Production, Process Investment and the Survival of Debt Financed Startup Firms

Transcription

1 Babson College Digital Knowledge at Babson Babson Faculty Research Fund Working Papers Babson Faculty Research Fund 00 Production, Process Investent and the Survival of Debt Financed Startup Firs S. Sinan Erzurulu Babson College, Fehi Tanrisever University of Texas at Austin Nitin Joglekar Boston University Follow this and additional works at: Part of the Business Adinistration, Manageent, and Operations Coons, and the Manageent Inforation Systes Coons This research was supported by the Babson Faculty Research Fund Suer Stipend / 009 Copyright held by authors. All rights reserved. Recoended Citation Erzurulu, S. Sinan; Tanrisever, Fehi; and Joglekar, Nitin, "Production, Process Investent and the Survival of Debt Financed Startup Firs" (00). Babson Faculty Research Fund Working Papers. Paper This Working Paper is brought to you for free and open access by the Babson Faculty Research Fund at Digital Knowledge at Babson. It has been accepted for inclusion in Babson Faculty Research Fund Working Papers by an authorized adinistrator of Digital Knowledge at Babson. For ore inforation, please contact digitalknowledge@babson.edu.

2 BABSON FACULTY RESEARCH FUND PRODUCTION, PROCESS INVESTMENT AND THE SURVIVAL OF DEBT FINANCED STARTUP FIRMS S. SINAN ERZURUMLU Babson College Technology, Operations and Inforation Manageent Division FEHMI TANRISEVER University of Texas at Austin NITIN JOGLEKAR Boston University No. WP 003 SS09 BFRF WORKING PAPER SERIES This research was supported by the Babson Faculty Research Fund Copyright Sinan Erzurulu, Fehi Tanrisever and Nitin Joglekar, 00. All rights reserved.

3 Production, Process Investent and the Survival of Debt Financed Startup Firs Fehi Tanrisever S. Sinan Erzurulu Nitin Joglekar University of Texas at Austin Babson College Boston University Version Whether to invest in process developent that can reduce the unit cost and thereby raise future profits or to conserve cash and reduce the likelihood of bankruptcy is a key concern faced by any startups firs that have taken on debt. We explore this concern by exaining the production uantity and cost-reducing R&D investent decisions in a two period odel. A startup fir ust ake a iniu level of profits at the end of the first period to survive and continue operating in the second period. We show that under a base case, with deterinistic deand, such a startup should produce the onopoly uantity and use an invest-all-or-nothing investent policy. However, under stochastic deand and allied survival constraint, the optial investent policy does not necessarily have an all-or-nothing character. We establish conditions for creating hedges through either aggressive or conservative investent alternatives. If the startup akes a conservative investent decision, it sacrifices soe first period expected profits to increase its survival chances and chooses an optial uantity less than the onopoly uantity. Further, if the startup decides to invest aggressively, then it produces ore than the onopoly uantity to cover the higher bankruptcy risk due to such aggressive investent. Keywords: Joint Production and Process Investent Decisions; Operational Hedging; Startup Operations; Survival under Debt.. Introduction According to a study by U.S. Bureau of the Census, it is estiated that over 700,000 startups are fored every year in the US (Acs and Arington 998). However, only a sall proportion of these startups are able to grow their revenues and becoe profitable, and even a saller proportion of these firs can show continued growth and ake initial public offerings (Acs and Arington 003). Startup firs are endowed with uniue characteristics regarding their asset structure, organization type and growth orientation (Gifford 005), and their operational decisions are often restricted by debt and other financial considerations (Berger and Udell 005). In practice, ost startups have very liited access to capital. Most of these firs take on debt and face iediate bankruptcy in case of a payback default. Hence, for

4 startup anagers it is necessary to generate adeuate short-ter cash flows by exploiting iediate business opportunities in order to keep up with the cash outflows and avoid bankruptcy. Further, startups are not erely focused on survival. They are also interested in long-ter growth. Indeed, ost startup firs are concerned with their ability to invest in research and developent (R&D) to iprove their products and services (Bhide 000). While such investents ay not generate iediate cash flows, they are likely to iprove the future prospects of the fir. In general, under bankruptcy risk, long-ter growth and short-ter survival are two intiately linked concerns. A key area of startup decision aking, involving short ter survival against long ter growth, is the R&D investent that is aied at reducing the fir s unit production cost. In this paper, we investigate the optial operating decisions of a startup under debt which can invest in production to exploit the current business opportunities and generate short-ter cash flows, or, it can also have a strategy under which it ay also invest in process iproveent to secure future arket share and long-ter profits. We have conducted a series of interviews in order to understand the key considerations that affect process R&D investent decisions in startup settings. For exaple, Faradox is an Austin based startup which provides high energy density capacitors using its niche production process. Faradox views process developent to reduce unit cost as a key copetitive aspect of its business. During our interviews, the VP of business operations at Faradox stated that there was treendous aount of on-going research in the field of high energy density capacitors and, it was uite likely that new copetitors ight enter the arket by developing new and possibly ore efficient production processes with lower unit costs. He also acknowledged that while process R&D was a key eleent of long ter survival of Faradox, it was very costly and its return was highly uncertain. Further, while aking investent decisions, predicting consuer deand also iposes a serious challenge for this copany since the arket is evolving and the custoer base is hard to analyze. Allied issues have also surfaced at other Austin startups, AccuWater, AxsTracker, Big Foot Networks etc. Managers at these firs indicated that their production and investent decisions are affected by risk created by cash flow and technology perforance (Erzurulu 3

