Part 3: Cost-Volume-Profit (CVP) Relationship/Analysis Cost Volume Profit Analysis is based on six assumptions: 1. A firm’s total revenue changes in direct proportion to changes in its unit sales volume. That is, the average sale price per unit of product is constant. (Linear Relationship concept) 2. Total costs can be separated into fixed costs and variable costs. 3. Total variable costs change in direct proportion to changes in sales volume. That is, the average variable cost per unit remains constant over the relevant range. 4. Total fixed costs (per month or per year) remain constant over the range of sales volume being considered. 5. Sales mix remains constant over the range of sales volume being considered. 6. Sales volume equals production volume; that is, inventory levels remain constant. The discussion deals with the relationship between cost, volume and profits and the various changes in the respective values dependent on the level of activity or volume of sales. An important element in the discussion of CVP is the concept of contribution margin. Contribution Margin – also known as marginal income or profit volume - it is used to recover fixed expenses and any excess are treated as profits. Formula: Sales – Variable Costs = Contribution Margin Traditional Income statement (Absorption Costing) Sales Xxx Less: Cost of Sales Xxx Gross Profit Xxx Less: Operating Expenses Xxx Net Income xxx Contribution Margin Income statement (Variable Costing) Per unit Totals Ratio Sales Xx XXXX 100% Less:Variable Cost Xx XXXX (VC/Sales) Contribution Margin Xx XXXX (CM/Sales) Less: Fixed Cost XXXX Net Income XXXX Illustration: 01 Alpha Bravo Charlie Selling Price 40 80 25 Units Sold 4,875 4,000 15,000 VC % 60% 75% 70% CM % 40% 25% 30% CM Peso Value 78,000 80,000 112,500 Fixed cost 60,000 90,000 62,500 Income/Loss 18,000 (10,000) 50,000 Cost Volume Profit Analysis – also known as Break-even Analysis Break-even point - a situation wherein a. Total Revenues = Total Costs; therefore NO LOSS, NO PROFIT. b. Total Sales = Total Variable Costs + Total Fixed Costs c. Total Sales – Total Variable Costs = Total Fixed Costs d. Total Contribution Margin = Total Fixed Costs Breakeven point (expressed in units) = Total Fixed Costs/Unit Contribution Margin Breakeven point (expressed in Pesos) = Total Fixed Costs/CM ratio OR = Breakeven units X Sales Price As mentioned earlier, Contribution Margin is used to recover fixed costs. The point where all fixed costs are recovered is known as the break even point. Any additional sale beyond the breakeven point will mean Profit represented by the Contribution Margin since the fixed cost have been fully recovered (paid for) by the CM at break even point. Sales with a desired profit Sales (in units) = Total fixed cost + Target Profit ------------------------------------CM / unit Sales (in Pesos) =Total Fixed Cost + Target Profit -------------------------------------CM ratio Effects of Income Tax on Break-even Sales At break-even point, income taxes are irrelevant or have no effect on the break-even sales because there are no profits at this level of sales. However, income tax will increase the desired sales volume if we include in our computation a target profit. The new formula will therefore be: Sales (in Pesos) =Total F Cost + Target Profit / (1-Tax rate) --------------------------------------------------CM ratio Whereby the Target Profit will be the Pre-tax Net Income. Illustration: 02 The Rapido Muncho Restaurant has two outlets that are open 24 hours a day. Fixed costs for the two restaurants together total P450,000 per year. Service varies from a cup of coffee to full meals. The average sales check per customer is P100. The average cost of food and other variable costs for each customer is P60. The income tax rate is 30%. Target net income is P105,000. Required: 1. Compute for Breakeven sales in units and in pesos assuming that the target net income is before taxes. a. BEP units b. BEP pesos 2. Compute for Breakeven sales in units and in pesos assuming that the target net income is after taxes. a. BEP units b. BEP peso Sales with Multiple Cost Drivers Bep = Cost Driver x Activty + Cost Driver x Activity + Other Fixed Cost Contribution Margin / unit or CM % In the previous examples, units produced has been used as the cost driver (cause of the incurrence) of all fixed costs. However, there