Chapter 10, Problem 17E

Consider the data for each of the following four independent companies:

Required:

1. 1. Calculate the missing values in the above table. (Round rates to four significant digits.)
2. 2. Assume that the cost of capital is 9 percent for each of the four firms. Compute the residual income for each of the four firms.

To determine

Calculate the missing amounts in the given table.

Explanation of Solution

Margin: It is an amount income generated by a dollar of sales. It is calculated as follows:

$\text{Margin}\text{=}\frac{\text{Operating Income}}{\text{Sales}}$

Turnover: It is an amount of sales generate by average operating assets. It is calculated by dividing the sales by the average operating assets in the assets, required to generate those sales.

$\text{Turnover = }\frac{\text{Sales}}{\text{Average Operating Assets}}$

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.

$\text{ROI = }\frac{\text{Operating}\text{Income}}{\text{Average}\text{TotalAssets}}$

Calculate the missing amounts in the given table:

Particulars	A		B		C		D
Revenue	$10,000		$48,000		$96,000		$19,200	k
Expenses	$8,000		$36,000	d	$90,000		$18,000	l
Operating income	$2,000		$12,000		$6,000	g	$1,200	m
Assets	$40,000		$96,000	e	$48,000		$9,600
Margin	20%	a	25%		6.25%	h	6.25%
Turnover	0.25	b	0.50		2.00	i	2.00
ROI	5.00%	c	12.5%	f	12.50%	j	12.50%	n

Table (1)

Notes to the above table:

a) Calculate margin for A:

$\begin{array}{c}\text{Margin}\text{=}\frac{\text{Operating Income}}{\text{Sales}}\\ =\frac{\$2,000}{\$10,000}\\ =0.20\text{or }20\%\end{array}$

b) Calculate the turnover for A:

$\begin{array}{c}\text{Turnover = }\frac{\text{Sales}}{\text{Average Operating Assets}}\\ =\frac{\$10,000}{\$40,000}\\ =0.25\end{array}$

c) Calculate the ROI for A:

$\begin{array}{c}\text{ROI = }\frac{\text{Operating}\text{Income}}{\text{Average}\text{TotalAssets}}\\ =\frac{\$2,000}{\$40,000}\\ =0.05\text{ or 5\%}\end{array}$

d) Calculate the expenses for B:

$\begin{array}{c}\text{Revenues}-\text{Expenses}\text{=}\text{Operating Income}\\ \text{\$48,000}-\text{Expenses}\text{=}\text{\$12,000}\\ \text{\$48,000}-\text{\$12,000}\text{=}\text{Expenses}\\ \text{Expenses = \$36,000}\end{array}$

e) Calculate the assets for B:

$\begin{array}{c}\text{Turnover = }\frac{\text{Sales}}{\text{Average Operating Assets}}\\ 0.50=\frac{\$48,000}{\text{Average Operating Assets}}\\ \text{Average Operating Assets}=\frac{\$48,000}{0.50}\\ \text{Average Operating Assets}=\$96,000\end{array}$

f) Calculate the ROI for B:

$\begin{array}{c}\text{ROI = }\frac{\text{Operating}\text{Income}}{\text{Average}\text{TotalAssets}}\\ =\frac{\$12,000}{\$96,000}\\ =0.125\text{ or 12}\text{.5\%}\end{array}$

g) Calculate the operating income for C:

$\begin{array}{c}\text{Revenues}-\text{Expenses}\text{=}\text{Operating Income}\\ \text{\$96,000}-\text{\$90,000}\text{=}\text{Operating Income}\\ \text{Operating Income}=\$6,000\end{array}$

h) Calculate margin for C:

$\begin{array}{c}\text{Margin}\text{=}\frac{\text{Operating Income}}{\text{Sales}}\\ =\frac{\$6,000}{\$96,000}\\ =0.0625\text{or 6}\text{.25}\%\end{array}$

i) Calculate the turnover for C:

$\begin{array}{c}\text{Turnover = }\frac{\text{Sales}}{\text{Average Operating Assets}}\\ =\frac{\$96,000}{\$48,000}\\ =2\end{array}$

j) Calculate the ROI for C:

$\begin{array}{c}\text{ROI = }\frac{\text{Operating}\text{Income}}{\text{Average}\text{TotalAssets}}\\ =\frac{\$6,000}{\$48,000}\\ =0.125\text{ or 12}\text{.5\%}\end{array}$

k) Calculate the Revenue for D:

$\begin{array}{c}\text{Turnover = }\frac{\text{Sales}}{\text{Average Operating Assets}}\\ 2.00=\frac{\text{Sales }\left(\text{Revenue}\right)}{\$9,600}\\ \text{Sales }\left(\text{Revenue}\right)=2.00\times \$9,600\\ \text{Sales }\left(\text{Revenue}\right)=\$19,200\end{array}$

m) Compute the Operating income for D:

$\begin{array}{c}\text{Margin}\text{=}\frac{\text{Operating Income}}{\text{Sales}}\\ 6.25\%=\frac{\text{Operating Income}}{\$19,200}\\ \text{Operating Income}=6.25\%\times \$19,200\\ \text{Operating Income}=\$1,200\end{array}$

l) Compute the expenses for D:

$\begin{array}{c}\text{Revenues}-\text{Expenses}\text{=}\text{Operating Income}\\ \text{\$19,200}-\text{Expenses}\text{=}\text{\$1,200}\\ \text{\$19,200}-\text{\$1,200}\text{=}\text{Expenses}\\ \text{Expenses = \$18,000}\end{array}$

n) Compute the ROI for D:

$\begin{array}{c}\text{ROI = }\frac{\text{Operating}\text{Income}}{\text{Average}\text{TotalAssets}}\\ =\frac{\$1,200}{\$9,600}\\ =0.125\text{ or 12}\text{.5\%}\end{array}$

To determine

Calculate the residual income for each of the four firms.

Explanation of Solution

Residual income: It is an amount by which an operating income (earnings) exceeds a minimum acceptable return on the average capital invested.

$\text{Residual income}\text{=}\text{Operating earnings}\text{–}\left(\text{Minimum acceptable return}\times \text{Invested capital}\right)$

Residual income for Firm A:

$\begin{array}{c}\text{Residual income}\text{=}\text{Operating earnings}\text{–}\left(\text{Minimum acceptable return}\times \text{Invested capital}\right)\\ =\$2,000-\left(9\%\times \$40,000\right)\\ =\$2,000-\$3,600\\ =\left(\$1,600\right)\end{array}$

Therefore, residual income of Firm A is ($1,600).

Residual income for Firm B:

$\begin{array}{c}\text{Residual income}\text{=}\text{Operating earnings}\text{–}\left(\text{Minimum acceptable return}\times \text{Invested capital}\right)\\ =\$12,000-\left(9\%\times \$96,000\right)\\ =\$12,000-\$8,640\\ =\$3,360\end{array}$

Therefore, residual income of Firm B is $3,360.

Residual income for Firm C:

$\begin{array}{c}\text{Residual income}\text{=}\text{Operating earnings}\text{–}\left(\text{Minimum acceptable return}\times \text{Invested capital}\right)\\ =\$6,000-\left(9\%\times \$48,000\right)\\ =\$6,000-\$4,320\\ =\$1,680\end{array}$

Therefore, residual income of Firm C is $1,680.

Residual income for Firm D:

$\begin{array}{c}\text{Residual income}\text{=}\text{Operating earnings}\text{–}\left(\text{Minimum acceptable return}\times \text{Invested capital}\right)\\ =\$1,200-\left(9\%\times \$9,600\right)\\ =\$1,200-\$864\\ =\$336\end{array}$

Therefore, residual income of Firm D is $336.