COST VOLUME PROFIT ANALYSIS
Many managerial decisions require a careful analysis of the behaviour of costs and profits as a function of the expected volume of sales. In the short run (less than a year), most of the costs and prices of a firm’s products will, in general, be determined. The principal uncertainty is not the cost price of a product but the quantity that will be sold. Hence the short-run profitability of a product line will be most sensitive to the volume of costs. CVP analysis highlights the effect of changes in sales volume on the organisation’s profitability. Fixed And Variable Costs CVP analysis requires a separation between fixed and variable costs. Fixed costs are those costs unaffected by variations in activity level in a given period. Fixed costs can be thought of a short run perhaps annual capacity costs, they represent the cost of resources required to perform a planned level of activities. Fixed costs can be committed costs or discretionary costs. Committed costs are the costs of long-term capacity resources, e.g. – depreciation, property taxes, salaries of senior supervisory personnel etc. These costs are not controllable or avoidable in the short run. Discretionary costs arise from decisions made during the periodic, usually annual, budgeting process. E.g. Advertising, R & D, factory support, maintenance etc. Once authorized, these costs are generally controllable by the periodic reporting system that compares actual with budgeted expenditures. Variable costs (also called engineered costs) fluctuate in response to changes in the underlying activity level or in response to changes in the scale of activity. E.g. materials, some components of labour (both direct and supervisory), overhead and marketing costs are typical examples of short-term variable costs. Some short-term variable costs like direct material and direct labour costs will increase proportionately with the level of output. Other short term variable costs may vary in steps, such as when an extra shift is added, with the level of output. E.g. - salaries of intermediate level supervisory personnel. Simple CVP model Gen. Profit Equation: Profit = Sales - VC - FC Define x = units produced and sold P = price per unit V = variable cost per unit F = fixed costs Profit = px - vx - f = (p – v) x - f This is the basic C – V – P equation. (p – v) is also referred to as contribution margin per unit from the basic c – v – p equation, we may derive BEP, defined as the level of output at which the contribution margin just covers the fixed costs i.e. the output level at which profits are zero. 0 = (p – v) BEP - f BEP = f/ (p - v) BEP in revenue rather than units sold, p *-BEP *-BEP = f/(p – v)/p) where (p – v)/p is called the contribution margin ratio.
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Example PARRY SOUND DISKETTES Parry Sound Diskettes (PSD) manufactures and sells a line of diskettes for microcomputers. Three models are produced: Economy, Standard and Premium. Unit cost and revenue data, as well as fixed costs, for PSD are as follows. Economy Standard Premium Selling price $10 $15 $25 Variable costs: Direct materials 2 3 5 Direct labor 2 4 6 Overhead 1 2 3 Selling 2 7 2 11 2 16 Contribution margin $3 $4 $9 = = = Product % of total 10% 50% 40% sales Fixed manufacturing $200,000 costs Advertising $100,000 Fixed administrative $100,000 costs Total expected sales 80,000 (units) (all products) Capacity (total all 100,000 (units) products) You have been asked by management to prepare a report analyzing each of the following issues: a. What is the projected profit given the initial data? b. Management is considering increasing the advertising budget by & 100,000 to increase total unit sales from 80,000 to 100,000. The mix of products would remain the same. Is the advertising campaign desirable? c. Management is considering altering the manufacturing budget so that more effort will be placed on selling the Premium model. The advertising budget could be increased by $150,000. While this would not increase the total unit sales, this campaign would result in the mix of Economy, Standard, and premium model being 5%, 30%, and 65%. Is this change desirable? d. Management is considering increasing the selling commissions paid to the sales force. The marketing manager believes that if the selling commission of each product is increased by 2%, the total level of sales will rise to 90000 units. Is the change desirable? e. Management is considering altering production process. By installing new manufacturing equipment, the direct materials, direct labor, and variable overhead costs can be reduced to 75% of their current levels for all products. Fixed manufacturing costs would rise by $200000, reflecting depreciation on the new equipment. What is the minimum level of total sales for which this change would be desirable? Limitations of CVP analysis Even the three product CVP model may seem somewhat transparent and perhaps too simplistic for practical problems. As long as we can develop a reasonably good model of cost-volume relationships, CVP analysis can be applied to complex multi-product situations. In general, cost estimation is the difficult part of the analysis, and not the modeling of extensive numbers of products. With the help of spreadsheets, we can input any complex model and obtain results. CVP analysis will be more realistic when applied to forecasting short-term costs and profits with existing product line.