are certain costs that may be variable in nature but whose cost driver may not be based on the units produced but on other cost drivers; thus should be treated as fixed cost taking into consideration that units produced serves as the primary cost driver. In this instance, we need to compute first the total cost of the fixed cost based on each cost driver to be able to get the Total Fixed Cost to be allocated to each unit produced. Illustration: 03 Sam Choy is a distributor of sticker books. For 200A, he plans to purchase sticker books for P30 each and sell them for P45 each. Sam’s fixed costs for 200A are expected to be P240,000. Sam’s only other costs will be variable costs of P60 per shipment for preparing the invoice and delivery documents, organizing the delivery and following up for collecting accounts receivable. The P60 cost will be incurred each time Sam ships an order of sticker books, regardless of the number of sticker books in the order. Required: Suppose Sam anticipates making 500 shipments in 200A, how many sticker books must Sam sell to breakeven in 200A? CVP Indifference Point CVP Analysis can compare alternative cost structures or selling prices such as: 1. high salary/low commission vs. lower salary/higher commission for sales persons 2. highly automated production process with low variable cost per unit vs. lower technology with higher variable costs per unit and lower fixed costs 3. broad advertising campaign with higher selling prices vs. minimal advertising and lower selling prices Indifference point between alternatives is the level of sales in units or sales pesos where the profits of the alternatives are equal Profit (A) = Profit (B) Formula: CM/unit (A) * Qty - Fixed Cost (A) = CM/unit (B) * Qty – Fixed Cost (B) Illustration: 04 Phoenix Company is involved in the importation and distribution of bottled health drinks. These drinks are sold for P200 each. Variable costs per bottle is P80. Salaries of sales person is fixed at P80,000 which is included in the total fixed costs of P360,000. Phoenix is considering an alternative compensation scheme where salaries are decreased to P20,000 and the commission per item sold is 20% of sales price. Required: 1. Compute for the breakeven points of the current and proposed salary scheme. a. Current: BEP b. Proposed BEP 2. Compute for the indifference point. Which is the more favorable salary scheme assuming current demand is at 2,000 units? Note: 1. The product/process with the higher contribution margin/unit is favorable if demand is greater than indifference point. It is because we are able to sell more help in the recovery of fixed cost. 2. The product/process with the lower fixed cost is favorable if demand is less than the indifference point. It is because we are selling less, it is better to have lower fixed cost that is needed to recover. Margin of Safety Concept Margin of Safety - excess of sales over breakeven that will bring forth profit; therefore all contribution margin derived from the margin of safety is regarded as profit. Formula: Total Budgeted (or Actual) Sales Less: Breakeven Sales Margin of Safety Margin of Safety Ratio = Break Even Ratio = PXX PXX PXX Margin of Safety/Actual or budgeted sales Break Even Sales/Actual or budgeted Sales Illustration: 05 Actual or Budgeted Sales Less Break Even Sales Margin of Safety CM Ratio NI Ratio 300 Qty. Peso Value 1,000 P10,000 100% 700 P7,000 70% -------- ---------------P3,000 30% x 40% ------------P1,200 12% ===== ==== % 40% Based on the illustration, we could derive a new formula for Margin of Safety Ratio which is Margin of Safety Ratio = Net Income Ratio/CM Ratio Break-even ratio = FC /CM Complementary ratios – ratios that combine to make a whole Variable Cost ratio Break-even ratio Contribution Margin ratio Margin of Safety ratio Total Sales (100%) Total Sales (100%) ============== ============= Net income ratio MOSR x CM ratio Net Income Fixed Cost ratio Breakeven Sales % x CM ratio FC ------------------------------Contribution Margin Ratio =============== Illustration: 06 Three independent situations involving cost volume profit situations follow. In each case you are to determine the amount where blank spaces appear. Case A Selling price Variable cost Fixed cost CM per unit Total fixed costs BEP in units BEP in sales CMR MOS unit NI(loss) Units sold Case B P2.00 