20. The solution to this problem requires a number of steps. First, remember that Current assets + Net
Current ratio = Current assets/Current liabilities
To find the total assets, we must first find the total debt and equity from the information given. So,
we find the net income using the profit margin:
Profit margin = Net income/Sales
Net income = Profit margin(Sales)
We now use the net income figure as an input into ROE to find the total equity:
ROE = Net income/Total equity
Total equity = Net income/ROE
CHAPTER 3 – 2
Next, we need to find the long-term debt. The long-term debt ratio is:
Inverting both sides gives:
Substituting the total equity into the equation and solving for long-term debt gives the following:
2.857 = 1 + ($3,419.60/LTD)
Now, we can find the total debt of the company:
Total debt = Current liabilities + LTD
And, with the total debt, we can find the TD&E, which is equal to TA:
Total assets = Total debt + Total equity
And finally, we are ready to solve the balance sheet identity as:
Net fixed assets = Total assets – Current assets
21. Child: Profit margin = Net income/Sales
Store: Profit margin = Net income/Sales
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)
CHAPTER 3 – 3
22. The solution requires substituting two ratios into a third ratio. Rearranging Debt/Total assets:
Firm A Firm B
D/TA = .65 D/TA = .45
Rearranging ROA = Net income/Total assets, we find:
Since ROE = Net income/Equity, we can substitute the above equations into the ROE formula, which
yields:
ROE = .05(TA)/.35(TA) ROE = .09(TA)/.55 (TA)
23. This problem requires us to work backward through the income statement. First, recognize that
Net income = (1 – TC)EBT. Plugging in the numbers given and solving for EBT, we get:
Now, we can add interest to EBT to get EBIT as follows:
EBIT = EBT + Interest
To get EBITD (earnings before interest, taxes, and depreciation), the numerator in the cash coverage
ratio, add depreciation to EBIT:
EBITD = EBIT + Depreciation
Now, we can plug the numbers into the cash coverage ratio and calculate:
Cash coverage ratio = EBITD/Interest
CHAPTER 3 – 4
24. The only ratio given that includes cost of goods sold is the inventory turnover ratio, so it is the last
ratio used. Since current liabilities are given, we start with the current ratio:
Current ratio = Current assets/Current liabilities
Using the quick ratio, we solve for inventory:
Quick ratio = (Current assets – Inventory)/Current liabilities
Inventory = Current assets – (Quick ratio × Current liabilities)
Inventory turnover = COGS/Inventory
25. Profit margin = Net income/Sales
As long as both net income and sales are measured in the same currency, there is no problem; in fact,
Net income = Profit margin × Sales
26. Short-term solvency ratios:
Current ratio = Current assets/Current liabilities
Quick ratio = (Current assets – Inventory)/Current liabilities
Cash ratio = Cash/Current liabilities
Asset utilization ratios:
Total asset turnover = Sales/Total assets
Inventory turnover = Cost of goods sold/Inventory
CHAPTER 3 – 5
Receivables turnover = Sales/Accounts receivable
Long-term solvency ratios:
Total debt ratio = (Total assets – Total equity)/Total assets
Debt-equity ratio = Total debt/Total equity
Equity multiplier = 1 + D/E
Times interest earned = EBIT/Interest
Cash coverage ratio = (EBIT + Depreciation)/Interest
Profitability ratios:
Profit margin = Net income/Sales
Return on assets = Net income/Total assets
Return on equity = Net income/Total equity
27. The DuPont identity is:
ROE = (PM)(TAT)(EM)
CHAPTER 3 – 6
28. SMOLIRA GOLF CORP.
Statement of Cash Flows
For 2018
Cash, beginning of the year $ 34,385
Operating activities
Net income $ 62,235
Plus:
Less:
Investment activities
Financing activities
Decrease in notes payable $ (2,808)
29. Earnings per share = Net income/Shares
PE ratio = Share price/Earnings per share
Dividends per share = Dividends/Shares
Book value per share = Total equity/Shares
CHAPTER 3 – 7
Market-to-book ratio = Share price/Book value per share
PEG ratio = PE ratio/Growth rate
30. First, we will find the market value of the company’s equity, which is:
Market value of equity = Shares × Share price
The total book value of the company’s debt is:
Total debt = Current liabilities + Long-term debt
Now we can calculate Tobin’s Q, which is:
Tobin’s Q = (Market value of equity + Book value of debt)/Book value of assets
Using the book value of debt implicitly assumes that the book value of debt is equal to the market
value of debt. This will be discussed in more detail in later chapters, but this assumption is generally
true. Using the book value of assets assumes that the assets can be replaced at the current value on
CHAPTER 26 – 8