Homework #10 Suggested Solutions

Size: px

Start display at page:

Download "Homework #10 Suggested Solutions"

Marianna Weaver
6 years ago
Views:

1 JEM034 Corporate Finance Winter Semester 2017/2018 Instructor: Olga Bychkova Homework #10 Suggested Solutions Problem 1. (28.2) The following table gives abbreviated balance sheets and income statements for Estée Lauder Companies. 1

2 Assume a 35 % tax rate. Calculate the following ratios: (a) Return on assets. (b) Operating profit margin. (c) Sales to assets ratio. (d) Inventory turnover. (e) Debt equity ratio. (f) Current ratio. (g) Quick ratio. after tax interest + net income (1 0.35) (a) ROA = = = 0.125, or 12.5%. total assets at start of year 4, 126 after tax interest + net income (b) Operating profit margin = = sales (1 0.35) = = 0.065, or 6.5%. 7, 911 sales 7, 911 (c) Sales to assets = = total assets 4, 126 = 1.9. cost of goods sold 1, 997 (d) Inventory turnover = = inventory at start of year 856 = 2.3. long term debt 1, 078 (e) Debt to equity ratio = = equity 1, 653 = current assets 2, 787 (f) Current ratio = = current liabilities 1, 699 = cash + marketable securities + receivables , 039 (g) Quick ratio = = = current liabilities 1, 699 Problem 2. (28.4) Look again at the table from the previous problem. At the end of fiscal 2008 Estée Lauder had 195 million shares outstanding with a share price of $45.5. The company s weighted average cost of capital was about 10%. Assume a 35 % tax rate. Calculate (a) Market value added. (b) Market to book ratio. (c) Economic value added. (d) Return on capital. (a) Market value added = market value of equity book value of equity = = 195 $45.5 $1, 653 = $7, 220 million. market value of equity 195 $45.5 (b) Market to book ratio = = = 5.4. book value of equity $1, 653 (c) EV A = (after tax interest + net income) (cost of capital capital) = = [(1 0.35) ] [0.1 (1, , 653)] = $177.7 million. 2

3 (d) ROC = after tax interest + net income total capital = (1 0.35) , , 653 = 0.19, or 19%. Problem 3. (28.5) There are no universally accepted definitions of financial ratios, but five of the following ratios are clearly incorrect. Substitute the correct definitions. long term debt + value of leases (a) Debt equity ratio = long term debt + value of leases + equity EBIT tax (b) Return on equity = average equity net income (c) P rofit margin = sales (d) Days in inventory = sales (e) Current ratio = inventory/365 current liabilities current assets (f) Sales to net working capital = average sales average net working capital current assets inventories (g) Quick ratio = current liabilities (h) T imes interest earned = interest earned long term debt The illogical ratios are (a), (b), (d), (e), and (h). The correct definitions are: Debt equity ratio = long term debt + value of leases equity Return on equity = net income average equity inventory at start of year Days in inventory = daily cost of goods sold current assets Current ratio = current liabilities EBIT T imes interest earned = interest payments Problem 4. (28.6) True or false? (a) A company s debt equity ratio is always less than 1. (b) The quick ratio is always less than the current ratio. (c) The return on equity is always less than the return on assets. (a) False (b) True (c) False 3

Problem 5. (28.7) Keller Cosmetics maintains an operating profit margin of 8% and a sales to assets ratio of 3. It has assets of $500,000 and equity of $300,000.

4 Problem 5. (28.7) Keller Cosmetics maintains an operating profit margin of 8% and a sales to assets ratio of 3. It has assets of $500,000 and equity of $300,000. Interest payments are $30,000 and the tax rate is 35%. (a) What is the return on assets? (b) What is the return on equity? sales (a) Sales to assets = sales = 3 $500, 000 = $1, 500, 000; total assets after tax interest + net income Operating profit margin = sales after tax interest + net income = 0.08 $1, 500, 000 = $120, 000; after tax interest + net income 120, 000 ROA = = = 0.24, or 24%. total assets 500, 000 (b) Net income = [after tax interest + net income] after tax interest = = $120, 000 (1 0.35) $30, 000 = $100, 500; net income 100, 500 ROE = = = 0.34, or 34%. equity 300, 000 Problem 6. (28.9) Magic Flutes has total receivables of $3,000, which represent 20 days sales. Total assets are $75,000. The firm s operating profit margin is 5%. Find the firm s sales to assets ratio and return on assets. Average collection period = receivables at start of year average daily sales Sales = receivables at start of year average collection period Sales to assets ratio = 365 = $3, sales $54, 750 = total assets $75, 000 = = $54, 750. ROA = sales to assets ratio operating profit margin = = , or 3.65%. Problem 7. (28.10) Consider this simplified balance sheet for Geomorph Trading: (a) Calculate the ratio of debt to equity. (b) What are Geomorph s net working capital and total long term capital? Calculate the ratio of debt to total long term capital. (Hint: Total long term capital = net working capital + long term assets.) 4