P2.10 P0.60 P.90 P180.000 Case C P8.00 P3.00 P200,000 P600,000 P90,000 100% 8,000 P16,000 12,000 25% 4,000 Illustration: 07 Additional Exercises: Based on the scanty information given in each problem below, determine the amount of each item required: Case A: Breakeven % is 64%, Net Profit is 12% of sales, Fixed Costs P128,000 Required: Actual Sales Case B: Net profit is 7.5% of sales, Variable ratio is 70%, Breakeven sales volume is P150,000 30%CMR, 7.5%NI. Required: Actual Sales Case C: Net Profit is 7% of sales, Breakeven % is 80%, Variable costs P260,000. Required: a. Margin of Safety Figure b. Fixed Costs Case D: Variable ratio is 65%, Breakeven % is 60%, Net Profit is P56,000 Required: a. Margin of Safety Figure b. Fixed Costs LEVERAGE In physics, leverage implies the use of a lever to raise a heavy object with a small amount of force. In politics, people have leverage if they can accomplish a great deal with their influence by simply making a phone call. We apply this concept of leverage in business as well taking into account a small increase in sales will generate a large effect on income. Operating Leverage - measure of how sensitive net income is to % change in sales. -serve as a multiplier effect as it measures at a given level of sales, how a percentage change in sales will affect profit Operating leverage results from the presence of fixed operating costs in a firm's income stream. The extent of the presence of fixed operating costs in a firm's income stream is measured by the degree of operating leverage (DOL). Degree of operating leverage = Contribution Margin Net Income Note: The DOL will never be less than 1 because CM will always be equal or greater than Net Income. Thus it is considered as a multiplier. % Change in Sales x Operating Leverage = % Change in NI Illustration: Markov Company has the following income statement for the year just ended expressed in ‘000s: Sales Variable Cost Contribution Margin Less Fixed Cost Net income 100 60 40 30 10 The operating leverage would be: Contribution Margin: 40/10 = 4 This simply means for every % change in sales volume, NI% will change 4 times. Therefore: if Sales Volume increases by 10%, Net income will improve not by 10% but by 40% (10% x 4 times) Sales Variable Cost Contribution Margin Less Fixed Cost Net income 100 60 40 x 110% = x 110% 110 = 10 x 140% = 30 14 30 66 44 It should be noted that companies with higher fixed cost levels will have a higher degree of operating leverage. Thus, other than providing ease in computation of projected net income, it serves as an indicator on the level of usage of fixed cost in generating sales. Relationship between Operating Leverage and Margin of Safety These two functions are inversely proportional to each other. Operating leverage = Contribution Margin / Net Income Margin of Safety = Net Income / Contribution Margin Thus: Operating leverage = 1/ Margin of Safety Margin of Safety = 1/ Operating leverage Illustration: 08 Fiesta Corporation is a manufacturer of fish crackers with catsup dip. Each pack of fish crackers with catsup dip sells for P35. Variable cost of producing one pack averages P15. Fixed costs are estimated to be at P1,000,000. For the previous year, sales reached P3,500,000. After careful market analysis, sales volume for the current year is targeted to increase by 10%. Required: 1. Determine the Net Income and Operating Leverage for Fiesta Corporation for the previous year. 2. Determine the Net Income and the Operating Leverage for the current year. 3. Determine the Margin of Safety and BEP in peso for the current year. Sales Mix Analysis - break-even analysis involving more than one product or involving multi products There may exist two scenarios in a Sales Mix situation whereby the product mix may be composed of: 1. Independent products. 