Chapter 22: Cost–volume–profit analysis for decision making Please note: GST versions of the end-of chapter questions are not appropriate for this chapter. Discussion questions 1. ‘It is reasonable to assume variable expenses approximate a straight line over the relevant range of operations (even if the overall variable expense line is curved)’. Discuss this statement. Variable expenses are likely to be curvilinear over their entire length because at higher levels of activity, and therefore higher quantities of purchases, an entity is likely to get larger discounts for buying in bulk. This means that as the level of activity increases the cost per unit to purchase variable inputs is likely to fall. The variable cost line is therefore likely to be curved and become less steep at higher levels of activity. Most entities do not regularly vary their output from zero units to hundreds of thousands within a normal operating period. It is more likely that entities operate within a fairly limited range of activity in any given period and are therefore operating on a limited section of their variable cost curve. Over a small section of a variable cost curve the line is likely to closely approximate a straight line. Hence the assumption that the variable expenses approximate a straight line is a reasonable assumption to make in normal operating conditions. 2. Fixed costs are not usually constant over all volumes of output. What are some of the factors that are likely to mean that fixed costs change over all volumes? Give an example. Many fixed costs are defined as discretionary fixed costs because they can be changed or discontinued by management if enough time is available. At low levels of activity, management may decide to reduce or eliminate such activities as advertising, research and development, and employee training programs. At an extremely low level of activity, such as one caused by a prolonged economic recession, drastic measures may be necessary to eliminate all but the committed fixed costs through layoffs and cutbacks. The committed fixed costs are required even if the operation is shut down temporarily. They consist of such items as depreciation of buildings and equipment, rates, insurance and senior management salaries. At an extremely high level of activity, added capacity will be necessary to satisfy the market demand for the entity’s products or services, so fixed costs such as depreciation and managerial salaries will increase. 3. Discuss the difficulties that would arise in CVP analysis if each of the six assumptions that underlie the analysis was totally unrealistic. If unit sales prices changed at different levels of sales then the formula for a straight revenue line would not be appropriate. In practice it is likely that prices change over the full range of production that is possible and that different customers may even be offered different prices depending on their market power. However, within a limited range of output prices can reasonably be assumed to be fairly constant. If this was not so then CVP analysis would become a complicated mathematical technique rather than a simple, but useful, business technique. If costs cannot be identified as fixed or variable with some degree of accuracy then it would make it difficult to draw up the intersection and slope of the cost curve. If variable costs cannot be assumed to change proportionally with volume then the cost curve would not be a straight line but could be a stepped line or a curved line. Either of these would make CVP calculation complicated. If total fixed costs do not remain constant over the relevant range then the intercept for the cost curve cannot be reasonably estimated. If efficiency does not remain relatively unchanged then the cost curve would not be a straight line and estimating the curve of the cost curve would be difficult. In practice higher levels of efficiency may be achieved at higher levels of output (economies of scale). If the total sales are not in some predictable proportion of sales mix when more than one product is sold then it would be difficult to estimate the total revenue curve. Each of the six assumptions cannot be said to hold over the full range of production from zero to infinity. However, the assumptions are not totally unrealistic within a limited range of output and most businesses don’t operate in a range from zero to infinity but rather within a narrow range of outputs. The assumptions simplify the analysis so that it is easy to calculate and understand but still useful in helping to frame broad policy decisions. 