5 and Tanrisever 007). These concerns are consistent with descriptions of startup decision aking in the extant literature (Bhide 000, Shane 007). However, in the absence of a odeling fraework, these anagers are not able to assess their production and process iproveent risks, and underlying tradeoffs, with precision. This has otivated our effort to foralize a class of factors that have been central for startup copanies while choosing their operating policies regarding production and process investent in the presence of survival considerations: uncertainties surrounding deand, technological perforance and likely entry of copetition. These factors for the core of our odel, and we exaine their ipact on the selection of operating (production and process investent) policies and the survival chances of the startup. For ease of exposition, odel specification and analysis are developed in two stages. In the first stage, we analyze a base case (BC) regarding our operating decisions under deterinistic deand with a two-period odel. BC provides bencharks for ore involved odels. In the second stage of our analysis, we allow stochastic realization of deand. This is tered as the stochastic deand and survival constraint (SDSC) case. With stochastic deand, profits after the first period are not guaranteed and a probabilistic survival constraint coes into play. SDSC is aenable to closed for solutions under liited conditions. Hence, we explore the underlying tradeoff between expected profit and bankruptcy risk through a cobination of analytical and nuerical solutions. The contributions fro our work are threefold. First, we specify a deterinistic-deand odel for a debt financed startup fir as a base case, and characterize an optial invest-all-or-nothing policy which derives the conditions for investent in process iproveent in order to enhance long-ter profits. Second, with deand uncertainty and the conseuent probabilistic survival constraint, we find that such a startup responds to the bankruptcy risk by increasing the investent threshold, i.e., the fir looks for ore favorable arket conditions to invest. Indeed, while balancing the bankruptcy risk with future growth opportunities, the startup ay either behave conservatively (aggressively) by investing and producing less (ore) than the BC level. In effect, a probabilistic survival constraint induces the startup to produce so as to create an operational hedge with respect to its process investent decision. Further, we 4

6 offer a probabilistic survival easure that reflects the riskiness of the startup s operating decisions under the threat of bankruptcy. Third, we explore the ipact of the existence of process investent opportunities, iediate profitability of the fir and liited debt availability on the optial operating decisions and the allied survival chances. In addition, we have circled back to soe startup anagers and sought their feedback on our findings. We discuss the anagerial iplications of these findings while we synthesize and discuss our results. The rest of our paper is organized as follows. provides a review of the related literature. In 3 we analyze the BC and characterize a closed for solution under deterinistic deand. We extend our discussion to SDSC case in 4. In 5 we discuss liited debt capacity. 6 addresses anagerial iplications, liitations and concludes our paper.. Relevant Literature Here we briefly review the streas of literature that are closely related to our work: investent in process R&D, startup operations and financing, and the entrepreneurial decision-aking. Investent in process R&D and allied cost reduction and capacity anageent decisions have long been key issues in the anufacturing technology anageent literature (De Groote 988, Fine and Porteus 989, Chand et al. 996, Li and Rajagopalan 998, Carrillo and Gaion 000, 004). In addition, a closely aligned literature explores the technology adoption decisions (McCardle 985, Milgro and Roberts 990, Fine and Freund 990, Gupta and Loulou 998). R&D investent under technology uncertainty in a single fir setting (Balcer and Lippan 984, Kornish, 999) and in copetitive settings (Maer and McCardle 987) usually yield an all-or-nothing type of policy: adopt the current best technology if the gap between current and state-of-the-art technology exceeds a certain threshold. In this paper, we will show that such all-or-nothing policies apply under liited conditions in startup settings to avoid bankruptcy. We illustrate that the incorporation of financial liitations in a startup setting lead to joint consideration of uantity and process investent decisions. 5

7 A recently growing body of literature deals with decision odels involving the financing and operations of startups. Archibald et al. (00) argue that if the startups are ore interested in surviving than axiizing their profits, they should eploy conservative strategies. On the contrary, we show that profit axiizing startups under a survival constraint could follow aggressive strategies when they have investent opportunities. Babich and Sobel (004) provide a odel to axiize the likelihood of a successful IPO for debt financed startups while Buzacott and Zhang (004) adopt an asset based financing schee for sall and start-up firs. However, they do not explicitly odel for strategic investent or copetition which is central to the long ter growth and survival of startups. Swinney et al. (006) build the case on how copetition between startup and established firs differs fro copetition between two established firs and show that a startup s preference to increase its survival affects the copetition. However, they consider a single period odel with a survival axiizing startup. Joglekar and Levesue (009) analyze the distribution of venture capital between product related R&D and arketing, but do not account for either survival constraint or copetition explicitly. Therefore, our research extends a growing literature on the theories of startup driven R&D and operational practices (Shane and Ulrich 004). Finally, an established topic of research in the entrepreneurship literature explores risk bearing as the key econoic role of entrepreneurs. On one hand, Kihlsto and Laffont (979) and Craer et al. (00) show that entrepreneurs are ore risk seeking, and on the other hand, Halek and Eisenhaur (00) finds that entrepreneurs do not differ fro wage earners and further, are ore risk-averse than others in soe cases. In a closely related epirical work, Wu and Knott (006) study the entrepreneur s decision of arket entry cobined with two distinct sources of uncertainty: deand uncertainty and uncertainty regarding entrepreneur s own ability. They argue that entrepreneurs are risk averse with respect to deand uncertainty and risk seeking with respect to perforance uncertainty. Recently, Corbett and Fransoo (008) also epirically investigate whether entrepreneurs follow the newsvendor logic and how their risk preferences affect their inventory decisions. We contribute to this strea of literature by explicitly odeling for operating decisions and bankruptcy which derives the risk preferences of the fir 6

