Chapter 3
Analysis of Financial Statements
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
3-1
DSO = 40 days; S = $7,300,000; AR = ?
AR
S
365
DSO =
AR
$7,300,000/365
40 = AR/$20,000
AR = $800,000.
40 =
3-2
A/E = 2.4; D/A = ?



D
1
= 1 - 
A
A



E
D
1 
= 1 

A
2.4
D
.
= 0.5833 = 58.33%.
A
3-3
3-4
ROA = 10%; PM = 2%; ROE = 15%; S/TA = ?; TA/E = ?
ROA = NI/A; PM = NI/S; ROE = NI/E.
ROA
NI/A
10%
S/TA
=
=
=
=
PM  S/TA
NI/S  S/TA
2%  S/TA
5.
ROE
NI/E
15%
15%
TA/E
=
=
=
=
=
PM  S/TA  TA/E
NI/S  S/TA  TA/E
2%  5  TA/E
10%  TA/E
1.5.
TA = $10,000,000,000; CL = $1,000,000,000; LT debt = $3,000,000,000; CE =
$6,000,000,000; Shares outstanding = 800,000,000; P0 = $32; M/B = ?
3-1
Book value =
M/B =
3-5
$6,000,000,000
= $7.50.
800,000,000
$32.00
= 4.2667.
$7.50
TA = $12,000,000,000; T = 40%; EBIT/TA = 15%; ROA = 5%; TIE = ?
EBIT
= 0.15
$12,000,000,000
EBIT = $1,800,000,000.
NI
= 0.05
$12,000,000,000
NI = $600,000,000.
Now use the income statement format to determine interest so you can
calculate the firm’s TIE ratio.
EBIT
$1,800,000,000 See above. INT = EBIT – EBT
= $1,800,000,000 - $1,000,000,000
INT
800,000,000
EBT
$1,000,000,000 EBT = $600,000,000/0.6
Taxes (40%)
400,000,000
NI
$ 600,000,000 See above.
TIE = EBIT/INT
= $1,800,000,000/$800,000,000
= 2.25.
3-6
We are given ROA = 3% and Sales/Total assets = 1.5.
ROA = Profit margin  Total assets turnover
3% = Profit margin(1.5)
Profit margin = 3%/1.5 = 2%.
From Du Pont equation:
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:
E
A
E
A
E
A
D
A
3-2
NI
E
D
E

and
= 1 , so
A
NI
A
A
1
= 3% 
0.05
=
= 60% .
= 1 - 0.60 = 0.40 = 40% .
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%.
3-7
Present current ratio =
$1,312,500
= 2.5.
$525,000
Minimum current ratio =
$1,312,500 + NP
= 2.0.
$525,000 + NP
$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, assuming that 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.
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
TA = $30,000,000,000; EBIT/TA = 20%; TIE = 8; DA = $3,200,000,000; Lease
payments = $2,000,000,000; Principal payments = $1,000,000,000; EBITDA
coverage = ?
EBIT/$30,000,000,000 = 0.2
EBIT = $6,000,000,000.
3-3
8 = EBIT/INT
8 = $6,000,000,000/INT
INT = $750,000,000.
EBITDA = EBIT + DA
= $6,000,000,000 + $3,200,000,000
= $9,200,000,000.
EBITDA  Lease payments
INT  Princ. pmts  Lease pmts
$9,200,000,000  $2,000,000,000
=
$750,000,000  $1,000,000,000  $2,000,000,000
$11,200,000,000
=
= 2.9867.
$3,750,000,000
EBITDA coverage ratio =
3-10
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)
- Cost
EBIT (given)
- INT (given)
EBT
- Taxes (34%)
NI
$10,000,000
na
$ 1,000,000
300,000
$
700,000
238,000
$
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%.
3-4
3-11
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.
