Long-term debt ratio
= Long-term debt / (Long-term debt + Total equity)
Long-term debt ratio 2008
= $25,000 / ($25,000 + 208,998) = 0.11
Long-term debt ratio 2009
= $32,000 / ($32,000 + 228,316) = 0.12
Intermediate
18.
This is a multi-step problem involving several ratios. The ratios given are all part of the DuPont
Identity. The only DuPont Identity ratio not given is the profit margin. If we know the profit margin,
we can find the net income since sales are given.
So, we begin with the DuPont Identity:
ROE = 0.15 = (PM)(TAT)(EM) = (PM)(S / TA)(1 + D/E)
Solving the DuPont Identity for profit margin, we get:
PM = [(ROE)(TA)] / [(1 + D/E)(S)]
PM = [(0.15)($3,105)] / [(1 + 1.4)( $5,726)] = .0339
Now that we have the profit margin, we can use this number and the given sales figure to solve for
net income:
PM = .0339 = NI / S
NI = .0339($5,726) = $194.06

B-24
SOLUTIONS
19.
This is a multi-step problem involving several ratios. It is often easier to look backward to determine
where to start. We need receivables turnover to find days’ sales in receivables. To calculate
receivables turnover, we need credit sales, and to find credit sales, we need total sales. Since we are
given the profit margin and net income, we can use these to calculate total sales as:
PM = 0.087 = NI / Sales = $218,000 / Sales; Sales = $2,505,747
Credit sales are 70 percent of total sales, so:
Credit sales = $2,515,747(0.70) = $1,754,023
Now we can find receivables turnover by:
Receivables turnover = Credit sales / Accounts receivable = $1,754,023 / $132,850 = 13.20 times
Days’ sales in receivables = 365 days / Receivables turnover = 365 / 13.20 = 27.65 days
20.
The solution to this problem requires a number of steps. First, remember that CA + NFA = TA. So,
if we find the CA and the TA, we can solve for NFA. Using the numbers given for the current ratio
and the current liabilities, we solve for CA:
CR = CA / CL
CA = CR(CL) = 1.25($875) = $1,093.75
To find the total assets, we must first find the total debt and equity from the information given. So,
we find the sales using the profit margin:
PM = NI / Sales
NI = PM(Sales) = .095($5,870) = $549.10
We now use the net income figure as an input into ROE to find the total equity:
ROE = NI / TE
TE = NI / ROE = $549.10 / .185 = $2,968.11
Next, we need to find the long-term debt. The long-term debt ratio is:
Long-term debt ratio = 0.45 = LTD / (LTD + TE)
Inverting both sides gives:
1 / 0.45 = (LTD + TE) / LTD = 1 + (TE / LTD)
Substituting the total equity into the equation and solving for long-term debt gives the following:
2.222 = 1 + ($2,968.11 / LTD)
LTD = $2,968.11 / 1.222 = $2,428.45

CHAPTER 3
B-25
Now, we can find the total debt of the company:
TD = CL + LTD = $875 + 2,428.45 = $3,303.45
And, with the total debt, we can find the TD&E, which is equal to TA:
TA = TD + TE = $3,303.45 + 2,968.11 = $6,271.56
And finally, we are ready to solve the balance sheet identity as:
NFA = TA – CA = $6,271.56 – 1,093.75 = $5,177.81
21.
Child:
Profit margin = NI / S = $3.00 / $50
= .06 or 6%
Store:
Profit margin = NI / S = $22,500,000 / $750,000,000
= .03 or 3%
The advertisement is referring to the store’s profit margin, but a more appropriate earnings measure
for the firm’s owners is the return on equity.
ROE = NI / TE = NI / (TA – TD)
ROE = $22,500,000 / ($420,000,000 – 280,000,000) = .1607 or 16.07%
22.
The solution requires substituting two ratios into a third ratio. Rearranging D/TA:
Firm A
Firm B
D / TA = .35
D / TA = .30
(TA – E) / TA = .35
(TA – E) / TA = .30
(TA / TA) – (E / TA) = .35
(TA / TA) – (E / TA) = .30
1 – (E / TA) = .35
1 – (E / TA) = .30
E / TA = .65
E / TA = .30
E = .65(TA)
E = .70 (TA)
Rearranging ROA, we find:
NI / TA = .12
NI / TA = .11
NI = .12(TA)
NI = .11(TA)

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