Success Repayable Loan under information symmetry

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However, according to the arguments of Admati and Pflerderer (1994), Ravid and Spiegel (1997), and the Korea Development Institute (2008), since only the exploration company, and not the investor, knows about the profit distribution of the exploration project, a compensation function similar in form to that of the Success Repayable Loan, rather than a general debt contract, may emerge as the optimal contract. However, the assumption that the company is fully aware of the profit distribution of its exploration project but the investor is not is a rather unreasonable assumption. Therefore, the application of an optimal contract with this form may be limited.⁴⁴ Therefore, we will proceed with this discussion by excluding the possibility of information asymmetry in relation to profit distribution.

Table 4-1. Form of optimal contract

Remarks (optimal contract form)

Information symmetry Success Repayable Loan: optimum can be derived

Information asymmetry General loan

3. Theoretical study on the Success Repayable Loan

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Repayable Loan are actually based on a general debt contract.⁴⁵ Second, most optimal contracts under information asymmetry are general debt contracts. Third, in the case of a Success Repayable Loan for an exploration project, the investor is the government, which is not necessarily aiming to maximize profit or utility. For example, for a government funding an exploration project, the goal may be to encourage more companies to participate in exploration projects at the same funding level (or expected funding level) as that provided through general debt contracts, rather than profit or utility maximization. In this case, the appropriate criteria for the effect of the Success Repayable Loan system would therefore be based on a general debt contract.

The Success Repayable Loan system is designed to encourage more exploration companies to participate in high-risk projects, which typically require significant investment costs but have relatively low probabilities of success. In the event a project fails, the loan will be repaid in whole or in part. If the project is successful, however, the government will impose excess returns, thereby making all or part of the risk shared.⁴⁶ The reason for an investor to impose excess returns is to cover losses from other projects that failed after spending financial resources that enable the sharing of risk. Thus, basically, the Success Repayable Loan system is a financing contract between a risk-neutral investor and a risk-averse exploration company. In the following, a simple model will be presented to explain the purpose of the Success Repayable Loan system.

Suppose that a resource exploration project can end in only one of two ways, success or failure, where is the profit generated by a successful project, and is the profit generated by a failed project (where ).

It is assumed that exploration success is a random variable, but both the investor and the exploration company know about the profit distribution. That is, the profit distribution of the successful exploration project is symmetrical information. The probability of exploration success is , while the probability of failure is , and these two probabilities are assumed to be symmetric information. Let’s say that the investment cost necessary to carry out the exploration project is , of which a certain portion is financed by the company itself and the remainder is financed by the investor. In other words, where is the investment procured independently by the

company and is the loan, their relation can be defined as , and . Thus, can be interpreted as the equity ratio, and as the loan rate. An interest amount ( ) is accrued for the loan. Since interest has no significant impact on our analysis of the core content of the Success Repayable

45 For example, the argument that the Success Repayable Loan system increases moral hazard can be interpreted as being the same as the argument that the Success Repayable Loan contract increases moral hazard more than a general debt contract.

46 These excess returns are called “special charges,” and both terms are used in this study.

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Loan system, we assume in order to proceed with our discussion.

The problems faced by the exploration company with a general loan can be expressed simply in the form of a lottery through the following.

(12)

The expected value of the lottery is calculated in a simple way, as follows.

(13)

Suppose that the utility function of the exploration company is a general Von Neumann-Morgenstern utility function ( ) based on the assumptions and . At this time, the expected utility of this

company can be defined as . Suppose that the exploration company’s

reserved utility is defined as . If the exploration company is risk-neutral, it will participate in the exploration project when ; if it is risk-averse, it will participate in the exploration project when . Whether holds or not generally depends on the extent of the company’s risk- aversion. If we define the certainty equivalent for the exploration project as , the company’s certainty equivalent ( ) will decrease as the company’s risk-aversion increases. This general lending system allows exploration companies to cover all risks associated with exploration projects. In other words, exploration companies must repay the funds they borrowed from investors regardless of whether the project is successful or not.

