Optimal investment and production decisions and the value of the firm

We explore the effects of uncertainty on a firm that can respond by modifying its investment or production schedule (or both simultaneously) to variations in output price. Investment may increase capacity and/or reduce costs. We consider a firm with finite resources.Our model uses option theory instead of the more traditional net present value framework. One of the early papers using this approach is Brennan and Schwartz (1985) in which an investment project to extract a finite natural resource is valued. In that paper, the value of the firm is a function of two state variables, the finite resource to be extracted (output to be produced in the future) and the commodity spot price. In order to maximize firm value, the manager can respond by modifying one control variable, the production level. In our model we handle instead three state variables (spot price, resources, accumulated investment) and two control variables (production rate and investment rate), and solve numerically.We obtain both the value and the optimal policy of a firm that has investment projects that increase capacity and/or reduce costs and illustrate optimal policies as resources and available investments decrease over the life of the firm. Firms may start by only investing, then invest and produce, to end only producing.We thank Scott Wo, the referee and the editor for their comments and suggestions. Cortázar and Lowener acknowledge the financial support from FONDECYT and FONDER.     

Dynamic Models of Investment Distortions

This paper studies the interaction between corporate financing decisions and investment decisions in a dynamic framework. When the production decision involves an expansion option, the firm trades off tax benefits of debt against two costs of debt financing, namely the investment distortion related to exercise of the expansion option and the loss of a valuable expansion opportunity if the firm defaults. The optimal capital structure is all equity for firms with more value in growth options (or intangible assets) and tends to involve debt financing for firms with more value in tangible assets. JEL Classification: D81, G13, G31, G32     

Technological advances and the decision to invest

Technological advances impact a firm’s investment decision, as they affect the investment cost. They can also affect the profitability due to demand shocks. We study a firm’s optimal investment decision when technological advances occur as surprises and induce uncertain reductions in the investment cost and in earnings. Despite this complex setting we derive closed-form solutions for the investment option value and the investment threshold. When technological advances only impact the investment cost, we demonstrate significant contributions compared to existing research, which restricts the analysis by keeping the expected investment cost path constant. For example, we show that, albeit the investment threshold is constant, the option value is very sensitive in the expected impact of technological advances. Leaving the restrictive setting, we obtain more intuitive results, e.g. that more frequent technological advances increase the option value. When technological advances impact future earnings we find important long-term effects: the investment threshold increases, whereas the option value decreases. Finally, earnings volatility postpones investment, while uncertainty due to technological advances expedites investment.     

Real options,agency conflicts,and optimal capital structure

We examine the impact of a stockholder–bondholder conflict over the timing of the exercise of an investment option on firm value and corporate financial policy. We find that an equity-maximizing firm exercises the option too early relative to a value-maximizing strategy, and we show how this problem can be characterized as one of overinvestment in risky investment projects. Equityholders’ incentive to overinvest significantly decreases firm value and optimal leverage, and significantly increases the credit spread of risky debt. Numerical solutions illustrate how the agency cost of overinvestment and its effect on corporate financial policy vary with firm and project characteristics.     

Optimal capital structure and the impact of time-to-build

We develop a dynamic investment options model with optimal capital structure and evaluate the effect of time-to-build on firm value and leverage choices. With time-to-build the firm increases initial leverage in order to reduce the impact of delayed cash flows resulting from time-to-build. The impact of time-to-build is more severe the higher the revenue volatility and competitive erosion, and when the firm issues long-term debt. Time-to-build is shown to have a substantial impact on firm values for plausible parameter values.     

Macroeconomic conditions and a firm’s investment decisions

We propose a model of a firm’s reversible investment decision with macroeconomic conditions based on optimal switching of a diffusion regime. The switching costs and the cash flow generated from the firm depend on a business cycle alternating via a Markov chain, and the triggers of investment and disinvestment in each state are determined endogenously. Provided the investment costs are cyclical due to high wages and rents in a boom, the investment tends to be delayed in boom, while the disinvestment is likely to be made earlier in terms of the level of switching triggers. This result shows us that the ‘hysteresis’ of investment is a rigorous phenomenon that does not change dramatically depending on business cycle. Yet, the business cycle may still amplify and propagate the exogenous shocks from macroeconomic conditions as far as the persistence of business cycle is concerned. In particular, the investment is deferred and the disinvestment occurs earlier when recession lasts longer and boom ends soon.     

The Relationship between Investment and Asset Life

Optimal investment in an asset and its optimal life are shown to be interrelated through operating cash flows and depreciation allowance, as well as book and salvage values upon termination; thus they are determined simultaneously. Asset life and investment are positively (negatively) related if delaying abandonment increases (reduces) the benefit of marginal investment. If investment and asset life are positively related, increased debt financing or allowable depreciation positively impact on them; otherwise, the impact is ambiguous in sign. Further, investment in a zero salvage value asset and its holding period increase with depreciation or leverage when (1) its cash flows form an annuity or (2) the firm employing it is tax-exempt.     

