Chapter 9, Problem 23PSB

a.

To determine

Indicate the division manager with the highest return on investment (ROI).

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 of companies.

Formula of ROI:

$\text{Return on investment = }\frac{\text{Operating income}}{\text{Operating assets}}$

Compute the ROI of Division AM, if operating income is $216,000, and operating assets are $1,800,000.

$\begin{array}{c}\text{Return on investment = }\frac{\text{Operating income}}{\text{Operating assets}}\\ \text{=}\frac{\text{\$216,000}}{\text{\$1,800,000}}\\ \text{= 0}\text{.12 or 12\%}\end{array}$

Compute the ROI of Division AS, if operating income is $100,000, and operating assets are $1,000,000.

$\begin{array}{c}\text{Return on investment = }\frac{\text{Operating income}}{\text{Operating assets}}\\ \text{=}\frac{\text{\$100,000}}{\text{\$1,000,000}}\\ \text{= 0}\text{.1 or 10\%}\end{array}$

Compute the ROI of Division E, if operating income is $96,000, and operating assets are $1,200,000.

$\begin{array}{c}\text{Return on investment = }\frac{\text{Operating income}}{\text{Operating assets}}\\ \text{=}\frac{\text{\$96,000}}{\text{\$1,200,000}}\\ \text{= 0}\text{.08 or 8\%}\end{array}$

Hence, the manager of Division AM produces highest ROI.

Conclusion

Hence, the manager of Division AM produces highest ROI.

b.

To determine

Indicate the manager that would be ready to accept the additional investment opportunity of $200,000, based on the ROI.

Explanation of Solution

The manager of Division E would be eager to accept the additional investment opportunity of $200,000 because it would increase the ROI of the division to 9%, which is greater than the current ROI of 8% (Refer Requirement (a)). The other two divisions would not be eager to accept because the ROI is reduced due to increased operating assets.

c.

To determine

Indicate the manager that would be the least to accept the additional investment opportunity of $200,000, based on ROI.

Explanation of Solution

The manager of Division AS would be the least eager to accept the additional investment opportunity of $200,000 because it would decrease the ROI of the division to 5.6%, which is lower than the current ROI of 10% (Refer Requirement (a)), and the ROI of the company, 6%, as well.

d.

To determine

Indicate the division that would provide the best investment opportunity for the company.

Explanation of Solution

Division AM would provide the best investment opportunity for the company because the ROI of the division would be higher amongst the three divisions, though decreased from the current 12% (Refer Requirement (a)), to 10%, and yet be higher than the ROI of the company, 6%.

e.

To determine

Mention the term used to explain the conflict referred in the Requirements (b) and (d).

Explanation of Solution

Sub-optimization: This is a condition in which the managers choose their personal benefit at the corporation’s expense. In the given case in Requirement (b), the manager of Division E eagerly accepts the investment opportunity to increase the ROI of his division. But according to Requirement (d), the company prospers, if Division AM is given the investment opportunity. So, the conflict in both the requirements to choose the personal benefit rather than the company benefit, at the corporation’s expense is termed as sub-optimization.

f.

To determine

Explain the way in which the managers could be convinced to use the additional investment opportunity by using the residual income approach.

Explanation of Solution

Residual income: The excess of income from operations over the desired acceptable income is referred to as residual income.

Formula of residual income:

$\text{Residual income = Operating income – }\left(\begin{array}{l}\text{Operating assets}\times \\ \text{Desired rate of return on investment}\end{array}\right)$

Company AT could convince the managers of the divisions to accept the investment opportunity because it would increase the residual income of the division, and yet achieving the desired rate of return. So, Company BT should introduce the residual income approach to evaluate the performance of the division.

g-1.

To determine

Compute the residual income of Company AT, before the additional investment.

Explanation of Solution

Compute the residual income of Company AT, if the operating income is $412,000, the operating assets are $4,000,000, and the desired rate of return is 6%.

$\begin{array}{c}\text{Residual income = Operating income – }\left(\begin{array}{l}\text{Operating assets}\times \\ \text{Desired rate of return on investment}\end{array}\right)\\ =\$412,000–\left(\$4,000,000\times 6\%\right)\\ =\$412,000–\$240,000\\ =\$172,000\end{array}$

2.

To determine

Compute the residual income of the divisions, before the additional investment.

Explanation of Solution

Compute the residual income of the Division AM, if the operating income is $216,000, the operating assets are $1,800,000, and the desired rate of return is 6%.