4. ‘In predicting the future profitability of a business, there is a basic limitation in the standard form of income statement’. Discuss this statement. If future analysis is based on the conventional income statement, then the statement is true. The conventional statement classifies costs on a functional basis, i.e. costs of sales, selling and distribution, administration, etc. No information is provided on the behaviour of costs in response to increasing production and sales volume. Costs and expenses will behave differently in response to volume changes, depending on whether they are fixed, variable or mixed. This fact must be considered when projecting profits. While it can be assumed that the fixed costs shown are fixed when considering future profitability, it can be appreciated the variable costs will fluctuate proportionately with volume changes. This allows future profitability analysis to be fairly meaningful. To be of any real assistance in planning, the conventional income statement will need supplementary cost behaviour information. Fixed costs are fixed only over a relevant range. 5. What type of cost behaviour describes the cost of operating a mobile phone? The answer to this question depends on the type of contract a person has. It would be useful to get a number of students to describe their phone contract and to explain what cost behaviour it exhibits. Some contracts have a base amount that is paid each month and includes a certain number of calls. The monthly payments will be a fixed cost and any calls over those allowed within the monthly payment will be variable. This type of contract will therefore have mixed costs. If a student prepays for calls then these are most often a straight variable cost if the student owns the phone. 6. Many airlines offer substantial discounts on some of their normal airfares. How can these discounts be justified on the basis of CVP relationships? Use relevant examples to explain your answer. Airlines such as Qantas have high fixed costs relative to the variable costs of operating a flight. Fixed costs include for example lease payments on the aircraft, salaries of pilots and cabin crew. By reducing price and limiting the number of seats at this lower price, revenue per flight and hence profitability may increase if providing a discount increases demand for a particular flight. Discount fares contribute to cover fixed costs assuming that the seats filled through discounting would remain empty if full fares are charged. 7. The owner–manager of a small business was heard to make the following remark: ‘Break-even analysis has little relevance for my business. I am not in business to break even, but to make profits.’ Do you agree with this statement? Explain your position. Should not agree with the opinion expressed by the owner manager. CVP and break-even analysis are about relationships of cost/volume/profit and are essential for future profit planning purposes. Note that break-even analysis is only one aspect of CVP analysis. The break-even point is only the focal point of attention, and the analysis of cost profit behaviour is the essential component. However, the break-even point does indicate the range of activity where losses are incurred and profits earned. Cost–volume–profit analysis can be used to maximise profits and can be a proficient tool in so doing. This analysis can be used to supplement other means of planning future profits. 8. As the marketing manager for a mobile phone company, explain how CVP analysis could be useful in determining the best mix of price, volume, sales mix and advertising. Starting from the initial mix of price, volume, sales mix and advertising, CVP analysis could be used to determine the current level of profit. This could be done both with numbers (mathematically) and with charts (diagrammatically). Each of the variables can then be changed one at a time or in combinations to see what impact this would have on profit. If the price of the mobile phones increased, this would increase total revenue (assuming no impact on sales), or alternatively as a marketing manager you should have some idea of the impact of a price increase