## Introduction

There is a strong relationship between the risk associated with a project and its net present value. Adequate and reasonable calculation of the net present value of an investment is possible only with an appropriate assessment of risk. Incorrect consideration of risk factors and wrong calculation of potential losses may entail misallocation of capital. Typically, risk adds uncertainty to future cash outflows and cash inflows, whereas the initial cost of investment is known with certainty.

The purpose of the given paper is to discuss cash flows, both positive and negative, that occur under different risk management decisions, such as risk retention, risk transfer, risk control, and risk avoidance. In the first part of the essay, the real-world components of the net present value formula, such as cash flows, the initial investment, and a suitable discount rate are identified for each type of risk management activity. In the second part of the paper, practical suggestions are provided for estimating realistic values for the variables determined in the first part.

## Main body

### Risk Retention

Risk-retention (also known as risk assumption or active retention) is a risk management technique that occurs when a company assumes some of the risks and decides to be responsible for all the damages or losses without transferring them to an insurance company. Under this risk management strategy, an organization establishes a self-insurance reserve to financial losses that are expected to happen (Baker and Flibeck, 2015, p. 34).

In some cases, risk retention can be more beneficial than risk transfer. In particular, risk retention is advantageous when a charge that a company has to pay for a risk transfer to an insurance company exceeds the expected losses.

Given that a company absorbs all the risks, risk retention can be financed through a captive insurance company, working capital, and a pre-planned loan from a bank. A captive insurance company is a subsidiary established by an organization in order to ensure its own risks. Working capital is calculated by subtracting the companyâ€™s total current liabilities from its total current assets. It is interconnected with the companyâ€™s liquidity and profitability reserves (Wieczorek-Kosmala *et al.*, 2016, p. 7). Apart from a pre-planned loan from a bank, a business entity can also take an ad hoc loan to cover future losses.

To calculate the net present value of a project, the following formula will be utilized:

It is important to assume that Ct is the net cash flows in period t, or, in other words, the difference between positive and negative cash flows. Positive cash flows include interest gained on reserve funds, revenues, as well as gains obtained due to the risk financing (for example, the cost of issues that have been avoided and insurance premium savings). However, it is worth mentioning that gains from risk financing are often difficult to calculate since they may be both tangible and intangible.

Among cash outflows (or negative cash flows) are a pre-determined premium for self-insurance, interest on a loan from a bank, administrative costs that are related to risk assumption, corporate income tax, depreciation, and the opportunity cost of capital employed. Other negative cash flows are policy administration and maintenance costs, premium taxes, a letter of credit, a reinsurerâ€™s margin, fronting, and other related cash flows (Ernst & Young, 2018, p. 39).

The initial investment is the cost of risk retention, which consists of a self-insurance premium or a fund that has been created by a company to finance potential risks. A suitable discount rate is the rate of return expressed as a percentage that an investor or a company expects to achieve on their investment. Usually, the determination of the effect of risk retention entails a comprehensive analysis along with profitability calculation.

### Risk Transfer

Risk transfer is a risk management strategy where a company shifts the risk to another person or entity. For example, by purchasing an insurance policy, an organization passes the pure risk of loss to the insurer. Other methods of risk transfer include judicial transfer and contractual transfer. If a risk is transferred due to legal action, this is judicial transfer. Contractual transfer occurs through a contractual agreement with the companyâ€™s business partners. For instance, two companies in a joint venture may decide to share potential losses. Risks of loss that can be transferred are associated with construction (damage to the building, work-related injuries, cost overruns, and losses due to delay) and carrier and bailee agreements (property damage due to natural disasters and non-negligent loss).

The transfer of risk does not completely liquidate risks or future costs. Instead, a company adopts this risk management strategy with a view to reducing potential risks and, consequently, future costs. One common element of risk transfer is insurance premiums that are paid on a regular basis to an insurer. Insurance premiums usually depend on the companyâ€™s insurance history, risk factors, and the type of coverage.