How to design down-and-out barrier option contracts so that firms invest when it is socially efficient

This paper investigates how to design down-and-out barrier options contracts so as firms invest when it is socially efficient. A government initially offers a firm a privileged right to exercise an investment opportunity that exhibits external benefits to society, but will eliminate this opportunity if its prospects are sufficiently bleak. The firm will invest at the date further away from that is socially efficient if the firm either is less uncertain about the return of the investment or incurs lower investment costs, or the government owns a more valuable knock-out option. Consequently, under these three scenarios the government can efficiently either offer the firm a higher investment tax credit or impose the firm a higher lease fee for holding the option to invest.     

On the neutrality of debt in investment intensity

This paper examines the interaction between investment and financing decisions of a firm using a real options approach. The firm is endowed with a perpetual option to invest in a project at any time by incurring an irreversible investment cost at that instant. The amount of the irreversible investment cost is directly related to the intensity of investment that is endogenously chosen by the firm. At the investment instant, the firm can finance the project by issuing debt and equity, albeit subject to an exogenously given credit constraint that prohibits the firm’s debt-to-asset ratio from exceeding a prespecified threshold. The optimal capital structure of the firm is determined by the trade-off between interest tax-shield benefits and bankruptcy costs of debt. Irrespective of whether the exogenously given credit constraint is binding or not, we show that leverage has no impact on the firm’s optimal investment intensity, thereby rendering the neutrality of debt in investment intensity. Similar to earlier work, we show that debt is not neutral to investment timing in general, and the levered firm invests earlier than the unlevered firm in particular.     

On the Interaction of Real and Financial Decisions of the Firm Under Uncertainty

This study analyzes the interaction between the optimal level of investment and debt financing. For this purpose, a model is structured in which a firm, facing an uncertain price, has to decide on its optimal level of investment and debt. The amount of investment sets a limit on output whose optimal level is determined after price is realized. The debt involved is risky (there exists a possibility of bankruptcy). The analysis proves that investment and its optimal financing have to be simultaneously determined and that a negative relationship exists between operating and financial leverage. We also demonstrate that as the tax rate increases, optimal capacity decreases and optimal leverage increases. An analysis of the impact of changes in the expected price shows that under some conditions, an increase in expected price would lead to an increase in optimal investment (firm size) and a decrease in optimal debt.     

Optimal Sequential Investment When Capital is Not Readily Reversible

When investment opportunities arrive one at a time and are reviewed sequentially, a corporation's optimal policy differs from a standard net present value rule if the corporation exercises control over an industry state variable and control is costly. The first condition presupposes a degree of market power for the firm; the second occurs if corporate investment decisions are imperfectly reversible. To address the problem of optimal investment in this context, a firm's investment decisions are modeled as a Markov reward process. The causes of economic irreversibility are discussed and general propositions concerning the optimal investment policy are derived. These propositions are then applied to the optimization of an exploration program by an oligopolistic firm (a price leader). Under particular demand and distributional assumptions, solutions for the optimal decision rule and the value of the exploration program are obtained and their properties examined.     

Heterogeneous beliefs and optimal ownership in entrepreneurial financing decisions

Our setting comprises one entrepreneurial firm with a growth opportunity seeking for external funding from a venture capitalist, where the entrepreneur and venture capitalist have homogeneous or heterogeneous beliefs about its growth prospects. We developed a real options model to determine the optimal ownership structure that triggers the simultaneous exercise of the growth option on the entrepreneurial firm by entrepreneurs and venture capitalists. Our results show that the more optimistic any of the parties is, the lower the post-money firm ownership that party will retain. However, optimism leads parties to delay their decision to invest in the entrepreneurial firm, by demanding higher profit triggers and investing only in more valuable entrepreneurial firms. The combination of these two effects leaves perceived returns on investment unchanged and not dependent on their own optimism.     

Preemption,leverage, and financing constraints

This paper investigates the interactions between preemptive competition and leverage in a duopoly market. We investigate both a case in which the firms have optimal financial structures, and a case in which financing constraints require firms to finance their investments by debt. Our findings are that the second mover always leaves the duopoly market before the leader, although the leader may exit before the follower's entry. The leverage effects of debt financing can increase the value of a firm and accelerate investment, even in the presence of preemptive competition. Notably, financing constraints can delay preemptive investment and improve firm values in preemptive equilibrium. Indeed, the leader's high leverage due to financing constraints can lower the first-mover advantage and weaken preemptive competition. Especially with strong first-mover advantage, the financing constraint effects can dominate the leverage effects. These findings are almost consistent with the empirical evidence, which shows that high leverage leads to competitive disadvantage and mitigates product market competition.     