on the likely level of sales that would be achieved. Diagrammatically an increase in price will shift the whole of the Total Revenue line up by the amount of the price increase. A change in the volume would be reflected in a move along the existing total cost and total revenue lines and the impact on profit could be seen. Alternatively the CVP equation could be recalculated at the higher volume level to determine the expected profit. A change in sales mix would require a recalculation of the assumed mix and therefore the weighted average contribution margin per unit. Using the CVP equation would predict the impact of these changes on profit. Advertising would normally be seen as part of the fixed costs and an increase in advertising will shift the total cost line up by the amount of the increase in this expense. Together with the resultant expected increase in sales the new predicted profit could be calculated. 9. Imagine you are the manager of a hotel. What are some of the fixed, variable and mixed costs of running the hotel and how could you use CVP relationships for profit planning? Fixed costs of running a hotel would include the manager’s salary, rates & taxes, advertising, depreciation, insurance, chefs salary and rent. Variable costs of running a hotel would include cleaning costs, food, drinks, and sales commissions. Mixed costs of running a hotel would include electricity, phone, water & sewerage, employee training, maintenance, and internet usage. Once an initial position was determined for CVP analysis management could then see what the impact of varying different factors such as fixed, variable and mixed costs and price and volume of patrons would have on the profitability of the hotel. 10. ‘Break-even analysis is all right if you have a one-product business, but it falls down badly if you want to derive a break-even point for several products.’ Discuss this statement. The existence of multiple products in CVP analysis causes a problem in that there are joint fixed production costs which are incurred in the production of the multiple products. Fixed costs form an important part of the calculation of the break-even point; that is, fixed costs are divided by contribution margin per product to determine break-even sales. The problem can be overcome by arbitrarily assigning fixed costs to particular products, and applying the normal single product formulae. However, this presents difficulties as mentioned above. Break-even analysis can still be used provided it is possible to assume a constant product mix for the products. Break-even point in sales dollars or total units can be determined by the normal formulae and the total break-even point broken down over various products, based on an assumed product mix. The advantages of using cost profit analysis can still be achieved even with multiple products, albeit without the same precision as for single products. Exercises Exercise 22.1 Linearity assumption of a step cost function Gavini’s Café is run by Alex and Lara Gavini. They usually run the business with three staff and this is sufficient when there are up to 30 customers in the café. When the bookings for an evening are higher than 30 customers, the Gavini’s hire an extra staff member for each extra 10 customers they expect, up to the café’s limit of 90 customers. For example, if between 31 and 40 customers book for the evening, one extra staff member is employed. It costs the café $80 per staff member for an evening, not including the Gavini’s. Required (a) Determine the variable cost function for the extra staff employed to cater for customers’ numbers between 30 and 90. (b) The Gavini’s would like to save some money and are considering employing extra staff at the rate of one for every 15 extra customers. What is the new cost function and what other qualitative factors should they consider in their decision? (LO1) (a) Customers Staff Costs High 90 (1) 720 Low 30 240 60 480 (1) $240 + $80 6 $480/60 = $8 y = $240 + $8 x (b) Customers Staff Costs High 90 (1) 560 Low 30 240 60 320 (1) $240 + $80 4 $320/60 = $5.33 y = $240 + $5.33 x Qualitative factors that need to be considered include: • Quality of customer service if staff have to serve 15 rather than 10 people. • Impact on speed of service and how this coordinates with the kitchen. • Possible loss of drink sales as customers are not attended to as often