In Guttentag and Herring's model, moral hazard can make a higher contractual interest rate reduce the lender's expected return; if the maximum achievable expected return is below the opportunity cost of funds, the borrower is rationed rather than financed at a still higher rate.

Evidence 2 passages

• groundsUntitled source

  maximizes the lender's expected return. Differentiating Equation (5) with respect to the contract rate, we find that: r (1- 7r)(1 -F(Z -K, wf))-(1-7r) f OF(R d (14) Or L o (w dr The creditor maximizes expected return at the point at which the expected value of the increase in the contract rate when the borrower does not default precisely offsets the expected loss due to the induced increase in the probability of default.15 If the creditor's expected return at this optimal contract rate r is less than the opportunity cost of funds, the borrower will be rationed, since raising the contract rate beyond r' will reduce the expected return to the creditor. In effect, rationing arises from the lender's concern with the moral hazard that, at a higher contract rate, the borrower will employ the funds in a riskier venture that will reduce the expected return to the lender. Note that if the borrower cannot increase the riskiness of the investment, raising the contract rate raises the expected return to the creditor until the rate reaches the level where it completely exhausts the expected return from the investment under the most favorable outcome plus the borrower's capital. No borrower would knowingly enter such a contract. The introduction of bankruptcy cost, which makes the borrower's capital position less valuable to the creditor than to the borrower, will result in an optimal contract rate to the lender that is

• groundsUntitled source

  it denies the possibility of trading off capital (or loan size) against interest rate. If there were no constraints on interest rates, there should be no minimum capital requirement. However, as we have shown, there are constraints on interest rates. If project returns could not be altered by borrowers, it would always be in the lender's interest to charge as high a loan rate as can be negotiated (up to the maximum possible rate where the lender would take everything, as noted above). If there is a probability greater than zero that the borrower can earn enough to cover the higher rate, the lender's expected return will be higher, even though the probability of a shortfall from the promised return will also be higher. But if the borrower can change the project returns in a way that increases risk to the lender, higher rates may not be in the interest of the lender because they provide the borrower with an incentive to make this type of adjustment. Hence, moral hazard may lead to an optimal rate of interest for a given prospective borrower. At contract rates above the optimum, the loss to the lender from higher default rates exceeds the gains from higher promised contractual returns, and at rates below the optimum, the opposite is the case. The optimal contract rate, r, given L, r, and the distribution of investment returns, defines a minimum acceptable capital position, Km:19 Km 1 rZ-Km, Km =rr* -(1 -ir)(F- r*) + (1 -ir) L f F(R, w)dR. (21)

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