5 long term debt (a) Debt to equity ratio = = 280 equity 190 = (b) Net working capital = current assets current liabilities = = $40. T otal long term capital = net working capital+long term assets = = $540. Debt to total long term capital ratio = = Problem 8. (28.12) Airlux Antarctica has current assets of $300 million, current liabilities of $200 million and a cash ratio of How much cash and marketable securities does it hold? cash + marketable securities Cash ratio = current liabilities Cash + marketable securities = cash ratio current liabilities = = 0.05 $200 million = $10 million. Problem 9. (28.13) On average, it takes Microlimp s customers 60 days to pay their bills. If Microlimp has annual sales of $500 million, what is the average value of unpaid bills? Average collection period = receivables at start of year average daily sales Receivables at start of year = average collection period average daily sales = = 60 $500 million 365 = $82 million. Problem 10. (28.26) Sometimes analysts use the average of capital at the start and end of the year to calculate return on capital. Provide some examples to illustrate when this does and does not make sense. (Hint: Start by assuming that capital increases solely as a result of retained earnings.) Recall that return on capital (ROC) equals the total profits earned for debt and equity investors divided by the amount of money contributed. It is calculated as after tax interest + net income. total capital Using an average of capital at the start and end of the year for the denominator will produce a reasonable result if the firm actively increases or reduces capital over the year in a manner consistent with past practices. 5

By contrast, if increases in capital over the year occur without additional debt or stock issuances (such as solely through retained earnings), the amount of money that has been contributed to the

6 By contrast, if increases in capital over the year occur without additional debt or stock issuances (such as solely through retained earnings), the amount of money that has been contributed to the firm by investors does not change during the year. Using an average that includes the higher year end figure will overstate the amount of capital contributed and will likely understate the ROC calculation. Problem 11. (29.2) State how each of the following events would affect the firm s balance sheet. State whether each change is a source or use of cash. (a) An automobile manufacturer increases production in response to a forecasted increase in demand. Unfortunately, the demand does not increase. (b) Competition forces the firm to give customers more time to pay for their purchases. (c) Rising commodity prices increase the value of raw material inventories by 20%. (d) The firm sells a parcel of land for $100,000. The land was purchased five years earlier for $200,000. (e) The firm repurchases its own common stock. (f) The firm doubles its quarterly dividend. (g) The firm issues $1 million of long term debt and uses the proceeds to repay a short term bank loan. (a) Inventories go up (use). (b) Accounts receivable go up (use). (c) No change shown on the firm s books. (d) Increase in cash (source) and reduction in assets. A loss of $100,000 is deducted from retained earnings. (e) Cash declines (use) and equity declines. (f) Cash declines (use). (g) Cash unchanged, although net working capital increases (the debt issue is a source of funds). Problem 12. (29.3) Here is a forecast of sales by National Bromide for the first four months of 2010 (figures in $ thousands): On the average 50% of credit sales are paid for in the current month, 30% are paid in the next month, and the remainder are paid in the month after that. What is the expected cash inflow from operations in months 3 and 4? Month 3: $18, $90, $120, $100, 000 = $119, 000. Month 4: $14, $70, $90, $120, 000 = $100,