2. Package (Composite) Products. A. Independent Products Scenario Break even units = Total Fixed Cost -------------------------*Weighted CM/ unit Using the Quantity Mix *Weighted contribution margin per unit is obtained by multiplying the individual Sales Mix Proportions (usually expressed as a percentage based on the Quantity) to the corresponding Contribution Margin per Unit. Break even sales can be derived by determining the break even units per product line and then multiply by the corresponding sales prices Or TOTAL FIXED COST Weighted Average CM% Using the Revenue Mix *Weighted contribution margin % = Total CM Total REVENUES Illustration: 09 Marvel Heroes Company is planning to sell two lines of stuffed toys, Fantastic Four and Avengers in the coming Holiday Season. The company budgets the following sales figures: Units Sold Revenues P200 and P100 per unit Variable Costs P120 and P70 per unit Contribution Margin P80 and P30 Fixed Costs Operating Income Fantastic Four 600 P120,000 P72,000 P48,000 Avengers 400 P40,000 P28,000 P12,000 Total 1,000 P160,000 P100,000 P60,000 P45,000 P15,000 Required: Determine the following: 1. Breakeven point in units: 2. Breakeven point in sales pesos: B. Package / Composite Units Certain products are sold in packages or components with a corresponding mix or ratio that has to be observed. Example would be a Gift Pack that must contain 1 bottle of champagne, 3 canned goods and 6 boxes of herbs and spices. Formula to compute for the break-even units will then be: Break even units = Total Fixed Cost -------------------------*Composite CM/ unit Composite Unit is computed as Sum of CM per unit * Product Mix (usually expressed in Qty.) Illustration: 10 * A company sells two products, X and Y. The sales mix consists of a composite unit of two units of X for every five units of Y (2:5). Fixed costs are P49,500. The unit contribution margins for X and Y are P2.50 and P1.20, respectively. 1. Considering the company as a whole, the number of composite units to breakeven is? 2. Compute the quantity of X and Y that must be produced to meet break-even sales. * HP Inc. formulates and sells three major chemicals: Supercali, Fragilistic, and Expialidocious. It sells to industrial users who use and buy these chemicals in the following ratio: three (3) measures of Supercali for (1) measure of Fragilistic, and (2) measures of Fragilistic per (1) measure of Expialidocious. The company makes the following contribution margin per measure: RPCPA Supercali: P30 Fragilistic: P45 Expialidocious: P90 Fixed costs amounted to P1.8 million. 1. How many (in units) of Supercali would be sold? 2. How many (in units) of Fragilistic would be sold? 3. How many (in units) of Expialidocious would be sold? Problem Solving: IP-1 (Moderate) The Soda Factory sells high energy bars to supermarkets for P80 per bar. Variable cost is P45 per bar and annual fixed cost are P854, 000. 1. Determine the breakeven point in units and pesos. 2. Determine the number of units required to earn a before tax profit of P120, 000. 3. Determine the required earn an after 40% tax profit of P120, 000. 4. Determine the volume required to earn a before tax return on sales of 13.25%. 5. Determine the volume required to earn an after tax return of 8.4%. (Assume 40% tax rate) 6. If the body Fit can sell 40, 000 bars, what price would it have to charge to earn a before tax profit of P260, 000. IP-2 (Moderate) Marcoleta & Co., makes a sign pen that sells for P20.00 per unit. Variable costs are P8.00 per unit, and fixed cost total P1, 800,000 per year. Required:Answer the following independent questions: 1. What is the product’s ratio? 2. Use the CM ratio to determine the break-even point in peso sales. 3. Due to an increase in demand, the company estimates that sales will increase by P1, 200,000 during the next year. By how much should net operating income (or net operating loss) charge, assuming that fixed cost do not change? Assume that the operating results for last year were: Sales ……………………………………………………… P4, 000, 000 Less variable expenses …………………………… 1, 600, 000 Contribution margin …………………………………. 2, 400, 000 Less fixed expenses ………………………………… 1, 800, 000 Net operating income ……………………………. P 600, 000 4. Compute the degree of operating leverage at the level of sales last year. 5. The president expects sales to increase by 20% next year. By what percentage should net operating income increase? 6. Refer to the original data. Assume that the company sold 180, 000 units last year. The sales manager is convinced that a 10% reduction in the selling price, combined with a 90, 000 increases in advertising, would cause annual sales in units to increase by one fourth. Prepare two contribution income statements, one showing the results of operation if these changes are made. Would you recommend that the company do as the sales manager suggest? 