EBIT
Interest
EBT
Tax (40%)
NI
D/A = 0%
$200,000
0
$200,000
80,000
$120,000
D/A = 50%
$200,000
40,000*
$160,000
64,000
$ 96,000
NI
$120,000
$96,000
=
= 12%
= 19.2%
Equity
$1,000,000
$500,000
Difference in ROE = 19.2% - 12.0% = 7.2%.
ROE =
*If D/A = 50%, then half of the assets are financed by debt, so Debt =
$500,000. At an 8 percent interest rate, INT = $40,000.
3-12
Statement a is correct. Refer to the solution setup for Problem 3-11 and
think about it this way: (1) Adding assets will not affect common equity
if the assets are financed with debt.
(2) Adding assets will cause
expected EBIT to increase by the amount EBIT = BEP(added assets). (3)
Interest expense will increase by the amount kd(added assets). (4) Pre-tax
income will rise by the amount (added assets)(BEP - kd). Assuming BEP >
kd, if pre-tax income increases so will net income. (5) If expected net
income increases but common equity is held constant, then the expected ROE
will also increase. Note that if kd > BEP, then adding assets financed by
debt would lower net income and thus the ROE. Therefore, Statement a is
true--if assets financed by debt are added, and if the expected BEP on
those assets exceeds the cost of debt, then the firm’s ROE will increase.
Statements b, c, and d are false, because the BEP ratio uses EBIT,
which is calculated before the effects of taxes or interest charges are
felt. Of course, Statement e is also false.
3-13
a. Currently, ROE is ROE1 = $15,000/$200,000 = 7.5%.
The current ratio will be set such that 2.5 = CA/CL. CL is $50,000,
and it will not change, so we can solve to find the new level of
current assets: CA = 2.5(CL) = 2.5($50,000) = $125,000. This is the
level of current assets that will produce a current ratio of 2.5.
At present, current assets amount to $210,000, so they can be
reduced by $210,000 - $125,000 = $85,000. If the $85,000 generated is
used to retire common equity, then the new common equity balance will
be $200,000 - $85,000 = $115,000.
Assuming that net income is unchanged, the new ROE will be ROE2 =
$15,000/$115,000 = 13.04%. Therefore, ROE will increase by 13.04% 7.50% = 5.54%.
b. 1. Doubling the dollar amounts would not affect the answer; it would
still be 5.54%.
3-5
2. Common equity would increase by $25,000 from the Part a scenario,
which would mean a new ROE of $15,000/$140,000 = 10.71%, which would
mean a difference of 10.71% - 7.50% = 3.21%.
3. An inventory turnover of 2 would mean inventories of $100,000, down
$50,000 from the current level.
That would mean an ROE of
$15,000/$150,000 = 10.00%, so the change in ROE would be 10.00% 7.5% = 2.5%.
4. If the company had 10,000 shares outstanding, then its EPS would be
$15,000/10,000 = $1.50. The stock has a book value of $200,000/10,000
= $20, so the shares retired would be $85,000/$20 = 4,250, leaving
10,000 - 4,250 = 5,750 shares. The new EPS would be $15,000/5,750 =
$2.6087, so the increase in EPS would be $2.6087 - $1.50 = $1.1087,
which is a 73.91 percent increase, the same as the increase in ROE.
5. If the stock was selling for twice book value, or 2  $20 = $40,
then only half as many shares could be retired ($85,000/$40 =
2,125), so the remaining shares would be 10,000 - 2,125 = 7,875, and
the new EPS would be $15,000/7,875 = $1.9048, for an increase of
$1.9048 - $1.5000 = $0.4048.
c. We could have started with lower inventory and higher accounts
receivable, then had you calculate the DSO, then move to a lower DSO
that would require a reduction in receivables, and then determine the
effects on ROE and EPS under different conditions. Similarly, we could
have focused on fixed assets and the FA turnover ratio. In any of
these cases, we could have had you use the funds generated to retire
debt, which would have lowered interest charges and consequently
increased net income and EPS.
