Chapter 25, Problem 5AP

a.

To determine

Identify the project that would be chosen by Person B for investment, if Person B’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 14% would be attractive to Person B and would improve the ROI of Person B’s location. Project A-1 and A-2 are having ROI of 14.1% and 20.0% respectively, which would be attractive to Person B to improve the ROI  of the current location.

b.

To determine

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

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 F of 12% would increase the value of Incorporation F. Projects A-1, A-2, A-3, and A-4 are likely to increase the value of Incorporation F. However, Project A-5 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-1	$\$150,000\times 14.1\%=\$21,150$	$\$21,150–\left(\$150,000\times 12\%\right)=\$ 3,150$
A-2	$\$300,000\times 20.0\%=\$60,000$	$\begin{array}{l}\$60,000–\left(\$300,000\times 12\%\right)=\$24,000\hfill \end{array}$
A-3	$\$250,000\times 13.5\%=\$33,750$	$\$33,750–\left(\$250,000\times 12\%\right)=\$3,750$
A-4	$\$400,000\times 12.5\%=\$50,000$	$\$50,000–\left(\$400,000\times 12\%\right)=\$2,000$
A-5	$\$500,000\times 9.8\%=\$49,000$	$\$49,000–\left(\$500,000\times 12\%\right)=\left(\$11,000\right)$

Table (1)

As per Table (1), Project A-5 is having residual income (Loss) of ($11,000).

d.

To determine

Create two rankings for the projects in order of acceptability if Person B 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-1	$150,000	14.1%	2
A-2	$300,000	20.0%	1
A-3	$250,000	13.5%	3
A-4	$400,000	12.5%	4
A-5	500,000	9.8%	5

Table (2)

On the basis of ROI, Project A-2 and Project A-1 would be acceptable by Person B because the ROI yields 14.1% and 20.0% respectively which is higher than the current ROI of 14%.

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

Project	Operating Income	Residual Income (loss)	Ranking
A-1	$\$150,000\times 14.1\%=\$21,150$	$\$21,150–\left(\$150,000\times 12\%\right)=\$ 3,150$	3
A-2	$\$300,000\times 20.0\%=\$60,000$	$\begin{array}{l}\$60,000–\left(\$300,000\times 12\%\right)=\$24,000\hfill \end{array}$	1
A-3	$\$250,000\times 13.5\%=\$33,750$	$\$33,750–\left(\$250,000\times 12\%\right)=\$3,750$	2
A-4	$\$400,000\times 12.5\%=\$50,000$	$\$50,000–\left(\$400,000\times 12\%\right)=\$2,000$	4
A-5	$\$500,000\times 9.8\%=\$49,000$	$\$49,000–\left(\$500,000\times 12\%\right)=\left(\$11,000\right)$	5

Table (3)

On the basis of residual income, Project A-2 and Project A-3 would be acceptable because the residual income is $24,000 and $3,750 respectively which are higher than the residual income of other projects.

e.

To determine

On the basis of the projects, explain the reasons behind the problem of under –investment using ROI as a tool of evaluation.

Explanation of Solution

As per Table (2), the Project A-1 would be preferred over Project A-3 because Project A-1 yields a ROI of 14.1% which is higher than the current ROI of 14%. On the other hand, Project A-3 yields a ROI of 13.5% which is lower than the current ROI of 14%.

As per Table (3), the Project A-3 would be preferred over Project A-1 because the residual income from Project A-3 is $3,750 with an invested capital of $250,000. On the other hand, the residual income from Project A-1 is $3,150 with an invested capital of $150,000. The residual income of Project A-3 is higher than the residual income of Project A-1.

If Person B is evaluated on the basis of ROI, then Project A-1 or Project A-2 would be considered because they are the projects that would raise the current ROI of 14%.