# Total shares at the end of ten years is 100*(1+5%) 10 =162.9.

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1 FCS5510 Sample Homework Problems Unit04 CHAPTER 8 STOCK PROBLEMS 1. An investor buys 100 shares if a \$40 stock that pays a annual cash dividend of \$2 a share (a 5% dividend yield) and signs up for the dividend reinvestment plan. a. If neither the price of the stock nor the dividend changes, how many shares will the investor have at the end of ten years? The dividend yield is 5 percent (\$2/\$40 = 5 percent). Given that neither the price of the stock nor the dividend changes, the number of shares in the dividend reinvestment plan will grow annually by 5 percent. Total shares at the end of ten years is 100*(1+5%) 10 = The income statement and balance sheet are presented as follows. Please compute various financial ratios. Then compare these results with the industrial averages listed in the textbook on page 298. What strengths and weaknesses are apparent? Income Statement for XYZ for the period ending December 31, 20XX Sales \$90,000 Cost of goods sold 54,000 Gross profit 36,000 Selling and administrative expense 13,500 Operating profit 22,500 Interest expense 4,500. Earnings before taxes 18,000 Taxes 2,880 Earnings available to stockholders \$15,120 Number of shares outstanding 9,000 Earnings per share \$1.51 (To compute the inventory turnover, assume that the prior year s inventory was \$36,000.) Firm XYZ Balance Sheet as of December 31, 20XX Assets Current assets Cash and marketable securities -- \$9,000 Accounts receivable \$28,800 --

2 . Less allowance for doubtful accounts 1,800 27,000 Inventory Finished goods 27, Work in progress 4, Raw materials 6,300 37,800 Total current assets -- \$73,800 Investments -- \$9,000 Long-term assets Plant and equipment 90, Less accumulated depreciation 27,000 63,000 Land -- 9,000 Total long-term assets -- \$72,000 Total assets -- \$ Liabilities & Stockholders Equity Current liabilities -- Accounts payable \$9,000 Accrued wages 9,900 Bank notes 13,500 Accrued interest payable 3,600 Accrued taxes 900 Total current liabilities \$36,900 Long-term debt 13,500 Total liabilities \$50,400 Stockholders equity -- Common stock(\$1 par value; 20,000 shares authorized; 10,000 shares outstanding) \$9,000 Additional paid-in capital 18,000 Retained earnings 77,400 Total stockholders equity \$104,400 Total liabilities and equity \$154,800 a) Current ratio: current assets = \$73,800 = 2 current liabilities \$36,900 b) Quick ratio (acid test): current assets minus inventory = \$36,000 = 0.98 current liabilities \$36,900

3 c) Inventory turnover: sales = \$90,000 = 2.4 average inventory (\$37,800 + \$36,000)/2 or cost of goods sold = \$54,000 = 1.5 average inventory (\$37,800 + \$36,000)/2 d) Receivables turnover: annual credit sales accounts receivable or annual sales = \$90,000 = 3.3 accounts receivable \$27,000 Average collection period: receivables = \$27,000 sales per day \$90,000/360 = 108 days Operating profit margin: earnings before interest and taxes = \$22,500 = 25% sales \$90,000 Net profit margin: earnings after taxes = \$15,120 = 16.8% sales \$90,000 Return on assets: earnings after taxes = \$15,120 = 9.8% total assets \$154,800 Return on equity: earnings after taxes = \$15,120 = 14.5% equity \$104,400 Return on investment: earnings x sales = \$15,120 x \$90,000 = 9.8% sales assets \$90,000 \$154,800 Debt/net worth: debt = \$50,400 = 48.3% equity \$104,400 Debt ratio: debt = \$50,400 = 32.6% total assets \$154,800 Times-interest-earned: earnings before interest and taxes = \$22,500 = 5.0 interest expense \$4,500 Strengths:

4 The current ratio, acid test, and inventory are comparable to the industry averages, and the operating profit margin exceeds the industry average. In general, the firm is performing acceptably. Weaknesses: There are two basic weaknesses. One is the slow collection of accounts receivable which are taking, on the average, 108 days to collect while the industry average is about 75 days. The firm is also using more debt financing than the industry (32.6 percent versus 25 percent for the industry). This increased debt financing may be financing the increased investment in accounts receivable. If the firm can collect its accounts receivable more rapidly, then it will be able to pay off some of its liabilities and thus reduce its debt ratio. The increased usage of debt may also explain why the net profit margin is below the industry average. Since the operating profit margin is comparable to the industry, the lower net profit margin can not be explained by the firm's operations. Either interest expense or higher taxes must be the source of the lower net profit margin. If the lower net profit margin is the result of increased interest expense, then this is probably the result of carrying too many accounts receivable. 5. You have taken the following information from a firm s financial statements. As an investor in the firm s debt instruments, you are concerned with its liquidity position and its use of financial leverage. What conclusions can you draw from this information? Sales \$1,700,000 \$1,500,000 \$1,000,000 Cash 18,000 7,000 5,000 Accounts receivable 152, , ,000 Inventory 200, , ,000 Current liabilities 225, , ,000 Operating income 170, ,000 90,000 Interest expense 27,000 23,000 20,000 Taxes 53,000 45,000 25,000 Net income 90,000 77,000 45,000 Debt 260, , ,000 Equity 330, , ,000

