# Residual Income (RI)

In management accounting, residual income represents any excess of a department's income over the opportunity cost of the capital that it employs. It is calculated by subtracting the product of a department's average operating assets and the minimum required rate of return from its controllable margin.

Residual income approach is useful in allocating resources among projects or investments. A positive residual income means that the department has met the minimum return requirement while a negative residual income means that the department has failed to meet it. Departments with positive residual income are good candidates for expansion.

Residual income also features in corporate finance and valuation where it equals the difference between a company's net income and the product of the company's equity capital and its cost of equity.

## Formula

Residual income of a department can be calculated using the following formula:

Residual Income = Controllable Margin - Required Return × Average Operating Assets

Controllable margin (also called segment margin) is the department's revenue minus all such expenses for which the department manager is responsible.

Required return is the opportunity cost of the funds for the company. It is based on the company's cost of capital and the risk of the project.

Average operating assets of the department represents the total capital employed by the department. It is calculated by dividing the sum of opening and closing balances of the operating assets of the department by 2.

## Residual Income vs ROI

Return on investment (ROI) is another performance evaluation tool which equals the operating income earned by a department divided by its asset base. Even though ROI is the most popular measure, it suffers from a serious drawback. It creates an incentive for managers to not invest in projects which reduce their composite ROI even though those projects generate a return greater than the minimum required return.

Let us consider a department whose current operating income is \$200,000 and its asset base is \$1,000,000. The minimum required return is 15% and the department manager is considering a project that will earn \$50,000 and require additional capital of \$300,000. The department manager would not accept the project because his current ROI is 20% (=\$200,000/\$1,000,000) and accepting the project will reduce his ROI to 19.23% (=(\$200,000 + \$50,000)/(\$1,000,000 + \$300,000)). However, from the company’s perspective, accepting the project is the right thing to do because the project's return of 16.67% is higher than the minimum required return.

If department managers are evaluated based on the residual income that their departments generate, they have an incentive to accept all such projects which earn a return greater than the minimum required rate of return. This is one of the advantages that the residual income approach has over the ROI approach.

But residual income itself suffers from a bias, it does not allow for ranking of departments based on the dollars they earn per \$100 of investment. Since capital is a scarce resource, a company may not be able to arrange money for all projects with positive residual income. It is quite possible that some departments may be able to accept a lower ROI project while a higher ROI project at another department may not get the required investment.

## Example

CP Inc. is a company engaged in production and distribution of computers and printers. It has two main operating departments: Department C specializes in design, production and marketing of computers and Department P deals in printers.

The following table lists the operating income and assets of the departments:

Department C Department P
Operating income \$300 million \$130 million
Opening operating assets \$1 billion \$0.5 billion
Closing operating assets \$1.1 billion \$0.7 billion

The company's weighted average cost of capital is 12% and the highest return available on new investment opportunities foregone equals 15%.

### Solution

Since the company can earn 15% on alternate projects, it is treated as the minimum required return.

Department C's average operating assets are \$1.05 billion on which the minimum required return is \$157.5 million (=\$1,050 million × 15%). Its residual income is hence \$142.5 million:

Residual Income (Department C)
= \$300 million - \$1,050 million × 15%
= \$142.5 million

Department P's average operating assets are \$0.6 billion on which the minimum required return is \$90 million. Its residual income is hence \$40 million (\$130 million minus \$90 million).

Residual Income (Department P)
= \$130 million - \$600 million × 15%
= \$40 million

Department C has earned \$142.5 million residual income as compared to \$40 million earned by department P. Residual income allows us to compare the dollar amount of excess return earned by different departments. Since the residual income in both cases is positive, we conclude that both have met the minimum return requirements. However, with residual income is not particularly useful in comparing performance.

Return on investment (ROI) calculates total return in percentage terms and is a better measure of relative performance. In this example, Department C has a return on investment (ROI) of 28.6% (\$300 million/\$1,050 million) while Department P has return on investment (ROI) of 21.67% (\$130 million/\$600 million).