In general, resource exploration projects are high-risk projects with a very low . Therefore, if exploration companies are risk-averse, few companies will want to bear the risks that exploration projects require. In other words, although an expected return on an exploration project is high, the company will abandon the exploration project under the general lending system, especially if the amount of funding secured independently by the exploration company does not cover the total investment cost (thus requiring external financing). In other words, in the case where but , the company will give up its profitable exploration business under the usual loan system. This is why the main purpose of the Success Repayable Loan system is to share the

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risks of exploration companies in a way that loss due to project failure is shared. In other words, as mentioned above, under the Success Repayable Loan system, the exploration company can be exempted from repayment of all or part of the loan if the exploration project fails, and the investor will be paid a certain percentage of the net profit in addition to the loan reimbursement if the exploration project is successful. Therefore, an exploration project under the Success Repayable Loan system can be simply expressed as a lottery, as follows.

(14)

, where if , 100% of the debt repayment will be exempted in the case of project failure, as under the Success Repayable Loan system, and if , full debt repayment will be required in the case of project failure, as under a general loan. represents the case where special charges are imposed or there is an excess return at the time of project success. The expected value of the lottery is as follows.

(15) The profit in the case of failure will be equal to or greater than the profit in the case of failure, while the profit in the case of success will be less than or equal to the profit in the case of success. That is, the variation in profit distribution in will be less than the variation in . Thus, if an investor imposes that satisfies , will always be a less risky exploration project than .⁴⁷ That is, there exists that makes the mean preserving spread (MPS) of . This can be derived as follows.

(16)

47 Here, as the investor’s excess return should not exceed the net profit (= ) of the exploration company upon project success, should be satisfied.

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Meanwhile, we can easily find that satisfies for the expected return of the company and is also a combination of the debt repayment ratio and the excess return that enables the investor to recover the exact expected loss ( ) through an expected excess gain ( , in the case of project success). Therefore, if the investor establishes exactly, will hold for all risk- averse exploration companies, and the investor’s net profit will be always zero. By using

, , and , we can confirm that

holds. Therefore, there may be a that satisfies , and for such , a company that would otherwise abandon an exploration project under a general loan might be able to carry out that same project under the Success Repayable Loan system, which is the main purpose of the loan system. Currently, compared to general loans, the Success Repayable Loan system offers no incentive for risk-neutral companies under

because risk-neutral companies are still indifferent to the choice between general loan and the Success Repayable Loan. In the case where , risk-sharing is impossible through the Success Repayable Loan system, because the success of the exploration project causes losses for the exploration company. Therefore, in order for the Success Repayable Loan system to fulfill its purpose, the project must satisfy the following.

This condition indicates that since the exploration business generally has a relatively low , must be sufficiently larger than or the debt reduction ratio ( ) should be sufficiently small when the project fails in order to fulfill the purpose of the Success Repayable Loan system.⁴⁸ The above discussion can be understood as a solution to an expected utility maximization problem under the following Success Repayable Loan system, based on the assumption that the investor can know the probability of success ( ) of the exploration project and the equity ratio ( ) of the exploration company.

48 Meanwhile, if the investor calculates the rate of return in relation to the loan ratio (that is, if ), the

expected values of the two cases can be matched by calculating .

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(17)

The first-order condition for this problem is:

(18)

Thus, when the constraints imposed by the investor are satisfied, the maximization of the company’s expected utility is determined regardless of the risk-aversion level of the company. In other words, since the investor is risk-neutral, the investor will bear all the risk, and since the risk-averse exploration company is guaranteed with a type of full insurance (meaning that it will earn the same profit regardless of its failure or success), will be determined, regardless of the risk-aversion level of the company. This means that, if the constraint imposed by the investor is satisfied, a general loan will always be the MPS of the Success Repayable Loan, meaning that all risk-averse companies can maximize their expected utility under and satisfy the given constraints. Through the above first-order condition and constraint, we can get as follows.