7 Problem 13. (29.6) True or false? (a) Financial planning should attempt to minimize risk. (b) The primary aim of financial planning is to obtain better forecasts of future cash flows and earnings. (c) Financial planning is necessary because financing and investment decisions interact and should not be made independently. (d) Firms planning horizons rarely exceed three years. (e) Financial planning requires accurate forecasting. (f) Financial planning models should include as much detail as possible. (a) False (it is a process of deciding which risks to take). (b) False (financial planning is concerned with possible surprises as well as expected outcomes). (c) True (financial planning considers both the investment and financing decisions). (d) False (a typical horizon for long term planning is 5 years). (e) True (perfect accuracy is unlikely to be obtainable, but the firm needs to produce the best available consistent forecasts). (f) False (excessive detail distracts attention from the crucial decisions). Problem 14. (29.11) If a firm pays its bills with a 30 day delay, what fraction of its purchases will be paid in the current quarter? In the following quarter? What if the delay is 60 days? 30 day delay: This quarter it will pay 1 /3 of last quarter s purchases and 2 /3 of this quarter s. 60 day delay: This quarter it will pay 2 /3 of last quarter s purchases and 1 /3 of this quarter s. Problem 15. (30.4) The Branding Iron Company sells its irons for $50 a piece wholesale. Production cost is $40 per iron. There is a 25% chance that wholesaler Q will go bankrupt within the next year. Q orders 1,000 irons and asks for six months credit. Should you accept the order? Assume that the discount rate is 10% per year, there is no chance of a repeat order, and Q will pay either in full or not at all. Reject because PV of Q s order = in total /2 40 = $4.25 per iron, or $4,250 Problem 16. (30.12) In October 2008, six month (182 day) Treasury bills were issued at an annual discount of 1.4%. What is the annual yield? Assume the initial price of Treasury bills is $100. 7

8 P rice of 6 month bill = $ $100 = $ Return = ( ) = , or 1.415% Problem 17. (30.23) Until recently, Augean Cleaning Products sold its products on terms of net 60, with an average collection period of 75 days. In an attempt to induce customers to pay more promptly, it has changed its terms to 2/10, EOM, net 60. The initial effect of the changed terms is as follows: Average Collection Periods, Days Percent of Sales with Cash Discount Cash Discount Net 60 30* 80 * Some customers deduct the cash discount even though they pay after the specified date. Calculate the effect of the changed terms. Assume Sales volume is unchanged and equals to $100. The interest rate is 12%. There are no defaults. Cost of goods sold is 80% of sales. Original terms: Changed terms: NP V per $100 sales = $80 + $ /365 = $17.7. NP V per $100 sales = $ $ $100 + = $ / /365 Problem 18. (30.24) Look back at the previous problem. Assume that the change in credit terms results in a 2% increase in sales. Recalculate the effect of the changed credit terms. For every $100 of prior sales, the firm now has sales of $102. Thus, the cost of goods sold increases by 2%, as do sales, both cash discount and net: NP V per $100 of initial sales = 1.02 $17.27 = $

9 Problem 19. (30.28) The financial manager of JAC Cosmetics is considering opening a lock box in Pittsburgh. Checks cleared through the lock box will amount to $300,000 per month. The lock box will make cash available to the company three days earlier than is currently the case. (a) Suppose that the bank offers to run the lock box for a $20,000 compensating balance. Is the lock box worthwhile? (b) Suppose that the bank offers to run the lock box for a fee of $0.1 per check cleared instead of a compensating balance. What must the average check size be for the fee alternative to be less costly? Assume an interest rate of 6% per year. (c) Why did you need to know the interest rate to answer (b) but not to answer (a)? (a) The lock box will collect an average of $300,000 /30 = $10, 000 per day. The money will be available three days earlier so this will increase the cash available to JAC by $30,000. Thus, JAC will be better off accepting the compensating balance offer. The cost is $20,000, but the benefit is $30,000. (b) Let x equal the average check size for break even. Then, the number of checks written per month is 300,000 /x and the monthly cost of the lock box is: 300, 000 x 0.1. The alternative is the compensating balance of $20,000. The monthly cost is the lost interest, which is equal to: 20, These costs are equal if x = $300. Thus, if the average check size is greater than $300, paying per check is less costly; if the average check size is less than $300, the compensating balance arrangement is less costly. (c) In part (a), we compare available dollar balances: the amount made available to JAC compared to the amount required for the compensating balance. In part (b), one cost is compared to another. The interest foregone by holding the compensating balance is compared to the cost of processing checks, and so here we need to know the interest rate. Problem 20. (30.29) A three month Treasury bill and a six month Treasury bill both sell at an annual discount of 10%. Which offers the higher annual yield? Assume the initial price of both Treasury bills is $100. P rice of three month T reasury bill = $ $100 = $ Y ield = ( ) = , or 10.66% P rice of six month T reasury bill = $ $100 = $

10 Y ield = ( ) = or 10.8%. 95 Therefore, the six month Treasury bill offers the higher yield. 10

Homework #3 Suggested Solutions

JEM034 Corporate Finance Winter Semester 2017/2018 Instructor: Olga Bychkova Homework #3 Suggested Solutions Problem 1. (6.6) When appraising mutually exclusive investments in plant and equipment, financial