8 together with the investent opportunities, in a fraework seuentially introducing technology, copetition and deand risks. In su, the effect of cost reducing R&D on the profitability of firs has been studied extensively for established firs that are unencubered by bankruptcy concerns. Further, cost reduction strategies adopted after the launch of a breakthrough product to axiize the profits is a relevant proble for any startup firs that take on debt and face the cash flow related threat of survival. However, this proble has not been explored forally. In the rest of this paper, we set up and study a startup s production and cost reducing investent decisions. 3. The Base Case When aking production and investent decisions, there are three key factors a typical startup considers: custoer deand, startup s technological perforance and copetitive pressures (Shane 007, Erzurulu and Tanrisever 007). To understand the interrelated ipact of these factors on the operating decisions, we consider a two period odel of a startup fir offering a single new product. This fir is financed by debt and ust generate pre-specified level of profit after the first period to ensure survival into the second period. The objective of the fir is to axiize the total of two-period profits under the survival reuireent. In this section we focus on a base case (BC) odel with no deand uncertainty, and study the ipact of technological perforance and copetitive pressures on the startup s operating decisions. In 3., we start with a siple odel which serves as a benchark for our analysis. Then we seuentially introduce uncertainty associated with the fir s process investent and second period copetition in 3. and 3.3, respectively. For generality, we use the ters return on process investent and technological perforance interchangeably throughout this anuscript. 3. A Benchark Model We start with soe key assuptions to set up our odel. Assuption. Product R&D is frozen at the beginning of the first period, i.e. at arket entry. 7

9 At least half of the startup firs in the US enter the arket with a novel product (GEM Report 007), and any of these firs continue to invest into product developent effort. We do not allow for such investents, so that our analysis is not confounded by the evolution of product uality. Assuption. The startup is financed by bank loans with a constant positive interest rate. We consider a bank-financed startup, but our odels and results trivially extend to bootstrapped startups. The interest rate is constant and positive, and upon fully paying its previous debt the startup can borrow in each period to cover its production cost and R&D investent. In general, once the loan is granted to a sall fir, the loan ters including interest rate and loan liit are deterined by industry practices and arket conditions and do not depend on the conditions of the borrower fir (Petersen and Rajan 994). For ease of exposure, we consider the effect of an explicit loan liit as an extension in 6. There is no tie discount on the profits of the second period. The analysis is unchanged, if we consider a discount paraeter between periods. Assuption 3. The startup goes bankrupt and gets liuidated if it cannot pay its debt at the end of each period. Most startups have liited access to capital arkets and cannot raise additional capital other than their initial funds (Chrisan et al. 998). In particular, inforational asyetries between the owners of the startups and the investors, and the uncertainties about the future prospects of the startup severely liit the fir s access to capital arkets (Shane 007). Hence, ost new businesses are built with liited capital and face iediate bankruptcy in case of a default. Based on these assuptions, the tiing of the gae is as follows. In the first period, the startup fir is a onopoly operating with a unit production cost of c and receives funds, y, with an interest rate of r. It allocates these funds at the beginning of the first period between production capacity,, and process R&D investent, A, which will in return linearly reduce the unit production cost in the second period to, c A c A, where denotes the return on investent (Gupta and Loulou 998). At the beginning of the consecutive period, the startup realizes revenues fro sales, observes reduction in unit 8

10 cost due to process investent, and akes the debt payents. In case, the revenues are not sufficient to cover the debt obligations, the fir goes bankrupt and gets liuidated. If the debt is paid in full then the fir goes into the second period and could receive a second round of funding, y to invest in production, as this is the final period. We adopt a linear inverse deand function for the startup s product as p ( ), t=,, where denotes the constant arket size. t t t We offer the following as the benchark odel: ax ( p ( ) c ) ry A ( ; A, ), A, y0 subject to c A y (a) where ( p ( ) c ) ry A 0 (b) ( ; A, ) ax ( p ( ) c ( A, )) ry, y0 subject to c y (c) In this odel, (a) and (c) represent the financial constraints in the first and second periods, respectively, such that the total expenditures of the fir in each period are liited by the aount of oney borrowed. (b) denotes the survival constraint reuiring that the oney borrowed in the first period should be paid back with interest at the end of the period. Based on our odel assuptions, (a) and (c) ust be binding. Therefore, we re-state () as follows: ax ( p ( ) ( r) c ) ( r) A ( ; A, ), A0 subject to ( p ( ) ( r) c ) ( r) A 0 () where ( ; A, ) ax( p ( ) ( r) c ( A, )) 0 Assuing that the return on investent is constant and eual to, we characterize the operating decisions and profits in Proposition 3.. We use the superscript bc to denote the benchark case. Later we will use c for the case with copetition and t for the case with uncertain return on 9