and glasses not filled as much. • Loss of reputation if meals take too long to serve or are cold when they arrive at the table. Exercise 22.2 High-low method and cost behaviour Tania’s Legal Services rents a photocopier. The company is charged a fixed annual rental plus a per-copy charge. If the company makes 120 000 copies per year, the overall per-copy cost is estimated to be $0.12. If 90 000 copies are made during a year, it is estimated that the cost per copy is $0.14. Required (a) Using the high-low method, estimate the variable rate per copy and the fixed annual rental fee. (b) What would be the total cost if 140 000 copies are made during a year? (c) If the variable rate per copy falls by $0.01 each time another 20 000 copies are made over and above 120 000 copies, can Tania’s Legal Services approximate the cost of photocopying with a straight line? (LO1) (a) No. units Cost per unit Total cost High 120 000 $0.12 $14 400 Low 90 000 $0.14 12 600 Differences 30 000 $1 800 Variable cost per unit: $1 800 30 000 = $0.06 per unit Fixed costs: $14 400 – (120 000 $0.06) = $7 200 (b) Total cost = $7 200 + (140 000 $0.06) = $7 200 + 8 400 = 15 600 (c) If the variable rate per copy falls by $0.01 each time another 20 000 copies are made over and above 120 000 copies then the cost of photocopying at those levels of output would become a curved line. Exercise 22.3 Reasonableness of the high-low method Lucerne Ltd sells feather quilts and has never used CVP analysis in its 4-year history. The manager provides you with the following sales and cost data for the first 4 years of operation. Required (a) Using the high-low method, estimate the cost function for the manufacture of quilts by Lucerne Ltd. (b) Check whether the cost function you calculated in requirement A would represent the actual costs of manufacturing for 2018 and 2019. What does this tell you about the high-low method of estimating a cost function? (LO1) (a) Cost of manufacturing Number of quilts High $1 790 000 32 500 Low 1 192 000 21 000 $598 000 11 500 $598 000 / 11 500 = $52 per quilt $1 790 000 – ($52 32 500) = $100 000 fixed costs y = 52 x + 100 000 (b) 2018 y = 52 (23 500) + 100 000 = $1 322 000 The estimated costs using the high-low method are $75 500 less than the actual costs of manufacturing in 2018 2019 y = 52 (27 000) + 100 000 = $1 504 000 The estimated costs using the high-low method are $114 000 less than the actual costs of manufacturing in 2019. This demonstrates that the high-low method of estimating a cost function is just that, an estimate, and will not give the exact actual costs for any level of production. The high-low method assumes that costs increase in a perfectly linear way and this is not likely to be true. Exercise 22.4 High-low method and cost behaviour Favero Ltd accumulates the following data concerning a mixed cost using kilometres as the activity level. Required (a) Compute the fixed and variable cost elements using the high-low method. (LO1) (a) Cost Kilometres driven High $17 550 8 500 Low 15 550 7 500 $2 000 1 000 Variable cost: $2000 / 1000 = $2 per kilometre. Fixed cost: $17 550 – ($2 8500) = $550. Exercise 22.5 Mixed costs with the high-low method Adam Leeman Ltd has determined total factory overhead costs at both minimum and maximum levels of production — 200 000 machine hours and 300 000 machine hours respectively. The total factory overhead, made up of variable costs, mixed costs and fixed costs, was $796 000 for 300 000 machine hours and $646 000 for 200 000 machine hours. At an activity level of 200 000 machine hours, the total factory overhead consists of the following components. Required (a) Determine the fixed and the variable portion (rate per machine hour) of the mixed costs. (b) What should be the total factory overhead cost for 240 000 machine hours? (LO1) (a) Variable cost per machine hour: $220 000 200 000 = $1.10/MHR At 300 000 machine hours: Total costs $796 000 Less: Fixed costs $230 000 Variable costs (300 000 $1.10) 330 000 560 000 Mixed costs $236 000 High low method: Variable cost per machine hour At 200 000 machine hours 196 000 = FC + 0.40 (200 000) FC = 196 000 – 80 000 = $116 000 (b) Total factory overhead for 240 000 machine hours: $230 000 + $116 000 + 1.10 (240 000) + 0.40 (240 000) $230 000 + $116 000 + $264 000 + $88 000 = $698 000 Exercise 22.6 Contribution margin income statement RingTone