7. Refer to the original data. Assume again that the company sold 180, 000 units last year. The president does not want to change the selling price. Instead, he wants to increase the sales commission by P1.25 per unit. He thinks that this move, combined with some increase in advertising be increase annual sales by 20%. By how much could advertising be increased with profits remaining unchanged? Do not prepare an income statement; use incremental analysis approach. 8. Assume that in the coming year there will be no change in the cost structure. The company can sell 220, 000 units next year. What selling price is required to have the company earn P 664, 000 before tax profit? IP-3 (Moderate) Mystery Company operates a chain of fancy pendant shops around the country. The shops carry many styles of pendants that are all sold at the same price. Sales personnel in the shops are paid a substantial commission on each pendant sold (in addition to small basic salary) in order to encourage them to be aggressive in their sales efforts. The following cost and revenue data relate to Shop 30 and are typical of one of the company’s many outlets: Per pendant Selling price P 50.00 Variable expenses: Invoice cost Sales commission Total variable expenses Fixed Expenses: Advertising Rent Salaries Total fixed expenses P 26.50 1.00 P 27.50 P 56, 000 122, 000 182, 000 P 360, 000 Required: 1. Calculate the annual break-even point in pesos sales and in unit sales for Shop 30. 2. If 15, 000 pendants are sold in a year, what would be Shop 30’s net operating income or loss? 3. The company is considering paying the store manager Shop 30 an incentive commission of P2.50 per watch (in addition to the salesperson’s commission). If this change is made, what will be the new break-even point in pesos sales and in unit sales? 4. Refer to the original data. As an alternative to (3) above, the company is considering paying the store manager at P4.00 commission on each pendant sold in excess of the break-even point. If this change is made, what will be the shop’s net operating income or loss if 17, 500 pendants are sold? 5. Refer to the original data. The company is considering eliminating sales commission entirely in its shops and increasing fixed salaries by P11,300 annually. If this change is made, what will be the new break-even point in pesos sales and in unit sales for Shop 30? Would you recommend that the change be made? IP-4 (fractional) - moderate Laurente & Co. of Bacolod makes two products, Mini and Giga. Present revenue, cost, and sales data on the two products follow: Mini Giga Selling price per unit P 10.00 P 5.00 Variable expenses per unit P 4.00 P 3.00 Number of units sold annually 30, 000 40, 000 Fixed expenses total P 228,000 per year. Required: 1. Assuming the sales mix given above, do the following: a. Prepare a contribution income statement showing both pesos and percent columns for each product and for the company as a whole. 2. The company has just developed a new product, Mega. Assume that the company could sell 5, 000 units at P20.00 each. The variable expenses would be P15.00 each. The company’s fixed expenses would not change. a. Prepare another contribution income statement, including sales of Mega (Sales of the other two products would not change). Carry percentage computations to one decimal place. IP-5 (Difficult) (RPCPA) Great Wall Ski Company recently expanded its manufacturing capacity, which will allow it to produce up to 15, 000 pairs of cross country skis of the mountaineering model or the touring model. The sales department assures management that it can sell between 9, 000 pairs and 13, 000 pairs either product this year. Because the models are very similar, Great Wall will produce only one of the two models. The following information was complied by the accounting department. Selling price Variable cost Per-Unit (pair) Data Mountaineering Touring P88.00 P 80.00 P 52.80 P 52.80 Fixed cost will total P 369, 600 if the mountaineering model is produced but will be only P 316, 800 if the touring model is produced. Siberian Ski is subject to a 40% income tax rate. Required: 1.Compute the contribution margin for each product line. 2. If the Great Wall desires an after-tax net income of P22,080, how many pairs of touring skis will the company have to sell? 3. How much would the variable cost per unit of the touring model have to change before it had the same breakeven point in units as the mountaineering model? 