Chapter 10, Problem 16E

A multinational corporation has a number of divisions, two of which are the North American Division and the Pacific Rim Division. Data on the two divisions are as follows:

Round all rates of return to four significant digits.

Required:

1. 1. Compute residual income for each division. By comparing residual income, is it possible to make a useful comparison of divisional performance? Explain.
2. 2. Compute the residual rate of return by dividing the residual income by the average operating assets. Is it possible now to say that one division outperformed the other? Explain.
3. 3. Compute the return on investment for each division. Can we make meaningful comparisons of divisional performance? Explain.
4. 4. Add the residual rate of return computed in Requirement 2 to the required rate of return. Compare these rates with the ROI computed in Requirement 3. Will this relationship always be the same?

To determine

Compute the residential income for each division and identify whether it is possible to make a useful comparison of divisional performance. Explain the same.

Explanation of Solution

Residual income: It is an amount by which an operating income (earnings) exceeds a minimum acceptable return on the average capital invested.

$\text{Residual income}\text{=}\text{Operating earnings}\text{–}\left(\text{Minimum acceptable return}\times \text{Invested capital}\right)$

Compute the residual income:

For NA:

$\begin{array}{c}\text{Residual income}\text{=}\text{Operating earnings}\text{–}\left(\text{Minimum acceptable return}\times \text{Invested capital}\right)\\ =\$1,250,000-\left(7\%\times \$15,000,000\right)\\ =\$1,250,000-\$1,050,000\\ =\$200,000\end{array}$

Therefore, the residual income is $200,000.

For PR:

$\begin{array}{c}\text{Residual income}\text{=}\text{Operating earnings}\text{–}\left(\text{Minimum acceptable return}\times \text{Invested capital}\right)\\ =\$610,000-\left(7\%\times \$6,700,000\right)\\ =\$610,000-\$469,000\\ =\$141,000\end{array}$

Therefore, the residual income is $141,000.

As the residual income is an absolute dollar amount, it is not adjust for the relative sizes of the division.

Therefore, it is not possible to make a useful comparison of divisional performance

To determine

Compute the residual rate of return and identify whether it is possible to make a useful comparison of divisional performance. Explain the same.

Explanation of Solution

Compute the residual rate of return:

$\text{Residual}\text{rate}\text{of}\text{return}\text{=}\frac{\text{Residual}\text{Income}}{\text{Average}\text{Operating}\text{Assets}}$

For NA:

$\begin{array}{c}\text{Residual}\text{rate}\text{of}\text{return}\text{=}\frac{\text{Residual}\text{Income}}{\text{Average}\text{Operating}\text{Assets}}\\ =\frac{\$200,000}{\$15,000,000}\\ =0.0133\text{or 1}\text{.33\%}\end{array}$

Therefore, residual rate of return of NA division is 1.33%.

For PR:

$\begin{array}{c}\text{Residual}\text{rate}\text{of}\text{return}\text{=}\frac{\text{Residual}\text{Income}}{\text{Average}\text{Operating}\text{Assets}}\\ =\frac{\$141,000}{\$6,700,000}\\ =0.0210\text{or 2}\text{.10\%}\end{array}$

Therefore, residual rate of return of NA division is 2.10%.

As the residual rate of return is a percentage, it is possible to make a useful comparison of divisional performance. The above calculations show that the PR Division is more profitable as compared to NA division.

To determine

Compute the ROI and identify that whether it makes meaningful comparisons of divisional performance. Explain the same.

Explanation of Solution

Return on investment (ROI): This financial ratio evaluates how efficiently the assets are used in earning income from operations. So, ROI is a tool used to measure and compare the performance of a units or divisions or a companies.

$\text{ROI = }\frac{\text{Operating}\text{Income}}{\text{Average}\text{TotalAssets}}$

Compute the ROI for each division:

For NA division:

$\begin{array}{c}\text{ROI = }\frac{\text{Operating}\text{Income}}{\text{Average}\text{TotalAssets}}\\ =\frac{\$1,250,000}{\$15,000,000}\\ =0.0833\text{or 8}\text{.33\%}\end{array}$

Therefore, ROI for NA division is 8.33%.

For PR division:

$\begin{array}{c}\text{ROI = }\frac{\text{Operating}\text{Income}}{\text{Average}\text{TotalAssets}}\\ =\frac{\$610,000}{\$6,700,000}\\ =0.0910\text{or 9}\text{.10\%}\end{array}$

Therefore, ROI for PR division is 9.10%.

Yes, it is used to makes meaningful comparisons of divisional performance. ROI of PR division is high.

To determine

Whether adding the residual rate of return computed in subpart 2 to the required rate of return. Compare these rates with the ROI computed in the subpart 3. Identify whether this relationship always should be same or not.

Explanation of Solution

Adding the residual rate of return computed in subpart 2 to the required rate of return:

For Division NA:

$\begin{array}{c}\text{Residual}\text{rate}\text{of}\text{return}\text{+}\text{Required}\text{Rate}\text{of}\text{return}\text{=}0.0133+0.0700\\ =0.0833\text{or}8.33\%\end{array}$

ROI for Division NA is 8.33%

For Division PR:

$\begin{array}{c}\text{Residual}\text{rate}\text{of}\text{return}\text{+}\text{Required}\text{Rate}\text{of}\text{return}\text{=}0.0210+\$.07\\ =0.0910\text{or}9.10\%\end{array}$

ROI for Division PR is 9.10%

ROI for the Division PR is a 9.10%.

The sum of residual rate of return and required rate of return is always equal to the ROI