Chapter 9, Problem 23PSA

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 Printer Division, if operating income is $96,000, and operating assets are $540,000.

$\begin{array}{c}\text{Return on investment = }\frac{\text{Operating income}}{\text{Operating assets}}\\ \text{=}\frac{\text{\$96,000}}{\text{\$540,000}}\\ \text{= 0}\text{.178 or 17}\text{.8\%}\end{array}$

Compute the ROI of Copier Division, if operating income is $90,000, and operating assets are $810,000.

$\begin{array}{c}\text{Return on investment = }\frac{\text{Operating income}}{\text{Operating assets}}\\ \text{=}\frac{\text{\$90,000}}{\text{\$810,000}}\\ \text{= 0}\text{.111 or 11}\text{.1\%}\end{array}$

Compute the ROI of Fax Division, if operating income is $54,000, and operating assets are $360,000.

$\begin{array}{c}\text{Return on investment = }\frac{\text{Operating income}}{\text{Operating assets}}\\ \text{=}\frac{\text{\$54,000}}{\text{\$360,000}}\\ \text{= 0}\text{.15 or 15\%}\end{array}$

Hence, the manager of Printer Division produces highest ROI.

Conclusion

Hence, the manager of Printer Division produces highest ROI.

b.

To determine

Indicate the manager that would be ready to accept the additional investment opportunity of $120,000, based on the ROI.

Explanation of Solution

The manager of Copier Division would be eager to accept the additional investment opportunity of $120,000 because it would increase the ROI of the division to 13%, which is greater than the current ROI of 11.1% (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 $120,000, based on ROI.

Explanation of Solution

The manager of Fax Division would be the least eager to accept the additional investment opportunity of $120,000 because it would decrease the ROI of the division to 12%, which is lower than the current ROI of 15% (Refer Requirement (a)), and the ROI of the company, 12.5%, as well.

d.

To determine

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

Explanation of Solution

Printer Division 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 17% (Refer Requirement (a)), to 14%, and yet be higher than the ROI of the company, 12.5%.

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 Copier Division eagerly accepts the investment opportunity to increase the ROI of his division. But according to Requirement (d), the company prospers, if Printer Division 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:

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

Incorporation 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, Corporation A should introduce the residual income approach to evaluate the performance of the division.

g-1.

To determine

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

Explanation of Solution

Compute the residual income of Incorporation AT, if the operating income is $240,000, the operating assets are $1,710,000, and the desired rate of return is 12.5%.

$\begin{array}{c}\text{Residual income = Operating income – }\left(\begin{array}{l}\text{Operating assets}\times \\ \text{Desired rate of return on investment}\end{array}\right)\\ =\$240,000–\left(\$1,710,000\times 12.5\%\right)\\ =\$240,000–\$213,750\\ =\$26,250\end{array}$

2.

To determine

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

Explanation of Solution

Compute the residual income of the Printer Division, if the operating income is $96,000, the operating assets are $540,000, and the desired rate of return is 12.5%.

$\begin{array}{c}\text{Residual income = Operating income – }\left(\begin{array}{l}\text{Operating assets}\times \\ \text{Desired rate of return on investment}\end{array}\right)\\ =\$96,000–\left(\$540,000\times 12.5\%\right)\\ =\$96,000–\$67,500\\ =\$28,500\end{array}$

Compute the residual income of the Copier Division, if the operating income is $90,000, the operating assets are $810,000, and the desired rate of return is 12.5%.

$\begin{array}{c}\text{Residual income = Operating income – }\left(\begin{array}{l}\text{Operating assets}\times \\ \text{Desired rate of return on investment}\end{array}\right)\\ =\$90,000–\left(\$810,000\times 12.5\%\right)\\ =\$90,000–\$101,250\\ =\$\left(11,250\right)\end{array}$

Compute the residual income of the Fax Division, if the operating income is $54,000, the operating assets are $360,000, and the desired rate of return is 12.5%.

$\begin{array}{c}\text{Residual income = Operating income – }\left(\begin{array}{l}\text{Operating assets}\times \\ \text{Desired rate of return on investment}\end{array}\right)\\ =\$54,000–\left(\$360,000\times 12.5\%\right)\\ =\$54,000–\$45,000\\ =\$9,000\end{array}$

3.

To determine

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

Explanation of Solution

Compute the residual income of the Printer Division, if the operating income is $120,000, the desired rate of return is 12.5% before investment, and 14% after investment.

$\begin{array}{c}\text{Residual income = }\left\{\begin{array}{l}\text{Operating income × }\\ \left(\begin{array}{l}\text{Desired rate of return on investment, after investment–}\\ \text{Desired rate of return on investment, before investment}\end{array}\right)\end{array}\right\}\\ \text{=\$120,000}\times \left(\text{14\%–12}\text{.5\%}\right)\\ =\$120,000\times 1.5\%\\ =\$1,800\end{array}$

Compute the residual income of the Copier Division, if the operating income is $120,000, the desired rate of return is 12.5% before investment, and 13% after investment.

$\begin{array}{c}\text{Residual income = }\left\{\begin{array}{l}\text{Operating income × }\\ \left(\begin{array}{l}\text{Desired rate of return on investment, after investment–}\\ \text{Desired rate of return on investment, before investment}\end{array}\right)\end{array}\right\}\\ \text{= \$120,000}\times \left(\text{13\%–12}\text{.5\%}\right)\\ =\$120,000\times 0.5\%\\ =\$600\end{array}$

Compute the residual income of the Fax Division, if the operating income is $120,000, the desired rate of return is 12.5% before investment, and 12% after investment.

$\begin{array}{c}\text{Residual income = }\left\{\begin{array}{l}\text{Operating income × }\\ \left(\begin{array}{l}\text{Desired rate of return on investment, after investment–}\\ \text{Desired rate of return on investment, before investment}\end{array}\right)\end{array}\right\}\\ \text{= \$120,000}\times \left(\text{12\%–12}\text{.5\%}\right)\\ =\$120,000\times \left(0.5\right)\%\\ =\$\left(600\right)\end{array}$

4.

To determine

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

Explanation of Solution

Compute the residual income of the Printer Division, if the residual income, before investment is $28,500 (From Requirement (2)), the residual income after investment is $1,800.

$\begin{array}{c}\text{Residual income = }\left\{\begin{array}{l}\text{Residual income before investment+}\\ \text{Residual income after investment }\end{array}\right\}\\ =\$28,500+\$1,800\\ =\$30,300\end{array}$

Compute the residual income of the Copier Division, if the residual income, before investment is $(11,250) (From Requirement (2)), the residual income after investment is $600.

$\begin{array}{c}\text{Residual income = }\left\{\begin{array}{l}\text{Residual income before investment+}\\ \text{Residual income after investment }\end{array}\right\}\\ =\$\left(11,250\right)+\$600\\ =\$\left(10,650\right)\end{array}$

Compute the residual income of the Fax Division, if the residual income, before investment is $9,000 (From Requirement (2)), the residual income after investment is $(600).

$\begin{array}{c}\text{Residual income = }\left\{\begin{array}{l}\text{Residual income before investment+}\\ \text{Residual income after investment }\end{array}\right\}\\ =\$9,000+\$\left(600\right)\\ =\$8,400\end{array}$

h.

To determine

 Indicate the manager that would be ready to accept the additional investment opportunity of $120,000, based on the residual income.

Explanation of Solution

The managers of Printer Division and Copier Division would be eager to accept the additional investment opportunity of $120,000 because it would increase the residual income of the divisions.