This Document Contains Chapters 26 to 27 Chapter 26 short-term finance and planning 1. Short-term financial planning is one of the cornerstones of corporate finance. If a company mismanages its current assets, it can run out of cash leading to bankruptcy. 2. The cash accounting equation is as follows: Non-current Net working capital Non-current Cash Equity = liabilities + − (excluding cash) − assets Thus, cash can be increased by growing non-current liabilities and equity. It is reduced by increasing net working capital and non-current assets. 3. Firms with a long operating cycle have relatively long inventory periods and/or relatively long receivables periods. Thus, such firms tend to keep inventory on hand, and they allow customers to purchase on credit and take a relatively long time to pay. Firms with a long cash cycle have a relatively long time between the time that purchased inventory is paid for and the time that inventory is sold and payment received. Thus, these are firms that have relatively short payables periods and/or relatively long receivable cycles. 4. Financing policies can be flexible or restrictive. Flexible short-term financial policies include keeping large balances of cash and marketable securities, making large investments in inventory, and granting liberal credit terms. Restrictive short-term financial policies are keeping low cash balances and no investment in marketable securities, making small investments in inventory, and allowing no credit sales and no accounts receivable. 5. The cash budget shows the cash inflows and outflows in future periods so that a finance manager can forecast their firm’s short-term financing requirements. 6. A firm can finance its short-term funding requirements through unsecured loans from banks, secured loans, banker’s acceptances, or commercial paper. 7. a. Use: The cash balance declined by €106.8 million to pay the dividend. b. Use: The cash balance declined by €301.5 million to pay for the assets. c. Source: The cash balance increased by €346 million, assuming the liabilities were used to increase cash. d. Use: The cash balance declined by €308.4 million to pay for the tax e. Use: The cash balance declined by €853 to pay for the property, plant and equipment. This Document Contains Chapters 26 to 27 8. The main effect of the new mobile phone payment system is that there is less need for cash and the management of cash becomes less problematic. 9. Since the cash cycle equals the operating cycle minus the trade payables period, it is not possible for the cash cycle to be longer than the operating cycle if the trade payables is positive. Moreover, it is unlikely that the trade payables period would ever be negative since that implies the firm pays its bills before they are incurred. 10. Shortage costs are those costs incurred by a firm when its investment in current assets is low. There are two basic types of shortage costs. 1) Trading or order costs. Order costs are the costs of placing an order for more cash or more inventory. 2) Costs related to safety reserves. These costs include lost sales, lost customer goodwill, and disruption of production schedules. Clearly in the miner’s case, a shortage of cash will result in mining disruption which would lead to the negative effects listed above. 11. A long-term growth trend in sales will require some permanent investment in current assets. Thus, in the real world, net working capital is not zero. Also, the variation across time for assets means that net working capital is unlikely to be zero at any point in time. This is a liquidity reason. 12. It shortened its payables period, thereby increasing its cash cycle. However, the operating cycle remained unaffected. 13. Their receivables period decreased, thereby decreasing their operating and cash cycles. 14. It is sometimes argued that large firms “take advantage of” smaller firms by threatening to take their business elsewhere. However, considering a move to another supplier to get better terms is the nature of competitive free enterprise. An 82-day payables period is not necessarily bad if that is the norm in the industry. 15. There could be a number of reasons. One, the industry norm may be nearer the shorter period and Power Assets was out of synch with other companies. Another explanation could be that they are looking to be sold and so wish to make the company’s financial management look good. Finally, they may actually be telling the truth! 16. Power Assets will need more financing because it is essentially borrowing less from its suppliers. Among other things, Power Assets will likely need more short-term borrowing from other sources, so it will pay more in interest expense. 17. a. No change. A dividend paid for by the sale of debt will not change cash since the cash raised from the debt offer goes immediately to shareholders. b. No change. The property is paid for by the cash raised from the short-term debt, so this will not change the cash balance. c. No change. Inventory and trade payables will increase, but neither will impact the cash account. d. Decrease. The short-term bank loan is repaid with cash, which will reduce the cash balance. e. Decrease. The payment of taxes is a cash transaction. f. Decrease. The preference shares will be repurchased with cash. g. No change. Trade receivables will increase, but cash will not increase until the sales are paid off. h. Decrease. The interest is paid with cash, which will reduce the cash balance. i. Increase. When payments for previous sales, or trade receivables, are paid off by the customer, the cash balance increases since the payment must be made in cash. j. Decrease. The trade payables are reduced through cash payments to suppliers. k. Decrease. Here, the dividend payments are made with cash, which is generally the case. This is different from part a, where debt was raised to make the dividend payment. l. No change. The short-term note will not change the cash balance. m. Decrease. The utility bills must be paid in cash. n. Decrease. A cash payment will reduce cash. o. Increase. If marketable securities are sold, the company will receive cash from the sale. 18. The total liabilities and equity of the company are the net book worth, or market value of equity, plus the long-term debt, so: Total liabilities and equity = $1,038 million + $1,161 million + $7,176 million Total liabilities and equity = $9,375 million This is also equal to the total assets of the company. Since total assets are the sum of all assets, and cash is an asset, the cash account must be equal to total assets minus all other assets, so: Cash = $9,375 million - $4,938 million - $2,098 million Cash = $2,339 million 19. a. Increase. If receivables go up, the time to collect the receivables would increase, which increases the operating cycle. b. Increase. If credit repayment times are increased, customers will take longer to pay their bills, which will lead to an increase in the operating cycle. c. Decrease. If the inventory turnover increases, the inventory period decreases. d. No change. The trade payables period is part of the cash cycle, not the operating cycle. e. Decrease. If the receivables turnover increases, the receivables period decreases. f. No change. Payments to suppliers affects the accounts payable period, which is part of the cash cycle, not the operating cycle. 