Pty Ltd produces phones. The company prepared the following budgeted income statement. The owner, Rhing Thonn, wants to use this income statement as the basis of projecting the profits for the forthcoming year. He needs to know what the projected profit will be if the unit sales of phones increase by 20%. The following relevant information is available. Required (a) Restructure the previous year’s income statement to present it in contribution margin format. (b) What is the contribution margin for each phone? (c) Assuming the selling price and all costs remain unchanged, what will be the projected profit for the forthcoming year? (LO2) RINGTONE PTY LTD Income Statement for the year ended (a) Sales revenue $2 560 000 Variable cost of sales ($2 560 000/$320) $96 $768 000 Variable selling expenses 0.2 ($260 000) 52 000 820 000 Contribution margin 1 740 000 Fixed expenses: Manufacturing costs 260 000 Selling expenses 208 000 Administrative expenses 120 000 588 000 Profit $1 152 000 (b) Contribution margin for each phone: Selling price per unit $320.00 Variable cost per unit: Manufacturing $96.00 Selling ($52 000/8 000) 6.50 102.50 Contribution margin in per unit $217.50 (c) Unit sales 1.2 (8 000) = 9 600 units Sales (9 600 $320) $3 072 000 Variable cost of sales (9 600 $96) 921 600 Variable selling expenses (9 600 $6.50) 62 400 984 000 Contribution margin 2 088 000 Fixed expenses: Manufacturing 260 000 Selling 208 000 Administrative 120 000 588 000 Profit $1 500 000 Note: This solution assumes production units equals sales units, i.e. no change in level of inventories held. Exercise 22.7 Contribution margin – interpretive skills Energy Experiences Pty Ltd runs camps for school children and sporting clubs that provide 3 days of canoeing, horse riding, abseiling and skiing. As a graduate with a sports and recreation degree, you have eventually worked your way up to managing the camps. The accountant has presented you with the following income statement and wants to work with you to improve the company’s financial position so that it may continue in business. Required (a) Taking into account the nature of the activities provided by Energy Experiences Pty Ltd, what costs are likely to be fixed regardless of the number of campers and what costs are likely to vary in total with the number of campers? (b) Suggest specific ways in which the company could make a profit by changing its pricing, reducing fixed costs and reducing variable costs. (LO2 and LO3) (a) Fixed costs: • management salaries • some Insurance • rates and taxes • some Electricity • some Water • animal maintenance such as food and vets • some maintenance costs • advertising • administration salaries • interest and finance costs. Variable costs: • staff for organising activities • food • cleaning costs • maintenance of sporting equipment • some insurance • some electricity. (b) The average price per camper is currently $300. It may be possible to increase this by up to 10% without affecting the demand for the campsite. It would require some market research to determine how much the price could be increased without affecting demand. A 10% increase in price, assuming it doesn’t reduce demand, would increase profit by $75 000. This would make the total revenue curve steeper and the break-even level of operations lower. Any reduction in fixed selling and site maintenance, administration or finance costs would directly affect the profit. Advertising could be reduced but this may have a negative impact on the number of campers. Site maintenance could be reduced in the short term but this may have long term costs and result in greater long term expenses. Administration costs could be reduced by reducing the number of staff, although this may impact on efficiency. Some administration could be outsourced to an accounting firm. The company should look at current financing of debt and discuss with the bank whether they can change their methods of financing. Insurance should be checked with an insurance broker to ensure that the best deal is being accessed. This needs to be weighed against the importance of ensuring adequate insurance coverage in what can essentially be a higher risk business. Reducing fixed costs moves the cost curve down and again leads to a lower break-even level. Variable costs could be reduced by trying to get contracts for bulk purchasing of food at