster icludes a large umber of firms. Clusters 3 ( = 804) ad 1 ( = 679) are the largest sub-groups of startups makig together 57.1% of the total sample. Table 6 presets statistics of total reveue (R) ad expediture (M) for the first ad ith data years of startups by cluster. For the first data year, F-statistics showed (ot preseted here) that the differeces i size measured either by R (p-value 0.279) or M (0.522) are ot statistically sigificat although startups i cluster 1 are relatively small. However, bakrupt startups are o average smaller tha active startups. Util ith data year the average size of startups i cluster 1 has icreased very strogly whereas that of startups i cluster 4 has seriously dimiished. I the ith data year, all the differeces i size betwee clusters are sigificat (p-value ). Table 5. Distributio of active startups by cluster. Cluster Active startups Percet Valid percet ,13 26, ,24 15, ,93 31, ,70 16, ,47 10,52 Total ,46 100,00 Missig 14 0,54 Total ,00 Table 6. Mea of total reveue ad expediture (TEUR) i active ad bakrupt startups by cluster. Mea of reveue (TEUR): Mea of expediture (TEUR): First data year Nith data year First data year Nith data year Active startups: Cluster 1 768,5 3260,7 839,7 3043, ,1 1305,1 1268,3 1232, ,8 1989,4 1346,4 1886, ,5 606,9 1094,0 561, ,3 1945,5 1147,0 1983,1 Total 1086,4 1981,8 1138,0 1877,9 Bakrupt startups: All 698,0 658,8 741,6 711,0 Appedix 3 presets the idustrial classificatio of startups by cluster. For the active firms, the cotigecy coefficiet (ot preseted here) idicated that the distributios (idustry & clusters) are highly statistically depedet (p = 0.000). The largest idustry groups for active startups are wholesale ad retail trade, repair of motor vehicles ad motor cycles (20.1%), costructio (16.7%), ad professioal, scietific ad techical activities (14.0%). Cluster 2 has exceptioally large umber of startups from huma health ad social work activities (14.1%) but icludes oly few costructio startups (10.6%). Cluster 3 icludes a large umber 15

18 of trasportatio ad storage startups (12.2%) while the umber of professioal, scietific, ad techical startups is relatively small (9.0%). Bakrupt startups iclude a lot of wholesale ad retail trade (30.4%), maufacturig (17.4%), ad accommodatio ad food service (13.0%) startups Estimatio results by cluster Table 7 presets descriptive statistics of the estimatio results by cluster. Pael A of the table shows the mea values of the fial estimates for the four parameters of the steady model. These average values represet the cetroids of the clusters ad they are used to demostrate differet types of startups. F-statistics (ot preseted here) showed that the differeces i the estimates betwee the clusters are all statistically sigificat (p-value ). The estimates of q are relatively high i clusters 1 (0.6146) ad 2 (0.5866) but exceptioally low i cluster 5 (0.0831). The average estimate of r is very high i cluster 4 (0.4063) but extremely low i cluster 5 ( ). The estimates of g show that startups i cluster 1 (0.1795) have grow very fast whereas startups i cluster 4 ( ) report very egative rates of growth. I geeral, the differeces i the average estimate of C are relatively small. However, startups i cluster 2 (0.4356) have a very low rate of expese. Bakrupt startups maily differ from average active startups i that r is slightly egative ( ) ad C is quite low (0.7421). Except for low C, their profile is close to the cetroid of startups i cluster 3. Pael B of Table 7 presets statistics for the steady growth of startups. The meas of golde path measure (1+r)/(1+g) reflectig R/M show large variatios betwee clusters. Cluster 5 (0.4387) that o average has a very low r has also a extremely low ratio while cluster 4 (1.5570) with a very high r reports a exceptioally high values for the ratio. The pael also shows that the coefficiet of determiatio of equatio (19) used to estimate r ad q is geerally high that is typical for distributed lag models. Thus, oly for cluster 2 (0.5900) it is quite low. However, the coefficiets for determiatio for logarithmic equatios i (18) to estimate g for R ad M are clearly lower. For cluster 1 ( & ) oly these coefficiets are relatively high. I geeral, the differeces i growth estimate betwee R ad M are quite large referrig to violatios agaist the steady state assumptio. The special characteristic of bakrupt startups is that the growth estimate for R exceeds that for M otably by 10 per cet uits Adjustmet processes by cluster Pael A of Table 7 shows that Cluster 1 (26.3% of startups) is characterized by a high growth rate (0.1795) ad a high reveue lag parameter (0.6146). The startups i this cluster ted to use a high rate of expese (0.8170) although reveue lag is high beig o average 1.6 periods (see Table 8). Pael B shows that i this cluster startups icely follow the steady growth paths with high coefficiets of determiatio. This coefficiet is also relatively high for the reveue geeratio model. Thus, this cluster ca called Rapidly growig steady startups with high reveue lag ad high rate of expese. Table 8 shows that i this cluster the iverse measure of adjustmet speed (S) for CFR idicates slow adjustmet. However, the differeces betwee steady values of profitability ratios ad their calculated values i early years are extremely large referrig to a strog adjustmet process. Thus, the time series of profitability ratios coverge towards steady values very slowly (see Table 9 ad Figure 1). These ratios refer to a very low egative profitability although average IRR is moderate (0.0792). The steady value of ROI ( ) strogly uderestimates profitability maily due to the high rate of expese. 16