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The short-term qualification implies that fluctuation in output mix and volume will not affect discretionary fixed costs, particularly indirect manufacturing costs such as setups, inspections, material handling, scheduling and expediting. The assumption will be violated if companies adjust spending on such categories as advertising, promotion, distribution, maintenance, training and education. R & D etc. in response to near term fluctuation in sales activity. In such a case, costs, classified as fixed, will vary with changes in output mix and volume. The assumptions of CVP analysis may also be violated if companies start to offer new products in their product line on apparent short-term contribution margins, since many discretionary costs appear to be fixed with respect to changes in output volume and mix, managers are tempted to increase profits through product proliferation, accepting special orders for products and introducing new variants of products. Thus the CVP analysis should be restricted to situations in which product proliferation will not occur and discretionary fixed costs will therefore remain fixed relative to assumed changes in output. CURVILINEAR BREAKEVEN ANALYSIS
In normal breakeven analysis, the usual assumption is that the total sales and variable cost line will have a linear relationship, that is, the lines will be straight. However, in practice, it is unlikely to have a linear relationship for two reasons: i) After the saturation point of existing demand, the sales value may show a downward trend; and ii) The average unit variable cost declines initially, reflecting the fact that as output increases the firm will be able to obtain bulk discounts on the purchase of raw materials and can also benefit from division of labour. When the plant is operated at further higher levels of output, the variable cost per unit tends to increase because of the greater likelihood of bottlenecks and breakdowns. Thus, the law of increasing costs may operate — with variable cost rising after reaching a particular level of output. In such cases, the contribution will not increase linearly — that is, based on the phenomenon of diminishing marginal productivity, the total cost line will not be straight but curvilinear. This situation will give rise to two breakeven points. The optimum profit is earned at the point where the distance between sales and total cost is the greatest. This session explores how various costs respond to changes in the volume of business activity whether it is a factory with additional units or a hotel with changes in occupancy levels. An understanding of these relationships is required for the formulation of business strategy, budgeting, and decision-making. The main focus will be on how managers may use Cost-Volume-Profit (CVP) analysis in a variety of business decisions including: Whether to reduce prices to increase sales? What sales level is required to cover the additional fixed interest charges on a long-term debt recently acquired to finance plant expansion? What combination of straight salary and commission should the firm offer to its sales people? What is the appropriate sales mix that will maximize the contribution margin per unit of the scarce resource? What will happen to our profitability if we expand capacity? Overall, CVP analysis is a technique that is used often by management accountants to both gain an understanding of the cost and profit structure in a company and to explain it to other managers theoretical basis underlying CVP analysis. Cost-volume-profit analysis examines the behaviour of total revenues, total costs, and operating income as changes occur in the output level, selling price, variable costs per unit or fixed costs. CVP uses one cost driver – volume of units produced and sold, and explores the behaviour of costs, variable or fixed, in relation to that cost driver. Many of the situations to which CVP analysis is applied are complex and this means that the models developed involve simplification but the conclusions can be reconciled with the economists’ position on cost, volume, profit behaviour.
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The Economist ’s Cost Volume Profit Graph 1. Curvilinear graph results in two break-even points. 2. The total cost function has an initial steep rise in costs before levelling off and finally exhibiting a further steep rise. 3. The total revenue line initially rises steeply then levels off and declines. 4. Two break-even points - B and C Economist’s Variable Cost Function. 1. Output levels between 0 and Q1 =Increasing returns to scale 2. Output levels between Q1 and Q2 =Constant returns to scale 3. Output levels beyond Q2 =Decreasing returns to scale The Accountant’s Cost Volume Profit Graph 1. Constant variable cost and selling price is assumed. 2. Only one break-even point and profit increases as volume increases. The position is reconcilable with the economists’ position as the accountants’ model is not intended to provide an accurate representation for all levels of output but has the objective of providing an accurate representation of cost and revenue behaviour only within the relevant range of output as dictated by known circumstances. Accountant’s Fixed Cost Function 1. Within the short term the firm anticipates that it will operate between output levels Q2 and Q3 and commits itself to fixed costs of 0A. 2. Costs are fixed in the short term but can be changed in the longer term.