favourable rates. Cleaning could be reduced or campers asked to keep the site clean during their visit and then only employ cleaners between groups of campers. Any reduction in variable costs will make the total cost curve less steep and reduce the break-even level of operations. Exercise 22.8 Contribution margin — calculations Use the same information for Energy Experiences Pty Ltd in exercise 22.7. The accountant can’t make decisions on the future of the company without your authority as manager, so he believes it is important to work through the possible solutions together so that you understand what you are authorising. Required (a) Using the contribution margin income statement from exercise 22.7, calculate the CVP equation for the operations of Energy Experiences Pty Ltd. (b) What is the break-even number of campers for Energy Experiences Pty Ltd? (c) You believe that the maximum number of campers that the camp site can accommodate in a year is 3000. What would you suggest to change the CVP equation for Energy Exercises Pty Ltd so that you can make a profit with this number of campers? (LO2 and LO3) (a) S = $750 000 / 2500 = $300 / camper V = ($375 000 + $150 000) / 2500 = $210 / camper F = $300 000 300 x = 210 x + 300 000 (b) 300 x = 210 x + 300 000 90 x = 300 000 x = 300 000 / 90 x = 3 334 customers (c) 300 (3 000) = 210 (3 000) + 300 000 + P P = $(30 000) To make a profit with 3 000 campers, the fixed costs have to be reduced by $30 000, or 10%. Alternatively the variable costs per unit have to be reduced by at least $10 ($30 000 / 3 000). The other option is to increase the price per camper by at least $10 (3 000 $10). A combination of the above alternatives could be used, particularly if Energy Experiences Pty Ltd wants to do more than break even and make a profit. Exercise 22.9 CVP analysis Big Beef BBQ Ltd sells a single product, a gas barbecue. The barbecue sells for $960 per unit. Annual fixed costs are $1 536 000, and the contribution margin rate is 40%. Required (a) What are the variable costs per unit? (b) How many units must the company sell to break even? (c) What is the break-even point in sales dollars? (d) If the company wants to earn a before-tax profit of $768 000, how many units must be sold? What sales dollar level is required? What is the company’s margin of safety at this sales level? (e) If the company wants to earn a before-tax profit of 20% of sales, how many units must be sold? What are the sales dollars? (f) Prepare a CVP chart for the company. (LO5) (a) Variable costs per unit $960 (1 – 0.40) = $576 (b) Break-even sales in units: $960 S = $576 S + $1 536 000 $384 S = $1 536 000 S = 4 000 barbeques (c) Break-even sales in dollars: 4 000 barbeques $960 = $3 840 000 (d) Units to sell to earn pre-tax profit of $768 000 $960 S = $576 S + $1 536 000 + $768 000 $384 S = $2 304 000 S = 6 000 Sales $’s: 6 000 $960 = $5 760 000 Margin of safety: Unit sales 6 000 – 4 000 = 2 000 units Dollar sales $5 760 000 – $3 840 000 = $1 920 000 (e) S = VC + FC + Target profit $960 S = $576 S + $1 536 000 + 0.2 $960 S 192 S = $1 536 000 S = 8 000 8 000 $960 = $7 680 000 (f) CVP Chart (Break-even should be $3.84M and Fixed costs $1.536M.) Exercise 22.10 CVP analysis with changes Warner Ltd sells its only product at a price of $200 per unit. Variable costs are $160 per unit and total fixed costs are $208 000. Current annual sales are 6500 units. Required (a) What is the company’s break-even point in sales units? What is the break-even point in sales dollars? (b) What is the company’s margin of safety? (c) Calculate the company’s profit under the following situations. Treat each case as independent of the others. i. Variable costs increase 10% ii. Sales volume decreases 20% iii. Fixed costs increase 10% iv. Sales price increases 15% v. Sales price increases 20%, sales volume decreases 20%, variable costs increase 20%, and fixed costs decrease 20% (LO6) (a) CM = $200 -$160 = $40 CM% = $40/$200 = 20% Break-even point units = $208 000/$40 = 5 200 units Break-even sales dollars = $208 000/0.20 = $1 040 000 Check: 5 200 ($200) = $1 040 000 (b) Units Sales dollars Sales 6 500 $1 300 000 Break even point 5 200 1 040 000 Margin of safety 1 300 $260 000 (c) 1. 6 500 ((200 – 1.10(160)) – 208 000 = $(52 000) Loss 2. 0.8 (6 500) [200 – 160] – 208 000 = $0 Break-even 3. 6 500 (200 – 160) – (208 000 1.10) = $31 200 Profit 4. 