20. a. Increase; Increase. If the terms of the cash discount are made less favourable to customers, the trade receivables period will lengthen. This will increase both the cash cycle and the operating cycle. b. Increase; No change. This will shorten the trade payables period, which will increase the cash cycle. It will have no effect on the operating cycle since the accounts payable period is not part of the operating cycle. c. Decrease; Decrease. If more customers pay in cash, the trade receivables period will decrease. This will decrease both the cash cycle and the operating cycle. d. Decrease; Decrease. Assume that the trade payables period does not change. Fewer raw materials purchased will reduce the inventory period, which will decrease both the cash cycle and the operating cycle. e. Decrease; No change. If more raw materials are purchased on credit, the trade payables period will tend to increase, which would decrease the cash cycle. We should say that this may not be the case. The trade payables period is a decision made by the company’s management. The company could increase the trade payables account and still make the payments in the same number of days. This would leave the trade payables period unchanged, which would leave the cash cycle unchanged. The change in credit purchases made on credit will not affect the inventory period or the trade payables period, so the operating cycle will not change. f. Increase; Increase. If more goods are produced for inventory, the inventory period will increase. This will increase both the cash cycle and operating cycle. 21. a. A 10-day collection period implies all receivables outstanding from the previous quarter are collected within 2 weeks and: (90 – 10)/90 = 8/9 of current sales are collected. So: Q1 Q2 Q3 Q4 Beginning receivables £145 £91.56 £102.22 £68.89 Sales £824 £920 £620 £1,600 Cash collections £(877.44) £(909.33) £(653.33) £(1,491.11) Ending receivables £91.56 £102.22 £68.89 £177.78 b. A 20-day collection period implies all receivables outstanding from the previous quarter are collected in the current month, and: (90-20)/90 = 7/9 of current sales are collected. So: Q1 Q2 Q3 Q4 Beginning Receivables 145.00 183.11 204.44 137.78 Sales 824.00 920.00 620.00 1,600.00 Cash Collections -785.89 -898.67 -686.67 -1,382.22 Ending Receivables 183.11 204.44 137.78 355.56 c. A 30-day collection period implies all receivables outstanding from the previous quarter are collected in the current quarter, and: (90-30)/90 = 2/3 of current sales are collected. So: Q1 Q2 Q3 Q4 Beginning Receivables 145.00 274.67 306.67 206.67 Sales 824.00 920.00 620.00 1,600.00 Cash Collections -694.33 -888.00 -720.00 -1,273.33 Ending Receivables 274.67 306.67 206.67 533.33 22. The operating cycle is the inventory period plus the receivables period. The inventory turnover and inventory period are: Inventory turnover = COGS/Average inventory Inventory turnover = £52,827/{[£8,413 + 10,158]/2} Inventory turnover = 5.6892 times Inventory period = 365 days/Inventory turnover Inventory period = 365 days/5.6892 Inventory period = 64.16 days And the receivables turnover and receivables period are: Receivables turnover = Credit sales/Average receivables Receivables turnover = £67,312/{[$5,108 + 5,439]/2} Receivables turnover = 12.7642 times Receivables period = 365 days/Receivables turnover Receivables period = 365 days/12.7642 Receivables period = 28.60 days So, the operating cycle is: Operating cycle = 64.16 days + 28.60 days Operating cycle = 92.75 days The cash cycle is the operating cycle minus the payables period. The payables turnover and payables period are: Payables turnover = COGS/Average payables Payables turnover = £52,827/{[$6,927 + 7,625]/2} Payables turnover = 7.2604 times Payables period = 365 days/Payables turnover Payables period = 365 days/7.2604 Payables period = 50.27 days So, the cash cycle is: Cash cycle = 92.75 days – 50.27 days Cash cycle = 42.48 days The firm is receiving cash on average 42.48 days after it pays its bills. 23. a. The payables period is zero since the company pays immediately. Sales in the year following this one are projected to be 15% greater in each quarter. Therefore, Q1 sales for the next year will be £540(1.15) = £621. The payment in each period is 30 percent of next period’s sales, so: Q1 Q2 Q3 Q4 Payment of accounts £189.00 £213.00 £235.50 £186.30 b. Since the payables period is 90 days, the payment in each period is 30 percent of the current period sales, so: Q1 Q2 Q3 Q4 Payment of accounts £162.00 £189.00 £213.00 £235.50 c. Since the payables period is 60 days, the payment in each period is 2/3 of last quarter’s orders, plus 1/3 of this quarter’s orders, or: Quarterly payments = 2/3(.30) times current sales + 1/3(.30) next period sales. Q1 Q2 Q3 Q4 Payment of accounts £171.00 £197.00 £220.50 £219.10 24. Since the payables period is 60 days, the payment of accounts in each period will be: Payment of accounts each period = 2/3(.75) times current sales + 1/3(.75) next period sales Q1 Q2 Q3 Q4 Payment of accounts £605.00 £682.50 £642.50 £637.50 Wages, taxes, other expenses £ 150.00 £ 184.00 £ 178.00 £ 158.00 Long-term financing expenses £ 60.00 £ 60.00 £ 60.00 £ 60.00 Total £815.00 £926.50 £880.50 £855.50 25. a. The November sales must have been the total uncollected sales minus the uncollected sales from December, divided by the collection rate two months after the sale, so: November sales = (£57,000 – £ 41,000)/0.15 November sales = £106,666.67 b. The December sales are the uncollected sales from December divided by the collection rate of the previous months’ sales, so: December sales = £41,000/0.35 December sales = £117,142.86 c. The collections each month for this company are: Collections = .15(Sales from 2 months ago) + .20(Last month’s sales) + .65 (Current sales) January collections = .15(£106,666.67) + .20(£117,142.86) + .65(£150,000) January collections = £136,928.57 February collections = .15(£117,142.86) + .20(£150,000) + .65(£173,000) February collections = £160,021.43 March collections = .15(£150,000) + .20(£173,000) + .65(£194,000) March collections = £183,200.00 26. The sales collections each month will be: Sales collections = .35(current month sales) + .60(previous month sales) Given this collection, the cash budget will be: January February March Beginning cash balance NKr280,000 NKr248,850 NKr317,840 Cash receipts Cash collections from credit sales NKr259,000 NKr 366,600 NKr 390,900 Total cash available NKr539,000 NKr615,450 NKr708,740 Cash disbursements Purchases NKr 156,000 NKr 147,000 NKr 175,500 Wages, taxes, and expenses NKr 39,750 NKr 48,210 NKr 50,300 Interest NKr 11,400 NKr 11,400 NKr 11,400 Equipment purchases NKr83,000 NKr 91,000 NKr 0 Total cash disbursements NKr290,150 NKr 297,610 NKr 237,200 Ending cash balance NKr248,850 NKr317,840 NKr471,540 27. Non-Current Assets: Source Current Assets: Source Equity: Source Non-current liabilities: Use Current liabilities: Use 28. First, we need to calculate the sales from the last quarter of the previous year. Since 50 percent of the sales were collected in that quarter, the sales figure must have been: Sales (last quarter of pervious year) = £81,000,000 / (1 – .50) Sales (last quarter of pervious year) = £162,000,000 Now we can estimate the sales growth each