BA 2802 – Principles of Finance

Solutions to Problems for Recitation 1

1. Use the following financial information to answer this question.

a. Using these financial statements, calculate all the ratios that you can for this
company in 2009 and 2010.

Ratios for 2009

Current Assets 620+340+1 , 360 2 ,320
= = =1. 1317
Current Ratio = Current Liabilities 1 ,250+800 2 , 050

Current Assets-Inventory 620+340 960

= = =0 . 4683
Quick Ratio = Current Liabilities 1 , 250+800 2 , 050

Cash 620 620

= = =0 .3024
Cash Ratio = Current Liabilities 1 , 250+800 2 ,050

Total Assets-Total Equity Total Liabilities 1 , 250+800+2 , 410

= =
Total Debt = T otal A sset s Total Assets 7 ,520
 4 , 460
=0 .5931
Total Debt = 7 , 520
Total Debt 4 , 460 4 , 460
= = =1. 4575
Debt to Equity = Total Equity 1, 200+1 , 860 3 , 060

Total Assets 7 ,520

= =2 . 4575
Equity Multiplier = Total Equity 3 , 060
Total Debt
1+ =1+1. 4575=2 . 4575
Equity Multiplier = Total Equity

Ratios for 2010

Current Assets 440+380+1 , 420 2 ,240
= = =1 . 009
Current Ratio = Current Liabilities 1 , 620+600 2 ,220

Current Assets-Inventory 440+380 820

= = =0 .3694
Quick Ratio = Current Liabilities 1 , 620+600 2 ,220

Cash 440 440

= = =0. 1982
Cash Ratio = Current Liabilities 1 , 620+600 2 ,220

Total Assets-Total Equity Total Liabilities 1 , 620+600+3 , 200

= =
Total Debt = T otal A sset s Total Assets 8 , 340

5 , 420
=0 . 65
Total Debt = 8 , 340

Total Debt 5, 420 5 , 420

= = =1.856
Debt to Equity = Total Equity 1, 500+1 , 420 2 , 920

Total Assets 8 ,340

= =2 . 856
Equity Multiplier = Total Equity 2 , 920

Total Debt
1+ =1+1. 856=2. 856
Equity Multiplier = Total Equity

EBIT 8 , 200−5 , 600−620 1, 980

= = =7 . 07
Times Interest Earned = Interest Expense 280 280

EBIT +Depreciation 1, 980+620 2 , 600

= = =9 . 2857
Cash Coverage = Interest Expense 280 280

Sales 8 , 200
= =0 . 9832
Total Asset Turnover = Total Assets 8 , 340
 Cost of Goods Sold 5 ,600
= =3. 9437
Inventory Turnover = Inventory 1 , 420

365 365
= =92. 5536
Days’ Sales in Inventory = Inventory Turnover 3 . 9437

Sales 8 , 200
= =21 .58
Receivable Turnover = Accounts Receivable 380

365 365
= =16 . 91
Days’ Sales in Receivables = Receivable Turnover 21 .58

Total Assets 1 8 , 340

= = =1. 017
Capital Intensity = Sales TAT 8 , 200

Net Income 1 ,220

= =0 .1488=14 . 88 %
Profit Margin = Sales 8 ,200

Net Income 1 ,220

= =0 .1463=14 . 63 %
Return on Assets = Total Assets 8 , 340

Net Income 1 , 220

= =0 . 4178=41 .78 %
Return on Equity = Total Equity 2 , 920

b. Prepare the DuPont decomposition of ROA and ROE for this company.
ROA = PM × TAT = 0.1488 × 0.9832 = 0.1463
ROE = PM × TAT × EM = 0.1488 × 0.9832 × 2.856 = 0.4178

c. Assume that the company distributes 40% of its net income as dividends to its
shareholders. Given this assumption, calculate the Internal and Sustainable Growth
Rates for this company.

Payout rate = 40%

Retention Rate = 1 – Payout Rate = 1 – 0.4 = 0.6 = 60%

ROA∗b 0 . 1463×0 . 6 0 . 08778

= = =9 .62 %
Internal Growth Rate = 1−ROA∗b 1−0 .1463×0 .6 1−0 .08778

ROE∗b 0 . 4178×0. 6 0 . 2507

= = =33 . 46 %
Sustainable Growth Rate = 1−ROE∗b 1−0. 4178×0 . 6 1−0 . 2507
2. a. ABC Company has total debt ratio of 0.6. Given this information, calculate the
Debt/Equity ratio of this firm.

Total Debt
Total Debt Ratio=
Total Assets

Total Equity
Total Equity Ratio=
Total Assets

From accounting identity:

Total Equity Total Debt

Total Equity Ratio+Total Debt Ratio= +
Total Assets Total Assets

Since Total Debt + Total Equity = Total Assets, we have,

Total Assets
Total Equity Ratio+Total Debt Ratio= =1
Total Assets

Then,
Total Equity Total Debt
=1− =1−0.60=0.40
Total Assets Total Assets

So,

Total Debt
Debt −Equity Ratio=
Total Equity

Now, divide both the numerator and the denominator of this ratio with total assets to
get:

Total Debt
Total Assets 0.6
Debt −Equity Ratio= = =1.5
Total Equity 0.4
Total Assets

b. A fire has destroyed a large percentage of the financial records of the Strongwell Co.
You have the task of piecing together information in order to release a financial
report. You have found the return on equity to be 13.8 percent. Sales were $979,000,
the total debt ratio was 0.42, and total debt was $548,000. Calculate the return on
assets for this firm.