11 investent. (See the Appendix for proofs of the leas, propositions and corollaries unless stated otherwise.) Proposition 3. When deand and the return on investent are deterinistic, the startup s total profits are axiized at the onopoly uantity, * ( rc ). Following, the process R&D investent of the startup is bounded by the discounted onopoly profits, A ax ( ( rc ) ) = = ( r) 4( r). Assuing that the cost cannot be driven to zero, the optial process investent for the startup, expected profits, *, are given by the following: * A, and the optial bc * Aax if 0 A, and 0 o/ w ( r)( c Aax ) bc if * ( ( rc ) ) o/ w 0 where bc ( ( r) c) 8 ( ( r) c) 6. A close exaination of () reveals that the startup s optiization proble is partially separable in production uantity and process investent. Conseuently, we find in Proposition 3. that it is optial to produce the onopoly uantity, and the onopoly profits liit the investent aount due to the survival constraint. To explain the investent decision, we define the fir s propensity to invest in process iproveent as. In particular, if 0 then, the fir does not invest in process iproveent. Therefore, the profits in each period are identical and eual to the onopoly profits. However, if the fir s propensity to invest is sufficiently high, 0, then it would allocate all of its funds in process iproveent and ake zero net profits after the debt payents, in the first period. It could later generate enough revenues with the second period sales to copensate for the issed earnings of the first period. In particular, the fir either chooses not to invest, A * = 0, or if it chooses to invest, it invests the axiu possible aount, A ax, which would axiize its profits without going bankrupt. Therefore, the optial 0

12 process investent decision can be characterized by an invest-all-or-nothing threshold policy. Further, as the ean return on investent and arket size increase, the fir s propensity to invest also increases. 3. Technology Uncertainty So far, we have assued that process investent reduces the future unit cost of the fir by a deterinistic aount. Nevertheless, for startups with niece processes like Faradox and BigFoot Networks return on process investent is inherently uncertain. To take this into consideration, we extend our discussion in the benchark case to consider the ipact of the return on investent uncertainty on the startup s operating decisions and profits. In particular, for every dollar invested, we assue that the second period cost is reduced by a rando aount described by, with a known distribution function, ( ), with a ean of and a variance of. The following proposition characterizes the optial production and investent decisions in the benchark odel with technology uncertainty. Proposition 3. When deand is deterinistic, but the return on investent is uncertain, then the startup s optial production uantity is eual to the onopoly uantity. And, the optial process investent and profits are, respectively, given by ( ( r)( c Aax )) ( r) A tu * Aax if 0 A, * and 4 0 o/ w ( ( rc ) ) ax if o/ w tu 0 where tu ( )( ( r) c) 8( ( r) c) 6. With return on investent uncertainty the fir s propensity to invest becoes larger than the case with no uncertainty in return on investent, i.e., tu bc ( ( rc ) ). Further, the fir profits are also non-decreasing in, so when selecting aong production technologies, the startup prefers technologies with ore variable return copared to the ones with relatively certain returns. This ay see like a counterintuitive result, but if this technology adoption proves to be successful, then the fir could obtain significant cost reduction and have a ajor increase in profits. That is, the startup disproportionately benefits fro upside deviation in return on process investent. In our odel, this is

13 driven by the convex onopoly profits, ( ( rc ) ) / 4, with respect to the unit cost in the second period. 3.3 Copetition In this section, we study the case with copetition. The seuence of events is precisely the sae as the case without copetition. The difference is that at the beginning of the second period a copetitor with an identical product enters the arket and firs play a Cournot gae where the copetitor s best response uantity is denoted by. The updated seuence of events and the startup s decisions are c suarized in Figure. Startup holds a onopoly position. () Startup realizes cost reduction due to process investent. () Rival fir enters the arket and firs engage in a uantity copetition. Period Period t = Start-up decides how uch : () oney to borrow (y ), () produce ( ) and (3) investent in process iproveent (A ), in period one. Startup (if survives) pays back the borrowed oney and decides how uch () oney to borrow (y ) and () produce ( ), in period two. Figure : Seuence of Events and Decisions in a Two Period Model with Copetition When a copetitor is to enter the arket, the startup ay not fully know the entrant s production syste for a new product, but it ay know the copetitor s cost through a probability distribution function. Indeed, Faradox Inc., a producer of high energy-density capacitors, entioned in our interview that there was treendous aount of theoretical research in the field of capacitor technologies and it was likely that soeone ight enter their arket by developing a new process to produce high energy-density capacitors. Hence, fro the perspective of Faradox, the efficiency of the prospective copetitor in the future is highly uncertain and exogenous.