5 An investor in debt instruments is primarily concerned with the firm's capacity to pay the interest and make the principal repayment. Emphasis will be placed on liquidity ratios and times-interest-earned. Emphasis may also be placed on the turnover of current assets, since such turnover generates the cash to make the creditor's payments. Current ratio: 2008: \$5, , ,000\$ = 1.9 \$175, : \$7, , ,000 = 1.5 \$210, : \$18, , ,000 = 1.6 \$225,000 There has been a decline in the current ratio. Quick ratio: 2008: \$5, ,000 = 0.7 \$175, : \$7, ,000 = 0.8 \$175, : \$18, ,000 = 0.8 \$225,000 There has been little change in the quick ratio. Inventory turnover (using average inventory): 2009: \$1,500,000 = 7.7 (\$200, ,000)/2 2010: \$1,700,000 = 8.7 (\$190, ,000)/2 Inventory turnover has increased. Days Sales Outstanding (Average collection period): 2008: \$125,000 = 45 \$1,000,000/ : \$130,000 = 31 \$1,500,000/ : \$152,000 = 32

6 \$1,700,000/360 Days sales outstanding has dramatically improved. Times-interest-earned: 2008: \$90,000/\$20,000 = : \$145,000/\$23,000 = : \$170,000/\$27,000 = 6.3 Times-interest-earned has improved. With the exception of the slight decline in the current ratio, there has been no change that indicates deterioration in the creditor's position. The creditor's position has probably improved. 6. What is the debt/equity ratio for a firm with total debt of \$500,000 and equity of \$200,000? Debt/Net worth: \$500,000/\$200,000 = 2.5 Debt ratio (Debt/Total assets): \$500,000/(\$500,000 + \$200,000) = 0.71 = 71% 7. A firm with sales of \$800,000 has average inventory of \$400,000. The industry average for inventory turnover is four times a year. What would be the reduction in inventory if this firm were to achieve a turnover comparable to the industry average? The firm wants to achieve the industry average given its level of sales. Thus: Industry average = Sales/Average inventory 4 = \$800,000/X X = \$200,000 Since the firm's inventory is \$400,000, the reduction in inventory will be \$400,000 - \$200,000 = \$200, Company A has three debt issues of \$3,000 each. The interest rate on issue A is 4 percent, on B the rate is 6 percent, and on C the rate is 8 percent. Issue B is subordinate to A, and issue C is subordinate to both A and B. The firm s operating income (EBIT) is \$500. What is the timesinterest-earned ratio for issue A and B, and C? Times interest earned = EBIT/Interest Issue A \$500/\$120 = 4.2 Issue B \$500/(\$ ) = 1.7

7 Issue C \$500/(\$ ) =.9 These answers indicate that the firm has insufficient operating income to meet all of its interest expense. If C is subordinated to A and B (and the above calculations are made based on that assumption), the interest payment to C may not be made unless the firm has cash or other sources of funds that may be used to meet the interest payment. 8. If a firm has sales of \$36,000,000 a year, and the average collection period for the industry is 30 days, what should this firm s accounts receivable be if the firm is comparable to the industry? Average collection period = Accounts receivable Sales per day To determine what the firm's accounts receivable should be to be comparable to the industry, solve the following equation: 30 = X/[(\$36,000,000/360)] X = \$3,000, Two firms have sales of \$1 million each. Other financial information is as follows: -- Firm A Firm B EBIT \$150,000 \$150,000 Interest 20,000 75,000 expense Income tax 50,000 30,000 Equity 300, ,000 What is the operating profit margin for Firm A? What is the net profit margin for Firm A? What is the return on equity for Firm B? Operating profit margin = EBIT/Sales Firm A: \$150,000/\$1,000,000 = 15% Net profit margin = Net earnings/sales Firm A: \$80,000/\$1,000,000 = 8% Return on equity = Earnings/Equity Firm B: \$45,000/\$100,000 = 45%

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