Chapter 3: Homework1. Which of the following statements is CORRECT?a. The ratio of long-term debt to total capital is more likely to experience seasonal fluctuations than iseither the DSO or the inventory turnover ratio.b. If two firms have the same ROA, the firm with the most debt can be expected to have the lower ROE.c. An increase in the DSO, other things held constant, could be expected to increase the total assetsturnover ratio.d. An increase in the DSO, other things held constant, could be expected to increase the ROE.e. An increase in a firm’s debt ratio, with no changes in its sales or operating costs, could beexpected to lower the profit margin.Answer: E is correctDebt ratio = Total liabilities ÷ Total assetsNet profit margin ratio = Net income ÷ SalesIf debt ratio↑, which mean either Total liabilities ↑ or Total assets ↓In case Total liabilities ↑, then Interest ↑ and Net income ↓, and, also, profit margin ↓A is incorrect. DSO is a measure of the average number of days that a company takes to collectrevenue after a sale has been made. A low DSO number means that it takes a company fewerdays to collect its accounts receivable. A high DSO number shows that a company is selling itsproduct to customers on credit and taking longer to collect money. This also happens to theinventory turnover.B is incorrect. If two firms have the same ROA, the firm with the most debt can be expected tohave the higher ROE.ROA = Net income available to common stockholders ÷ Total assetsROE = Net income available to common stockholders ÷ Common equityFor example, ROA = $110 ÷ $2,000 = 5.5%Total assets = Total liabilities + equity Company A Company BTA = TL + Equity $1,064 + $896 $800 + $1,200ROE $110 ÷ 896 = 12.27% $110 ÷ $1,200 = 9.16%
C is incorrect.An increase in the DSO, other things held constant, could be expected to decreasethe total assets turnover ratio.DSO = Receivables ÷ Ave. sales per day = Receivables ÷ [Annual sales/365]Total assets turnover ratio = Sales ÷ Total assetsFor example, DSO = $375 ÷ [$3,000/365] = 45.6 → 46 daysTotal assets turnover ratio = $3,000 ÷ $2,000 = 1.5If DSO ↑ = 50 days, Sales ↓1) $375 ÷ 50 = 7.5 => Sales = 7.5 * 365 = $2,7372) Receivables ↑ = $400 => $400 ÷ 50 = 8 => Sales = 8 * 365 = $2,920Then, Total assets turnover ratio will decrease by => $2,737 ÷ $2,000 = 1.37D is incorrect.An increase in the DSO, other things held constant, could be expected to decreasethe ROE.ROE = Net income available to common stockholders ÷ Common equityIf DSO ↑, which mean either Receivables ↑ or the average sales per day ↓In case the average sales per day ↓, then Sales ↓, which will lead to Net income ↓ and ROE ↓2. Companies HD and LD have the same tax rate, sales, total assets, and basic earning power. Bothcompanies have positive net incomes. Company HD has a higher debt ratio and, therefore, a higherinterest expense. Which of the following statements is CORRECT?a. Company HD has a lower equity multiplier.b. Company HD has more net income.c. Company HD pays more in taxes.d. Company HD has a lower ROE.e. Company HD has a lower times interest earned (TIE) ratio.Answer: E is correctTIE ratio = EBIT÷ Interest expenseFor example EBIT = $ 283.8 and Interest expense = $ 88, TIE ratio = 283.8 ÷ 88 = 3.2
If Interest expense = $ 95, TIE ration = 238.88 ÷ 95 = 2.51A is incorrect.Equity multiplier = Total assets ÷ Common equityDebt ratio = Total liabilities ÷ Total assetsEven HD and LD have the same Total assets, but HD has a higher debt ratio.That means HD has higher Total liabilities, and has a higher Equity multiplier.For example HD LDTotal liabilities 1,500 1,064Common equity 500 936Total Liabilities and equity 2,000 2,000Equity multiplier 2,000 ÷ 500 = 4 2,000 ÷ 936 = 2.14B is incorrect.Since HD has a higher debt ratio, therefore, higher interest expense.Then HD should have lower EBT, and pay less in taxes than LD because they have the same tax rate.However, HD still has less Net incomeFor example, HD LDEBIT 500 500Interest 200 100EBT 300 400Tax (40%) 120 160Net income 180 240C is incorrect.BEP ratio = EBIT ÷ Total assetsBoth HD and LD have the same BEP, and Total assets, which means that both have the same EBITSince HD has a higher debt ratio, therefore, higher interest expense.Then HD should have lower EBT, and pay less in taxes than LD because they have the same tax rate.