quarter, and calculate the net sales including the seasonal adjustments. The sales figures for each quarter will be: Quarter 1 Quarter 2 Quarter 4 Quarter 4 Sales (basic trend) £100,000,000 £120,000,000 £144,000,000 £172,800,000 Seasonal adjustment £0 £–10,000,000 £–5,000,000 £15,000,000 Sales projection £100,000,000 £110,000,000 £139,000,000 £187,800,000 Since 50 percent of sales are collected in the quarter the sales are made, and 45 percent of sales are collected in the quarter after the sales are made, the cash budget is: Quarter 1 Quarter 2 Quarter 4 Quarter 4 Collected within quarter £50,000,000 £55,000,000 £69,500,000 £93,900,000 Collection from previous quarter £72,900,000 £45,000,000 £49,500,000 £62,550,000 Cash collections from sales £122,900,000 £100,000,000 £119,000,000 £156,450,000 29. a. A 45-day collection period means sales collections each quarter are: Collections = 1/2 current sales + 1/2 old sales A 36-day payables period means payables each quarter are: Payment of accounts = 3/5 current orders + 2/5 old orders So, the cash inflows each quarter are: Q1 =€79 + 1/2(€230) – 2/5(.45)(€230) – 3/5(.45)(€195) – .30(€230) – €15 Q1 = €15.95 Q2 = 1/2(€230) + 1/2(€195) – 2/5(.45)(€195) – 3/5(.45)(€270) – .30(€195) – €15 – 90 Q2 = –€59.00 Q3 = 1/2(€195) + 1/2(€270) – 2/5(.45)(€270) – 3/5(.45)(€290) – .30(€270) – €15 Q3 = €9.60 Q4 = 1/2(€270) + 1/2(€290) – 2/5(.45)(€295) – 3/5(.45)(€250) – .30(€290) – €15 Q4 = €58.30 The company’s cash budget will be: WILDCAT SA. Cash Budget (in millions) Q1 Q2 Q3 Q4 Beginning cash balance €73.00 €88.95 €29.95 €39.55 Net cash inflow 15.95 (59.00) 9.60 58.30 Ending cash balance €88.95 €29.95 €39.55 €97.85 Minimum cash balance (30.00) (30.00) (30.00) (30.00) Cumulative surplus (deficit) €58.95 (€0.05) € 9.55 €67.85 b. With a €30M minimum cash balance, the short-term financial plan will be: WILDCAT SA Short-Term Financial Plan (in millions) Q1 Q2 Q3 Q4 Beginning cash balance €30.00 €30.00 €30.00 €30.00 Net cash inflow 15.95 –59.00 9.60 58.30 New short-term investments –16.81 0 –9.64 –58.53 Income on short-term investments 0.86 1.20 0.04 0.23 Short-term investments sold 0 57.80 0 0 New short-term borrowing 0 0 0 0 Interest on short-term borrowing 0 0 0 0 Short-term borrowing repaid 0 0 0 0 Ending cash balance €30.00 €30.00 €30.00 €30.00 Minimum cash balance –30.00 –30.00 –30.00 –30.00 Cumulative surplus (deficit) €0 €0 €0 €0 Beginning short-term investments €43.00 €59.81 €2.01 €11.65 Ending short-term investments €59.81 €2.01 €11.65 €70.18 Beginning short-term debt 0 0 0 0 Ending short-term debt 0 0 0 0 Below you will find the interest paid (or received) for each quarter: Q1: excess funds at start of quarter of €43 invested for 1 quarter earns .02(€43) = €0.86 income Q2: excess funds of €59.81 invested for 1 quarter earns .02(€59.81) = €1.20 in income Q3: excess funds of €2.01 invested for 1 quarter earns .02(€2.01) = €0.04 in income Q4: excess funds of €111.65 invested for 1 quarter earns .02(€11.65) = €0.23 in income 30. a. With a minimum cash balance of €45M, the short-term financial plan will be: WILDCAT SA Short-Term Financial Plan (in millions) Q1 Q2 Q3 Q4 Beginning cash balance €45.00 €45.00 €45.00 €45.00 Net cash inflow 15.95 (59.00) 9.60 58.30 New short-term investments (16.51) 0 0 (53.76) Income on short-term investments .56 .89 0 0 Short-term investments sold 0 44.51 0 0 New short-term borrowing 0 13.60 0 0 Interest on short-term borrowing 0 0 (0.41) (0.13) Short-term borrowing repaid 0 0 (9.19) (4.41) Ending cash balance €45.00 €45.00 €45.00 €45.00 Minimum cash balance (45.00) (45.00) (45.00) (45.00) Cumulative surplus (deficit) 0 0 0 0 Beginning short-term investments €28.00 €44.51 0 0 Ending short-term investments €44.51 0 0 €53.76 Beginning short-term debt 0 0 €13.60 €4.41 Ending short-term debt 0 €13.60 €4.41 0 b. And with a minimum cash balance of €15M, the short-term financial plan will be: WILDCAT SA Short-Term Financial Plan (in millions) Q1 Q2 Q3 Q4 Beginning cash balance €15.00 €15.00 €15.00 €15.00 Net cash inflow 15.95 (59.00) 9.60 58.30 New short-term investments (17.11) 0 (9.95) (58.85) Income on short-term investments 1.16 1.50 .35 0.55 Short-term investments sold 0 €57.50 0 0 New short-term borrowing 0 0 0 0 Interest on short-term borrowing 0 0 0 0 Short-term borrowing repaid 0 0 0 0 Ending cash balance €15.00 €15.00 €15.00 €15.00 Minimum cash balance (15.00) (15.00) (15.00) (15.00) Cumulative surplus (deficit) 0 0 0 0 Beginning short-term investments €58.00 €75.11 €17.61 €27.56 Ending short-term investments €75.11 €17.61 €27.56 €86.41 Beginning short-term debt 0 0 0 0 Ending short-term debt 0 0 0 0 Since cash has an opportunity cost, the firm can boost its profit if it keeps its minimum cash balance low and invests the cash instead. However, the trade-off is that in the event of unforeseen circumstances, the firm may not be able to meet its short-run obligations if enough cash is not available. 31. This question is designed to make students collect their own data and carry out an analysis using real companies. As such, there is no correct answer because each year the data will be different. Chapter 26 case study Wolgemut Manufacturing Working Capital Management 1. The cash flow each quarter will consist of the sales collection, minus the suppliers paid, expenses, dividends, interest, and capital outlays. The cash flows for each quarter will be: Cash Flow Q1 Q2 Q3 Q4 Collections from previous quarter €383,400.00 €386,460.00 €400,140.00 €429,552.00 Collections from current quarter sales 223,740.00 231,660.00 248,688.00 215,820.00 Payments to suppliers for previous quarter –179,670.00 –186,030.00 –199,704.00 –173,310.00 Payments to suppliers for current quarter –129,870.00 –139,416.00 –120,990.00 –135,464.40 Expenses –152,550.00 –157,950.00 –169,560.00 –147,150.00 Dividends and interest –120,000.00 –120,000.00 –120,000.00 –120,000.00 Outlay –200,000.00 Net cash flow €25,050.00 €14,724.00 –€161,426.00 €69,447.60 Cash Balance Q1 Q2 Q3 Q4 Beginning cash balance €115,000.00 €140,050.00 €154,774.00 –€6,652.00 Net cash inflow 25,050.00 14,724.00 161,426.00 69,447.60 Ending cash balance €140,050.00 €154,774.00 –€6,652.00 €62,795.60 Minimum cash balance 90,000.00 90,000.00 90,000.00 90,000.00 Cumulative surplus –deficit €50,050.00 €64,774.00 –€96,652.00 –€27,204.40 The short-term financial plan looks like this: Short-term Financial Plan Q1 Q2 Q3 Q4 Target cash balance €90,000.00 €90,000.00 €90,000.00 €90,000.00 Net cash inflow 25,050.00 14,724.00 –161,426.00 69,447.60 New short-term investments –25,175.00 –14,974.88 0 0 Income on short-term investments 125.00 250.88 325.75 0 Short-term investments sold 0 0 65,149.88 0 New short-term borrowing 0 0 95,950.38 0 Interest on short-term borrowing 0 0 0 –1,151.40 Short-term borrowing repaid 0 0 0 –68,296.20 Ending cash balance €90,000.00 €90,000.00 €90,000.00 €90,000.00 Minimum cash balance –90,000.00 –90,000.00 –90,000.00 –90,000.00 Cumulative surplus –deficit €0 €0 €0 €0 Beginning short-term investments €25,000.00 €50,175.00 €65,149.88 €0 Ending short-term investments 50,175.00 65,149.88 0 0 Beginning short-term debt 0 0 0 95,950.38 Ending short-term debt €0 €0 €95,950.38 €27,654.18 The interest calculations for each quarter and the net cash cost are: Q1: Excess funds at start of quarter of €25,000.00 earns €125.00 in income. Q2: Excess funds at start of quarter of €50,175.00 earns €250.88 in income. Q3: Excess funds at start of quarter of €65,149.88 earns €325.75 in income. Q4: Shortage of funds at start of quarter of €95,950.38 costs €1,151.40 in interest. Net cash cost Q1 €125.00 Q2 250.88 Q3 325.75 Q4 –1,151.40 Cash generated by short-term financing –€449.78 2. If Wolgemut reduces its target cash balance to €70,000, the cash flows each quarter will remain the same, so they will not be repeated here. The cash balance and short-term financial plan will be: Cash Balance Q1 Q2 Q3 Q4 Beginning cash balance €115,000.00 €140,050.00 €154,774.00 –€6,652.00 Net cash inflow 25,050.00 14,724.00 –161,426.00 69,447.60 Ending cash balance €140,050.00 €154,774.00 –€6,652.00 €62,795.60 Minimum cash balance 70,000.00 70,000.00 70,000.00 70,000.00 Cumulative surplus –deficit €70,050.00 €84,774.00 –€76,652.00 –€7,204.40 Short-term Financial Plan Target cash balance €70,000.00 €70,000.00 €70,000.00 €70,000.00 Net cash inflow 25,050.00 14,724.00 –161,426.00 69,447.60 New short-term investments –25,275.00 –15,075.38 0 0 Income on short-term investments 225.00 351.38 426.75 0 Short-term investments sold 0 0 85,350.38 0 New short-term borrowing 0 0 75,648.87 0 Interest on short-term borrowing 0 0 0 –907.79 Short-term borrowing repaid 0 0 0 –68,539.81 Ending cash balance €70,000.00 €70,000.00 €70,000.00 €70,000.00 Minimum cash balance –70,000.00 –70,000.00 –70,000.00 –70,000.00 Cumulative surplus –deficit €0 €0 €0 €0 Beginning short-term investments €45,000.00 €70,275.00 €85,350.38 €0 Ending short-term investments 70,275.00 85,350.38 0 0 Beginning short-term debt 0 0 0 75,648.87 Ending short-term debt €0 €0 €75,648.87 €7,109.06 Q1: Excess funds at start of quarter of €45,000.00 earns €225.00 in income. Q2: Excess funds at start of quarter of €70,275.00 earns €351.38 in income. Q3: Excess funds at start of quarter of €85,350.38 earns €426.75 in income. Q4: Shortage of funds at start of quarter of €75,648.87 costs €907.79 in interest. Net cash cost Q1 €225.00 Q2 351.38 Q3 426.75 Q4 –907.79 Cash generated by short-term financing €95.34 3. If the sales growth rate is 11 percent, the cash flows for each quarter will be: Cash Flow Q1 Q2 Q3 Q4 Collections from previous quarter €383,400.00 €397,195.00 €411,255.00 €441,484.00 Collections from current quarter sales 229,955.00 238,095.00 255,596.00 221,815.00 Payments to suppliers for previous quarter –184,660.83 –191,197.50 –205,251.33 –178,124.17 Payments to suppliers for current quarter –133,477.50 –143,288.67 –124,350.83 –143,094.73 Expenses –156,787.50 –162,337.50 –174,270.00 –151,237.50 Dividends and interest –120,000.00 –120,000.00 –120,000.00 –120,000.00 Outlay –200,000.00 Net cash flow €18,429.17 €18,466.33 –€157,021.17 €70,842.61 Cash Balance Q1 Q2 Q3 Q4 Beginning cash balance €115,000.00 €133,429.17 €151,895.50 –€5,125.67 Net cash inflow 18,429.17 18,466.33 –157,021.17 70,842.61 Ending cash balance €133,429.17 €151,895.50 –€5,125.67 €65,716.94 Minimum cash balance 90,000.00 90,000.00 90,000.00 90,000.00 Cumulative surplus –deficit €43,429.17 €61,895.50 –€95,125.67 –€24,283.06 The short-term financial plan looks like this: Short-term Financial Plan Target cash balance €90,000.00 €90,000.00 €90,000.00 €90,000.00 Net cash inflow 18,429.17 18,466.33 –157,021.17 70,842.61 New short-term investments –18,554.17 –18,684.10 0 0 Income on short-term investments 125.00 217.77 311.19 0 Short-term investments sold 0 0 62,238.27 0 New short-term borrowing 0 0 94,471.70 0 Interest on short-term borrowing 0 0 0 –1,133.66 Short-term borrowing repaid 0 0 0 –69,708.95 Ending cash balance €90,000.00 €90,000.00 €90,000.00 €90,000.00 Minimum cash balance –90,000.00 –90,000.00 –90,000.00 –90,000.00 Cumulative surplus –deficit €0 €0 €0 €0 Beginning short-term investments €25,000.00 €43,554.17 €62,238.27 €0 Ending short-term investments 43,554.17 62,238.27 0 0 Beginning short-term debt 0 0 0 94,471.70 Ending short-term debt €0 €0 €94,471.70 €24,762.76 The interest calculations for each quarter and the net cash cost are: Q1: Excess funds at start of quarter of €25,000.00 earns €125.00 in income. Q2: Excess funds at start of quarter of €43,554.17 earns €217.77 in income. Q3: Excess funds at start of quarter of €62,238.27 earns €311.19 in income. Q4: Shortage of funds at start of quarter of €94,471.70 costs €1,133.66 in interest. Net cash cost Q1 €125.00 Q2 217.77 Q3 311.19 Q4 –1,133.66 Cash generated by short-term financing –€479.70 If the sales growth rate is 5 percent, the cash flows for each quarter will be: Cash Flow Q1 Q2 Q3 Q4 Collections from previous quarter €383,400.00 €375,725.00 €389,025.00 €417,620.00 Collections from current quarter sales 217,525.00 225,225.00 241,780.00 209,825.00 Payments to suppliers for previous quarter –174,679.17 –180,862.50 –194,156.67 –168,495.83 Payments to suppliers for current quarter –126,262.50 –135,543.33 –117,629.17 –128,043.13 Expenses –148,312.50 –153,562.50 –164,850.00 –143,062.50 Dividends and interest –120,000.00 –120,000.00 –120,000.00 –120,000.00 Outlay –200,000.00 Net cash flow €31,670.83 €10,981.67 €–165,830.83 €67,843.54 Cash Balance Q1 Q2 Q3 Q4 Beginning cash balance €115,000.00 €146,670.83 €157,652.50 –€8,178.33 Net cash inflow 31,670.83 10,981.67 –165,830.83 67,843.54 Ending cash balance €146,670.83 €157,652.50 –€8,178.33 €59,665.21 Minimum cash balance 90,000.00 90,000.00 90,000.00 90,000.00 Cumulative surplus –deficit €56,670.83 €67,652.50 –€98,178.33 –€30,334.79 The short-term financial plan looks like this: Short-term Financial Plan Target cash balance €90,000.00 €90,000.00 €90,000.00 €90,000.00 Net cash inflow 31,670.83 10,981.67 –165,830.83 67,843.54 New short-term investments –31,795.83 –11,265.65 0 0 Income on short-term investments 125.00 283.98 340.31 0 Short-term investments sold 0 0 68,061.48 0 New short-term borrowing 0 0 97,429.05 0 Interest on short-term borrowing 0 0 0 –1,169.15 Short-term borrowing repaid 0 0 0 –66,674.39 Ending cash balance €90,000.00 €90,000.00 €90,000.00 €90,000.00 Minimum cash balance –90,000.00 –90,000.00 –90,000.00 –90,000.00 Cumulative surplus –deficit €0 €0 €0 €0 Beginning short-term investments €25,000.00 €56,795.83 €68,061.48 €0 Ending short-term investments 56,795.83 68,061.48 0 0 Beginning short-term debt 0 0 0 97,429.05 Ending short-term debt €0 €0 €97,429.05 €30,754.65 The interest calculations for each quarter and the net cash cost are: Q1: Excess funds at start of quarter of €25,000.00 earns €125.00 in income. Q2: Excess funds at start of quarter of €56,795.83 earns €283.98 in income. Q3: Excess funds at start of quarter of €68,061.48 earns €340.31 in income. Q4: Shortage of funds at start of quarter of €97,429.05 costs €1,169.15 in interest. Net cash cost Q1 €125.00 Q2 283.98 Q3 340.31 Q4 1,169.15 Cash generated by short-term financing –€419.86 4. Since the only period in which there is borrowing is the third period, we can set the ending short- term debt in quarter 3 equal to zero and use Solver. Doing so, we find the necessary target cash balance is –€54,000, which implies it is not possible for the company to eliminate short-term borrowing during the next year. The short-term financial plan would be: Cash Flow Q1 Q2 Q3 Q4 Collections from previous quarter €383,400.00 €386,460.00 €400,140.00 €429,552.00 Collections from current quarter