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Problems 1. Multiple-Product Cost-Volume-Profit Analysis Hewtex Electronics manufactures two products, tape recorders and electronic calculators, and sells them nationally to wholesalers and retailers. The Hewtex management is very pleased with the company’s performance for the current fiscal year. Projected sales through December 31, 1989 indicate that 70,000 tape recorders and 140,000 electronic calculators will be sold this year. The projected earnings statement, which appears below, shows that Hewtex will exceed the earnings goal of 9% on sales after taxes. The tape recorder business has been fairly stable for the last few years and the company does not intend to change the tape recorder price. However, the competition among manufacturers of electronic calculators has been increasing. Hewtex’s calculators have been very popular with consumers. In order to sustain this interest in its calculators and to meet the price reductions expected from competitors, management has decided to reduce the wholesale price of its calculator from $22.50 to $20.00 per unit effective January 1, 1990. At the same time, the company plans to spend an additional $57,000 on advertising during fiscal year 1990. As a consequence of these actions, management estimates that 80% of its total revenue will be derived from calculator sales as compared to 75% in 1989. As in prior years, the sales mix is assumed to be the same at all volume levels. The total fixed overhead costs will not change in 1990, nor will the variable overhead cost rates (applied on a direct labor hour base). However, the cost of materials and direct labor is expected to change. The cost of solid state electronic components will be cheaper in 1990. Hewtex estimates that material costs will drop 10% for the tape recorders and 20% for the calculators in 1990. However, direct labor costs for both products will increase 10% in the coming year. Required: 1. How many tape recorder and electronic calculator units did Hewtex Electronics have to sell in 1989 to break even? 2. What volume of sales is required if Hewtex Electronics is to earn a profit in 1990 equal to 9% on sales after taxes? 3. Derive the equation describing the level of profits in 1990 as a function of the number of tape recorders and electronic calculators sold. Plot the breakeven line and the line representing a profit of 9% of sales after taxes.
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HEWTEX ELECTRONICS Projected Earnings Statement For the Year Ended December 31, 1999 Tape Recorders -----------------------Total Amount (000 omitted) Per Unit Sales $ 1,050 $15.00 Production costs: Materials $ 280 $ 4.00 Direct labor 140 2.00 Variable overhead 140 2.00 Fixed overhead 70 1.00 ------------ --------Total production Costs $ 630 $ 9.00 Gross margin $ 420 $ 6.00 Fixed selling and Administrative Net income before Income taxes Income taxes (55%) Net income
Electronic Calculators Total ----------------------------------- -------------------------Total Amount (000 omitted) Per Unit (000 omitted) $3,150 .$22.50 $4,200.0 $ 630 420 280 210 ---------$ 1,540 $ 1,610
$ 4.50 3.00 2.00 1.50 ----------
$ 910.0 560.0 420.0 280.0 ------------
$11.00 $ 11,50
$ 2,170.0 $ 2,030.0 1,040.0 990.0 544.5 $ 445.5
2. Working Capital Management – The Management of Accounts Receivable Lockport Produce is a wholesale produce company whose customers are mainly small grocery stores. Recently, Gail MacDonald, the general manager and owner of Lockport Produce, has become concerned about the firm’s level of accounts receivable. Because Lockport Produce handles a variety of produce, sales are stable throughout the year, averaging $ 1,000,000 per month, 90% of which are credit sales. Credit sales are billed immediately to customers upon delivery. The average collection period for credit sales is 40 days, and bad debts usually amount to 4% of credit sales. The average markup over variable costs is 50%. Lockport Produce has been very successful and has grown rapidly in the six years since its inception. Because Gail has resisted issuing further equity capital, funds for working capital purposes have often been tight and the firm has had to borrow constantly from the bank, both for operating and for intermediate financing purposes. The firm’s average cost of debt has been 14%. Gail is now considering some alternatives to reduce the firm’s level of accounts receivable. Consider each of the following questions separately 1. By hiring an accounts receivable clerk to manage collections, Gail figures that the average collection period for credit sales can be reduced to 30 days. If the clerk’s salary would be $20,000 per year, would hiring back the clerk be a good idea? 2. If credit sales are eliminated, monthly sales will fall to $970,000. Assuming that the administrative cost savings from eliminating credit sales would be negligible, would eliminating credit sales be a good idea? 3. MULTIPLE-PRODUCT AND MULTI-DECISION COST VOLUME PROFIT ANALYSIS
Rich Gogan, a promoter, is considering the possibility of booking the Wild World of Wrestling (WWW) in the Oxford Futuredome. Currently, due to intense television exposure, the WWW is enjoying great popularity. Rich figures that the possibility of earning money, which would be donated to the building drive to replace the roof on the local curling arena, is pretty good.