If we had to increase assets, then we would have had to finance this
increase by adding either debt or equity, which would have lowered ROE
and EPS, other things held constant.
Finally, note that we could have asked some conceptual questions
about the problem, either as a part of the problem or without any
reference to the problem.
For example, “If funds are generated by
reducing assets, and if those funds are used to retire common stock,
will EPS and/or ROE be affected by whether or not the stock sells
above, at, or below book value?”
3-14
TA = $7,500,000,000; EBIT/TA = 10%; TIE = 2.5; DA = $1,250,000,000; Lease
payments = $775,000,000; Principal payments = $500,000,000; EBITDA coverage = ?
EBIT/$7,500,000,000 = 0.10
EBIT = $750,000,000.
2.5 = EBIT/INT
2.5 = $750,000,000/INT
INT = $300,000,000.
3-6
EBITDA = EBIT + DA
= $750,000,000 + $1,250,000,000
= $2,000,000,000.
EBITDA  Lease payments
INT  Princ. pmts  Lease pmts
$2,000,000,000  $775,000,000
=
$300,000,000  $500,000,000  $775,000,000
$2,775,000,000
=
= 1.7619  1.76.
$1,575,000,000
EBITDA coverage ratio =
3-15
TA = $5,000,000,000; T = 40%; EBIT/TA = 10%; ROA = 5%; TIE ?
EBIT
 0.10
$5,000,000,000
EBIT  $500,000,000.
NI
 0.05
$5,000,000,000
NI  $250,000,000.
Now use the income statement format to determine interest so you can
calculate the firm’s TIE ratio.
EBIT
$500,000,000
INT
83,333,333
EBT
$416,666,667
Taxes (40%) 166,666,667
NI
$250,000,000
See above.
INT = EBIT – EBT
= $500,000,000 - $416,666,667
EBT = $250,000,000/0.6
See above.
TIE = EBIT/INT
= $500,000,000/$83,333,333
= 6.0.
3-16
Total market value = $3,750,000,000(1.9) = $7,125,000,000.
Market value per share = $7,125,000,000/50,000,000 = $142.50.
Alternative solution:
Book value per share = $3,750,000,000/50,000,000 = $75.
Market value per share = $75(1.9) = $142.50.
3-17
Step 1:
Solve for
55 =
55Sales =
Sales =
current annual sales using the DSO equation:
$750,000/(Sales/365)
$273,750,000
$4,977,272.73.
3-7
Step 2:
If sales fall by 15%, the new sales level will be
$4,977,272.73(0.85) = $4,230,681.82.
Again, using the DSO
equation, solve for the new accounts receivable figure as follows:
35 = AR/($4,230,681.82/365)
35 = AR/$11,590.91
AR = $405,681.82  $405,682.
3-18
The current EPS is $2,000,000/500,000 shares or $4.00. The current P/E ratio
is then $40/$4 = 10.00.
The new number of shares outstanding will be
650,000. Thus, the new EPS = $3,250,000/650,000 = $5.00. If the shares are
selling for 10 times EPS, then they must be selling for $5.00(10) = $50.
3-19
Step 1:
Calculate total assets from information given.
Sales = $6 million.
3.2 = Sales/TA
$6,000,000
3.2 =
Assets
Assets = $1,875,000.
Step 2:
Calculate net income.
There is 50% debt and 50% equity, so Equity = $1,875,000  0.5 =
$937,500.
ROE = NI/S  S/TA  TA/E
0.12 = NI/$6,000,000  3.2  $1,875,000/$937,500
6.4NI
0.12 =
$6,000,000
$720,000 = 6.4NI
$112,500 = NI.
3-20
Given ROA = 8% and net income of $600,000, total assets must be $7,500,000.
NI
TA
$600,000
8% =
TA
TA = $7,500,000.