6 500 ((200 1.15) – 160) – 208 000 = $247 000 Profit 5. 0.8(6 500)[1.20(200) – 1.20(160)] – 0.8(208 000) = $83 200 Profit Exercise 22.11 CVP analysis with changes Cruz Manufacturing Ltd’s sales slumped badly in 2019. For the first time in its history, it operated at a loss. The company’s income statement showed the following results from selling 600 000 units of product: Net sales $2 400 000; total costs and expenses $2 610 000; and loss $210 000. Costs and expenses consisted of the following. Management is considering the following independent alternatives for 2020: 1. increase unit selling price 25% with no change in costs, expenses, and sales volume 2. change the compensation of salespersons from fixed annual salaries totalling $210 000 to total salaries of $70 000 plus a 3% commission on net sales 3. purchase new high-tech machinery that will change the proportion of cost of sales to 55% of net sales variable and fixed cost of goods to $767 748 in total. Required (a) Calculate the break-even point in dollars for 2020 for each of the three alternatives. (b) Which course of action to you recommend? (LO6) (a) Break-even point in dollars: CM = $4 – $2.6 = $1.4 CM% = $1.4 / $4 = 0.35 Break even sales dollars = $1 050 000 / 0.35 = $ 3 000 000 Alternative 1: CM = $5 – $2.6 = $2.4 CM% = $2.4 / $5 = 0.48 Break even sales dollars = $1 050 000 / 0.48 = $ 2 187 500 Alternative 2: CM = $4 – $2.72 = $1.28 CM% = $1.28 / $4 = 0.32 Break even sales dollars = $910 000 / 0.32 = $2 843 750 Alternative 3: CM = $4 – $2.4 = $1.6 CM% = $1.6 / $4 = 0.4 Break even sales dollars = $1 157 748 / 0.4 = 2 894 370 (b) Alternative 1 should be recommended because the break-even point in sales dollars is lowest. Exercise 22.12 Cost–volume–profit analysis with two products Flaherty Ltd sells two types of shoes, men’s shoes and women’s shoes. During the financial year ended 30 June 2019, fixed costs were $460 800 and sales were in the ratio of three units (pairs) of men’s shoes to one unit (pair) of women’s shoes. Men’s shoes sell for $180 per pair, and the variable costs are $116 per pair. Women’s shoes sell for $300 per pair, and the variable costs are $204 per pair. Required (a) Calculate the break-even point in total units, and the number of units of each type of shoe that must be sold at the break-even point. (b) How many units of men’s shoes and how many pairs of women’s shoes must the firm sell to achieve a profit of $57 600? (LO7) (a) CM — X = $180 – $116 = $64 CM — Y = $300 – $204 = $96 Weighted average contribution margin: WACM = 3/4 ($64) + 1/4 ($96) = $72 Break-even point in total units $460 800/$72 = 6 400 units Units of X 3/4 (6 400 ) = 4800 units Units of Y 1/4 (6 400 ) = 1600 units 6 400 (b) Break even + DNP = ($460 800 + $57 600)/$72 = $518 400/$72 = 7 200 units Units of X 3/4 (7 200 = 5 400 units Units of Y 1/4 (7 200 ) = 1 800 units 7 200 units Exercise 22.13 Cost–volume–profit analysis with two products Aussie Sporting Company Pty Ltd produces two types of sporting balls: basketballs and footballs. During the year ended 30 June 2019 it sold the balls in the proportion of three basketballs for every two footballs sold. The basketballs are high-quality balls and sell for $120 each and the variable costs per ball are $80. The footballs sell for $110 each and the variable costs per ball are $55. The fixed costs for Aussie Sporting Company are $432 400 per year. Required (a) Calculate the break-even point in total units and the number of units of each type of ball that must be sold. (b) How many basketballs and how many footballs must the firm sell to achieve an after-tax profit of $579 600 if the tax rate is 30%? (LO7) (a) CM — BB = $120 – $80 = $40 CM — FB = $110 – $55 = $55 Weighted average contribution margin: WACM = 3/5 ($40) + 2/5 ($55) = $46 Break-even point in total units $432 400/$46 = 9 400 units Units of BB 3/5 (9 400) = 5 640 units Units of FB 2/5 (9 400) = 3 760 units 9 400 (b) $579 600 / (1 – 0.3) = $828 000 Break even + DNP = ($432 400 + $828 000)/$46 = $1 260 400/$46 = 27 400 units Units of BB 3/5 (27 400) = 16 440 units Units of FB 2/5 (27 400) = 10 960 units 27 400 Exercise 22.14 Contribution margin variance analysis SJM Ltd has prepared the following income statement information showing the actual contribution margin earned from the sale of its only product, and the planned contribution margin. Required (a) Calculate