Residual income valuation and management remuneration under uncertainty: a note

The so-called Residual Income Valuation theorem states that the value of a project or a firm can be determined either on the basis of cash flows between the firm and its owners or by using residual incomes, provided that cash flows and residual incomes are derived from a set of accounting data that fulfills certain regularity conditions. Residual income is defined as accounting earnings reduced by a capital charge on book equity capital. In this paper it is shown that this theorem also applies when residual incomes and in particular the discount factors are uncertain. Risk-aversion of principals and agents is taken into account on the basis of properly defined risk-adjusted discount rates. This approach is preferred as it facilitates practical application. Implications are drawn with regards to valuation but also to the design of management remuneration systems. It is shown that the capital charge rate used to determine the performance-related compensation component should be reduced below the risk-adjusted rate, if the fixed component falls below a certain threshold. Absent agency cost or other externalities, the reduction of the capital charge rate is required to avoid underinvestment.