There is only a slight difference between the components of cash inflows and cash outflows for risk transfer and risk retention. Cash outflows may consist of money that a company will pay to the insurance company (insurance premiums) and expected opportunity losses (the value of a potential profit that could have been realized if alternative action had been taken). Other negative cash flows are depreciation and corporate income tax.

Positive cash flows include revenues and tax savings on insurance premiums (Ernst & Young, 2018, p. 39). The amount of initial investment is equal to the amount of insurance premium which a company will pay to its insurer. A suitable discount rate is the interest rate which investors expect to achieve. The discount rate does not depend on the type of risk transfer financing and is determined by an insurer that uses a yield curve to calculate the current market rate of return on the companyâ€™s assets.

### Risk Control

Risk control is a risk management activity that is aimed at minimizing the probability, frequency, and severity of potential losses at optimal cost. Usually, it occurs after hazards have been identified and risk assessment has been conducted. It is worth mentioning that risk control is the most common risk management strategy employed by businesses. Risk control involves the identification of potential risk factors both in the organizationâ€™s operations and financial policies and the implementation of changes to reduce risk. The main objective of this method is to reduce the amount of lost income and assets.

Among the methods of risk, control is loss prevention (reduction of the frequency of losses), loss elimination (decreasing the severity of losses), and loss avoidance (minimization of the probability of losses).

Some real-life examples of the implementation of risk control strategies are investments in staff training, materials, and safety equipment, which may reduce risk and potential losses. Despite the fact that each of these investments will incur additional costs, both tangible and intangible assets will increase. Negative cash flows include initial investment (for example, in materials or equipment), expenses associated with the maintenance of materials or equipment, as well as the opportunity cost. In this case, the opportunity cost is related to any disruption in the normal production process caused by the purchase and installation of equipment and the purchase and use of materials.

Positive cash flows include a decrease in insurance premiums and tax savings due to the depreciation of the equipment or materials that can be listed as an expense on a tax return. A drop in the insurance premium will occur if an insurance company sees that an organization has taken specific steps in order to eliminate or just mitigate the potential risk factors. The initial investment is equal to the cost of materials and/or equipment that were bought to minimize future losses, as well as other expenditures associated with risk control. A suitable discount rate represents the percentage of return that investors may expect to achieve on the cost of the initial investment.

### Risk Avoidance

Risk avoidance is a risk management strategy that provides for the elimination of activities and hazards that can adversely affect the organizationâ€™s assets. Risk avoidance may be considered as the opposite of risk retention or risk acceptance, where a company assumes all the possible losses. In contrast to risk control that is aimed at minimizing losses, risk avoidance involves complete avoidance of compromising events and does not allow for performing activities that may carry any amount of risk. However, the entire elimination of all the risk factors cannot always be possible, which is why risk avoidance seeks to deflect the maximum possible number of threats in order to prevent the damaging consequences.

Risk avoidance is assumed to be the most expensive risk management activity, which does not make it feasible for the majority of risks. In fact, it is the least popular risk management strategy employed by businesses. Nevertheless, it can make potential losses equal to zero, reducing the cost of downtime and recovery. An example of risk avoidance is a company refusing to use promising innovative technology due to potential technological risk and thus choosing a proven technology that has fewer benefits. The utilization of risk avoidance strategy is justified only in case potential gains from it outweigh the opportunity costs.

Cash inflows include savings or gains from avoiding the risk. For instance, if a company decides to close the production line due to its low profitability, positive cash flows would include fixed and variable costs required for sustaining the production line. If a company decides to sell the equipment that is not functioning properly, cash inflows would be equal to the cost at which this equipment is sold.

Among cash, outflows are the opportunity costs which the company would earn if it decided to assume the risk. For example, if the company closed the production line, the opportunity cost would be the net income generated from that production line. If the company sold the malfunctioning equipment, the opportunity cost would be additional revenues generated from utilizing the equipment. Other negative cash flows can include tax savings associated with depreciation, as most types of tangible property (land, equipment, vehicles, and furniture) can be depreciated on a regular basis. Typically, if an organization opts to avoid risk, it does not have to make any initial investment, so its cost is equal to zero. A suitable discount rate is equal to the opportunity costs under the risk retention strategy.

