Chapter 25, Problem 5BP

a.

To determine

Identify the project that would be chosen by Person F for investment, if Person F’s objective were to maximize the location’s 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 or a companies. The formula for ROI is as follows:

$\text{Return on investment}\left(\text{ROI}\right)\text{ = }\frac{\text{Operating income }}{\text{Average total investment}}$

The projects that are having ROI greater than or equal to 15% would be attractive to Person F and would improve the ROI of Person F’s location. Project A and B are having ROI of 16.2% and 15.0% respectively, which would be attractive to Person F to improve the ROI  of the current location.

b.

To determine

Identify the project that would increase the value of Incorporation S.

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. The formula for ROI is as follows:

$\text{Return on investment}\left(\text{ROI}\right)\text{ = }\frac{\text{Operating income }}{\text{Average total investment}}$

The projects that are having ROI above the minimum required return established for Incorporation S of 12% would increase the value of Incorporation S. Projects A, B, C, and D are likely to increase the value of Incorporation S. However, Project E would not be acceptable.

c.

To determine

Identify the project that would have a negative residual income.

Explanation of Solution

Residual income: Residual income is the excess of income over the minimum acceptable return on average capital invested. The minimum rate of return shows the opportunity cost of using the invested capital. The formula for residual income is as follows:

$\text{Residual income = Operating earnings}-\left\{\left(\begin{array}{l}\text{Minimum }\\ \text{acceptable }\\ \text{return}\end{array}\right)\times \text{Invested capital}\right\}$

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. The formula for ROI is as follows:

$\text{Return on investment}\left(\text{ROI}\right)\text{ = }\frac{\text{Operating income }}{\text{Average total investment}}$

Determine the residual income (loss) of each project.

Project	Operating Income	Residual Income (loss)
A	$\$200,000\times 16.2\%=\$32,400$	$\begin{array}{c}\$32,400-\left(\$200,000\times 12\%\right)=\$8,400\end{array}$
B	$\$400,000\times 15\%=\$60,000$	$\$60,000-\left(\$400,000\times 12\%\right)=\$12,000$
C	$\$300,000\times 14\%=\$42,000$	$\$42,000-\left(\$300,000\times 12\%\right)=\$6,000$
D	$\$200,000\times 13\%=\$26,000$	$\$26,000-\left(\$200,000\times 12\%\right)=\$2,000$
E	$\$600,000\times 10\%=\$60,000$	$\$60,000-\left(\$600,000\times 12\%\right)= \left(\$12,000\right)$

Table (1)

As per Table (1), Project E is having residual income (Loss) of ($12,000).

d.

To determine

Create two rankings for the projects in order of acceptability if Person F is evaluated (1) on ROI and (2) on residual income.

Explanation of Solution

Residual income: Residual income is the excess of income over the minimum acceptable return on average capital invested. The minimum rate of return shows the opportunity cost of using the invested capital. The formula for residual income is as follows:

$\text{Residual income = Operating earnings}-\left\{\left(\begin{array}{l}\text{Minimum }\\ \text{acceptable }\\ \text{return}\end{array}\right)\times \text{Invested capital}\right\}$

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. The formula for ROI is as follows:

$\text{Return on investment}\left(\text{ROI}\right)\text{ = }\frac{\text{Operating income }}{\text{Average total investment}}$

Rank the projects in order of acceptability based (1) on ROI.

Project	Required capital	ROI	Ranking
A	$200,000	16.2%	1
B	$400,000	15.0%	2
C	$300,000	14.0%	3
D	$200,000	13.0%	4
E	$600,000	10.0%	5

Table (2)

On the basis of ROI, Project A and Project B would be acceptable by Person F because the ROI yields 16.2% and 15.0% respectively which is higher than the current ROI of 15%.

Rank the projects in order of acceptability based (2) on residual income.

Project	Operating Income	Residual Income (loss)	Ranking
A	$\$200,000\times 16.2\%=\$32,400$	$\begin{array}{c}\$32,400-\left(\$200,000\times 12\%\right)=\$8,400\end{array}$	2
B	$\$400,000\times 15\%=\$60,000$	$\$60,000-\left(\$400,000\times 12\%\right)=\$12,000$	1
C	$\$300,000\times 14\%=\$42,000$	$\$42,000-\left(\$300,000\times 12\%\right)=\$6,000$	3
D	$\$200,000\times 13\%=\$26,000$	$\$26,000-\left(\$200,000\times 12\%\right)=\$2,000$	4
E	$\$600,000\times 10\%=\$60,000$	$\$60,000-\left(\$600,000\times 12\%\right)= \left(\$12,000\right)$	5

Table (3)

On the basis of residual income, Project A and Project B would be acceptable because the residual income is $12,000 and $8,400 respectively which are higher than the residual income of other projects.

e.

To determine

Explain the components of ROI and explain the manner by which the combination of components of ROI is useful for evaluating the success of business processes within a firm

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. The components of Return on Investment (ROI) are shown in the equation given below:

$\begin{array}{c}\begin{array}{l}\text{Return on }\\ \text{Investment (ROI)}\end{array}\}=\text{Capital turnover}\times \text{Return on sales}\\ \frac{\text{Operating income}}{\text{Average total assets}}\text{=}\frac{\text{Net sales}}{\text{Average total assets}}\times \frac{\text{Operating earnings}}{\text{Net sales}}\end{array}$

Return on sales ratio evaluates the operating income that can be expected from one dollar of sales. This ratio is helpful to management because it indicates how much operating profit is being generated from each dollar of sales.

Capital turnover is a ratio that measures the amount of sales generated from each dollar of capital investment. Thus, it shows the relationship between the net sales and the average capital invested. This ratio is useful in evaluating how efficiently a company is utilizing the invested capital to generate sales dollars.

Thus, the combination of capital turnover and return on sales allows a company to assess the success of the investments that are used to generate sales, and the profitability of each dollar with respect to sales.