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# Functions from tables. Find a simple function that fits ISBN: 9780321570567 2

## Solution for problem 42E Chapter 1.2

Calculus: Early Transcendentals | 1st Edition

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Problem 42E

Functions from tables. ?Find a simple function that fits the data in the tables.

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Exam 2 Study Guide Chapters 5-7 Contribution margin (CM=sales-variable expenses) o It is the amount available to cover fixed expense and whatever remains from it, goes toward profit o If the amount of contribution margin isn’t enough, then there is a loss Example: Here is an example of a company that sales furniture. The cost of one table is S300 and since the variable expense is \$200, the CM is \$100. For every additional table sold, there is \$200 more of CM that goes to cover the fixed expenses. If one more table is sold, the loss becomes \$19,800. Income Statement (Sale of one Table) Total Per unit Sales \$300 300 Variable expenses \$200 200 Contribution Margin \$100 100 Fixed expenses \$20,000 Net operating \$(19,900) loss income/loss When the company manages to sell 200 units, then that is the point at which the CM covers all of the fixed expenses. This means that company has reached breakeven for that month. If 201 units are sold, that means that there would be a Net Operating Profit of \$100. For every unit sold, after the amount that breaks even, there will be \$100 profit for each unit. Changes in activity  if the company currently sales 300 speakers, but plans to sell 350 in the next month, the increase in net operating income would be 50 units x \$100 which is \$5000 increase in income. Break-even point o Level of sales at which profit is zero o Once this point is reached, net operating income will increased by the amount of the unit contribution margin for each additional unit sold Contribution Margin Ratio Income Statement (Sale of one Table) Total Per unit Percent of Sales Sales (300 tables) \$90,000 (300 x 300 100% \$300) Variable expenses \$60,000 200 60,000/90,000= 67% Contribution \$30,000 100 30,000/90,000= Margin 33% Fixed expenses \$20,000 Net operating \$10,000 income/loss CM ratio = Contribution Margin / Sales In this case the CM ratio is 33%. This means that for each dollar increase in sales, the total CM will increase by 33 cents because it is (\$1 x 33%). Each dollar increase in sales will increase the CM and the net operating income by the CM ratio amount. Change in CM = CM Ratio x Change in Sales Example: If the furniture company plans to increase sales by 30,000 in the next month, then the CM should increase by \$9,900 (which is 30,000 x 33%) Income Statement (Sale of one Table) Total Expected Increase Sales (300 tables) \$90,000 \$120,000 \$30,000 Variable expenses \$60,000 \$80,000 \$20,000 Contribution \$30,000 40,000 \$10,000 Margin Fixed expenses \$20,000 20,000 0 Net operating \$10,000 \$20,000 \$10,000 income/loss ** The expected variable expenses is calculate by dividing the expected sales by the cost of the unit (which is 120,000 / 300 = 400 units) and then multiplying that by the original variable expense of each item (which is 400 x 200 = \$80,000) Changes in Fixed Cost and Sales Volume o Would an increase in advertising budget, in this case \$10,000 to the fixed expenses, increase the monthly sales by \$30,000, which would be a total of 400 units sold. o As seen in the table above, if the expected sales increase by 30,000, which means that it would be \$120,000. In this case, if \$10,000 is added to the fixed expense the change in fixed expense of \$10,000 would result in 0 increase in profits. Changes in Variable Costs and Sales Volume o The current cost of each table is \$300, but to make them of higher quality they would have to increase the variable costs by \$20 and therefore, reducing the CM. o Would the increase in quality, increase sales to 380 tables a month CM = 100 – 20 = \$80 Expected total CM with higher-quality tables  380 x \$80 = \$30,400 Present total CM  300 x 100 = \$30,000 The increase in total CM is \$400, which means that the net operating income would increase and therefore, the quality should be improved. Change in Selling Price o The company is currently selling 300 units but they have an opportunity to make a bulk sale of 150 units to a wholesales, with an acceptable price. This sale doesn’t affect the fixed costs of the company or the regular sales. o What is the price that should be quoted, if the company is seeking a profit of 4,000 Variable cost = \$200 