$\begin{array}{c}\text{Residual income = Operating income – }\left(\begin{array}{l}\text{Operating assets}\times \\ \text{Desired rate of return on investment}\end{array}\right)\\ =\$216,000–\left(\$1,800,000\times 6\%\right)\\ =\$216,000–\$108,000\\ =\$108,000\end{array}$

Compute the residual income of the Division AS, if the operating income is $100,000, the operating assets are $1,000,000, and the desired rate of return is 6%.

$\begin{array}{c}\text{Residual income = Operating income – }\left(\begin{array}{l}\text{Operating assets}\times \\ \text{Desired rate of return on investment}\end{array}\right)\\ =\$100,000–\left(\$1,000,000\times 6\%\right)\\ =\$100,000–\$60,000\\ =\$40,000\end{array}$

Compute the residual income of the Division E, if the operating income is $96,000, the operating assets are $1,200,000, and the desired rate of return is 6%.

$\begin{array}{c}\text{Residual income = Operating income – }\left(\begin{array}{l}\text{Operating assets}\times \\ \text{Desired rate of return on investment}\end{array}\right)\\ =\$96,000–\left(\$1,200,000\times 6\%\right)\\ =\$96,000–\$72,000\\ =\$24,000\end{array}$

3.

To determine

Compute the residual income of the divisions, after the additional investment.

Explanation of Solution

Compute the residual income of the Division AM, if the operating income is $200,000, the desired rate of return is 6% before investment, and 10% after investment.

$\begin{array}{c}\text{Residual income = }\left\{\begin{array}{l}\text{Operating income × }\\ \left(\begin{array}{l}\text{Desired rate of return on investment, after investment–}\\ \text{Desired rate of return on investment, before investment}\end{array}\right)\end{array}\right\}\\ \text{=\$200,000}\times \left(\text{10\%–6\%}\right)\\ =\$200,000\times 4\%\\ =\$8,000\end{array}$

Compute the residual income of the Division AS, if the operating income is $200,000, the desired rate of return is 6% before investment, and 5.6% after investment.

$\begin{array}{c}\text{Residual income = }\left\{\begin{array}{l}\text{Operating income × }\\ \left(\begin{array}{l}\text{Desired rate of return on investment, after investment–}\\ \text{Desired rate of return on investment, before investment}\end{array}\right)\end{array}\right\}\\ \text{= \$200,000}\times \left(\text{5}\text{.6\%–6\%}\right)\\ =\$200,000\times \left(0.4\right)\%\\ =\$\left(800\right)\end{array}$

Compute the residual income of the Division E, if the operating income is $200,000, the desired rate of return is 6% before investment, and 9% after investment.

$\begin{array}{c}\text{Residual income = }\left\{\begin{array}{l}\text{Operating income × }\\ \left(\begin{array}{l}\text{Desired rate of return on investment, after investment–}\\ \text{Desired rate of return on investment, before investment}\end{array}\right)\end{array}\right\}\\ \text{= \$2000,000}\times \left(\text{9\%–6\%}\right)\\ =\$200,000\times 3\%\\ =\$6,000\end{array}$

4.

To determine

Compute the residual income of the divisions, after the additional investment.

Explanation of Solution

Compute the residual income of the Division AM, if the residual income, before investment is $108,000 (From Requirement (2)), the residual income after investment is $8,000.

$\begin{array}{c}\text{Residual income = }\left\{\begin{array}{l}\text{Residual income before investment+}\\ \text{Residual income after investment }\end{array}\right\}\\ =\$108,000+\$8,000\\ =\$116,000\end{array}$

Compute the residual income of the Division AS, if the residual income, before investment is $40,000 (From Requirement (2)), the residual income after investment is $(800).

$\begin{array}{c}\text{Residual income = }\left\{\begin{array}{l}\text{Residual income before investment+}\\ \text{Residual income after investment }\end{array}\right\}\\ =\$40,000+\$\left(800\right)\\ =\$39,200\end{array}$

Compute the residual income of the Division E, if the residual income, before investment is $24,000 (From Requirement (2)), the residual income after investment is $6,000.

$\begin{array}{c}\text{Residual income = }\left\{\begin{array}{l}\text{Residual income before investment+}\\ \text{Residual income after investment }\end{array}\right\}\\ =\$24,000+\$6,000\\ =\$30,000\end{array}$

h.

To determine

 Indicate the manager that would be ready to accept the additional investment opportunity of $200,000, based on the residual income.

Explanation of Solution

The managers of Division AM and Division E would be eager to accept the additional investment opportunity of $200,000 because it would increase the residual income of the divisions.