14 To incorporate this into our benchark odel, we assue that the unit variable cost of the copetitor, ~, is distributed with a probability density function of ( ), and has a ean of and a variance of. For ease of exposure, we exclude technology uncertainty in this section, but our findings here also trivially extend to the case with both technology uncertainty and copetition. The following proposition characterizes the startup s optial production and investent decisions for the benchark odel with copetition. Proposition 3.3 Under deterinistic deand and return on investent, when there is copetition in the future period, then the startup s optial production uantity is eual to the onopoly uantity. The optial process investent and the optial profits are, respectively, given by c * Aax if 0 A, and 0 o/ w ( ( ) ) 4 ax ( ( ) ) c r c A r c Aax if 0 * 9, ( rc ) ( ( r ) c ) o / w 4 9 where c ( ( ( r) c) ) 4 (( r) c ) 3. Fro Proposition 3.3, we observe that the propensity of the startup to invest increases with the c expected unit cost of the copetitor, i.e., / 0. In other words, when faced with a strong copetitor, the startup is less willing to invest since the benefits of investent is reduced under copetition. According to our investent policy, the variance of the copetitor s cost would have no effect on the investent decision so long as the uantity response function is linear in the realization of copetitor s cost. However, since Cournot profits are convex in the copetitor s cost, the optial profits increase as the strength of copetition gets ore variable because the startup disproportionately benefits fro high cost entrants. 3

15 Coparing the fir s propensity to invest with and without copetition for various levels of copetitor s unit cost, we can further explain the ipact of the strength of future copetition on the fir s propensity to invest: Corollary 3.4 In the presence of copetition the startup s propensity to invest increases copared to the benchark case, if the expected copetitor is relatively weak. In particular: bc c i) if 7/ 4, bc c ii) if 7/ 4. Corollary 3.4 shows that the fir ay find it optial to invest in the presence of copetition bc c when it is better off with no investent in the benchark case, i.e., 0. Therefore, the shadow of future copetition ay encourage investent by the startup depending on the expected strength of the copetitor. 4. The Stochastic Deand and Survival Case In the BC, we studied the startup fir s operating decisions under deterinistic deand. However, in ost cases the startup would have very liited inforation about the deand, especially for a brand new product. In this section, we exaine our odel with stochastic deand in each period, and replace the deterinistic survival constraint of the BC with a probabilistic survival reuireent. 4. The Model with Stochastic Deand and Survival In this case, we assue a deand shock, t, in each period t (t =, ) with a noral probability density function, (.), with ean zero and variance v, and cuulative distribution function, (.). The iniu profit level reuired for the survival denoted by is exogenous and includes the overhead costs like rents and wages. We define the first period net expected onopoly profits,, as the iediate econoical viability of the fir (Note that the expected onopoly profits is given by 4

16 E[( p(, ) ( r) c) ]). Under the SDSC case with copetition, technology uncertainty and stochastic deand, the two-period expected profit axiization proble of the startup is given as: * z ax E p c r c A A E, A, A s. t., A 0 where ( A;,, ) ax E ( p (, ) ( r) c ( A, ; A )) c 0, I ( ( ; ) ) ( ) ( ;,, ) s. t. ( ) M ( I ) MI 0, I{0,} Stochastic survival constraints (3) where I is the first period survival indicator (= if the fir survives the first period) and M is a large nuber. In (3), the constraints in the second stage of the proble only hold if the startup has survived the first period. In particular, unless the first period profit for the startup eets the iniu level reuired for survival, the startup cannot play the second period uantity gae. In this case, the survival indicator variable I in (3) has to be zero and conseuently, is also forced to zero. We solve the optiization proble in (3) by backward induction. In the second period, firs play a Cournot gae to axiize their expected profits. Hence, the startup s euilibriu profit, if it could play the second period gae, is given by A rc A ;,,, / 9 where E( ). By assuption, 0. For the startup to participate in the second period, first it has to survive in the first period only if ( ) startup s proble in (3) becoes. After substituting the optial second period solution, the * ( ( r) c ( A, )) z ax E ( p(, ) c ) r c A A E,, ( ), A0 9 (4) 5

17 Unlike the BC, the axiization proble is not separable in production and investent decisions, and it is non-convex. Nevertheless, we can still prove the following iportant relationship for the optial decisions. Proposition 4. When deand is stochastic, the startup fir in the first period either adopts a conservative operating policy by producing and investing less than the onopoly levels i.e., ( rc ), * A A r, or an aggressive operating policy by producing and investing ore than the onopoly levels, i.e.,, * A A. r Proposition 4. provides an interesting risk based justification linking production and investent decisions of a startup under stochastic deand and bankruptcy risk. The fir is aggressive in investent decision A A, if and only if it is also aggressive in production. Or, the fir is conservative in investent decision A A if and only if it is also conservative in production. If an aggressive investent is planned, then the expected cash flows under the onopoly production plan is not sufficient to cover the debt payents. Hence, the fir increases its production uantity above the onopoly level so as to benefit fro upside deand realizations and to increase its survival chances and conversely, a conservative investent reduces production below the onopoly level. In the following proposition, we establish the intiate connection between the optial operating policy of the fir and the survival probability. Proposition 4. An optial operating policy is aggressive (conservative) if and only if its survival probability, P ( ra ) ( ) r c, is less (ore) than fifty percent. Proposition 4. provides an euivalent survival-based definition for optial aggressive and conservative operating decisions. That is, optial operating policies that survive less (ore) than 50% 6