the sales price variance, the sales volume variance and the variable expense variance. Report to your manager on what is revealed in the analysis. (LO8) (a) Sales price variance: Budgeted selling price $480 000/3 200 = $150 Actual selling price $468 000/3 000 = 156 Difference $6 Sales price variance $6 (3 000) $18 000 Favourable Sales volume variance: Budgeted CM = $150 – (256 000/3 200) = $70 Sales volume variance $70 (3 200 – 3 000) = $14 000 Unfavourable Variable cost variance: Budgeted variable cost ($256 000/3 200) = $80 per unit Actual variable cost ($255 000/3 000) = $85 per unit Difference $5 Variable cost variance $5 (3 000) = $15 000 Unfavourable Summary Favourable variance $18 000 Unfavourable variances ($14 000 + $15 000) (29 000) Unfavourable CM variance $(11 000) Contribution Margin variance Actual CM – budgeted CM ($213 000 – 224 000) $(11 000) Unfavourable The combined effects of favourable sales price variance, an unfavourable sales volume variance and an unfavourable variable cost variance explain the net unfavourable overall contribution margin of $(11 000). The increase in the selling price is more than offset by the decrease in sales volume and further exacerbated by the increase in variable costs. Exercise 22.15 Contribution margin variance analysis Assume you are marketing manager for SJM Ltd in exercise 22.14, and the accountant explains that when the actual results were compared with budget results he found a favourable sales price variance, an unfavourable sales volume variance and an unfavourable variable expense variance. Required (a) For which of these three variances would it be reasonable for the accountant to expect you, as marketing manager, to take responsibility? (b) Explain what could have caused the sales price variance, the sales volume variance and the variable expense variance. (LO8) (a) It would be reasonable for the accountant to expect the marketing manager to take responsibility for the favourable sales price variance and the unfavourable sales volume variance. (b) The positive sales price variance suggests that the firm has been able to sell its product for $2 more than the budgeted amount and this could be due to a successful marketing campaign allowing the firm to increase its selling price. Alternatively it could be due to the market price for the product increasing by $2 and the marketing manager not being aware that the price increase was coming so that the budget was set at the wrong price. The unfavourable sales volume variance suggests that the actual quantity of products sold is less than budget and could reflect an advertising campaign that has not been as successful as budgeted for. The unfavourable variable expense variance could be due to any unexpected increase in variable expenses. The nature of variable expenses would depend on what product SJM Ltd actually sold. Problems Problem 22.16 Cost behaviour analysis using high-low method The factory overhead of TJD Ltd has fluctuated significantly from year to year in relation to the direct machine hours. The average costs at the average high and low levels of activity during the past 3 years are as follows. Factory overhead consists of indirect materials, repairs and maintenance, rates and taxes, and power. The company has analysed these costs at the low level of activity and determined that the costs are incurred as follows at that level. Required (a) Determine the cost function for factory overhead using the format y = a+ bx. (b) If direct machine hours of 300 000 are expected for the next year, what is the estimate of factory overhead? (c) Calculate how much of the factory overhead is maintenance cost at the high activity level of 480 000 direct machine hours. (LO1) (a) a = 2 120 000 – 6(320 000) = $200 000 y = 200 000 + 6X (b) y = 200 000 + 6(300 000) = $2 000 000 (c) Indirect materials (variable) = 832 000/320 000 = $2.6 per DMH Power (variable) = $384 000/320 000 = $1.20 per DMH Factory overhead at high level $3 360 000 Indirect materials 480 000 ($2.6) $1 248 000 Power 480 000 ($1.20) 576 000 Rates and taxes (fixed) 184 000 Maintenance (1) 1 352 000 $3 360 000 (1) $3 360 000 – (1 248 000 + 576 000 + 184 000) = $1 352 000 Problem 22.17 CVP analysis Slip Shod Ltd has provided the following production and sales information for each pair of its dress shoes. The fixed costs for the period are $1 125 000. