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Chapter 3

SOLUTIONS TO END-OF-CHAPTER PROBLEMS

3-1 CA = $3,000,000; [pic] = 1.5; [pic] = 1.0;

CL = ?; I = ?

[pic]

[pic]

3-2 DSO = 40 days; S = $7,300,000; AR = ?

[pic]

3-3 A/E = 2.4; D/A = ?

[pic]
3-4 ROA = 10%; PM = 2%; ROE = 15%; S/TA = ?; A/E = ?
ROA = NI/A; PM = NI/S; ROE = NI/E

ROA = PM ( S/TA
NI/A = NI/S ( S/TA10% = 2% ( S/TA
S/TA = 5.

ROE = PM ( S/TA ( TA/E
NI/E = NI/S ( S/TA ( TA/E
15% = 2% ( 5 ( TA/E
15% = 10% ( TA/E
TA/E = 1.5.

3-5 We are given ROA = 3% and Sales/Total assets = 1.5(.

From Du Pont equation: ROA = Profit margin ( Total assets turnover
3% = Profit margin(1.5)
Profit margin =3%/1.5 = 2%.

We can also calculate the company’s debt ratio in a similar manner, given the facts of the problem. We are given ROA(NI/A) and ROE(NI/E); if we use the reciprocal of ROE we have the following equation:

[pic]
Alternatively,

ROE = ROA ( EM
5% = 3% ( EM
EM = 5%/3% = 5/3 = TA/E.

Take reciprocal:

E/TA = 3/5 = 60%;therefore,

D/A = 1 - 0.60 = 0.40 = 40%.

Thus, the firm’s profit margin = 2% and its debt ratio = 40%.

3-6 Present current ratio = [pic] = 2.5.

Minimum current ratio = [pic] = 2.0.

$1,312,500 + (NP = $1,050,000 + 2(NP
(NP = $262,500.

Short-term debt can increase by a maximum of $262,500 without violating a 2 to 1 current ratio, assumingthat the entire increase in notes payable is used to increase current assets. Since we assumed that the additional funds would be used to increase inventory, the inventory account will increase to $637,500, and current assets will total $1,575,000.

Quick ratio = ($1,575,000 - $637,500)/$787,500 = $937,500/$787,500 = 1.19(.

3-7 1. [pic] = 3.0(
[pic] = 3.0(
Current liabilities= $270,000.

2. [pic] = 1.4(
[pic] = 1.4(
Inventories = $432,000.

3. Current assets = Cash + [pic] + [pic] + Inventories
$810,000 = $120,000 + Accounts receivable + $432,000
Accounts receivable = $258,000.

4. [pic] = 6.0(
[pic] = 6.0(
Sales = $2,592,000.

5. DSO = [pic] = [pic] = 36.33 days ( 36days.

3-8 TIE = EBIT/INT, so find EBIT and INT.
Interest = $500,000 ( 0.1 = $50,000.

Net income = $2,000,000 ( 0.05 = $100,000.
Pre-tax income (EBT) = $100,000/(1 - T) = $100,000/0.7 = $142,857.
EBIT = EBT + Interest = $142,857 + $50,000 = $192,857.

TIE = $192,857/$50,000 = 3.86(.

3-9 ROE = Profit margin ( TA turnover ( Equity multiplier
=NI/Sales ( Sales/TA ( TA/Equity.
Now we need to determine the inputs for the equation from the data that were given. On the left we set up an income statement, and we put numbers in it on the right:

Sales (given) $10,000,000
- Cost na
EBIT (given) $ 1,000,000
- INT(given) 300,000
EBT $ 700,000
- Taxes (34%) 238,000
NI $ 462,000

Now we can use some ratios to get some more data:
Total assets turnover = 2 = S/TA; TA = S/2 = $10,000,000/2 = $5,000,000.

D/A = 60%; so E/A = 40%; and,therefore,
Equity multiplier = TA/E = 1/(E/A) = 1/0.4 = 2.5.

Now we can complete the Du Pont equation to determine ROE:
ROE = $462,000/$10,000,000 ( $10,000,000/$5,000,000 ( 2.5 = 0.231 = 23.1%.

3-10 Known data:

TA = $1,000,000; kd = 8%; T = 40%
BEP = 0.2 = EBIT/Total assets, so EBIT = 0.2($1,000,000) = $200,000;
D/A = 0.5 = 50%, so Equity = $500,000....
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