Where there is information symmetry between investors (government) and an exploration company

Here, we assume that an exploration company is going to secure amount of money from an investor in order to carry out a project that will generate a profit of . In this case, is a random variable, and it is assumed that the exploration company and investor know exactly how much profit will be generated by the end of the exploration project. That is, the information on project profit is uncertain but is assumed to be symmetric information. The funding contract and its terms, , between the exploration company and investor must be established before the project begins. Therefore, this case will fall under that of a principal-agent framework, where the investor plays the role of the principal, and the exploration company acts as the agent.⁴⁰ The contract

40 Some are also of the opinion that, as an investor, the government cannot play the role of an owner. Although the government is an agent of the people, our discussion will proceed under the premise that, to some extent, the government can play the role of an investor.

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between the exploration company and investor can be seen as a compensation function, , that specifies how much of the profit, , generated from the project by the exploration company will be returned to the investor for the money he or she invested.

Now, the utility of returns for the investor and exploration company is expressed as a Von Neumann–

Morgenstern utility function. The utility function of the investor is , and the utility function of the

exploration company is . Here, we assume . In the context of

information symmetry, the exploration company must guarantee the minimum expected utility level required by the investor by providing compensation for its investment.⁴¹ This condition is known as a rationality constraint.

Therefore, we have an optimal compensation function, , as a solution to the following problem.

(1)

If the Lagrangian multiplier for this problem is , the first-order condition is as follows.

(2)

From this first-order condition, the following condition can be derived.

(3)

In this case, and are the absolute risk aversion coefficients of the exploration company and investor, respectively. Therefore, in the case of information symmetry, it can be confirmed that the compensation for the investor in the exploration company depends on the relative risk aversion of both the exploration company and the investor. In other words, the compensation function of the exploration company is determined only by the sharing of risk. For example, if the absolute risk aversion coefficient of the exploration company and investor is

41 Likewise, the investor should seek compensation to meet the minimum expected utility level required by the exploration company.

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a constant absolute risk aversion (CARA), the exploration company’s compensation function can be expressed as

, which does not have exactly the same form as the Success Repayable Loan but is similar to it in that it is somewhere between a general debt contract and equity contribution. In other words, the compensation function, , of an exploration company that borrows from an investor can be defined as follows.

(4)

However, while this compensation function is applied to all profits, the compensation function of the Success Repayable Loan system differs somewhat in that the exploration company’s earnings are exempt from debt, , when the project is not profitable. In other words, the Success Repayable Loan can be defined as a compensation function, in consideration of the fact that the exploration company has limited liability for reimbursement under information symmetry. When considering the limited liability of the exploration company, the constraint is added to the utility maximization problem (3.1), allowing the following compensation function to be obtained using the Kuhn-Tucker conditions.

(5)

Therefore, if the exploration company’s limited liability for repayment is considered in the case of information symmetry, an optimal compensation function for the Success Repayable Loan can be derived. However, in general, information between exploration companies and investors is asymmetric, as the exploration companies usually have exclusive information on their projects. As adverse selection or moral hazard can occur in the case of information asymmetry, investors first consider these issues before agreeing to enter into funding contracts.

Assuming the limited liability of exploration companies and the risk-neutral utility function of exploration companies and investors, it is known that a compensation function in the form of a general debt contract is optimal in cases of information asymmetry.

First, if an exploration company has information on the profitability of a certain project in advance, but the

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investor does not, such information asymmetry can cause adverse selection problems. In other words, the exploration company can take advantage of such asymmetry of information because the investor cannot distinguish a high-profit project from a low-profit one. Therefore, when entering into a financing contract for an exploration project, the investor should take into consideration the incentive of the company. The Korea Development Institute (2008) derived the optimal contract in this case, assuming that both the company and investor are risk-neutral. Let be the probability density function for the profit distribution ( ) of a high- profit project (h), and be the probability density function for the profit distribution ( ) of a low-profit project. It is assumed that, based on Assumption 1 below, the probability of achieving high profitability from a high-profit project must be higher than that of a low-profit project.

Assumption 1. Monotone likelihood ratio property (MLRP)⁴²

The likelihood ratio is an increasing function of .

Therefore, if Assumption 1 is satisfied, the expected profit of a high-profit project must be higher than that of a low-profit project. That is, holds. Here, is assumed. In this case, an optimal contract can be derived by solving the optimization problem below.

(6)

, where “I” is the amount invested in the exploration project, and “A < I” is the equity capital of the company.

The first constraint is the rationality constraint of the investor, while the second constraint is the condition that the exploration company will not participate in a less-profitable project. The third constraint is the condition of the limited liability of the company. The Korea Development Institute (2008) showed that the optimal contract under such constraints can be derived as follows.

42 For further discussion of this assumption, see Milgrom (1981).

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(7)

Therefore, in the case of the ex-ante asymmetry of information on the profitability of an exploration project, it can be confirmed that the optimal contract takes the form of a general liability contract.

Meanwhile, the asymmetry of information on profits can also occur ex-post. For example, an exploration company is aware of an ex-post realized profit ( ), but the investor, who is under an asymmetry of information where he cannot observe such profit, has an incentive to spend cost to conduct an accounting audit in response to the potential for adverse selection. Townsend (1979) and Gale and Hellwig (1985) showed that the optimal contract here takes the form of a general debt contract. Townsend (1979) showed that the optimal contract (if the audit cost of a risk-neutral investor is above zero ( ) and an exploration company has a minimum profit ( )) must be one in which in the case where , an audit will not be conducted, and the company will pay a fixed amount ( ) to the investor, while in the case where , an audit will be conducted, and the company will provide compensation ( ) satisfying . If the company is risk-neutral, the expression will be . However, if the company is risk-averse, the expression will be , meaning that the investor will be exempted from repaying a portion of the debt as a result of risk-sharing. Gale and Hellwig (1985) developed the optimal contract by expanding these discussions into credit markets under the assumption that both the investor and company are risk-neutral. Under this model, the optimal contract can be derived using the solution of the following enterprise problem.⁴³

(8)

, where is the state of nature and the company knows about this, but the investor incurs an auditing cost ( ) in order to confirm it. is the total income of the company; , the initial wealth of the company; , the total investment cost; , the investment amount of the investor; , the interest rate; and , the audit plan of the

43 Here, the credit market is perfectly competitive and therefore investors’ long-term profits are assumed to be zero.

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investor. It is assumed that non-monetary costs ( ) will be incurred by the company in the event an audit is conducted. In the above optimization problem, the first constraint is the individual-rationality constraint (IR), the second constraint is the ex-post feasibility of the contract, and the third constraint is the incentive-compatibility constraint (IC). In the optimal contract that can be expressed as a solution to this optimization problem, because there exists a minimum amount ( ) that triggers an audit, an audit will not be conducted in the case where

, and the compensation function will satisfy ,

if a case does not fall under the conditions of audit, the compensation function will be and a fixed compensation amount will be provided by the company. These results are basically the same as those of Townsend (1979) for a risk-neutral company, showing that the optimal contract appears in the form of a standard debt contract.

In general, the profit of an exploration project will be influenced by that company’s effort. An investor, however, suffers from an asymmetry of information, as he or she cannot observe the level of effort being made by the exploration company, thus giving rise to the possibility of moral hazard on the part of the exploration company. The investor should thus take this into consideration when entering into a funding contract. Innes (1990) showed that, in the case of a risk-neutral investor and company, limited liability of the company for repayment, and a compensation function with an increasing function of profit, the optimal contract takes the form of a general debt contract. When a company’s profit is a continuous random variable ( ), the profit of the company will be affected by the level of the company’s effort. Therefore, profit ( ) can be defined as the probability density function when the company exerts the level of effort . At this time, satisfies the above- mentioned MLRP assumption.

Assumption 2. Monotone likelihood ratio property (MLRP)

For all , a likelihood ratio is an increasing function of .

The MLRP assumption implies that the greater the realized profit, the greater the likelihood that the effort level has been higher, meaning that a realized profit provides appropriate information on the level of effort. Meanwhile, it is assumed that, since the level of effort of the company will cause cost or disutility, the cost or disutility can be denoted as (and assuming ). Therefore, when the compensation function of the company is expressed as , the expected utility function of the company ( ) can be expressed as follows.

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(9)

Therefore, the company will determine the level of effort ( ) necessary to maximize its expected utility ( ) for a given , and the relation will hold for all . Therefore, if the minimum expected return required by the investor is , the optimal contract can be derived from the following problem.

(10)

The first constraint is the company’s limited liability for reimbursement, and the third constraint is the rationality condition. The incentive-compatibility constraint of the company is included in the process of deriving

. The form of the optimal compensation function that emerges as a solution to this problem is as follows.

(11)

, where is the profit that can be achieved through a level of effort . Furthermore, Innes (1990) proved that, if the above Assumption 2 is added as a constraint in the above problem, the form of the optimal compensation function is that of a general debt contract; that is, in the case , and in the case

.

The compensation function ( ) of the company is a weakly increasing function of (where ).

An important assumption in Innes’ conclusion (1990) is the risk-neutrality of the company. If both the investor and the company are risk-neutral, the discussion of risk-sharing can be discarded and only the incentive effect of moral hazard can be considered. However, if a company is risk-averse, ineffectiveness in risk-sharing must be suffered in order to present an appropriate incentive to a company under moral hazard.

As such, the optimal contract under most situations of information asymmetry is a general debt contract.

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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