18 chances always involve producing and investing ore (less) than the onopoly levels, and vice versa. This iplies that an aggressive fir is expected to go bankrupt on average while a conservative fir is expected to survive. In general, an operating policy is considered to be riskier as the survival probability decreases. In the reinder of this section and in 5, we explore the factors that that drive the optial operating decisions of the startup under stochastic deand. In Proposition 4. we iplicitly assue that the startup would find an investent opportunity. However, that ay not be the case. Corollary 4. considers the ipact of the existence of investent opportunities (with positive NPV) on the operating decision of econoically viable startup firs. Recall that iediate econoical viability eans the fir s first period net expected onopoly profits are non-negative. Corollary 4. Suppose the startup fir is iediately econoically viable in the first period, i.e., 0, then i) If there are no process investent opportunities, A 0, the fir always adopts a conservative operating policy. That is, the fir produces less than the onopoly uantity. ii) If there is an opportunity for process investent, A 0, then the startup ay either adopt an aggressive or conservative operating policy. According to Corollary 4., when there are no investent opportunities, iediately econoically viable startups always choose a conservative operating policy. To better illustrate our finding, we exaine a siple situation with no iniu level of profits, = 0 and we let the deand shocks in each period ( t for t =, ) be uniforly distributed with U[-b, +b]. Then, the optiization proble takes the following for: 0, A0 ax f (, A) ( ) ( r )( c A) ( ra ) ( ) b r c ( kc) ( kc) ka k ( ) A 9 b 7

19 When there are no investent opportunities (A = 0), f(,0) is concave in and the optial uantity is given by * ( r) c ( ( r) c) 4b 9, which agrees with our finding that in the absence of investent opportunities, the fir always behaves conservatively. The positive second ter of the optial uantity, *, above represents the under-production aount due to stochastic bankruptcy risk in order to increase the probability of survival. In particular, if the bankruptcy risk is to be reoved fro the decision fraework, the fir siply produces the first best production level, i.e., the onopoly uantity. That is, the bankruptcy risk drives an econoically viable startup to adopt a conservative policy in the absence of investent opportunities. In addition, startups with high expected future prospects, such as a large arket base, an already efficient process technology or a relatively weak copetitor, focus ore on survival in anticipation of future profits. That is, they deviate ore fro their first best operating plans and choose a ore conservative policy. We will nuerically investigate the optial operating policies for this case in 5. We now turn our attention to a fir that is not econoically viable in the first period. We iplicitly assue that the fir is econoically viable over the planning horizon. Otherwise, it is optial to liuidate the fir at tie zero. Corollary 4.: Suppose the startup fir is not iediately econoically viable in the first period, i.e., 0, then the fir always adopts an aggressive operating policy, regardless of the existence of investent opportunities. When the fir is not iediately viable, e.g., due to high operating costs relative to iediate profits, its survival is contingent on the upside deviations in arket deand. To benefit fro these upside deviations and survive, the fir should increase its production above the onopoly uantity. Conseuently, even with no investent opportunities the fir would always choose an aggressive operating policy. We suarize the effects of the iediate econoical viability and investent opportunities on the operating policy of the startup in Table. 8

20 Our results show that an iediately viable startup with investent opportunities ay either adopt a conservative or an aggressive operating policy depending on the arket paraeters. To further investigate this case and the ipact of arket paraeters on the optial operating decisions, we present a coprehensive coputational analysis in the next section. We also note that this case is not analytically tractable. There are several reasons for this, including that the objective function in (4) is neither jointly convex nor concave in and A for all feasible set of paraeter settings. Table : Operating Policy of the Startup With Investent Opportunities With No Investent Opportunities Iediately Viable Startup ( 0 ) Conservative or aggressive operating policy depending on arket paraeters Conservative operating policy Iediately Non-viable Startup ( 0 ) Aggressive operating policy Aggressive operating policy 4. Coputational Analysis In this section, we focus on a set of nuerical analyses to illustrate the ipact of key arket factors (deand uncertainty, technological perforance, copetition and iniu reuired level of profits), on the optial operating policies (production and process investent) of the iediately viable startups with investent opportunities. We also provide insights that link the BC to SDSC. 4.. Design of Nuerical Experients Our design of experient focuses on the optial survival probability as the relevant easure of the risk taken by the fir. The survival probability is an endogenous variable deterined by the fir s production and investent policy. Recall that a conservative policy survives with probability ore than 50% while an aggressive strategy bankrupts with probability ore than 50%. And, a conservative (aggressive) policy involves producing less (ore) than the onopoly uantity and investing less (ore) than the expected net onopoly profits. 9

21 We begin with exaining the ipact of ean return on investent in 4.. in an experiental setup that has no copetition, deterinistic return on investent and zero interest rate as in BC. In this case the optiization proble in (4) reduces to ( ca) c A ax f (, A) ( ) c A F A, 0 4 Following, we explore the ipact of technological uncertainty and copetition on the operating decisions in 4..3 and 4..4, respectively. For ease of exposition, throughout our nuerical analysis we fix the arket size and initial unit cost (θ = 0, c = 7), so =.5 and =.5. The standard deviation of deand shock is set to v =.. The ipact of different levels of v is investigated in We present a selective set of our results, but we have tested and confired siilar results with entire sets of values that the odel paraeters can take. 4.. Benchark Case with Stochastic Deand In this section we exaine the ipact of ean return on investent,, and the iediate econoical viability of the fir through iniu reuired profits,. Figure illustrates the optial operating decisions and the associated survival probabilities for all reasonable levels of. We observe in Figure that it is optial to invest if hen, as in the BC, a threshold type of investent policy is optial, but the policy does not have an invest-all-or-nothing structure. As the fir s potential efficiency in cost reduction increases, the fir raises its investent aount in process technology leading to riskier operating decisions with lower survival probability. Indeed, aggressive investent becoes the optial policy for. In addition, the production uantity ay either increase or decrease with the investent level to create an operational hedge in response to optial investent decision. 0