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The Oxford Futuredome is a domed arena that will seat 60,000 fans as a wrestling or boxing venue. Rich figures that there would be three types of seating: ringside, reserved, and rush. The distribution and the ticket prices for these seats are expected to be as follows: Seat Type % Total Capacity % Total Ticket Sales Price Ringside 10% 10% $50 Reserved 70 70 25 Rush 20 20 10 At these prices, total ticket sales are expected to be 45,000. The costs, associated with such a promotion are high. He rent for the Futuredome is $10,000. The cost of hiring the private security personnel will be $30,000. In addition, a city ordinance requires that police be in attendance. The number of police required depends on the number of customers, and the police cost will be about $1 per customer. The cost of hiring ushers for the event will be $20,000. Clean-up and the repair of property damage caused by the fans is expected to cost $80,000 plus about $2 per fan. Insurance and other incidental costs will be $10,000. The promotional fee for the event will be $10,000. The basic fee for the wrestlers who will appear on the card is $400,000. In addition, the wrestlers demand, and get, 10% of the gross receipts. The restaurant, snack bars and vendors are controlled by the owners of the Futuredome. Futuredome management requires a flat fee of $100,000 to provide food services for the evening plus 25% (15% for the owners, 10% for the vendors) of the total food sales. The lessor, in this case Rich, must also pay the variable cost of the food provided, which averages $3 per fan. The average sales are $8 per fan. Finally, total sales taxes are 8% on any sales, food or tickets. (All prices provided above include taxes.) Required: Consider each case below separately. 1. What is the expected profit from this promotion? 2. Given the anticipated prices and distribution of sales, how many tickets, in total, must be sold for the promotion to break even? 3. An alternative and more expensive, seating plan will increase the rent for the event to $150,000. Under this seating plan, the distribution of seats and sales, would be ringside, 15%; reserved, 70%; and rush, 15%. Is the upgrade to the more expensive seating plan worthwhile? 4. If the food prices were cut so that the average revenue from each customer was $6, the total ticket sales would rise to 48,000. Is this price cut worthwhile? 5. Cutting all ticket prices by 10% is expected to increase total ticket sales by 10%. Is this change worthwhile? 6. One of the main attractions of the event would be a feature match between the Mighty Hercules, the current WWW heavyweight champion, and his archrival. Warren the Weasel. Hercules and Warren could be brought in a few days before the event in order to appear on local television and in some shopping centres. The total cost of the promotion would be $50,000 and would increase ticket sales by 10%. Is the promotion worthwhile? 7. One possibility is to organize a lottery for the available tickets. Under this scheme all tickets to the event would sell for $20, and the names of the customers to be assigned the seats would be drawn randomly by a computer. The additional cost of
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this alternative would be $50,000, which includes the cost of promoting the lottery, as well as the fee to be paid to the accounting firm that would supervise the lottery. If the lottery were used, all 60,000 seats to the event would probably be sold. Is the lottery worthwhile?
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Assignments 1. NONLINEAR COST STRUCTURE AND BREAKEVEN ANALYSIS
Bill Alexander is president of the Mason Company, a small producer of valves in a highly competitive market. A recent drop in the price of the valves has caused him great concern, since the price is now below the Mason Company’s standard cost. Standard cost was determined from operating at 80% of the maximum capacity of 20,000 valves per month. The company does not normally operate above this level (of 8,000 valves per month), since the higher production requires overtime work that significantly increases variable costs. The fixed costs of the Mason Company are $40,000 per month, and variable costs are $15 per valve for production levels up to 8,000 valves per month. Consequently, the standard cost of the valve is set at $20, based on operating at the desired level of 80% of capacity. Normally the price of the valve ranges from $21 to $23, allowing a small but adequate return on the Mason Company’s modest investment in machinery and facilities. For production above the standard volume, unit variable costs for the additional units increase by 15% above the normal variable cost for volume between 80% and 85% of capacity 20% above the normal variable cost for volume between 86% and 90% of capacity 30% above the normal variable cost for volume between 90% and 100% of capacity Recently the price of valves has dropped about 10% to $29 per valve. Bill feels that he is now in a no-win situation, since he is losing money on every valve he is selling. While he sees some opportunities for increasing his sales volume above the current level of 8,000 units per month, he believes this would only make matters worse, since he feels that he is losing money at current volumes and the variable costs on the additional units produced will be even greater. • • •
Required:
1. Comment on Bill’s analysis of the price-cost squeeze in which he now finds himself. At what point would you recommend that he actually turn down orders at $19 per valve? 2. Assuming the price returns to its previous level of $21, at what volumes will the Mason Company operate profitably? 2. CHOOSING THE SCALE OF OPERATIONS WITH DECLINING MARGINAL REVENUE Penticton Oil Products Limited (POPL) operates a small oil refinery that refines crude oil produced in the immediate geographical vicinity of the refinery. POPL processes the crude oil in batches. Each batch of crude oil refined produces five different products. The number of units of each product produced, per batch of crude oil processed, is as follows:
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Product Number Units Produced per Batch --------------------------------------------------------------------------1 100 2 50 3 10 4 20 5 40 The marketing manager has indicated that the price received for each product is a function of the number of units sold. The marketing manager has provided the following schedule of estimated market prices for the upcoming month for each of the five products where, in each case, x is the number of units of that product sold during the month: Product Number Estimated Market Price per Unit -----------------------------------------------------------------------------------1 (150—0.01x) 2 (80 ---0.006x) 3 (400—0.02x) 4 (600---0.05x) 5 (250---0.015x) For example, if 1,000 units of product 3 were sold, the price per unit that would be received would be $380 (computed as 400 – 0.02 * 1,000). In addition, the marketing manager has stated that, apart from any price considerations, an upper limit exists on the number of units of each product that can be sold during the upcoming month. These limits are: Product Number Maximum Sales Units -------------------------------------------------------------------------1 5,000 2 4,000 3 550 4 1,500 5 2,500 The cost of each batch of crude oil that is processed through the refinery is estimated as $15,000 for the cost of the crude oil and $7,000 for the out-of-pocket cost of refining. Finally, the production manager has advised you that a disposal cost must be paid for any products that are produced and not sold. The disposal cost per unit for each of the products is: Product Number Disposal Cost per Unit ---------------------------------------------------------------------1 $10 2 5 3 20 4 50 5 15 Required:
1. How many batches of crude oil should the refinery process this month? 2. The president of POPL is concerned that at the current market prices, some of the products may not be covering their costs. How would you respond to the president? 10
3. CHOOSING THE SCALE OF OPERATIONS WITH SALES CONSTRAINTS
Grande Cache Office Products Limited (GCOP) produces a line of ten products that are distributed to stationery supply retailers for resale in the office products industry. The selling price, variable costs, and estimated maximum sales for each of the ten products are as follows: Product Price Variable Costs Maximum Sales 1 $ 7.65 $ 3.07 125,000 2 11.72 5.39 75,000 3 4.41 1.21 350,000 4 15.12 10.32 95,000 5 19.65 11.75 105,000 6 8.54 3.76 450,000 7 15.97 9.90 80,000 8 13.96 7.96 200,000 9 5.86 1.87 600,000 10 10.78 6.97 120,000
The planning committee, consisting of the vice-president of marketing and the vice president of production, has devised five alternative operating plans for the upcoming year. The potential production levels and the total fixed manufacturing and selling costs for each of the five alternatives are given below (the potential production levels are given in the column corresponding to each plan, and the total fixed costs are given at the bottom of the column corresponding to each plan). Plan Number (Maximum Possible Production)
Product 1 2 3 4 5 6 7 8 9 10
1 119,000 85,000 289,000 68,000 102,000 374,000 34,000 204,000 323,000 102,000
Fixed costs $4,000,000
2 154,000 110,000 374,000 88,000 132,000 484,000 44,000 264,000 418,000 132,000
3 170,000 51,000 323,000 51,000 34,000 408,000 17,000 153,000 357,000 136,000
4 68,000 85,000 255,000 102,000 136,000 323,000 68,000 255,000 289,000 119,000
5 105,000 75,000 255,000 60,000 90,000 330,000 30,000 180,000 285,000 90,000
$6,000,000
$3,000,000
$5,000,000
$3,500,000
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The maximum sales potential for each product is independent of the plan number chosen. Required:
1. Compute the net income associated with each of the five plans. 2. The corporate controller has made the following comments: I feel that you are making a mistake by ignoring the fixed cost per unit of production. By not allocating the fixed marketing and production costs to the individual products, you do not know if all these products are profitable. The fixedcost allocation may point out some products that are unprofitable. Why not allocate the fixed production and marketing costs associated with each plan to the individual products in proportion to the production of each product? You can then eliminate those products whose price is less than the resulting full cost. Only by considering the full cost of each product will you make the proper decisions. Furthermore, you have ignored the general and administrative expenses. These costs are fixed and amount to $2,500,000, irrespective of which plan you choose. You have to find a way of allocating these costs to the products in order to evaluate overall profitability. You should allocate these costs to the individual products in proportion to the relative profitability of each product. On behalf of the planning committee, draft a reply to the company controller. 3. The marketing staff believes that if $100,000 is spent promoting Grande CacheOfficeProducts Limited’s corporate image, the maximum sales potential for all products will increase by 15%. Assuming that this belief is correct, should the promotion be undertaken?
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