4. Suppose the variable cost per unit of touring skis decreases by 10 percent, and the total fixed cost of touring skis increases by 10 percent. Compute the new breakeven point. 5. Suppose management decided to produce both products. If the two models are sold in equal proportion, and total fixed cost amount to P 343, 200, what is the firm’s breakeven point in units? 6. Suppose the Great Wall decided to produce only one model of ski. What is the total sales revenue at which great Wall make the same profit or loss regardless of the ski model it decided to produce? 7. If the Great Wall sales department could guarantee the annual sale of 12, 000 pairs of either model, which model would the company produce & why? Mountaineering because of highest CM per unit IP 8 (Easy, Moderate to Difficult) Solve each as independent problem. 1. The Childers Co. sells widgets. At an annual sales volume of 75,000 units the company breaks even. At annual sales volume of 100, 000 units the company reports a profit of P200, 000. The annual fixed costs for the Childers Co. are? (M) 2. Batman Co. earned P40, 000 on sales of P400, 000. It earned P55, 000 on sales of P450, 000. Variable costs as a percentage of sales and total fixed cost are? (M) 3. At a sales level of P90, 000, Violeta Company’s contribution margin is p24, 000. If the degree of operating leverage is 6 at a P90, 000 sales level, net income must be? (M) 4. The Siamese Company has an operating leverage of 2. Sales for 2005 are p2, 000, 000 with a contribution margin of P1, 000, 000. Sales are expected to be P3, 000, 000 in 2006. Net income for 2006 can be expected to increase by what amount over year 2005? (M) 5. The Makatao Marketing Co., is expecting an increase of the fixed costs by P78, 750 upon moving their place to business to the downtown area. Likewise it is anticipating that the selling price per unit and the variable expenses will not change. At present, the sales volume necessary to breakeven is P750, 000 but with the expected increase in fixed costs, the sales volume necessary to breakeven would go up to P975, 000. Based on this projection, what was the total fixed cost before the increase of P78, 750? (D) 6. Alla Co. is considering dropping a product. Variable costs are P75.00 per unit. Fixed overhead costs, exclusive of depreciation, have been allocated at a rate of p5.00 per unit and will continue whether or not production ceases. Depreciation on the equipment is P60, 000 a year. If production is stopped, the equipment can be sold for P140, 000. If production continues, however, it will be useless at the end of 1st year and will have no salvage value. The selling price is P100 a unit. Ignoring the tax effect, what is the minimum unit to be sold in the current year to breakeven on cash flow basis? 7. In 2004 Lucia Company had a net loss of P8, 000. The company sells one product with selling price of P80 and variable cost per unit of P60. In 2005, the company would like to earn a before tax profit of P40, 000. How many additional units must the company sell in 2005 than it sold in 2004? Assume that the tax rate is 40%. (M) 8. Mars Co. is considering two processes. The first process is highly manual with variable cost per unit of P24 and fixed costs of P640, 000 per annum. The second process is highly mechanized with variable cost of P15 and fixed costs of P1, 200, 000 per annum. The selling price is P60. Compute the difference point. In quantity & in peso (D) 9. ABE, Inc. sells a product for P8 per unit. The fixed costs are P160, 000 and the variable costs are 60% of the selling price. What would be the amount of sales if ABE were to realize a profit of 12% of sales? (M) 10. Pyramid Company would like to market a new product at a selling price of P15 per unit. Fixed costs for this product are P1, 000, 000 for less than 500, 000 units of output & P1, 500, 000 for 500, 000 or more units output. The contribution margin percentage is 20%. How many units of this product must be sold to: a. Breakeven? (E) b. Earn a target operating income of P1 million? (E) 11. Cadet Company had is a manufacturer of its only one product line. It had a sale of P400, 000 for 2006 with a contribution margin ratio of 20 percent. Its margin of safety ratio was 10 percent. What was the company’s fixed cost? (E) DONE!