Compiled by Jeemit Shah

# What is Residual Income Valuation?

Residual income valuation (also known as residual income model or residual income method) is an equity valuation method that is based on the idea that the value of a company’s stock equals the present value of future residual incomes discounted at the appropriate cost of equity.

The main assumption underlying residual income valuation is that the earnings generated by a company must account for the true cost of capital (i.e., both the cost of debt and cost of equity). Although the accounting for net income considers the cost of debt (interest expenses are included in the calculation of net income), it does not take into account the cost of equity since the dividends and other equity distributions are not included in the net income calculation.

Due to the above reason, the net income does not represent the company’s economic profit. Moreover, in some cases, even when a company reports accounting profits, such profits may turn out to be economically unprofitable after the consideration of equity costs.

On the other hand, residual income is the company’s income adjusted for the cost of equity. Remember that the cost of equity is essentially the required rate of return asked by investors as compensation for the opportunity cost and corresponding level of risk. Therefore, the value of a company calculated using the residual income valuation is generally more accurate since it is based on the economic profits of a company.

## Benefits of using Residual Income Valuation

The residual income approach offers both positives and negatives when compared to the more often used dividend discount and discounted cash flows (DCF) methods. On the plus side, residual income models make use of data readily available from a firm’s financial statements and can be used well with firms that do not pay dividends or do not generate positive free cash flow. Most importantly, as we discussed earlier, residual income models look at the economic profitability of a firm rather than just its accounting profitability.

## Limitations of Residual Income Valuation

The biggest drawback of the residual income method is the fact that it relies so heavily on forward-looking estimates of a firm’s financial statements, leaving forecasts vulnerable to psychological biases or historic misrepresentation of a firm’s financial statements.

## Calculation of Residual Income Valuation

The first step required to determine the intrinsic value of a company’s stock using residual income valuation is to calculate the future residual incomes of a company.

Recall that residual income is the net income adjusted for the cost of equity. In most cases, the residual income can be calculated as the difference between the net income and equity charge. Mathematically, it can be expressed through the following formula:

Residual Income = Net Income – Equity Charge

Essentially, the equity charge is a deduction from net income accounted for the cost of equity. The equity charge is a multiple of the company’s equity capital and the cost of equity capital. The formula of the equity charge is:

Equity Charge = Equity Capital x Cost of Equity

### Single stage Residual Income Valuation

In the residual income model, the intrinsic value of a share of common stock is the sum of book value per share and the present value of expected future per-share residual income. In the residual income model, the equivalent mathematical expressions for intrinsic value of a common stock are

Where:

- V
_{ 0}= value of a share of stock today (t = 0) - B
_{ 0}= current per-share book value of equity - B
_{t}= expected per-share book value of equity at any time t - r = required rate of return on equity (cost of equity)
- E
_{t}= expected earnings per share for period t - RI
_{t}= expected per-share residual income - ROE
_{T}= return on equity

### Continuing equity value with persistence factor

The final valuation formula adjusts the previous multi-period formula by adding a continuing value (similar to terminal value) which incorporates a persistence factor. The persistence factor attempts to capture competitive forces which will drive return on equity down towards cost of equity capital over the long-term as new entrants will look to compete in any market that offers high returns.

The persistence factor ranges between 0 and 1 with 1 representing a business with a perfect economic moat that will persist into the future. The persistence factor can be estimated taking into account the competitive forces in the industry.

It can be calculated as:-

Where:-

- V
_{ 0}= value of a share of stock today (t = 0) - B
_{ 0}= current per-share book value of equity - B
_{t}= expected per-share book value of equity at any time t - r = required rate of return on equity (cost of equity)
- E
_{t}= expected earnings per share for period t - RI
_{t}= expected per-share residual income - ROE
_{T}= return on equity - ω = persistence factor