8.5  Residual Income

There is a re-interpretation of the term a_t that brings out the intuition that the company is only making money (or adding value) only if it provides a return that compensates the shareholders for the risks they take.   The compensation for risk is measured by the (expected) rate of return required by shareholders in order to hold the stock.

In Chapter 4, the cost of equity capital was introduced within the context of the Capital Asset Pricing Model (CAPM).  Under CAPM, the cost of equity capital equals the investors’ required rate of return.  

Residual Income is defined relative to opportunity costs as follows:

Residual Income = Comprehensive Income – Cost of Equity Capital * Book Value of Equity

Formally,

RI_t = CI_t – k_e*BV_t-1

You can see residual income is positive if the comprehensive income generated at time t exceeds the shareholders required rate of return on book value at time t-1, in which the firm created positive shareholder value at time t.

The concept of residual income was discussed by Marshall as early as the 1890.  He defined “economic profit” as “what remains of his profits after deducting interest on his capital at the current rate.”  Note that this takes into account the cost of capital directly in the definition.