Desired profit = 40,000 / 200 = 200 Quoted price should be \$200 Break-even analysis o There are two different approaches that could be used o Both will always result in the same number of units needed to break-even 1. Equation Method • Profit = Unit CM x Q – Fixed Expenses • Where: o Unit CM: unit contribution margin o Q: number of units Example: The CM is \$100 per table and the fixed expenses are \$20,000. Profit = 0 0 = \$100 x Q – S20,000 Q = \$20,000 / \$100 Q = 200 units would need to be sold in order to break-even (as mentioned at the beginning of the notes) 2. Formula Method • Unit sales to break even = Fixed expenses / Unit CM Break-Even in Dollar Sales There are three different methods 1. Use the equation method or formula method to find the break-even point in unit sales and then multiply the result by the selling price 2. Use the equation method to compute break-even point in dollar sales Profit = CM ratio x Sales – Fixed Expenses o Where you would place a 0 for profit and then solve for sales Example: 0 = .33 x Sales – \$20,000 Sales = \$20,000 / .33 Sales = \$60,606.06 3. Use the formula method to compute dollar sales need to break even Dollar sales to break even = Fixed expenses^4 / CM Ratio Margin of Safety • It is the excess of budgeted or actual sales dollars over the break-even volume of sales dollars • In other words, it is the amount by which sales can drop before losses are incurred • Higher margin of safety  lower risk of not breaking-even and incurring a loss Margin of safety in dollars = (total budgeted sales) – (Break-even sales) Margin of safety percentage = margin of safety in dollars / total budgeted sales Variable Costing vs. Absorption Costing • Variable o Product costs  direct materials, direct labor, variable manufacturing overhead (only manufacturing costs that vary with output) o Period costs  fixed manufacturing overhead, variable selling and administrative expenses, fixed selling and administrative expenses • Absorption o Product costs  direct materials, direct labor, variable manufacturing overhead, fixed manufacturing overhead (all manufacturing costs) o Period costs  variable selling and administrative expenses, fixed selling and administrative expenses *Main difference: absorption costing includes fixed manufacturing overhead in product costs *Absorption costing = highest values for work in process and finished goods inventory Unit Product Costs Reconciliation of Variable Costing with Absorption Costing Income o Units produced exceed unit sales  inventories increase  net operating income is higher under absorption costing • Why Because some of the fixed manufacturing overhead of the period is deferred in inventories o Unit sales exceed units produced  inventories decrease - net operating income is lower under absorption costing • Why Because some of the fixed manufacturing overhead of previous periods is released from inventories o To reconcile the two costing methods, we need to determine how much fixed manufacturing overhead was deferred or released from inventories Manufacturing overhead deferred (released) inventory = Fixed manufacturing overhead in ending inventories – fixed manufacturing overheard in beginning inventories o Once you have the fixed manufacturing overhead deferred or released from inventories, then you add that amount to the variable costing net operating income (loss) to get the absorption costing net operating income (loss) Variable costing net operating income (loss) Add (deduct) fixed manufacturing overhead deferred (released) from inventory under absorption Absorption costing net operating income (loss) Manufacturing overhead deferred in (released from) inventory = Fixed manufacturing overhead in ending inventories / fixed manufacturing overhead in beginning inventories Example: Absorption costing Fixed manufacturing overhead deferred in (released from) inventory January February March Fixed M.O in ending \$0 \$40,000 \$0 inventories Fixed M.O in 0 0 \$40,000 beginning inventories Fixed M.O deferred \$0 \$(40,000) \$40,000 in or released from • Cost per unit = fixed manufacturing overhead / units produced • The cost per unit is then multiplied by the units in beginning inventory to get the amount deferred or released o Units in beginning inventory = units produced – units sold Units produced = Units sold No change in inventories Absorption net operating income = variable net operating income Units produced > Units sold Inventories increase Absorption net operating income > variable net operating income Units produced < Units sold Inventories decrease Absorption net