sales 223,740.00 231,660.00 248,688.00 215,820.00 Payments to suppliers for previous quarter –179,670.00 –186,030.00 –199,704.00 –173,310.00 Payments to suppliers for current quarter –129,870.00 –139,416.00 –120,990.00 –135,464.40 Expenses –152,550.00 –157,950.00 –169,560.00 –147,150.00 Dividends and interest –120,000.00 –120,000.00 –120,000.00 –120,000.00 Outlay –200,000.00 Net cash flow €25,050.00 €14,724.00 €–161,426.00 €69,447.60 Cash Balance Q1 Q2 Q3 Q4 Beginning cash balance €115,000.00 €140,050.00 €154,774.00 €–6,652.00 Net cash inflow 25,050.00 14,724.00 –161,426.00 69,447.60 Ending cash balance €140,050.00 €154,774.00 €–6,652.00 €62,795.60 Minimum cash balance –54,000.00 –54,000.00 –54,000.00 –54,000.00 Cumulative surplus –deficit €194,050.00 €208,774.00 €47,348.00 €116,795.60 The short-term financial plan looks like this: Short-term Financial Plan Target cash balance –€54,000.00 –€54,000.00 –€54,000.00 –€54,000.00 Net cash inflow 25,050.00 14,724.00 –161,426.00 69,447.60 New short-term investments –25,895.00 –15,698.48 0 –69,698.70 Income on short-term investments 845.00 974.48 1,052.97 251.10 Short-term investments sold 0 0 160,373.03 0 New short-term borrowing 0 0 0 0 Interest on short-term borrowing 0 0 0 0 Short-term borrowing repaid 0 0 0 0 Ending cash balance –€54,000.00 –€54,000.00 –€54,000.00 –€54,000.00 Minimum cash balance 54,000.00 54,000.00 54,000.00 54,000.00 Cumulative surplus –deficit €0 €0 €0 €0 Beginning short-term investments €169,000.00 €194,895.00 €210,593.48 €50,220.44 Ending short-term investments 194,895.00 210,593.48 50,220.44 119,919.14 Beginning short-term debt 0 0 0 0 Ending short-term debt €0 €0 €0 €0 The interest calculations for each quarter and the net cash cost are: Q1: Excess funds at start of quarter of €169,000.00 earns €845.00 in income. Q2: Excess funds at start of quarter of €194,895.00 earns €974.48 in income. Q3: Excess funds at start of quarter of €210,593.48 earns €1,052.97 in income. Q4: Excess funds at start of quarter of €50,220.44 earns €251.10 in income. Net cash cost Q1 €845.00 Q2 974.48 Q3 1,052.97 Q4 251.10 Cash generated by short-term financing €3,123.54 Chapter 27 Short Term Capital Management 1. Yes. Once a firm has more cash than it needs for operations and planned expenditures, the excess cash has an opportunity cost. It could be invested (by shareholders) in potentially more profitable ways. 2. Baumol Model: We obtain the solution for the general cash balance, C*, by solving this equation for C: 2 2 * 2 R TF C C TF/R = = Where R is the opportunity cost of holding cash, T is the total amount of new cash needed for transaction purposes over the relevant planning period, F is the fixed cost of selling securities to replenish cash Miller-Orr Model: Given L, which is set by the firm, the Miller–Orr model solves for the target cash balance, Z, and the upper limit, U. Expected total costs of the cash balance return policy (Z, U) are equal to the sum of expected transaction costs and expected opportunity costs. The values of Z (the return cash point) and U (the upper limit) that minimize the expected total cost have been determined by Miller and Orr: Z *=3 3Fs2 / (4R) +L U* = 3Z* − 2L Here * denotes optimal values, and σ2 is the variance of net daily cash flows. The average cash balance in the Miller–Orr model is: 4 Average cash balance = 3 Z − L 3. Net disbursement float is more desirable because the bank thinks the firm has more money than it actually does, and the firm is, therefore, receiving interest on funds it has already spent. 4. If it has too much cash it can simply pay a dividend, or, more likely in the current financial environment, buy back shares. It can also reduce debt. If it has insufficient cash, then it must either borrow, sell shares, or improve profitability. 5. The terms of sale refer to the period for which credit is granted, the cash discount, and the type of credit instrument. For example, suppose a customer is granted credit with terms of 5/30, net 90. This means that the customer has 90 days from the invoice date within which to pay. In addition, a cash discount of 5 percent from the stated sales price is to be given if payment is made in 30 days. If the stated terms are net 60, the customer has 60 days from the invoice date to pay and no discount is offered for early payment. 6. A firm must consider three factors in setting a credit period: The probability that the customer will not pay, the size of the account, and the extent to which the goods are perishable. 7. It is definitely true that a company can have an optimal credit policy. This will be a function of the strategic and corporate goals of the company, as well as the tax system, bankruptcy costs and agency costs. The credit cost curve expresses the total cost of granting credit as a function of the carrying costs and opportunity costs of granting credit. A credit cost curve is provided in Figure 28.6 of the main text. The level of credit corresponding to the minimum point on the total credit cost curve is the optimum level of credit. If a firm's present level of credit is less (more) than the optimum level, the firm should keep on increasing (decreasing) the level of credit unless it reaches the optimum level. 8. The five Cs of credit are Character, Capacity, Capital, Collateral, and Conditions. Other factors could be related to political and strategic decisions. For example, in 2009, the British government forcibly told banks to extend credit to small companies in an attempt to re-galvanise the UK economy. 9. An ageing schedule allows a firm to focus their collection efforts on a subset of outstanding credit. Companies spend a lot of time following up on debtors, especially when their payments are overdue. By having different collection strategies for each category of debtor, the firm can maximise its collections. 10. The holding cost is the average daily cash balance times the interest rate, so: Holding cost = (£10,500)(.03) Holding cost = £315 The trading costs are the total cash needed times the replenishing costs, divided by the average daily balance times two, so: Trading cost = [(£65,000)(£17)]/[(£10,500)(2)] Trading cost = £210.48 The total cost is the sum of the holding cost and the trading cost, so: Total cost = £315.00 + £210.48 Total cost = £525.48 The target cash balance using the Baumol model is: Z* = [(2T × F)/R]1/2 Z* = [2(£65,000)(£17)/.03]1/2 Z* = £8,582.93 They should increase their average daily cash balance to: New average cash balance = €£8,582.93/2 New average cash balance = £4,291.47 This would minimize the costs. The new total cost would be: New total cost = (£4,291.47)(.03) + [(£65,000)(£17)]/[2(£4,291.47)] New total cost = £257.49 11. a. The opportunity costs are the amount transferred times the interest rate, divided by two, so: Opportunity cost = (€20,000)(.03)/2 Opportunity cost = €300 The trading costs are the total cash balance times the trading cost per transaction, divided by the amount transferred, so: Trading cost = (€54,000)(€100)/€20,000 Trading cost = €270 The firm keeps too little in cash because the trading costs are lower than the opportunity costs. b. The target cash balance using the Baumol model is: Z* = [(2T × F)/R]1/2 Z* = [2(€54,000)(€100)/.03]1/2 Z* = €18,973.67 12. a. The disbursement float is the average monthly cheques written