Optimal Investment Threshold Research Articles

Optimal investment timing and size decision‐making with jump risk and time‐inconsistent preferences

AbstractThis paper analyzes a firm's investment timing and capacity decision by considering the manager's time‐inconsistent preferences and continuous economic depreciation of the capital stock cannot be completely offset. The demand shock of the underlying product evolves according to a double exponential jump‐diffusion process. Within a real options framework, we derive the explicit expressions for the optimal investment threshold and investment size when the manager is sophisticated. We find that time‐inconsistent preferences will lead the firm to delay investment when capital depreciation rate is low and accelerate investment when the rate of capital depreciation is high. Further, we show that capital depreciation rate has a monotonic positive effect on the investment size of a time‐consistent manager but a non‐monotonic effect on that of a sophisticated manager. A sophisticated manager tends to choose a smaller investment size than a time‐consistent manager. Finally, we demonstrate that compared with the geometric Brownian motion, the firm invests later with a larger capacity under the jump‐diffusion model.

A Real Option Analysis of the “Flats for Land” System - an Idiosyncratic Equity Financing Mechanism on Real Estate Investments

A typical real estate development project encounters an entrée capital expense for land purchase that is not immediately recovered until the allocated capital for the land acquisition is replaced with new capital that converts the land to a rentable building space. This article presents an idiosyncratic equity financing scheme that eliminates the sunk cost for a land purchase over a real estate development, within a real options framework. The study provides a model solution, numerical results of the option value, and the optimal investment threshold of a real estate development that is initiated through the “flats for land” scheme.

A Real Option Analysis of the “Flats for Land” System - an Idiosyncratic Equity Financing Mechanism on Real Estate Investments

A typical real estate development project encounters an entrée capital expense for land purchase that is not immediately recovered until the allocated capital for the land acquisition is replaced with new capital that converts the land to a rentable building space. This article presents an idiosyncratic equity financing scheme that eliminates the sunk cost for a land purchase over a real estate development, within a real options framework. The study provides a model solution, numerical results of the option value, and the optimal investment threshold of a real estate development that is initiated through the “flats for land” scheme.

The effect of cutting interest rates on corporate investments: A real options model

AbstractWe propose a real options model with regime shifts to investigate the effect of cutting interest rates on corporate investments when a financial crisis occurs. Cutting interest rates would lower the investment project's hurdle rate. The reduction in hurdle rate is positively related to the magnitude of interest rate cuts and the persistence of the financial crisis. The hurdle rate becomes lower in the financial crisis state because the reduction in interest rate would lower the cost of capital and the opportunity cost of immediate investment. In the numerical analysis of this study, we show that the change in the opportunity cost accounts for most of the change in the hurdle rate. Upon taking into consideration the firm's financing constraints, we find that cutting interest rates accelerates investments for firms with high liquidity. However, for firms with low liquidity, the optimal investment threshold is not affected by the variation in interest rates. Instead, the investments of low‐liquidity firms are affected by the change in the friction of credit supply.

Optimal Investment and Financing Decisions Under Cost Uncertainty

In this paper, we employ the real options approach to study the impact of cost uncertainty on a firm’s optimal investment and financing decisions. The firm owns a perpetual right to an irreversible investment project, and the firm’s goal is to determine the optimal investment timing and level of coupon payments when the investment cost jumps upward at a random time. We find that the optimal investment threshold and level of coupon payments decrease with the jump intensity and the magnitude of the jump. The cost uncertainty gives the firm a stronger incentive to accept projects with risky cash flows. Furthermore, we examine the conflict of interests between the share- and bond-holders. We show that the debt overhang distortion and the asset substitution incentive decrease with the cost uncertainty. However, the effect of cost uncertainty on the incentive of asset substitution reverses in the region of low operating profits

Discount-Rate Uncertainty and Cost-Benefit Analysis: Should Long-Lived Projects Be Treated Differently?