19 Table 7. Mea values of the estimated steady model parameters by cluster. Cluster: Estimate All Pael A. Parameters of the model Bakrupt startups q 0,6146 0,5866 0,2754 0,2411 0,0831 0,3862 0,3468 r 0,0792 0,0972-0,0162 0,4063-0,5165 0,0445-0,0093 g 0,1795-0,0037 0,0540-0,0847 0,1112 0,0609 0,0573 C 0,8170 0,4356 0,8188 0,8232 0,8599 0,7647 0,7421 Nr. of firms Pael B. Measures of steady growth (1+r)/(1+g) 0,9284 1,1159 0,9398 1,5570 0,4387 1,0147 0,9775 R/M 0,9560 1,1245 0,9822 1,1466 0,8969 1,0157 0,9811 R 2 (q, r) 0,8191 0,5900 0,7947 0,8298 0,8868 0,7853 0,8066 g (R) 0,2041 0,0179 0,0701-0,0691 0,1345 0,0807 0,1091 R 2 (g (R)) 0,7360 0,4695 0,4579 0,4511 0,4152 0,5271 0,5249 g (M) 0,1556-0,0300 0,0369-0,1048 0,0859 0,0392 0,0055 R 2 (g (M)) 0,6644 0,3113 0,4138 0,4725 0,3959 0,4719 0,4941 Note: R 2 (.) = coefficiet of determiatio of the equatio used to estimate (.) g (.) = growth of (.) R = total reveue M = total expediture R/M = estimate for the reveue-expediture ratio Table 8. Statistics of adjustmet processes by cluster. Cluster: Bakrupt startups L 1,5950 1,4190 0,3800 0,3178 0,0906 0,5309 S 0,5211 0,5888 0,2612 0,2635 0,0748 0,3280 r 0,0792 0,0972-0,0162 0,4063-0,5165-0,0093 ROI -0,3713 0,0970-0,0676 0,4370-0,6158-0,0444 PMR -0,0759 0,1121-0,0144 0,0930-0,0993-0,0148 CFR -0,1125 0,1164-0,0259 0,1110-0,1172-0,0339 ROI-ROI 1 1,4913-0,0035 0,2310 0,1025 0,0045 0,2014 PMR-PMR 0 0,8221 0,0481 0,1227 0,0866-0,0610 0,1269 CFR-CFR 0 1,2106 1,2653 0,3628 0,3180 0,0903 0,5046 Notes: L = q/(1-q) = average lag betwee expediture ad reveue S = q/(1+g) = iverse measure of adjustmet speed for CFR ROI = steady retur o ivestmet ratio ROI 1 = retur o ivestmet ratio i period 1 PMR = steady profit margi ratio PMR 0 = profit margi ratio i period 0 CFR = steady cash flow ratio CFR 0 = cash flow ratio i period 0 17

20 Table 9. Theoretical time series of profitability ratios for the five clusters ad bakrupt startups. Pael 1. Clusters 1-3 Cluster 1 (r = 0,0792) Cluster 2 (r = 0,0972) Cluster 3 (r = -0,0162) Period PMR ROI CFR PMR ROI CFR PMR ROI CFR 0-0,8980-1,3231 0,0639-1,1489-0,1371-0, ,4414-1,8627-0,5273 0,0771 0,1006-0,3525-0,0565-0,2987-0, ,2485-1,0700-0,2959 0,0872 0,0885-0,1103-0,0276-0,1310-0, ,1608-0,7319-0,2011 0,0947 0,0882-0,0043-0,0183-0,0858-0, ,1188-0,5593-0,1570 0,1002 0,0899 0,0491-0,0155-0,0727-0, ,0978-0,4693-0,1353 0,1041 0,0917 0,0780-0,0147-0,0690-0, ,0872-0,4224-0,1243 0,1068 0,0933 0,0942-0,0145-0,0680-0, ,0818-0,3980-0,1186 0,1086 0,0945 0,1034-0,0144-0,0677-0, ,0789-0,3852-0,1157 0,1098 0,0953 0,1088-0,0144-0,0677-0, ,0775-0,3786-0,1142 0,1106 0,0959 0,1119-0,0144-0,0676-0, ,0767-0,3751-0,1134 0,1112 0,0963 0,1138-0,0144-0,0676-0,0259 Steady state -0,0759-0,3713-0,1125 0,1121 0,0970 0,1164-0,0144-0,0676-0,0259 Pael 2. Clusters 4-6 ad bakrupt startups Cluster 4 (r = 0,4063) Cluster 5 (r = -0,5165) Bakrupt startups (r = -0,0093) Period PMR ROI CFR PMR ROI CFR PMR ROI CFR 0 0,0064-0,2070-0,0383-0,2074-0,1418-0, ,0617 0,3344 0,0447-0,0879-0,6203-0,1235-0,0695-0,2459-0, ,0828 0,3966 0,0945-0,0975-0,6145-0,1176-0,0367-0,1128-0, ,0899 0,4233 0,1067-0,0990-0,6155-0,1172-0,0231-0,0694-0, ,0921 0,4328 0,1099-0,0992-0,6158-0,1172-0,0178-0,0534-0, ,0927 0,4357 0,1107-0,0992-0,6158-0,1172-0,0159-0,0476-0, ,0929 0,4366 0,1110-0,0993-0,6158-0,1172-0,0152-0,0455-0, ,0930 0,4369 0,1110-0,0993-0,6158-0,1172-0,0149-0,0448-0, ,0930 0,4369 0,1110-0,0993-0,6158-0,1172-0,0149-0,0446-0, ,0930 0,4370 0,1110-0,0993-0,6158-0,1172-0,0148-0,0445-0, ,0930 0,4370 0,1110-0,0993-0,6158-0,1172-0,0148-0,0445-0,0340 Steady state 0,0930 0,4370 0,1110-0,0993-0,6158-0,1172-0,0148-0,0444-0,