The variables that have been determined and discussed in the paper are components of positive and negative cash flows, initial investments, and suitable discount rates under four types of risk management decisions. The given part will present some suggestions for the appropriate evaluation of each variable. One may note that the value of the initial investment and the time period is known with certainty, which is why there is no need to provide recommendations for estimating these components.

Regardless of the risk management strategy which the company decides to follow, todayâ€™s value of invested cash and the number of time periods can be easily calculated. For example, if a company wants to build a plant with a risk of production hazard and the building process will take three years, the time period is equal to three years. The initial investment is equal to the self-insurance premium (in case of risk retention), insurance premium (in case of risk transfer), or the cost of safety equipment (in case of risk control).

One may find it helpful to analyze cash flows using the Brealey-Myers adjusted present value approach. It considers tax relief on debt capital and the financial effects specific to a particular project. The adjusted present value of a project is thus calculated by adding the net present value, which it would produce under all-equity financing, to the PV of financing-related cash flows. A suitable discount rate k is determined by a projectâ€™s Î² coefficient, which should be appropriately estimated.

If a company issues securities to finance the project for risk control or risk avoidance, it should add this amount to the negative cash flows. The interest payment on a loan that can be taken if a company decides to assume risk or finance a project can be calculated by dividing the interest rate by the number of payments and multiplying the result by the loan principal. Disruption costs are the component of negative cash flows, which can be calculated using the critical path method (CPM) or the measured mile analysis. CPM is helpful in assigning a cost to delays under discrete work item planning. The measured mile analysis identifies two parts of work for comparison, one of which is impacted by a delay.

Tax savings associated with depreciation are positive cash flows. They can be calculated by estimating an increase in the depreciation, which is related to the purchase of equipment, materials, or other tangible assets, and multiplying it by the corporate tax rate. Indirect benefits, such as insurance premium reductions, cannot be calculated by a company and are determined only by an insurance company.

If a company assumes the risk, this means that the self-insurance premium has already been determined. Administrative costs linked to risk management may include payments to third-party administrators, consultants, and attorneys, as well as risk management payroll. Corporate income tax is calculated by multiplying the corporate income by the current tax rate. The opportunity cost of capital employed can be estimated by multiplying the market rate by the cost of the initial investment. In other words, this is a forgone benefit which a company loses by investing capital in a project.

When calculating the discount rate, one needs to take into account risks related to the project and the rate of return which investors can expect to gain. The k variable from the net present value formula depends on the risk-free interest rate and Î² coefficient. The risk-free interest rate does not depend on the decisions made by a company and is calculated by subtracting the inflation rate from the Treasury bond yield for the selected period of time.

To estimate the market risk premium, one needs to subtract the risk-free rate from the expected rate of return on investment. The Î² coefficient reflects the risk of a particular project instead of the risk of the organization. It depends on the rate of return, cash outflows, and cash inflows, as well as the current state of the economy. To identify a reliable Î² coefficient, one needs to analyze all the aspects of a particular project and consider all possible risks. It is also recommended to take into account potential losses, which may lead to a negative Î² coefficient.

## Conclusion

In summary, the net present value method is an effective tool that can be employed to quantify the profitability of an investment decision based on the initial investment, expected positive and negative cash flows, as well as an appropriate discount rate. This method can be used in such risk management activities as risk retention, risk transfer, risk control, and risk avoidance. However, it is important that projected positive and negative cash flows include indirect benefits and other side effects of a project.

## Reference List

Baker, H. and Flibeck, G. (eds.) (2015) *Investment risk management. *New York: Oxford University Press.

Ernst & Young (2018) *Applying IFRS 17.* Web.

Wieczorek-Kosmala, M. *et al. *(2016) â€˜Working capital management and liquidity reserves: the context of risk retentionâ€™, *Journal of Economics and Management, *23(1), pp. 5â€“20.