There are many different methods of valuing a company or its stock. One could opt to use a relative valuation approach, comparing multiples and metrics of a firm in relation to other companies within its industry or sector. Another alternative would be valuing a firm based upon an absolute estimate, such as implementing discounted cash flow (DCF) modeling or the dividend discount method, in an attempt to place an intrinsic value on said firm.

One absolute valuation method which may not be so familiar to most, but is widely used by analysts, is the residual income method. In this article, we will introduce you to the underlying basics behind the residual income method and how it can be used to place an absolute value on a firm.

### Key Takeaways

- Residual income is the income a company generates after accounting for the cost of capital.
- The residual income valuation formula is very similar to a multistage dividend discount model, substituting future dividend payments for future residual earnings.
- Residual income models make use of data readily available from a firm's financial statements.
- These models look at the economic profitability of a firm rather than just its accounting profitability.

#### Valuing A Company Using The Residual Income Method

## An Introduction to Residual Income

When most hear the term residual income, they think of excess cash or disposable income. Although that definition is correct in the scope of personal finance, in terms of equity valuation residual income is the income generated by a firm after accounting for the true cost of its capital.

You might be asking, "but don't companies already account for their cost of capital in their interest expense?" Yes and no. Interest expense on the income statement only accounts for a firm's cost of its debt, ignoring its cost of equity, such as dividend payouts and other equity costs.

Looking at the cost of equity another way, think of it as the shareholders' opportunity cost, or the required rate of return. The residual income model attempts to adjust a firm's future earnings estimates to compensate for the equity cost and place a more accurate value on a firm. Although the return to equity holders is not a legal requirement, like the return to bondholders, in order to attract investors firms must compensate them for the investment risk exposure.

In calculating a firm's residual income, the key calculation is to determine its equity charge. Equity charge is simply a firm's total equity capital multiplied by the required rate of return of that equity, and can be estimated using the capital asset pricing model (CAPM).

## Computing Residual Income and the Equity Charge

The formula below shows the equity charge equation:

Equity Charge = Equity Capital x Cost of Equity

Once we have calculated the equity charge, we only have to subtract it from the firm's net income to come up with its residual income. For example, if Company X reported earnings of $100,000 last year and financed its capital structure with $950,000 worth of equity at a required rate of return of 11%, its residual income would be:

Equity Charge - $950,000 x 0.11 = $104,500

Net Income | $100,000 |
---|---|

Equity Charge | -$104,500 |

Residual Income | -$4,500 |

As you can see from the above example, using the concept of residual income, although Company X is reporting a profit on its income statement, once its cost of equity is included in relation to its return to shareholders, it is actually economically unprofitable based on the given level of risk. This finding is the primary driver behind the use of the residual income method. A scenario where a company is profitable on an accounting basis, may still not be a profitable venture from a shareholder's perspective if it cannot generate residual income.

Given the opportunity cost of equity, a company can have positive net income but negative residual income.

## Intrinsic Value With Residual Income

Now that we've found how to compute residual income, we must now use this information to formulate a true value estimate for a firm. Like other absolute valuation approaches, the concept of discounting future earnings is put to use in residual income modeling as well. The intrinsic, or fair value, of a company's stock using the residual income approach, can be broken down into its book value and the present values of its expected future residual incomes, as illustrated in the formula below.

$\begin{aligned} &\text{V}_0 = BV_0 + \left \{ \frac {RI_1}{(1+r)^n} + \frac {RI_2}{(1+r)^{n+1}} + \cdots \right \}\\ &\textbf{where:}\\ &\textit{BV} = \text{Present book value}\\ &\textit{RI} = \text{Future residual income}\\ &\textit{r} = \text{Rate of return}\\ &\textit{n} = \text{Number of periods}\\ \end{aligned}$

As you may have noticed, the residual income valuation formula is very similar to a multistage dividend discount model, substituting future dividend payments for future residual earnings. Using the same basic principles as a dividend discount model to calculate future residual earnings, we can derive an intrinsic value for a firm's stock. In contrast to the DCF approach which uses the weighted average cost of capital for the discount rate, the appropriate rate for the residual income strategy is the cost of equity.

## What Are the Pros of the Residual Income Method?

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.

## What Are the Limitations of the Residual Income Method?

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.

## How Is a Firm's Residual Income Calculated?

Residual income is calculated as a company's net income less a charge for its cost of capital (known as the equity charge). The equity charge is computed from the value of equity capital multiplied by the cost of equity (often its required rate of return).

## The Bottom Line

The residual income valuation approach is a viable and increasingly popular method of valuation and can be implemented rather easily by even novice investors. When used alongside the other popular valuation approaches, residual income valuation can give you a clearer estimate of the true intrinsic value of a firm maybe.