22 Miniu Profit Level No Investent Conservative Policy Aggressive Policy No Investent Conservative Policy Aggressive Policy Mean Return on Investent, * A* A P Mean Return on Investent, Figure : Optial Operating Decisions and Survival Probability as a Function of for 0 Figure 3 illustrates the interactive ipact of and on the optial policy. We observe that no investent region expands as increases. In particular, when is high, investent creates a very high bankruptcy risk consuing the liited short-ter profits of the fir. Therefore, the fir avoids investent. On the hand, if is low, then the fir is expected to have cash in the future and, it ay invest soe of this cash in process iproveent without diinishing its survival probability. Further, depending on its ean return on investent, the optial policy is either conservative or aggressive No Investent * * ( A 0,, P 0.5 ) Iediately non-viable region Iediately viable region No Investent * * ( A 0,, P 0.5 ) Aggressive Policy * * ( A A,, P 0.5 ) Conservative Policy * * ( A A,, P 0.5 ) Mean Return on Investent () Figure 3: Interaction of and under SDSC Case

23 Conservative Policy Aggressive Policy Conservative Policy Aggressive Policy 4..3 Technology Uncertainty In the previous section we discuss the ipact of ean return on investent on the operating decisions of the fir, but we did not exaine the associated uncertainty. We coplete this discussion by illustrating the effect of technology uncertainty, in Figure 4. For ease of discussion, in the reinder of this section we set 0, but siilar results can be obtained for other values. Under deterinistic deand, fro Proposition 3., we know that as the return on investent gets ore variable and the chances of upside deviations increase, the fir is ore willing to invest. Siilarly, when deand is uncertain, Figure 4 leads to the observation that for a given level of, an increase in technology uncertainty decreases the survival chances of the fir, by inducing ore aggressive operating decisions with higher production and investent levels *.5 A P A* Technology uncertainty, Technology uncertainty, Figure 4: Optial Production Quantity and Process Investent as a Function of =.5) 4..4 Copetition In this section we explore the ipact of copetition on the operating decision of the fir under stochastic deand and deterinistic return on investent. In Figure 5 we present the optial operating decisions as well as the associated survival probabilities as the copetitor s expected cost changes for a given level of return on investent.

24 No Investent Aggressive Investent Conservative Investent No Investent Aggressive Investent Conservative Investent A* A P * Copetitor s Expected Cost, Copetitor s Expected Cost, Figure 5: Optial operating decisions and survival probability as a function of (=.5). Siilar to the BC, Figure 5 shows that the fir starts investing when the copetitor is sufficiently weak and benefits fro investent in the future period. However, the fir ay invest (and produce) either aggressively or conservatively depending on the level of. Further, for a given level of it does not necessarily keep raising its investent aount as the copetition gets weaker because although the expected arginal second period profit of the fir is increasing with, a higher investent aount also increases fir s exposure to bankruptcy. Figure 5 illustrates this tradeoff that fir chooses a conservative investent policy when faced with very weak copetitors to control the bankruptcy risk. Figure 6 further explores the interrelated ipact of copetition and the ean return on process iproveent on the optial operating policy of the fir. The startup akes no process investent if it is not efficient to engage in copetition with a relatively strong copetitor. A conservative policy is chosen when the future entrant would not intensify copetition because it has relatively high cost production process. Further, an aggressive policy is adopted when the startup is sufficiently efficient in cost reduction and the copetitor is neither too strong nor too weak. In this case, the second period profits are distributed ore eually between the firs. Hence, by following an aggressive strategy (if it is not too costly) the startup ay significantly increase its share of expected profits in the second period and obtain a strong future arket position. 3

25 Copetitor s Expected Cost ( Copetitor s Expected Cost () Conservative Policy A A,, P 0.5 ) * * ( No Investent A 0,, P 0.5 ) ( * * Aggressive Policy A A,, P 0.5 ) * * ( Mean Return on Investent () Figure 6: Interaction of - under SDSC Case 4..5 Deand Uncertainty Deand uncertainty is an exogenous factor influencing the bankruptcy risk. Recall that with deand uncertainty investent aount ay be either less or ore than onopoly investents. Figure 7 illustrates that deand uncertainty shrinks investent regions when it is optial to start investing in process R&D, and the thresholds for process investent in the SDSC are higher than the BC, ceteris paribus Invest only in BC Invest both in BC and SDSC Investent threshold for SDSC (v=.) Do not Invest Investent threshold for BC (v=0) Mean Return on Investent () Figure 7: Partitioning of the Process Investent Space under the BC and SDSC 4

