# EQL Model Mathematics & Economics Math Problem Paper (Math Problem Sample)

MBA 655 Quiz 3 Cranston Dispensers, Inc. In the early 1990s, Cranston Dispensers, Inc. was quick to realize that concern for the environment would cause many consumer product manufacturers to move away from aerosol dispensers to mechanical alternatives that pose no threat to the ozone layer. In the following decades, most countries banned the most popular aerosol propellants, first chlorofluorocarbons and then hydrocholrofluorocarbons. As the leading manufacturer of specialized pump and spray containers for a variety of products in cosmetics, household cleaning supplies, and pharmaceutical industries, Cranston experienced a rapid increase in sales and profitability after it made this strategic move. At that time, the firm focused much of its attention on capturing market share and keeping up with demand. For most of 20x4 and 20x5, however, Cranston’s share price was falling while shares of other companies in the industry were rising. At the end of fiscal 20x5, the company hired Susan McNulty as the new treasurer, with the expectation that she would diagnose Cranston’s problems and improve the company’s financial performance relative to that of its competitors. She decided to begin the task with a thorough review of the company’s working capital management practices. While examining the company’s financial statements, she noted that Cranston had a higher percentage of current assets on its balance sheet than other companies in the packaging industry. The high level of current assets caused the company to carry more short-term debt and to have higher interest expense than its competitors. It was also causing the company to lag behind its competitors on some key financial measures, such as return on assets and return on equity. In an effort to improve Cranston’s overall performance, Susan has decided to conduct a comprehensive review of working capital management policies, including those related to the cash conversion cycle, credit policy, and inventory management. Cranston’s financial statements for the three most recent years follow. Cranston Dispensers Income Statement ($ in thousands) Account 20x5 20x4 20x3 Sales 3,784 3,202 2,760 Cost of Goods Sold 2,568 2,172 1,856 Gross Profit 1,216 1,030 904 Selling & Administrative 550 478 406 Depreciation 247 230 200 Earnings Before Interest and Taxes 419 322 298 Interest Expense 20 25 14 Taxable Income 399 297 284 Taxes 120 89 85 Net Income 279 208 199 Cranston Dispensers Balance Sheet ($ in thousands) Account 20x5 20x4 20x3 Current Assets Cash 341 276 236 Accounts Receivable 722 642 320 Inventory 595 512 388 Total Current Assets 1,658 1,430 944 Net Fixed Assets 1,822 1,691 1,572 Total Assets 3,480 3,121 2,516 Current Liabilities Accounts Payable 332 288 204 Accrued Expenses 343 335 192 Short-term Notes 503 491 243 Total Current Liabilities 1,178 1,114 639 Long-term Debt 398 324 289 Other Long-term Liabilities 239 154 147 Total Liabilities 1,815 1,592 1,075 Owners’ Equity Common Equity 1,665 1,529 1,441 Total Liabilities & Equity 3,480 3,121 2,516 Required: 1. Determine Cranston’s average production cycles for 20x4 and for20x5. 2. Determine Cranston’s average collection cycles for 20x4 and for 20x5. Assume that all sales are credit sales. 3. Determine Cranston’s average payment cycles for 20x4 and for 20x5. 4. Using your answers to questions 1 through 3, determine Cranston’s cash conversion cycles for 20x4 and for 20x5. 5. Cranston now bills its customers with terms of net 45. Although most customers pay on time, some routinely stretch the payment period to sixty or even ninety days. What steps can Cranston take to encourage clients to pay on time? What is the potential risk of implementing penalties for late payment? 6. Suppose Cranston institutes a policy of granting a 1% discount for payment within fifteen days with the full amount due in 45 days. Half the customers take the discount, the other half take an average of sixty days to pay. a. What is the length of Cranston’s collection cycle under this new policy? b. In dollars, how much would the policy have cost Cranston in 20x5? c. If this policy had been in effect during 20x5, by how many days would Cranston have shortened the cash conversion cycle? 7. An image-based lockbox system could accelerate Cranston’s cash collections by three days. Cranston can earn an annual rate of 6% on the cash freed by accelerated collections. Using sales for 20x5, determine the most that Cranston should pay per year for the lockbox system. 8. One of Cranston’s principal raw materials is plastic pellets, which it purchases in lots of 100 pounds at $0.35 per pound. Annual consumption is 8,000,000 pounds. Within a broad range of order sizes, ordering and shipping costs are $120 per order. Carrying costs are $1.50 per year per 100 pounds. Compute the EOQ for plastic pellets. If Cranston used the EOQ model, how often would it order pellets?

source..

Cranston Dispensaries, Inc.

Student’s Name

Institutional Affiliation

The Average Production Cycle is 365/Inventory Turnover ratio= 365/ (Cost of Goods/Average Inventory) = (in simple terms) 365* Average Inventory/COGS

For 20*4

1.

Average Inventory (Average of Opening and Closing Inventory for the year 2004)

= (388+512)/2

=450

Production Cycle

= 365*450/2172

=75.62 days or 76 days

For 20*5

Average Inventory

= (595+512)/2=553.5

Production Cycle

= 365*553.5/2568

=78.67 days or 79 days

2.

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