(19)

This discussion can be explained by the following diagram.

Figure 4-1. Risk-neutral company (information symmetry)

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원문 번역문

기울기 Slope

위헙중립적 기업의 무차별곡선 Indifference curve of a risk-neutral company 투자자에 의해 주어진 제약선 Constraint line imposed by an investor

Figure 4-2. Risk-averse company (information symmetry)

원문 번역문

기울기 Slope

위험기피도 낮은 기업의 무차별곡선 Indifference curve of a company with low risk- aversion

위험기피도 높은 기업의 무차별곡선 Indifference curve of a company with a high risk- aversion

대칭정보 하에서의 투자자에 의해 주어진 Constraint line imposed by an investor under

information symmetry

62 제약선

If the company is risk-neutral, the indifference curve of the company’s expected utility appears in the form of a downward sloping straight line on a plane. Therefore, if the investor’s constraint is satisfied, the Success Repayable Loan will be the MPS of a general loan. A risk-neutral company is indifferent to the Success Repayable Loan or general loan for satisfying all constraints of the investor, as can be seen in the diagram above. On the other hand, if the firm is risk-averse, the indifference curve for the firm’s expected utility appears to be concave downward to the origin, with the expected utility increasing more toward the left side of the curve. Here, the degree of concavity depends on the degree of corporate risk-aversion. Therefore, there can be an interior solution

or a corner solution ( , but ), depending on the given

success probability ( ), corporate equity ratio ( ), profit upon success ( ), and exploration investment amount ( ). In this case, we can confirm that the optimal satisfying the investor’s constraints is determined by the exogenous variables given above, regardless of the degree of risk-aversion.⁴⁹ Whether it is an interior or corner solution, companies will always prefer the Success Repayable Loan as long as they are risk-averse and the investor-imposed constraints are satisfied. For example, as seen in the above diagram, we can easily understand that the expected utility of a firm at in the presence of an interior solution is always higher than the expected utility of a general loan at , regardless of the degree of risk-aversion.

In the Success Repayable Loan, the investor, as a public institution, imposes an excess return to compensate for the expected loss from an exploration project rather than for the purpose of maximizing profit (Chulkyu Lee, 2008). Therefore, considering the purpose of the Success Repayable Loan, it is more appropriate that an investor always chooses to secure an expected profit to exactly cover the expected loss under the Success Repayable Loan system, rather than maximize the expected profit. That is, it is ideal to always meet for any given .⁵⁰ However, as shown in the investor constraint, since and that satisfy the constraints of an exploration project do not always exist (for example, in the case of , there may be a case where an that satisfies the constraints is more than 1), and as can be seen later in the analysis, there is a practical

49 It should be remembered that the values of these exogenous variables also affect investors’ constraint line.

50 This means that, in the long term, the investor’s profit (normal profit) should be zero. This condition is the same as the condition of a fund provider in a fully competitive fund market.

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difficulty in determining such when there is information asymmetry and the current system has a fixed level of for policy convenience, which leaves open the possibility of the Success Repayable Loan not achieving its intended purpose even under information symmetry. Since means that , in terms of a company, will be less risky than and at the same time will become an exploration project company with higher expected returns, so both risk-neutral and risk-averse firms will prefer . In other words, there may be some risk-neutral and risk-averse companies willing to undertake an exploration project that would abandon that same project under the general loan system. However, since an investor cannot recover the entire expected loss, the Success Repayable Loan System will become unsustainable in the long term. If , then , and will become an exploration project company with lower expected returns (although with less risk than ), meaning that all risk-neutral companies will prefer (general loan). In the case of risk- averse firms, whether or not for a given is satisfied depends on the firms’ degree of risk-aversion. In other words, relatively risk-averse firms prefer the Success Repayable Loan, while those that are relatively less risk-averse tend to favor a general loan.