Evaluating the benefits of investment projects related to climate change is complicated by disagreements surrounding the discount rate. It is widely known that greater discount-rate heterogeneity increases the weighted-average present value of investing, and therefore reduces the minimum internal rate of return needed to justify now-or-never investment. A larger adjustment is appropriate for projects with longer lives. I extend this analysis in two directions, first by giving the decision-maker the option to delay investment. Greater discount-rate heterogeneity also increases the weighted-average present value of the option to wait and reevaluate investment in the future. This weakens the relationship between discount-rate heterogeneity and the optimal investment threshold---and in some cases actually reverses it. When discount rates are low and the project's lifetime is short, increases in discount-rate heterogeneity can lead to tougher (not easier) optimal investment tests. The second extension examines the effect on these results of using different approaches to aggregate opinions about the discount rate, including the $\alpha$-maxmin, minimax-regret, and multi-utilitarian criteria.

Feed-in Tariff Contract Schemes and Regulatory Uncertainty

This paper presents a novel analysis of two feed-in tariffs (FIT) under market and regulatory uncertainty, namely a sliding premium with cap and floor and a minimum price guarantee. Regulatory uncertainty is modeled with a Poisson process, whereby a jump event may reduce the tariff before the signature of the contract. Using a semi-analytical real options framework, we derive the project value, the optimal investment threshold, and the value of the investment opportunity for these schemes. Taking into consideration the optimal investment threshold, we also compare the two aforementioned FITs with the fixed-price FIT and the fixed-premium FIT, which are policy schemes that have been extensively studied in the literature. Our results show that increasing the likelihood of a jump event lowers the investment threshold for all the schemes; moreover, the investment threshold also decreases when the tariff reduction increases. We also compare the four schemes in terms of the corresponding optimal investment thresholds. For example, we find that the investment threshold of the sliding premium is lower than the minimum price guarantee. This result suggests that the first regime is a better policy than the latter because it accelerates the investment while avoiding excessive earnings to producers.

Effects of Knightian Uncertainty on Interactions between Investment and Financing Decisions

This study examines the interactions between investment and financing decisions under Knightian uncertainty. We first derive the optimal coupon and investment threshold under Knightian uncertainty. When financing and investment decisions interact, the jointly optimal coupon decreases with the degree of Knightian uncertainty, which supports empirical research. We show that the tax effect on investment decisions increases as the degree of Knightian uncertainty increases. We also find that the jointly determined coupon is less influenced by Knightian uncertainty.

Photovoltaic Smart Grids in the prosumers investment decisions: a real option model

The digitization of power system represents one of the main instruments to achieve the target set by the European Union 2030 climate and energy Agenda of affordable energy transition. During the last years, such innovation process has been associated with the Smart Grid (SG) term. In this context, efficiency and flexibility of power systems are expected to increase and energy consumers to be active also on the production side, thus becoming prosumers (agents that both produce and consume energy). This paper provides a theoretical real option framework with the aim to model prosumers’ decision to invest in photovoltaic power plants, assuming that they are integrated in a SG. Our main focus is to study the optimal plant size and the optimal investment threshold, in a context where exchange of energy among prosumers is possible. The model was calibrated and tested with data from the Northern Italy energy market. Our findings show that the possibility of selling energy between prosumers, via the SG, increases investment values. This opportunity encourages prosumers to invest in a larger plant compared with the case without exchange possibility and that there is a positive relation between optimal size and (optimal) investment timing. The effect of uncertainty is in line with the literature, showing increasing value to defer with volatility. Our comparative statics stress the need for policies to push the PV efficiency.

Jointly Held Investment Options and Vertical Relationships

We find the optimal time for exercising a jointly held investment option. When the input market is competitive, the investment can take place earlier, later, or exactly when the optimal investment threshold is reached depending on how the option holders interact and on the bargaining power distribution. When instead the input supplier has market power, the game-theoretic framework downstream is shown to be of secondary importance. The timing effect that is attributed to the vertical relationship is always prevailing, which dictates the inefficient postponement of the investment.