times the average number of days for the cheques to clear, so: Disbursement float = 3(€125,000) Disbursement float = €375,000 The collection float is the average monthly cheques received times the average number of days for the cheques to clear, so: Collection float = 4(–€140,000) Collection float = –€560,000 The net float is the disbursement float plus the collection float, so: Net float = €375,000 – €560,000 Net float = -€185,000 b. The new collection float will be: Collection float = 2(–€140,000) Collection float = –€280,000 And the new net float will be: Net float = €375,000 – €280,000 Net float = €95,000 13. a. Total float = 4(£12,000) + 6(£7,000) + 5(£3,000) Total float = £105,000 b. The average daily float is the total float divided by the number of days in a month. Assuming 30 days in a month, the average daily float is: Average daily float = £105,000/30 Average daily float = £3,500 c. The average daily receipts are the average monthly cheques received divided by the number of days in a month. Assuming a 30 day month: Average daily receipts = (£12,000 + £7,000 + £3,000)/30 Average daily receipts = £733.33 The weighted average delay is the sum of the days to clear a cheque, times the amount of the cheque divided by the average monthly receipts, so: Weighted average delay = 4(£12,000/£22,000) + 6(£7,000/£22,000) + 5(£3,000/£22,000) Weighted average delay = 4.77 days 14. a. The average daily float is the sum of the percentage each cheque times the number of cheques received times the amount of the cheque times the number of days until the cheque clears, divided by the number of days in a month. Assuming a 30 day month, we get: Average daily float = [.34(50,000)(€20)(2) + .66(50,000)(€30)(3)]/30 Average daily float = €121,666.67 On average, there is €121,666.67 that is uncollected and not available to the firm. b. The total collections are the sum of the percentage of each cheque amount received times the total cheques received times the amount of the cheque, so: Total collections = .34(50,000)(€20) + .66(50,000)(€30) Total collections = €1,330,000 The weighted average delay is the sum of the average number of days a cheque of a specific amount is delayed, times the percentage that cheque amount makes up of the total cheques received, so: Weighted average delay = 2(€340,000 /€1,333,000) + 3(€990,000/€1,333,000) Weighted average delay = 2.74 days The average daily float is the weighted average delay times the average cheques received per day. Assuming a 30 day month, we get: Average daily float = 2.74(€1,333,000/30 days) Average daily float = €121,747 c. The most the firm should pay is the total amount of the average float, or €121,747. d. The average daily interest rate is: 1.03 = (1 + R)365 R = .0081% per day The daily cost of float is the average daily float times the daily interest rate, so: Daily cost of the float = €121,747(.000081) Daily cost of the float = €985.99 e. The most the firm should pay is still the average daily float. Under the reduced collection time assumption, we get: New average daily float = 1.20(€1,333,000/30) New average daily float = €53,320 15. a. The reduction in cash balance from adopting the new system is the number of days it reduces collection time times the average daily collections, so: Cash balance reduction = 4(SFr640,000) Cash balance reduction = SFr2,560,000 b. The Swiss franc return that can be earned is the average daily interest rate times the cash balance reduction. The average daily interest rate is: Average daily rate = 1.121/365 – 1 Average daily rate = .0311% per day The daily return that can be earned from the reduction in days to clear the cheques is: Daily return = SFr2,560,000(.000311) Daily return = SFr794.98 c. If the company takes the new system, it will receive four payments early, with the first payment occurring today. We can use the daily interest rate from part b, so the savings are: Savings = SFr640,000 + SFr640,000(PVIFA.0311%,3) Savings = SFr2,558,808 If the new system payments occur at the end of the month, we need the effective monthly interest rate, which is: Monthly interest rate = 1.121/12 – 1 Monthly interest rate = 0.9489% Assuming the new system payments occur at the end of the month, the payments, which are a perpetuity, will be: PV = C/R SFr2,558,808.15 = C / .009489 C = SFr24,280 It could also be assumed that the payments occur at the beginning of the month. If so, we would need to use the PV of a perpetuity due, which is: PV = C + C / R Solving for C: C = (PV × R) / (1 + R) C = (SFr2,558,808 × .009489) / (1 + .009489) C = SFr24,051.79 16. The interest that the company could earn will be the amount of the cheques times the number of days it will delay payment times the number of weeks that cheques will be disbursed times the daily interest rate, so: Interest = £370,000(7)(52/2)(.0003) Interest = £20,202 17. The benefit of the new arrangement is the Rm640 million in accelerated collections since the new system will speed up collections by one day. The cost is the new compensating balance, but the company will recover the existing compensating balance, so: NPV = Rm640,000,000 – (Rm30,000,000 – Rm20,000,000) NPV = Rm630,000,000 The company should proceed with the new system. The savings are the NPV times the annual interest rate, so: Net savings = Rm630,000,000(.07) Net savings = Rm44,100,000 18. The total cash needed is the cash shortage per month times twelve months, so: Total cash = 12(€360,000) Total cash = €4,320,000 The target cash balance using the Baumol model is: Z* = [(2T × F)/R]1/2 Z* = [2(€4,320,000)(€500)/.065]1/2 Z* = €257,801.35 The company should invest: Invest = €700,000 – €257,801.35 Invest = €442,198.65 of its current cash holdings in marketable securities to bring the cash balance down to the optimal level. Over the rest of the year, sell securities: Sell securities = €4,320,000/€257,801.35 Sell securities = 16.76 17 times. 19. The target cash balance using the Miller-Orr model is: Z* = L + (3/4 × F × 2 / R)1/3 Z* = £1,100 + [3/4(£100)(£75)2/.00021]1/3 Z* = £2,361.79 The upper limit is: U* = 3 × Z* – 2 × L U* = 3(£2,361.79) – 2(£1,100) U* = £4,885.38 When the balance in the cash account drops to £1,100, the firm sells of marketable securities: Sell = £2,361.79 – £1,100 Sell = £1,261.79 20. Using the Baumol model and solving for R, we get: Z* = [(2T × F)/R]1/2 €2,200 = [2(€21,000)(€10)/R]1/2 R = [2(€21,000)(€10)]/€2,2002 R = .0868 or 8.68% 21. a. There are 30 days until account is overdue. If you take the full period, you must remit: Remittance = 200(£95) Remittance = £19,000 b. There is a 2 percent discount offered, with a 10 day discount period. If you take the discount, you will only have to remit: Remittance = (1 – .02)(£19,000) Remittance = £18,620 c. The implicit interest is the difference between the two remittance amounts, or: Implicit interest = £19,000 – £18,620 Implicit interest = £380 The number of days’ credit offered is: Days’ credit = 30 – 10 Days’ credit = 20 days 22. a. The average collection period is the percentage of accounts taking the discount times the discount period, plus the percentage of accounts not taking the discount times the days until full payment is required, so: Average collection period = .65(10 days) + .35(30 days) Average collection period = 17 days b. And the average balance is: Average balance = 