Using the relations developed in part (a) of this question,

Total Equity Total Debt

=1− =1−0.42=0.58
Total Assets Total Assets

Total Assets
Equity Multiplier=
Total Equity
 1 1
Equity Multiplier= = =1.7241
Total Equity 0.58
Total Assets
ROA = PM × TAT
ROE = PM × TAT × EM
ROE 0.138
ROE = ROA × EM → ROA = = ≈8%
EM 1.7241

c. Global Ventures has a return on equity of 9.8 percent, a retention ratio of 60 percent,
and a profit margin of 4.5 percent. The company paid $378 in dividends and has net
working capital of $100. Net fixed assets are $18,550 and current liabilities are
$520. Calculate the total equity of the firm.

Dividend Per Share Total Dividends /Number of Shares

=
Payout Rate = Earnings Per Share Net Income /Number of Shares

Total Dividends Total Dividends 378

⇒ Net Income= =
Payout Rate = Net Income Payout Ratio 1−0 . 6

Net income = $945

Net Income 945 945

⇒ 0 .045= ⇒ Sales= =$ 21 , 000
Profit Margin = Sales Sales 0. 045

Net Working Capital = Current Assets – Current Liabilities

100 = Current Assets – 520
Current Assets = 510 + 100 = $620
Total Assets = Current Assets + Net Fixed Assets = 620 + 18,550
Total Assets = $19,170

21,000 19,170
ROE = PM × TAT × EM ¿ 0.045 × × =0.098
19,170 Total Equity

0.045 ×21.000
Total Equity= =$ 9,642.86
0.098
3. You have been working for just few days as an analyst in the credit department of a major
investment bank. You and your boss are working on analysis of financial statement of two local
companies, The ABC Inc., and The XYZ Corp. During lunch, your boss got into an argument with
the CEO and got fired. Now, it is your responsibility to finish the analysis of financial positions of
these two companies.

Income Statement, 2015 The ABC Inc. The XYZ Corp.

Sales 3,500,000 4,750,000
Cost of Goods Sold 2,800,000 3,610,000
Earnings Before Interest and Taxes (EBIT) 700,000 1,140,000
Interest Expense 77,700 94,800
Earnings Before Taxes (EBT) 622,300 1,045,200
Taxes 248,920 418,080
Net Income 373,380 627,120

Balance Sheet, 2015 The ABC Inc. The XYZ Corp.

Cash 210,000 285,000
Accounts Receivable 350,000 475,000
Inventory 700,000 1,140,000
Fixed Assets 1,000,000 1,600,000
Total 2,260,000 3,500,000

Accounts Payable 455,000 760,000

LT Debt 555,000 790,000
Stockholders’ Equity 1,250,000 1,950,000
Total 2,260,000 3,500,000

a. Compute the ratios your boss has been unable to compute before being fired.
The ABC Inc. The XYZ Corp.

Current Ratio 2.77 2.50

Quick Ratio ________ ________

Total Asset Turnover 1.55 1.36

Inventory Turnover ________ ________

Debt/Equity Ratio ________ 0.79

Times Interest Earned 9 ________

Profit Margin ________ ________

 Return on Equity 0.30 0.32

Cash + Accounts Receviable 210 , 000+350 , 000

= =1. 231
Quick RatioABC = Accounts Payable 455 , 000

Cash + Accounts Receviable 285 , 000+475 ,000

= =1 . 000
Quick RatioXYZ = Accounts Payable 760 , 000

Cost of Goods Sold 2 , 800 , 000

= =4 . 000
Inventory TurnoverABC = Inventory 700 , 000

Cost of Goods Sold 3 , 610 , 000

= =3 . 167
Inventory TurnoverXYZ = Inventory 1, 140 , 000
Total Debt 455 , 000+555 , 000
= =0 . 808
Debt to EquityABC = Total Equity 1 , 250 , 000

EBIT 1,140 , 000

= =12. 03
Times Interest EarnedXYZ = Interest Expense 94, 800
Net Income 373 , 380
= =10 . 67 %
Profit MarginABC = Sales 3 ,500 , 000
Net Income 627 , 120
= =13 . 20 %
Profit MarginXYZ = Sales 4 , 750 , 000

b. Comment on the difference between the return on equity of these two firms. Indicate one
area which might be a potential problem for each firm and briefly discuss why you consider
it as a potential problem.

ROE = PM × TAT × EM
ROE = PM x TAT x (1+Debt to Equity Ratio)

ROEABC=0.1067*1.55*1.808 = 0.2990 = 29.90%

ROEXYZ=0.1320*1.36*1.79 = 0.3213 = 32.13%

XYZ has higher Profit Margin, better at turning their sales into profits.
ABC has higher Total Asset Turnover, manage their assets efficiently.
Problem Area: ABC has higher Equity Multiplier. Therefore it has higher leverage and it
is riskier than XYZ.
Problem Area: XYZ has lower TAT than ABC. It is not managing its assets as
efficiently as ABC.

c. Calculate how much the ABC company can grow the next year by using the
retained earnings and borrowing while keeping its debt ratio constant if the ABC
company distributes $210,000 worth dividends.

Payout rate = 210,000/373,380 = 56.24%

Retention Rate = 1 – Payout Rate = 1 – 0.5624 = 0.4376

 ROE∗b 0 .30×0 . 4376 0 . 1313
= = =15. 12 %
Sustainable Growth Rate = 1−ROE∗b 1−0. 30×0 . 4376 1−0 .1313
d. Calculate how much the XYZ company can grow the next year by using only the
retained earnings if the company keeps 50% of its net income as retained earnings.

Retention Rate = 0.50

Net Income 627 , 120

= =0. 1792=17 .92 %
Return on Assets = Total Assets 3 ,500 ,000

ROA∗b 0 . 1792×0 .5 0 .0896

= = =9. 84 %
Internal Growth Rate = 1−ROA∗b 1−0 .1792×0 .5 1−0 . 0896