21 Figure 1. Developmet of profitability ratios i cluster 1 of active startups Startup age PMR ROI CFR r Cluster 2 (15.3% of startups) is also characterized by a high reveue lag parameter (0.5866) with a high average lag of 1.4 periods. However, its rate of expese is very low (0.4356) cosistetly with the high lag parameter. The coefficiet of determiatio for the distributed lag model is low idicatig a weak depedece betwee expediture ad reveue. I additio, the average estimates for growth rates i R ad M are of differet sig reflectig a o-steady state. Because the average rate of growth i this cluster is close to zero, this cluster ca be etitled as Zero-growth o-steady startups with high reveue lag ad low rate of expese. Table 8 shows that i this cluster the adjustmet process (S) is very slow. However, the differeces betwee the steady values ad values i early years for ROI ad PMR are very small. Thus, the adjustmet process for these ratios is very weak (see Table 9 ad Figure 2). However, the steady value of CFR is far from its early values, which leads to a strog ad log adjustmet process. I this cluster, ROI gives a satisfactory estimate of r (0.0972) already i the early years. Figure 2. Developmet of profitability ratios i cluster 2 of active startups Startup age PMR ROI CFR r 19

22 Cluster 3 (31.1%) is the largest sub-group of active firms. It is characterized by a egative iteral rate of retur ( ) ad a low reveue lag parameter (0.2754) givig a average lag of 0.38 periods. Therefore, the cluster ca be called as Uprofitable startups with a low reveue lag. The rate of growth (0.0540) i these startups is average. Table 8 shows that the adjustmet process (S) due to the low reveue lag is quick. However, the differeces betwee the steady values of profitability ratios ad their early values are large. Therefore, the adjustmet processes are strog although beig quick (Table 9 ad Figure 3). The three profitability ratios refer i the early years to a very uprofitable startup due to the adjustmet process. I the steady state, ROI ( ) still uderestimates IRR. Figure 3. Developmet of profitability ratios i cluster 3 of active startups Startup age PMR ROI CFR r Cluster 4 (16.8%) is characterized by a very high iteral rate of retur (0.4063), a egative growth rate ( ) ad a low reveue lag parameter (0.2411) with a average lag of 0.32 periods. Thus, this cluster ca be etitled as Very profitable shrikig startups with a low reveue lag. Table 8 shows that the adjustmet process (S) is as quick as i cluster 3. The differeces betwee the steady state values ad the early values of ROI ad PRM are small leadig to weak adjustmet processes. However, for CFR the adjustmet process is strog (Table 9 ad Figure 4). I already early years, the three profitability ratios correctly refer to a profitable startup. The steady rate of ROI (0.4370) gives a good proxy of r. Cluster 5 (10.5%) is the smallest sub-group of active startups. This cluster is characterized by a very low iteral rate of retur ( ), a high growth rate (0.1112) ad a very low reveue lag parameter (0.0831) leadig to a average lag of 0.1 periods (oe moth). Cosistetly with the low reveue lag parameter, the rate of expese is high (0.8599). For this cluster, the differece betwee g ad r is very large leadig to a low steady reveue-expediture ratio R/M (0.8969). Thus, this cluster ca be called as Very uprofitable rapidly growig startups with a low reveue lag. Table 8 shows that the speed of adjustmet process (S) is extremely quick. Because the steady values of the profitability ratios are quite close to their values i early years, the adjustmet processes are very weak (Table 9 ad Figure 5). These ratios correctly give a isight of very uprofitable startup already i the early years. Especially, the steady ROI ( ) uderestimates iteral rate of retur but ayway gives a reasoable proxy. 20