Feed-in tariff contract schemes and regulatory uncertainty

This paper presents a novel analysis of two feed-in tariffs (FIT) under market and regulatory uncertainty, namely a sliding premium with cap and floor and a minimum price guarantee. Regulatory uncertainty is modeled with a Poisson process, whereby a jump event may reduce the tariff before the signature of the contract. Using a semi-analytical real options framework, we derive the project value, the optimal investment threshold, and the value of the investment opportunity for these schemes. Taking into consideration the optimal investment threshold, we also compare the two aforementioned FITs with the fixed-price FIT and the fixed-premium FIT, which are policy schemes that have been extensively studied in the literature. Our results show that increasing the likelihood of a jump event lowers the investment threshold for all the schemes; moreover, the investment threshold also decreases when the tariff reduction increases. We also compare the four schemes in terms of the corresponding optimal investment thresholds. For example, we find that the investment threshold of the sliding premium is lower than the minimum price guarantee. This result suggests that the first regime is a better policy than the latter because it accelerates the investment while avoiding excessive earnings for producers or excessive payments for consumers.

Feed-in Tariff Contract Schemes and Regulatory Uncertainty

This paper presents a novel analysis of two feed-in tariffs (FIT) under market and regulatory uncertainty, namely a sliding premium with cap and floor and a minimum price guarantee. Regulatory uncertainty is modeled with a Poisson process, whereby a jump event may reduce the tariff before the signature of the contract. Using a semi-analytical real options framework, we derive the project value, the optimal investment threshold, and the value of the investment opportunity for these schemes. Taking into consideration the optimal investment threshold, we also compare the two aforementioned FITs with the fixed-price FIT and the fixed-premium FIT, which are policy schemes that have been extensively studied in the literature. Our results show that increasing the likelihood of a jump event lowers the investment threshold for all the schemes; moreover, the investment threshold also decreases when the tariff reduction increases. We also compare the four schemes in terms of the corresponding optimal investment thresholds. For example, we find that the investment threshold of the sliding premium is lower than the minimum price guarantee. This result suggests that the first regime is a better policy than the latter because it accelerates the investment while avoiding excessive earnings to producers.

Guarantee-Investment Combination Financing Contract Design for Entrepreneurship

Recently, a guarantee-investment combination financing mode is popular. This paper considers an entrepreneur who has exclusively an option to invest in a project. The investment is irreversible but delayable with a growth option. Thanks to the financing mode, the initial investment cost is borrowed from a bank with an insurer's guarantee and the growth investment cost is provided by the insurer. In return, the entrepreneur pays the insurer a guarantee fee upon initial investment and a fraction of equity upon growth investment. We assume that the cash flow is increased by a growth factor once the growth investment is exercised. We explicitly derive all the values of firm securities, optimal investment thresholds, optimal default thresholds and fair guarantee costs. We derive optimal guarantee contract design. The welfare level increases considerably if insurers instead of entrepreneurs determine growth investment time. The increased welfare level rises quickly with growth factor.

Investment decisions and debt financing under information uncertainty

This study examines how information uncertainty influences investment decisions. In contrast to prior studies, which assume no information uncertainty, our model includes a discrepancy in valuing debt between shareholders and debtholders at the time of debt issuance. We derive the values of corporate securities and the optimal investment threshold and coupon under information uncertainty. We show that compared with the absence of information uncertainty, debtholders value debt less than shareholders do, and hence, shareholders should contribute more investment funds. Debt financing restraints due to information uncertainty lead to delayed investment. We find that information uncertainty plays a mitigating role in shareholder-debtholder conflicts over investment policy. Moreover, the information uncertainty costs that shareholders incur increase sharply with the level of information uncertainty.

Company stock rewards on the evaluation of investor’s remuneration package with stochastic income

We consider a risk averse investor as are who has a bond, is rewarded with [Formula: see text] units of company stock option and is endowed with stochastic income. First, we derive and analyzes the optimal investment threshold and investment value function of the investor. Second, we determine a remuneration package and the utility indifference pricing of this risk averse investor and analyze the results for two utility functions; the exponential and logarithmic utilities. From these results, we conclude that the more units of company stock the investor receives, the higher the chances of increasing the total wealth or profit.

