Question

company has the following operating data for the past 2 years:

	Year 1	Year 2
Residual Income	$600	?
Return on Investment	10%	87.5%
Required Rate of return	8%	9%
Average operating assets	?	$42,000

Sales in year 1 is $70,000 less than sales in year 2.

The Company had the same capital turnover in both years.

Q.) What is the sales margin in Year 2

Answer 1

Year 1:

Residual Income = Average Operating Assets * (Return on Investment - Required Rate of Return)

$600 = Average Operating Assets * (10% - 8%)

Average Operating Assets = $600 / 2%

Average Operating Assets = $30,000

Net Profit = Average Operating Assets * Return on Investment

= $30,000 * 10% i.e. $3,000

Year 2:

Residual Income = Average Operating Assets * (Return on Investment - Required Rate of Return)

Residual Income = $42,000 * (9% - 8.75%)

Residual Income = $105

Net Profit = Average Operating Assets * Return on Investment

= $42,000 * 8.75% i.e. $3,675

Combined Analysis:

Let Sales in Year 1 be X

It is provided that capital turnover is same in both years, i.e.

X / $30,000 = (X + $70,000) / $42,000

(X * $42,000) / $30,000 = X + $70,000

$1.4 * X = X + $70,000

X = $70,000 / 0.4

X = $175,000

Sales Margin in Year 2 = Net Profit / Sales

= $3,675 / ($175,000 + $70,000)

= 1.5%

(It is assumed that return on Investment in Year 2 is 8.75% instead of 87.5% as return on Invest @ 87.5% is very unreasonable. Moreover, it is assumed that all the assets of the firm are financed by Equity i.e. No debt firm.)

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