1,200(£2,200)(17)(12/365) Average balance = £1,475,506.85 23. The interest rate for the term of the discount is: Interest rate = .02/.98 Interest rate = .0204 or 2.04% And the interest is for: 40 – 9 = 31 days So, using the EAR equation, the effective annual interest rate is: EAR = (1 + Periodic rate)m – 1 EAR = (1.0204)365/31 – 1 EAR = .2685 or 26.85% a. The periodic interest rate is: Interest rate = .03/.97 Interest rate = .0309 or 3.09% And the EAR is: EAR = (1.0309)365/31 – 1 EAR = .4314 or 43.14% b. The EAR is: EAR = (1.0204)365/51 – 1 EAR = .1556 or = 15.56% c. The EAR is: EAR = (1.0204)365/25 – 1 EAR = .3431 or 34.31% 24. The receivables turnover is: Receivables turnover = 365/Average collection period Receivables turnover = 365/52 Receivables turnover = 7.02 times And the annual credit sales are: Annual credit sales = Receivables turnover × Average daily receivables Annual credit sales = 7.02(€46,000) Annual credit sales = €322,884.62 25. The total sales of the firm are equal to the total credit sales since all sales are on credit, so: Total credit sales = 4,000(£400) Total credit sales = £1,600,000 The average collection period is the percentage of accounts taking the discount times the discount period, plus the percentage of accounts not taking the discount times the days until full payment is required, so: Average collection period = .60(15) + .40(40) Average collection period = 25 days The receivables turnover is 365 divided by the average collection period, so: Receivables turnover = 365/25 Receivables turnover = 14.60 times And the average receivables are the credit sales divided by the receivables turnover so: Average receivables = £1,600,000/14.60 Average receivables = £109,589.04 If the firm increases the cash discount, more people will pay sooner, thus lowering the average collection period. If the ACP declines, the receivables turnover increases, which will lead to a decrease in the average receivables. 26. The average collection period is the net credit terms plus the days overdue, so: Average collection period = 25 + 9 Average collection period = 34 days The receivables turnover is 365 divided by the average collection period, so: Receivables turnover = 365/34 Receivables turnover = 10.7353 times And the average receivables are the credit sales divided by the receivables turnover so: Average receivables = £8,000,000/10.7353 Average receivables = £745,205.1 27. a. The cash outlay for the credit decision is the variable cost of the engine. If this is a one-time order, the cash inflow is the present value of the sales price of the engine times one minus the default probability. So, the NPV per unit is: NPV = –€$1,500,000 + (1 – .005)(€1,800,000)/1.025 NPV = €247,317.07 per unit The company should fill the order. b. To find the breakeven probability of default, , we simply use the NPV equation from part a, set it equal to zero, and solve for . Doing so, we get: NPV = 0 = –€1,500,000 + (1 – )(€1,800,000)/1.025 = .1458 or 14.58% We would not accept the order if the default probability was higher than 14.58 percent. c. If the customer will become a repeat customer, the cash inflow changes. The cash inflow is now one minus the default probability, times the sales price minus the variable cost. We need to use the sales price minus the variable cost since we will have to build another engine for the customer in one period. Additionally, this cash inflow is now a perpetuity, so the NPV under these assumptions is: NPV = –€1,500,000 + (1 – .005)(€1,800,000 – €1,500,000)/.025 NPV = €10,440,000.00 per unit The company should fill the order. The breakeven default probability under these assumptions is: NPV = 0 = –€1,500,000 + (1 – )(€1,800,000 – €1,500,000)/.025 = .8750 or 87.50% We would not accept the order if the default probability was higher than 87.50 percent. This default probability is much higher than in part b because the customer may become a repeat customer. d. It is assumed that if a person has paid his or her bills in the past, they will pay their bills in the future. This implies that if someone doesn’t default when credit is first granted, then they will be a good customer far into the future, and the possible gains from the future business outweigh the possible losses from granting credit the first time. 28. The cost of switching is the lost sales from the existing policy plus the incremental variable costs under the new policy, so: Cost of switching = €800(1,130) + €475(1,195 – 1,130) Cost of switching = €934,875 The benefit of switching is the new sales price minus the variable costs per unit, times the incremental units sold, so: Benefit of switching = (€800 – €475)(1,195 – 1,130) Benefit of switching = €21,125 The benefit of switching is a perpetuity, so the NPV of the decision to switch is: NPV = –€934,875 + €21,125/.015 NPV = £473,458.33 Since NPV is positive, Champions should proceed. The firm will have to bear the cost of sales for one month before they receive any revenue from credit sales, which is why the initial cost is for one month. Receivables will grow over the one month credit period and will then remain stable with payments and new sales offsetting one another. 29. The cash flow from the old policy is the quantity sold times the price, so: Cash flow from old policy = 70,000(£530) Cash flow from old policy = £37,100,000 The cash flow from the new policy is the quantity sold times the new price, all times one minus the default rate, so: Cash flow from new policy = 70,000(£552)(1 – .02) Cash flow from new policy = £37,867,200 The incremental cash flow is the difference in the two cash flows, so: Incremental cash flow = £37,867,200 – £37,100,000 Incremental cash flow = £767,200 The cash flows from the new policy are a perpetuity. The cost is the old cash flow, so the NPV of the decision to switch is: NPV = –£37,100,000 + £767,200/.02 NPV = £1,260,000 Since NPV is positive, the change is a good idea. 30. a. The old price as a percentage of the new price is: €90/€91.84 = .98 So the discount is: Discount = 1 – .98 = .02 or 2% The credit terms will be: Credit terms: 2/10, net 30 b. We are unable to determine for certain since no information is given concerning the percentage of customers who will take the discount. However, the maximum receivables would occur if all customers took the credit, so: Receivables = 3,000(€90) Receivables = €270,000 (at a maximum) c. Since the quantity sold does not change, variable cost is the same under either plan. d. No, because: d – = .02 – .10 d – = –.08 or –8% Therefore the NPV will be negative. The NPV is: NPV = –3,000(€90) + (3,000)(€91.84)(.02 – .10)/(.01) NPV = -€2,474,160 The breakeven credit price is: P(1 + r)/(1 – ) = €90(1.01)/(.9) P = €101 This implies that the breakeven discount is: Breakeven discount = 1 – (€90/€101) Breakeven discount = .1089 or 10.89% The NPV at this discount rate is: NPV = –3,000(€90) + (3,000)(€101)(.1089 – .10)/(.01) NPV 0 31. We must first find the expected revenue per invoice since there is a probability of default. The expected revenue per invoice is the invoice price times one minus the probability of default, or: Expected revenue per invoice = €1,500(1 – .025) Expected revenue per invoice = €1,462.5 The cost per invoice is the price paid, or: Cost per invoice = €1,500(1 – .035) Cost per invoice = €1,447.50 The EBIT is