'Cost of Capital' in Residual Income for Performance Evaluation

Posted: 11 Jul 2000

See all articles by Peter O. Christensen

Peter O. Christensen

Copenhagen Business School - Department of Finance

Gerald A. Feltham

University of British Columbia

Martin G. H. Wu

University of Illinois at Urbana-Champaign

Date Written: June 21, 2000

Abstract

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

Christensen, Peter Ove and Feltham, Gerald A. and Wu, Martin G. H., 'Cost of Capital' in Residual Income for Performance Evaluation (June 21, 2000). Sauder School of Business Working Paper, Available at SSRN: https://ssrn.com/abstract=233993 or http://dx.doi.org/10.2139/ssrn.233993

Peter Ove Christensen

Copenhagen Business School - Department of Finance ( email )

Solbjerg Plads 3
Frederiksberg, DK-2000
Denmark
+45 6140 3237 (Phone)

Gerald A. Feltham (Contact Author)

University of British Columbia ( email )

2053 Main Mall
Vancouver, BC V6T 1Z2
Canada
604-822-8397 (Phone)
604-822-9470 (Fax)

Martin G. H. Wu

University of Illinois at Urbana-Champaign ( email )

1206 South Sixth Street
Champaign, IL 61820
United States
(217) 333-5957 (Phone)
(217) 244-0902 (Fax)

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