26 Standard Deviation of Deand () Figure 8 shows the ipact of deand variability and ean return on investent on the optial policy when there is no copetition and technological variability. As shown in Figure 8, when v is very low, the startup either chooses not to invest or invests conservatively. A higher variability of deand provides the fir with the opportunity of survival under aggressive investent plans. Hence, aggressive policies are only possible if deand is sufficiently variable to provide high deand and the fir is efficient in cost reduction. Indeed, when deand is deterinistic as in the BC, aggressive policies are infeasible. These observations cobined with our earlier findings support that deand variability is necessary to induce iediately viable firs to increase their investent aount and adopt aggressive policies if the increased second period profits due to aggressive investent copensate the excess risk taken by the fir. Also note that Figure 8 generalizes Figure which is constructed for v =. only No Investent * * ( A 0,, P 0.5) Aggressive Policy A A,, P 0.5 ) * * ( =. Conservative Policy A A,, P 0.5 ) * * ( = 0.9 = Mean Return on Investent () Figure 8: Interaction of under SDSC Case 5. Debt Capacity To isolate the ipact of bankruptcy risk, we have assued throughout the paper that the startup fir is able to borrow enough to finance its optial operating policy in the first period. In this section we 5

27 introduce a debt capacity, L, which liits the total cash available to the fir ( c A L ), and exaine its effect on the risk preferences of the startup. In Proposition 5. we characterize the ipact of debt capacity on the base case results under deterinistic deand. Proposition 5. Under deterinistic deand and return on investent, with no future copetition, i) If L c Aax, the debt capacity is never binding. ii) If L c, the debt capacity is always binding. iii) If c L c A, the debt capacity ay or ay not be binding depending on the arket ax paraeters. If the debt capacity is larger than the axiu aount of cash that ay be needed by the fir, i.e., L c A, additional cash has no value to the fir. In this case, the optial operating decisions ax are characterized by Proposition 3. and the fir s propensity to invest is unaffected. However, if debt capacity is not sufficient to finance the onopoly production level, the fir ay invest additional capital into production and increase profits. Also, when the debt capacity is oderately tight ax c L c A, the fir ay benefit fro additional cash if investent is optial when there is no debt capacity. Further, in the following corollary we discuss the fir s propensity to invest with a binding debt capacity. Corollary 5. Under deterinistic deand, when there is a binding debt capacity, startup s propensity to invest decreases. We show (Proposition 3.) that the startup s operating policy with no debt capacity can be described as an all-or-nothing policy, i.e., whether to invest nothing or to invest all of the net onopoly profits, A ax. However, under a binding debt capacity, the startup can never finance to invest as uch as A ax. Besides, since the arginal return on investent is increasing in A, reducing the axiu investent level decreases the benefits of scale econoies in investent and hence, decreases the fir s 6

28 Copetitor s Expected Cost () propensity to invest. Figure 9 presents the ipact of debt capacity on the optial operating policy of the startup under stochastic deand and survival. 9 8 No Debt capacity L= 7 Conservative Policy 6 Aggressive Policy L= No Investent Mean Return on Investent () Figure 9: Ipact of Debt Capacity on the Operating Policy in SDSC L=0 L=0 L= L= No Debt capacity Figure 9 is identical to Figure 6 for no debt capacity case. We observe that, our discussion in 4..4 still holds, but the liiting effect of a tighter debt capacity is clear. Aggressive and conservative policy regions shrink and no-investent region expands with a tighter debt capacity. Overall, our observations suggest that the fir s propensity to invest is reduced with the debt capacity in the deterinistic deand case, and the debt capacity akes the fir ore conservative under stochastic deand. However, the basic results we have shown for the BC and SDSC reain valid under reasonably tight debt capacities. 6. Discussion and Concluding Rearks Existing organizational theories (Bhide 000) have arshaled evidence to argue that startup anagers ake yopic choices in their long ter investent decisions when faced with uncertainty and financial pressure. Our analysis explores the ipact of three key risk drivers (deand, technology and copetition) on the short and long ter production and process investent decisions of startups under the presence of 7

29 explicit financial constraints. Since financial liitations alter optial operating decisions; our results provide a risk based justification for startups linking their production with their process R&D investent. 6. Optial Operating Decisions of Startups with Deterinistic Deand Under deterinistic deand we find that the startup always produces the onopoly uantity and uses a process investent threshold policy involving an invest-all-or-nothing type of structure. The investent policy is described by the fir s propensity to invest. We investigate the ipact of deand, technological perforance and copetition on the fir s propensity to invest in process iproveent. In a large arket the fir has high potential to recover the process investent. Siilarly, higher expected return on investent (better expected technological perforance) increases the potential benefits of investent and akes the fir ore willing to invest. Further, as in new technology developent, the fir disproportionately benefits ore fro upside deviations of return on investent. Hence, the fir s propensity to invest increases as the process technological perforance gets ore variable. Ipact of copetition is ore involved. As the expected copetitor in the future gets stronger, it chips off future profits and the startup s propensity to invest decreases. However, copared to the onopoly situation, the startup ay invest to itigate the ipact of copetition and secure its future earnings if the copetitor is not very strong. We suarize the ipact of key paraeters on the optial process investent of the startup under deterinistic deand (base case) in Table. Recall that in BC the fir always produces the onopoly uantity. Table : Ipact of Key Factors on the Optial Operating Policy under Deterinistic Deand Factor Return on process investent Copetition Debt Capacity Ipact on Optial Operating Policy The fir s propensity to invest increases with ean () and standard deviation () of return on process technology investent. decreases with expected level of copetition (). increases copared to the onopoly case, if the copetitor is not very strong. decreases with debt capacity (L). 8