'Cost of Capital' in Residual Income for Performance Evaluation
Posted: 11 Jul 2000
Date Written: June 21, 2000
We examine the determinants of the optimal "cost of capital" in residual income for measuring performance in a moral hazard setting with both firm-specific and systematic risks. The recommendation in the literature is that the "cost of capital" should be the riskless interest rate adjusted for systematic risk. We show that, if the manager is risk averse and can personally trade in market securities, and if there is firm-specific risk, the optimal "cost of capital" for performance evaluation is the riskless interest rate adjusted for firm-specific risk.
The manager provides unobservable and personally costly effort. Its inducement creates a need for performance evaluation based on the firm's (residual) income which is affected by both firm-specific and systematic risk. The manager also selects a capital investment that is costly to shareholders and increases the firm's risk. If the manager can personally trade in market securities, he can offset the systematic component of the firm's risk. He bears his efficient share of the market risk and his risk-return preferences for that type of risk are perfectly aligned with those of well-diversified shareholders. However, he bears the firm-specific component of the firm's risk, which is of no direct concern to the well-diversified shareholders.
Therefore, the "cost of capital" levied in residual income by shareholders must mitigate the manager's incentive to under-invest in capital due to its impact on the firm-specific risk in the residual income. If the manager receives no private firm-specific information, the optimal "cost of capital" is lower than the riskless interest rate. On the other hand, if the manager receives perfect firm-specific information after signing the incentive contract but before choosing the capital investment, he will chose first-best investments if he is charged the riskless interest rate. However, in this setting, the optimal "cost of capital" is set higher than the riskless interest rate to induce lower variations in capital investments in order to reduce the risk premium paid to the manager for ex-ante firm-specific information risk. We conclude the paper by examining a setting in which the manager can allocate the capital provided by shareholders among investments in the firm's production technology and in market securities. If the allocation is not contractible, the optimal "cost of capital" is the riskless interest rate so as to avoid arbitrage opportunities.
Keywords: Cost of capital; Residual income; Performance evaluation
JEL Classification: G32, J33, M40, M41, M46
Suggested Citation: Suggested Citation