Real Option 모형을 활용한 풍력발전 에너지 저장장치 추가의 최적 투자 분석

This paper proposes areal option model to analyze optimal investment time to adopt an energy storage system (ESS) for wind power systems. Using the suggested model, we can derive the optimal threshold to invest the ESS. According to our results, when REC weight and the ratio of REC to total profit decreases, the optimal investment threshold increases significantly. This implies that the decrements can be barriers to promoting adoption of ESS. Also,it is shown that higher volatility and discount rate can be another obstacles to the investment.

Photovoltaic Smart Grids in the Prosumers Investment Decisions: A Real Option Model

The digitization of power system represents one of the main instruments to achieve the target set by the European Union 2030 climate and energy Agenda of affordable energy transition. During the last years, such innovation process has been associated with the Smart Grid (SG) term. In this context, efficiency and flexibility of power systems are expected to increase and energy consumers to be active also on the production side, thus becoming prosumers (agents that both produce and consume energy). This paper provides a theoretical real option framework with the aim to model prosumers’ decision to invest in photovoltaic power plants, assuming that they are integrated in a Smart Grid. Our main focus is to study the optimal plant size and the optimal investment threshold, in a context where exchange of energy among prosumers is possible. The model was calibrated and tested with data from the Northern Italy energy market. Our findings show that the possibility of selling energy between prosumers, via the Smart Grid, increases investment values. This opportunity encourages prosumers to invest in a larger plant compared with the case without exchange possibility and that there is a positive relation between optimal size and (optimal) investment timing. The effect of uncertainty is in line with the literature, showing increasing value to defer with volatility.

The interaction of debt financing, cash grants and the optimal investment policy under uncertainty

Significant progress has been made toward understanding a levered firm's optimal investment policy under uncertainty. To date, however, not much work has concentrated on the time scale trade-off and collectively held real options. We employ a game-theoretic real option model between a firm and a government to analyze the effect of uncertainty and investment stimulus in the form of cash grants on optimal investment timing, financing and investment scaling. We find that the jointly held real option between the firm and the government leads to underinvestment, regardless of whether the firm has the possibility to issue debt. Subsidies, however, reduce the level of underinvestment. Notably, the results indicate that even though levered firms receive less support, they invest more than unlevered firms. This challenges recent findings that a firm's optimal investment level is not affected by the way it finances a project. Similarly, we find that for realistic parameter constellations the levered firm's optimal investment threshold can be higher than that of its unlevered counterpart. This indicates that the availability of tax shield benefits does not necessarily serve as an incentive to invest earlier. Finally, we show that the effect of cash flow uncertainty on the equilibrium level of grants is ambiguous and triggers the switch from a subsidy to non-subsidy regime.

수익 불확실성하의 풍력발전 최적 투자 시점 분석 : Real Option 모형을 활용

This paper proposes a new model for determining optimal investment time for wind power systems. The model, with characteristics of a real option model, explicitly incorporates profit uncertainty and an investor’s option to defer investment. By using the real option model, we can derive the optimal threshold for wind power investment. Theoretical analysis is performed with respect to uncertainty. In addition, by using the real option model, we show that the optimal investment threshold increases with increasing volatility, mean-drift, and investment cost. A comparison between this study and those that adopted the traditional NPV method shows that the decision derived by NPV underestimates investment value.

Study on the investment timing of carbon capture and storage under different business modes

AbstractIn this paper, the optimal investment timing decision in carbon capture and storage (CCS) is studied under different business modes. Two analytical models of the optimal CCS investment threshold are presented: one is the ‘single mode,’ meaning that CCS investment is performed only by the power producer; the other is the ‘cooperation mode,’ referring to CCS investment can be conducted by cooperation between the power producer and the CCS operator. In the single mode, this study pictures the investment decision for a CCS project based on real options theory considering uncertainties in carbon prices, government incentives, and CCS investment costs. On this basis, a model for the cooperation mode is proposed by integrating real options theory and game theory to analyze the CCS investment threshold. The results of a numerical example show that CCS investment in cooperation mode requires a much larger threshold than in single mode. Moreover, the CCS investment threshold is positively affected by carbon price volatility and the transfer payments coefficients, but negatively affected by government incentives and learning effects. These conclusions provide a theoretical foundation for decision making regarding CCS investment and related policy making. © 2018 Society of Chemical Industry and John Wiley & Sons, Ltd.