D is incorrect.HD has a higher ROE.ROA = Net income ÷ Total assetsROE = ROA * Equity multiplierFor example HD LDROA 180 ÷ 2,000 = 0.09 = 9% 240 ÷ 2,000 = 0.12 = 12%ROE 9% * 4 = 0.36 = 36% 12% * 2 = 0.24 = 24%3. Companies HD and LD have the same total assets, sales, operating costs, and tax rates, and they paythe same interest rate on their debt. However, company HD has a higher debt ratio. Which of thefollowing statements is CORRECT?a. Given this information, LD must have the higher ROE.b. Company LD has a higher basic earning power ratio (BEP).c. Company HD has a higher basic earning power ratio (BEP).d. If the interest rate the companies pay on their debt is more than their basic earning power (BEP), thenCompany HD will have the higher ROE.e. If the interest rate the companies pay on their debt is less than their basic earning power (BEP), thenCompany HD will have the higher ROE.Answer: B is correct.A is incorrect. LD must have the lower ROE. (See question #2, choice D)4. Muscarella Inc. has the following balance sheet and income statement data:Cash $ 14,000 Account payable $ 42,000Receivables 70,000 Other current liabilities 28,000Inventories 210,000 Total CL $ 70,000Total CA $ 294,000 Long-term debt 70,000Net fixed assets 126,000 Common equity 280,000Total assets $ 420,000 Total liability & equity $ 420,000Sales $ 280,000Net income $ 21,000The new CFO thinks that inventories are excessive and could be lowered sufficiently to cause the currentratio to equal the industry average, 2.70, without affecting either sales or net income. Assuming thatinventories are sold off and not replaced to get the current ratio to the target level, and that the fundsgenerated are used to buy back common stock at book value, by how much would the ROE change?a.4.28%
b.4.50%c. 4.73%d. 4.96%e. 5.21%Answer: B is correct5. Quigley Inc. is considering two financial plans for the coming year. Management expects sales to be$301,770, operating costs to be $266,545, assets to be $200,000, and its tax rate to be 35%. Under Plan Ait would use 25% debt and 75% common equity. The interest rate on the debt would be 8.8%, but the TIEratio would have to be kept at 4.00 or more. Under Plan B the maximum debt that met the TIE constraintwould be employed. Assuming that sales, operating costs, assets, the interest rate, and the tax rate wouldall remain constant by how much would the ROE change in response to the change in the capitalstructure?a. 3.83%b. 4.02%c. 4.22%d. 4.43%e. 4.65%Answer: A is correctPlan ASales $301,770Less: Operating costs 266,545EBITDA $35,255Less: Interest 4,400EBT $30,855Less: Tax (35%) 10,799Net income $20,05625% debt = $200,000 * 0.25 = $50,00075% common equity = $200,000 * 0.75 = $150,000Interest = $50,000 * 8.8% = $4,400TIE ratio = EBIT ÷ Interest = $35,255 ÷ $4,400 = 8.01
ROE = Net income available to common stockholders ÷ Common equity = $20,056 ÷ $150,000 = 13.37%Plan BTIE ratio = 4.0 = $35,255 ÷ InterestSo, Interest = $8,813.75 = Debt * 8.8% and then, Debt = $100,156.25 => 50.078% debtCommon equity = $200,000 - $100,156 = $ 99,844Sales $301,770Less: Operating costs 266,545EBITDA $35,255Less: Interest 8,814EBT $26,441Less: Tax (35%) 9,254Net income $17,187ROE = Net income available to common stockholders ÷ Common equity = $17,187 ÷ $99,844 = 17.20%The ROE change = 17.20% - 13.37% = 3.83%