Question

1. Consider the data for each of the following four independent companies. Calculate the missing values in the table below. For margin and ROI, enter your answers as percentages, rounded to two decimal places. For example, the decimal value .03827 would be entered as "3.83" percent. For turnover, enter your answer as a decimal value rounded to two decimal places.

	A		B		C		D
Revenue	$10,000		$49,000		$96,000		$
Expenses	$8,000		$		$90,240		$
Operating income	$2,000		$12,250		$		$
Assets	$40,000		$		$48,000		$9,800
Margin		%	25	%		%	6.00	%
Turnover			0.50				2.00
ROI		%		%		%		%

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. If the residual income is negative, enter a negative amount.

A's residual income	$
B's residual income	$
C's residual income	$
D's residual income	$

Answer 1

Solution

	A	B	C	D
Revenue	$10,000	$49,000	$96,000	$19,600
Expenses	$8,000	$36,750	$90,240	$18,424
Operating Income	$2,000	$12,250	$5,760	$1,176
Assets	$40,000	$98,000	$48,000	$9,800
Margin	20%	25%	6%	6%
Turnover	2.5	0.50	2	2
ROI	50%	12.50%	12%	12%

Residual Income –

	A	B	C	D
Residual Income	($1,600)	$3,430	$1,440	$294

Computation of missing values and residual incomes for A, B, C and D:

Missing Values for A –

Margin = operating income/revenue

= ($2,000/$10,000) x 100 = 20%

Turnover = sales revenue/assets

= 10,000/40,000 = 2.5

ROI = margin x turnover

= 20% x 2.5 = 50%

-Residual Income

Cost of capital = 9%

Return on assets = 40,000 x 9% = $3,600

Residual income = operating income – minimum return

= $2,000 - $3,600 = ($1,600)

Missing Values for B –

Expenses = revenue – operating income

= 49,000 – 12,250 = $36,750

Assets –

Given turnover = 0.50

Turnover = revenue/assets

0.50 = 49,000/assets

Assets = 49,000/0.50

Assets = $98,000

ROI = margin x turnover

Margin = 25%

ROI = 25% x 0.50 = 12.5%

Residual Income -
return on assets = 98,000 x 9% = $8,820

Residual income = 12,250 – 8,820 = $3,430

Missing Values for C –

Operating income = revenues – expenses

Operating income = 96,000 – 90,240 = $5,760

Margin = (5,760/96,000) x 100 = 6%

Turnover = 96,000/48,000 = 2 times

ROI = 6% x 2 = 12%

Residual Income –

Return on assets = 48,000 x9% = $4,320

Residual income = 5,760 – 4,320 = $1,440

Missing Values for D –

Revenue ?

Turnover = 2

Assets = $9,800

2 = Revenue/9,800

Revenue = 2 x 9,800 = $19,600

Operating income –

Margin = 6%

Margin = operating income/revenue

6% = income/19,600

Operating income = 19,600 x 6% = $1,176

Expenses = revenue – operating income

= 19,600 – 1,176 = $18,424

ROI = margin x turnover

= 6% x 2 = 12%

Residual income –

Minimum return on assets = 9,800 x 9% = $882

Residual income = 1,176 – 882 = $294