Torrid Romance Publishers has total receivables of $3,120, which represents 20 days’ sales. Total assets are $94,900. The firm’s operating profit margin is 5.5%. Find the firm's ROA and asset turnover ratio.

A firm has a debt-to-equity ratio of .84 and a market-to-book ratio of 3.0. What is the ratio of the book value of debt to the market value of equity?
 
Explanation

Book debt / Book equity × [1 / (Market equity / Book equity)] = Book debt / Market equity
.84 × (1 / 3) = .28


Torrid Romance Publishers has total receivables of $3,120, which represents 20 days’ sales. Total assets are $94,900. The firm’s operating profit margin is 5.5%. Find the firm's ROA and asset turnover ratio.
 

Explanation

Total sales = $3,120 × 365 / 20 = $56,940
Asset turnover ratio = $56,940 / $94,900 = .60
ROA = Asset turnover × Operating profit margin = .60 × .06 = .0330, or 3.30%

Keller Cosmetics maintains an operating profit margin of 8% and asset turnover ratio of 2.

a. What is its ROA?
 
 b. If its debt-equity ratio is 1, its interest payments and taxes are each $8,700, and EBIT is $23,500, what is its ROE?

 
Explanation
a.
ROA = Asset turnover × Operating profit margin = 2 × .08 = .1600, or 16%

b.
If Debt / Equity = 1, then Debt = Equity, so total assets are twice equity.

Net income = EBIT – Interest – Taxes = $23,500 – 8,700 – 8,700 = $6,100

ROE =	Assets	× ROA ×	Net income
	Equity		After-tax operating income

Tax rate =	Taxes	=	$8,700	= .5878, or 59%
	EBT		$23,500 – 8,700

ROE =	2	× ROA ×	$6,100	= .2015, or 20%
	1		$6,100 + 8,700 × (1 – .59)