资本支出、公司规模与账面市值比效应——基于A股上市公司的研究

基于成熟资本市场的理论及实证研究表明,在不确定的环境下,公司最优资本支出提高了市场价值,降低了账面市值比,账面市值比对收益率的预测作用可以通过公司的最优投资行为来解释。基于这一机制,本文对我国上市公司规模、资本支出及账面市值比效应进行了研究。我们发现,第一,按照Fama-French(1992,1993)方法构建投资组合的潜在条件同样是公司前期的资本支出,本期资本支出在提高公司市场价值的同时,非但没有降低反而提高了小规模组公司期末账面市值比;第二,控制规模的情况下,资本支出较显著降低了公司的预期收益,在大规模公司中表现最明显;第三,本期资本支出对规模效应具有一定解释力,但对账面市值比效应并不具有显著解释力;第四,我国上市公司股票价格变动更多由会计业绩变动决定而非风险变动所决定,据此对上述发现作出了尝试性的解释。     

The Relationship Between Equity-Based Compensation and Managerial Risk Taking: Evidence from China

The authors analyze the impact of equity-based compensation on managerial risk-taking behavior in Chinese listed firms from January 2006 to July 2011. They find that greater risk-taking incentives lead executives to invest more in research and development (R&D) projects and less in capital expenditures. Greater managerial risk-taking incentive increases firm focus. Managerial risk-taking incentives have positive effects on firms' leverage. Overall, increasing the sensitivity of chief executive officers' portfolio value to stock return volatility helps incentivize executives to work harder, as sharing gains and losses with shareholders aligns the interests of executives and shareholders. In addition, the results indicate that state control of firms has a negative effect on R&D investment, and this suggests that state-controlled firms should take more initiative to innovate.     

Organisational change and performance in long-lived small firms: a real options approach

This paper supports two key principles of real options reasoning: (a) the value of waiting and (b) the value of staging. It tests whether real options logic applies to small firms implementing significant changes (e.g. in technology) in a model of small firm performance, estimated on data collected by interviews with entrepreneurs. We found that to achieve a higher value by waiting, a delicate balance of precipitators of change against time until exercise is necessary (e.g. if there were just one or two precipitators, then waiting would certainly raise the value). Similarly, to achieve a higher value by staging, the entrepreneur needs to balance embedding against investment time. Thus, provided that investment time is less than 1¼ years, we found that embedding will raise the value. Overall, this implies that strategic flexibility in investment decisions is necessary for good long-run performance of small firms.     

Some results on relocation policies

In this paper, we derive general results concerning optimal relocation policy under some assumptions. We consider a firm that is located in a specific location, producing at a certain level of efficiency. With time, the firm can decide to change its location to a new and more efficient site, paying relocation costs. Moreover, we assume that these new sites become available according to a Poisson process, and that the levels of efficiency improvement inherent to each one of these sites are random variables. With this framework, we characterise certain parameters of the optimal relocation policy. In particular, we characterise the expected relocation time and we prove that it depends on the distribution of the level of efficiency improvement only through an expected value. Therefore, the optimal policy shows a kind of robustness in terms of the stochastic assumptions of the problem, which has a major impact in the application of relocation policies. In addition, we also characterise the optimal relocation time. Impacts on the final results driven by the characteristics of the firm's original location site, the market environment and the way in which risk is modelled are studied numerically. The overall results are in line with economic intuition.     

INFLATION,INVESTMENT, AND DEBT

In this paper the effect of inflation on firms' investment and debt-financing decisions is examined. Inflation affects optimal investment and financing directly through the probability of accounting loss and the real value of depreciation and interest tax shields. In addition, when corporate and differential personal taxes cause investment and financing decisions to interact, inflation has indirect effects on these decisions through their interactions. In general, the overall effects of inflation on optimal investment and debt are ambiguous in sign. For tax-exempt firms, however, optimal investment and debt are independent of inflation. For firms that are always in a tax-paying position, higher inflation reduces optimal investment without affecting optimal debt. Furthermore, inflation causes total firm value to decrease if the depreciation rate exceeds the firm's debt/asset ratio.     

Dominant institutional owners and firm value

This research analyzes the impact of control by dominant institutional owners (banking institutions and investment funds) on firm value. The analysis considers the level of voting rights in the hands of the dominant institutional owner and other large shareholders. The results reveal a different effect on value depending on whether the dominant institutional investor is a banking institution or an investment fund. Moreover, the results show that the presence of other large shareholders affects firm value when a dominant institutional owner controls the firm.     

Agency cost of debt overhang with optimal investment timing and size

The concept of debt overhang (that is, an equity‐maximizing levered firm will under‐invest relative to a firm‐value‐maximizing firm) is well established in the literature. A number of papers have demonstrated it as delayed investment (when investment size is specified) or smaller investment (when investment time is specified). However, there is no work on the underinvestment effect when the firm chooses both size and timing of investment, as it usually does in real life. This is what our paper focuses on. When the firm has the flexibility to choose both size and time, the effect is complicated by the fact that delayed investment results in larger investment, which suggests that the underinvestment problem might be mitigated. We find, however, that the effect depends on how underinvestment is measured. When measured by the expected present value of investment, flexibility can mitigate or exacerbate the underinvestment problem, depending on the cost of installing capacity. But when measured by the agency cost, flexibility always exacerbates the underinvestment problem. It is shown numerically that, at the optimal leverage ratio, the agency cost with plausible parameter values can be economically significant. Thus, with the flexibility of choosing both time and size of investment, the debt overhang problem can be of significant practical relevance in corporate investment decisions.