the revenue minus expenses, or: EBIT = Revenue – Variable costs – Fixed costs EBIT = 100,000(€1,462.5) – 100,000(€1,447.50) – €400,000 EBIT = €1,100,000 32. If we factor immediately, we receive cash on an average of 34 days sooner. The number of periods in a year are: Number of periods = 365/34 Number of periods = 10.73529 The EAR of this arrangement is: EAR = (1 + Periodic rate)m – 1 EAR = (1 + 2/98)10.73529 – 1 EAR = .2422 or 24.22% 33. a. The cost of the credit policy switch is the quantity sold times the variable cost. The cash inflow is the price times the quantity sold, times one minus the default rate. This is a one-time, lump sum, so we need to discount this value one period. Doing so, we find the NPV is: NPV = –12(£1,200) + (1 – .2)(12)(£1,850)/1.02 NPV = £3,011.76 The order should be taken since the NPV is positive. b. To find the breakeven default rate, , we just need to set the NPV equal to zero and solve for the breakeven default rate. Doing so, we get: NPV = 0 = –12(£1,200) + (1 – )(12)(£1,850)/1.02 = .3384 or 33.84% c. Effectively, the cash discount is: Cash discount = (£1,850 – £1,700)/£1,850 Cash discount = .0811 or 8.11% Since the discount rate is less than the default rate, credit should not be granted. The firm would be better off taking the £1,700 up-front than taking an 80% chance of making £1,850. 34. a. The cash discount is: Cash discount = (£55 – £51)/£55 Cash discount = .0727 or 7.27% The default probability is one minus the probability of payment, or: Default probability = 1 – .90 Default probability = .10 Since the default probability is greater than the cash discount, credit should not be granted; the NPV of doing so is negative. b. Due to the increase in both quantity sold and credit price when credit is granted, an additional incremental cost is incurred of: Additional cost = (3,300)(£31 – £29) + (3,500 – 3,300)(£31) Additional cost = £12,800 The breakeven price under these assumptions is: NPV = 0 = –£12,800 – (3,300)(£51) + {3,500[(1 – .10)P – £31] – 3,300(£51 – £29)}/(1.00753 – 1) NPV = –£12,800 – £168,300 + 138,955.23P – £7,988,822.93 £8,169,922.93 = 138,955.23P P = £58.80 c. The credit report is an additional cost, so we have to include it in our analysis. The NPV when using the credit reports is: NPV = 3,300(29) – .90(3,500)31 – 3,300(51) – 7,000 + {3,500[0.90(55 – 31) – 2] – 3,300(51 – 29)}/(1.00753 – 1) NPV = £95,700 – £97,650 – £168,300 – £184,400 – £176,451.09 NPV = –£353,701.09 So, credit should not be extended. 35. We can express the old cash flow as: Old cash flow = (P – v)Q And the new cash flow will be: New cash flow = (P – v)(1 – )Q + Q [(1 – )P – v] So, the incremental cash flow is Incremental cash flow = –(P – v)Q + (P – v)(1 – )Q + Q [(1 – )P – v] Incremental cash flow = (P – v)(Q – Q) + Q [(1 – )P – P] Thus: NPV = (P – v)(Q – Q) – PQ + + R (P - v)(Q - Q) Q {(1 - )P - P 36. If the cost of subscribing to the credit agency is less than the savings from collection of the bad debts, the company should subscribe. The cost of the subscription is: Cost of the subscription = £500 + £4(400) Cost of the subscription = £2,100 And the savings from not selling bad credit risks will be: Savings from not selling to bad credit risks = (£280)(400)(0.03) Savings from not selling to bad credit risks = £3,360 So, the company’s net savings will be: Net savings = £3,360 – £2,100 Net savings = £1,260 The company should subscribe to the credit agency. 37. The cash flow from the old policy is: Cash flow from old policy = (€75 – €43)(3,200) Cash flow from old policy = €102,400 And the cash flow from the new policy will be: Cash flow from new policy = (€80 – €43)(3,500) Cash flow from new policy = €129,500 The incremental cash flow, which is a perpetuity, is the difference between the old policy cash flows and the new policy cash flows, so: Incremental cash flow = €129,500 – €102,400 Incremental cash flow = €27,100 The cost of switching credit policies is: Cost of new policy = [PQ + Q (v – v) + v(Q – Q)] In this cost equation, we need to account for the increased variable cost for all units produced. This includes the units we already sell, plus the increased variable costs for the incremental units. So, the NPV of switching credit policies is: NPV = –[(€75)(3,200) + (3,200)(€43 – €43) + (€43)(3,500 – 3,200)] + (€27,100/.03) NPV = €650,433 Since the NPV of new credit policy is negative, Dschungel AG should not proceed with new credit policy. 38. Using the Baumol model and solving for T, we get: Z* = [(2T × F)/R]1/2 $10,000,000 = [2(T)($5,000)/.058]1/2 T = [($10,000,000)2(.058)] / [2($5,000)] T = $580,000,000 So, the average weekly disbursement is: Average weekly disbursement = $580,000,000 / 52 Average weekly disbursement = $11,153,846.15 39. a. Since the upper limit, U, is set by the firms, use that to find Z: U = 3Z – 2L Z = (U + 2L) / 3 So for Gold Star, the target cash balance is: Z = [£205,000 + 2(£95,000)] / 3 Z = £131,666.67 And for Silver Star, the target cash balance is: Z = [£230,000 + 2(£120,000)] / 3 Z = £156,666.67 b. We can use the Miller-Orr model to solve for the variance of the cash flows for each firm. Solving the Miller-Orr model for the variance, we find: Z* = L 4R 3 3Fσ2 + Z* – L = 2 3 3Fσ 4R (Z* – L)3 = 4R 3Fσ2 2 = (Z* L)3 4 R 3F - To find the variance of Gold Star’s cash flows, we first need to find the daily interest rate, which is: R = (1.058)1/365 – 1 R = 0.000154 And the variance of Gold Star’s cash flows is: 2 = (£131,666.67 £95,000)3 4 .000154 3 £2,800 - 2 = £3,626,296.53 The daily interest rate for Silver Star is: R = (1.061)1/365 – 1 R = 0.000162 And the variance of Silver Star’s cash flows is: 2 = (£156,666.67 £120,000)3 4 .000162 3 £2,500 - 2 = £4,265,442.41 40. The company should adopt the new credit policy if its PV, PVNew, is greater than the PV of the current policy, PVOld. Note that we can write the general formula as: PV = + 365 Avg. days to pay 1 (Discount rate) (Avg. sales)(1 - Discount) So, the PV of the current policy is: PVOld = (R50,000,000/365) / [1 + 0.06(45/365)] PVOld = R135,980.42 Now, find we can find the PV of the new policy. Under the new policy, we expect 2 groups of customers: 1) those that take the discount and pay early, and 2) those that do not take the discount and pay "late". Since we are only given the average collection for all customers, we need to find the average collection period for each group. For those who take the discount, we will assume they pay on day 10. Let T = the average number of days until payment for those customers who do not take the discount. This means the average collection period for those customers who do not take the discount will be: 0.7(10 days) + 0.3T = 28 days T = 70 days Now apply this to our general formula for PV, allowing for the fact that we have two kinds of customers, the PV of the new policy will be: PVNew = PV of customers who take discount + PV of customers who do not take discount PVNew = 0.7(R50,000,000/365)(1 0.02) 1 (0.06)(10/365) - + + 0.3(R50,000,000/365) 1 + (0.06)(70/365) PVNew = R134,446.77 Because PV of the current policy is greater than the PV of the new policy, the company should not adopt the new policy. Solution Manual for Corporate Finance David Hillier, Stephen Ross, Randolph Westerfield, Jeffrey Jaffe, Bradford Jordan 9780077139148
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