Chapter 25, Problem 12E

To determine

Compute the missing data for Companies X, Y and Z.

Answer to Problem 12E

The missing data for Companies X, Y and Z are as follows:

Particulars	Company X	Company Y		Company Z
Operating income	$220,000	e. $1,200,000	i. $4,800,000
Sales	a. $687,500	f. $3,000,000	j. $9,600,000
Invested capital	b. $3,437,500	$6,000,000	$32,000,000
Return on sales	32%	40%	k. 50%
Capital turnover	20%	g. 50%	30%
Return on investment	c. 6.4%	20%	15%
Minimum acceptable return	10%	12%	l. 12 %
Residual income (loss)	d. ($123,750)	h. $480,000	$960,000

Table (1)

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:

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

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:

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

Capital turnover:   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. The formula to calculate capita turnover is as follows:

$\text{Capital turnover ratio}=\frac{\text{Net sales}}{\text{Average total assets}}$

Return on sales: This financial ratio evaluates the operating income that can be expected from one dollar of sales. The formula to calculate the return on sales is as follows:

$\text{Return on sales = }\frac{\text{Operating earnings}}{\text{Net sales}}$

Working Note:

a. Compute sales for Company X.

$\begin{array}{c}\text{Return on sales}=\frac{\text{Operating income}}{\text{Net sales}}\\ 32\%=\frac{\$220,000}{\text{Net sales}}\\ \text{Net sales}=\frac{\$220,000}{32}\times 100\\ =\$687,500\end{array}$

(1)

b. Compute invested capital for Company X.

$\begin{array}{c}\text{Capital turnover}=\frac{\text{Net sales}}{\text{Average investment}}\\ 20\%=\frac{\$687,500\left(1\right)}{\text{Average investment}}\\ \text{Average investment}=\frac{\$687,500}{20}\times 100\\ =\$3,437,500\end{array}$

(2)

c. Compute return on investment for Company X.

$\begin{array}{c}\text{Return on investment}=\text{Capital turnover}\times \text{return on sales}\\ =20\%\times 32\%\\ =6.4\%\end{array}$

d. Compute residual income for Company X.

$\begin{array}{c}\text{Residual income = Operating earnings}-\left\{\left(\begin{array}{l}\text{Minimum }\\ \text{acceptable }\\ \text{return}\end{array}\right)\times \text{Invested capital}\right\}\\ =\$220,000-\left(10\%\times \$3,437,500\left(2\right)\right)\\ =\$220,000-\$343,750\\ =(\$123,750)\end{array}$

e. Compute operating income for Company Y.

$\begin{array}{c}\text{Return on investment}=\frac{\text{Operating income}}{\text{Average capital invested}}\\ 20\%=\frac{\text{Operating income}}{\text{\$6,000,000}}\\ \text{Operating income}=\text{\$6,000,000}\times 20\%\\ \text{Operating income}=\text{\$}1,200,000\end{array}$

(3)

f. Compute sales for Company Y.

$\begin{array}{c}\text{Return on sales}=\frac{\text{Operating income}}{\text{Net sales}}\\ 40\%=\frac{\$1,200,000\left(3\right)}{\text{Net sales}}\\ \text{Net sales}=\frac{\$1,200,000}{40}\times 100\\ =\$3,000,000\end{array}$

g. Compute capital turnover for Company Y.

$\begin{array}{c}\text{Capital turnover}=\frac{\text{Net sales}}{\text{Average investment}}\\ =\frac{\text{\$3,000,000}}{\text{\$6,000,000}}\\ =50\%\end{array}$

h. Compute residual income for Company Y.

$\begin{array}{c}\text{Residual income = Operating earnings}-\left\{\left(\begin{array}{l}\text{Minimum }\\ \text{acceptable }\\ \text{return}\end{array}\right)\times \text{Invested capital}\right\}\\ =\$1,200,000\left(3\right)-\left(12\%\times \$6,000,000\right)\\ =\$1,200,000-\$720,000\\ =\$480,000\end{array}$

i. Compute operating income for Company Z.

$\begin{array}{c}\text{Return on investment}=\frac{\text{Operating income}}{\text{Average capital invested}}\\ 15\%=\frac{\text{Operating income}}{\text{\$32,000,000}}\\ \text{Operating income}=\text{\$32,000,000}\times 15\%\\ \text{Operating income}=\text{\$}4,800,000\end{array}$

(4)

j. Compute sales for Company Z.

$\begin{array}{c}\text{Capital turnover}=\frac{\text{Net sales}}{\text{Average investment}}\\ 30\%=\frac{\text{Net sales}}{\$32,000,000}\\ \text{Net sales}=\$32,000,000\times 30\%\\ =\$9,600,000\end{array}$

(5)

k. Compute return on sales for Company Z.

$\begin{array}{c}\text{Return on sales}=\frac{\text{Operating income}}{\text{Net sales}}\\ =\frac{\$4,800,000\left(4\right)}{\$9,600,000\left(5\right)}\\ =50\%\end{array}$

l. Compute minimum acceptable return for Company Z.

$\begin{array}{c}\text{Residual income = Operating earnings}-\left\{\left(\begin{array}{l}\text{Minimum }\\ \text{acceptable }\\ \text{return}\end{array}\right)\times \text{Invested capital}\right\}\\ \$960,000=\$4,800,000\left(4\right)-\left\{\left(\begin{array}{l}\text{Minimum }\\ \text{acceptable }\\ \text{return}\end{array}\right)\times \$32,000,000\right\}\\ \$4,800,000-\$960,000=\left\{\left(\begin{array}{l}\text{Minimum }\\ \text{acceptable }\\ \text{return}\end{array}\right)\times \$32,000,000\right\}\\ \$3,840,000=\left(\begin{array}{l}\text{Minimum }\\ \text{acceptable }\\ \text{return}\end{array}\right)\times \$32,000,000\end{array}$

$\begin{array}{l}\text{Minimum acceptable return}=\frac{\$3,840,000}{\$32,000,000}\\ \text{Minimum acceptable return}=12\%\end{array}$