operating income < variable net operating income Break-Even Analysis Companywide break-even point Dollar sales for company to breakeven = (traceable fixed expenses + common fixed expenses) / overall CM ratios • Overall CM ratio = overall contribution margin / total sales Segment break-even point Dollar sales for a segment to break even = segment traceable fixed expenses / segment CM raito Activity-based Costing Tool Traditional absorption costing  provide data for external financial reports Activity-based costing (ABC) provide information to internal decision making Three ways it differs from traditional absorption costing: 1) Nonmanufacturing costs • Many nonmanufacturing costs relate to selling, distributing, and servicing • ABC includes nonmanufacturing and manufacturing costs when calculating the entire cost of a product i. Traces all direct nonmanufacturing costs to products 1. Commissions to salespersons, shipping costs, warranty repair costs ii. Allocates indirect nonmanufacturing costs to products whenever the product have caused the costs to be incurred 2) Manufacturing costs • ABC doesn’t assign two types of manufacturing overhead costs to products i. Organization-sustaining costs 1. They are treated as period expenses rather than product costs a. Factory security guard’s wages, cost of supplies used by plant manager’s secretary ii. Products are only charged for the costs of the capacity they use 3) Cost pools and Allocation Bases • Activity: event that causes consumption of overhead resources • Activity cost pool: “bucket” in which costs are accumulated that relate to a single activity measure in the ABC system • Activity measure: allocation based (cost driver) i. Transaction drivers: number of ties an activity occurs (example: number of bill sent out to customers) ii. Duration drivers: amount of time required to perform an activity (example: time spend preparing individual bills for customers) Activity-Based Costing (ABC) System • Strong top management support + cross-functional involvement + link to evaluation and rewards = successful ABC implementations Cost objects (products and customers) Activities Consumption of Resources Cost Steps: • Defining activities, activity cost pools, activity measures Activity Cost Pools Activity cost pool Activity measure Customer orders Number of customer orders Product design Number of product designs Order size Machine-hours Customer relations Number of active customers Other Not applicable • Assign overhead costs to activity cost pools o First-stage allocation: process of assigning functionally organized overhead costs derived from a company’s general ledger to activity cost pools • Calculate activity rates o Determine total activity for each pool hat would be required to product the company’s present product mix and serve its present customers o Activity rates = total cost for each activity / total activity • Assign overhead costs to cost objects using activity rates and activity measures o Second-stage allocation: activity rates are used to apply overhead costs to products and customers Example: A company has two different products and each year there are two production runs for each product. Manufacturing Overhead has a set-up cost of a total of \$52,000. There are some changes made to the products technology each year amounting to \$26,000 per year to the manufacturing overhead. Total overhead is \$175,000 per year. Direct labor hours total 7,000 for the year. Given: Product A Product B Units produced 1,000 1,000 Direct material cost per unit\$24 \$24 Direct labor cost per unit \$36 \$48 Machine hours per unit 6 8 Direct labor hours 3 4 Changes made during the 6 2 year  Direct labor hour cost = 175,000 / 7,000 = \$25 The cost per unit for each product using traditional overhead allocation: Product A: 24 + 36 + 3(25) = \$135 Product B: 24 + 48 + 4(24) = \$172

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##### ISBN: 9780321570567

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: tables, function, fits, Find, functions. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The full step-by-step solution to problem: 42E from chapter: 1.2 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. The answer to “Functions from tables. ?Find a simple function that fits the data in the tables.” is broken down into a number of easy to follow steps, and 14 words. Since the solution to 42E from 1.2 chapter was answered, more than 345 students have viewed the full step-by-step answer.

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Functions from tables. Find a simple function that fits