# Residual income model

A residual income model values securities using a combination of book value of the company (i.e. its NAV), and a present value based on accounting profits. The value of a company is the sum of:

• the NAV at the time of valuation, and,
• the present value of the residual income: the amounts by which profits are expected to exceed the required rate of return on equity.

The latter, like most present value calculations, ends with a terminal value which is calculated on a different basis to the other future amounts.

The residual return is:

(R - r) × B

Where:
B is the NAV
R is the return based on accounting profits and owners equity (net profit ÷ B), and
r is the required rate of return on equity.

This can also be expressed as net profit - (r × B)

The terminal value is somewhat differnt from that used in an NPV. Rather than being the actual value of the company at that time, it is the actual value minus the NAV at that time.

The significance of the extra profit over the required rate of return is that it is a measure of the wealth the company creates for shareholders. This is what the company adds to the value of is assets, and what justifies a company being worth more than the value of its assets. Therefore, the value of a company should be the sum of this and its assets.

The NAV will vary from year to year, which affects the calculation of the returns. The change is the net profit, less dividends and other returns to shareholders, plus capital raised.

Basing valuation on wealth creation is conceptually similar to EVA. Residual income models are better suited to securities valuation (whereas EVA is primarilly useful to management).

The advantage of the residual income model is that it is entirely based on accounting measures of profit and value of assets.

The most obvious objection to the residual income model is that it is based on accounting numbers that often fail to reflect the true economic value of assets and cash flows.

For a more detailed analysis, including the derivation of the model, see this tutorial on residual income models.