ROA =
To calculate BEP, we still need EBIT.
income statement:
EBIT
Interest
EBT
Taxes (35%)
NI
3-8
$1,148,077
225,000
$ 923,077
323,077
$ 600,000
To calculate EBIT construct a partial
($225,000 + $923,077)
(Given)
$600,000/0.65
EBIT
TA
$1,148,077
=
$7,500,000
= 0.1531 = 15.31%.
BEP =
3-21
1. Debt = (0.50)(Total assets) = (0.50)($300,000) = $150,000.
2. Accounts payable = Debt – Long-term debt = $150,000 - $60,000
= $90,000.
3. Common stock =
Total liabilities
- Debt - Retained earnings
and equity
= $300,000 - $150,000 - $97,500 = $52,500.
4. Sales = (1.5)(Total assets) = (1.5)($300,000) = $450,000.
5. Inventories = Sales/5 = $450,000/5 = $90,000.
6. Accounts receivable = (Sales/365)(DSO) = ($450,000/365)(36.5)
= $45,000.
7. Cash + Accounts receivable + Inventories
Cash + $45,000 + $90,000
Cash + $135,000
Cash
=
=
=
=
(1.8)(Accounts payable)
(1.8)($90,000)
$162,000
$27,000.
8. Fixed assets = Total assets - (Cash + Accts rec. + Inventories)
Fixed assets = $300,000 - ($27,000 + $45,000 + $90,000)
Fixed assets = $138,000.
9. Cost of goods sold = (Sales)(1 - 0.25) = ($450,000)(0.75) = $337,500.
3-9
3-22
a. (Dollar amounts in thousands.)
Firm
DSO =
Industry
Average
Current assets
Current liabilities
=
$655,000
$330,000
=
1.98
Accounts receivable
Sales/365
=
$336,000
$4,404.11
=
76.3 days
Sales
Inventories
=
$1,607,500
$241,500
=
6.66
6.7
Sales
Total assets
=
$1,607,500
=
$947,500
1.70
3.0
Net income
Sales
=
$27,300
=
$1,607,500
1.7%
1.2%
Net income
Total assets
=
$27,300
$947,500
=
2.9%
3.6%
Net income
Common equity
=
$27,300
$361,000
=
7.6%
9.0%
Total debt
Total assets
=
$586,500
$947,500
=
61.9%
60.0%
2.0
35 days
b. For the firm,
ROE = PM  T.A. turnover  EM = 1.7%  1.7 
$947,500
= 7.6%.
$361,000
For the industry, ROE = 1.2%  3  2.5 = 9%.
Note: To find the industry ratio of assets to common equity, recognize
that 1 - (total debt/total assets) = common equity/total assets. So,
common equity/total assets = 40%, and 1/0.40 = 2.5 = total
assets/common equity.
c. The firm’s days sales outstanding is more than twice as long as the
industry average, indicating that the firm should tighten credit or
enforce a more stringent collection policy. The total assets turnover
ratio is well below the industry average so sales should be increased,
assets decreased, or both. While the company’s profit margin is higher
than the industry average, its other profitability ratios are low compared
to the industry--net income should be higher given the amount of equity
and assets. However, the company seems to be in an average liquidity
position and financial leverage is similar to others in the industry.
3 - 10
d. If 2002 represents a period of supernormal growth for the firm, ratios
based on this year will be distorted and a comparison between them and
industry averages will have little meaning. Potential investors who
look only at 2002 ratios will be misled, and a return to normal
conditions in 2003 could hurt the firm’s stock price.
3-23
a.
Firm
Current ratio
=
Debt to
total assets
=
Times interest
=
earned
Current assets
=
Current liabilities
Industry
Average
$303
$111
=
2.73
2
Debt
Total assets
=
$135
$450
=
30.00%
30.00%
EBIT
Interest
=
$49.5
$4.5
=
11
7
$61.5
$6.5
=
9.46
9
$795
$159
=
5
10
EBITDA
coverage
=
EBITDA  Lease pymts
=
Princ. Lease
INT  pymts  pymts
Inventory
turnover
=
Sales
Inventories
=
Accounts receivable
$66
=
Sales/365
$795/365
DSO
=
F.A.
Turnover
=
Sales
Net fixed assets
=
$795
$147
=
5.41
6
T.A.
Turnover
=
Sales
Total assets
=
$795
$450
=
1.77
3
Net income
Sales
=
$27
$795
=
3.40%
3.00%
Net income
Total assets
=
$27
$450
=
6.00%
9.00%
= 6%  1.4286 =
8.57%
12.90%
Profit margin =
Return on
total assets =
Return on
common equity =
ROA  EM
= 30.3 days 24 days
Alternatively,
ROE =
Net income
$27
=
= 8.57%  8.6%.
Equity
$315
3 - 11
b. ROE = Profit margin  Total assets turnover  Equity multiplier
=
Total assets
Net income
Sales


Common equity
Sales
Total assets
=
$27
$795
$450


= 3.4%  1.77  1.4286 = 8.6%.
$795
$450
$315
Profit margin
Total assets turnover
Equity multiplier
Firm
3.4%
1.77
1.4286
Industry
3.0%
3.0
1.43*
Comment
Good
Poor
O.K.
D
E
=
TA
TA
1 – 0.30 = 0.7
TA
1
EM =
=
= 1.43.
0.7
E
* 1 -
Alternatively, EM = ROE/ROA = 12.9%/9% = 1.43.
c. Analysis of the Du Pont equation and the set of ratios shows that the
turnover ratio of sales to assets is quite low. Either sales should be
increased at the present level of assets, or the current level of
assets should be decreased to be more in line with current sales.
d. The comparison of inventory turnover ratios shows that other firms in
the industry seem to be getting along with about half as much inventory
per unit of sales as the firm. If the company’s inventory could be
reduced, this would generate funds that could be used to retire debt,
thus reducing interest charges and improving profits, and strengthening
the debt position. There might also be some excess investment in fixed
assets, perhaps indicative of excess capacity, as shown by a slightly
lower-than-average fixed assets turnover ratio. However, this is not
nearly as clear-cut as the overinvestment in inventory.
e. If the firm had a sharp seasonal sales pattern, or if it grew rapidly
during the year, many ratios might be distorted.
Ratios involving
cash, receivables, inventories, and current liabilities, as well as
those based on sales, profits, and common equity, could be biased. It
is possible to correct for such problems by using average rather than
end-of-period figures.
3 - 12
3-24
a. Here are the firm’s base case ratios and other data as compared to the
industry:
Current
Inventory turnover
Days sales outstanding
Fixed assets turnover
Total assets turnover
Return on assets
Return on equity
Debt ratio
Profit margin on sales
EPS
Stock Price
P/E ratio
P/CF ratio
M/B ratio
Firm
2.3
4.8
37.4 days
10.0
2.3
5.9%
13.1
54.8
2.5
$4.71
$23.57
5.0
2.0
0.65
Industry
2.7
7.0
32.0 days
13.0
2.6
9.1%
18.2
50.0
3.5
n.a.
n.a.
6.0
3.5
n.a.
Comment
Weak
Poor
Poor
Poor
Poor
Bad
Bad
High
Bad
--Poor
Poor
--
The firm appears to be badly managed--all of its ratios are worse than the
industry averages, and the result is low earnings, a low P/E, a low stock
price, and a low M/B ratio. The company needs to do something to improve.
b. A decrease in the inventory level would improve the inventory turnover,
total assets turnover, and ROA, all of which are too low. It would have
some impact on the current ratio, but it is difficult to say precisely how
that ratio would be affected. If the lower inventory level allowed the
company to reduce its current liabilities, then the current ratio would
improve.
The lower cost of goods sold would improve all of the
profitability ratios and, if dividends were not increased, would lower the
debt ratio through increased retained earnings. All of this should lead
to a higher market/book ratio, a higher stock price, a higher
price/earnings ratio, and a higher price/cash flow ratio.
3 - 13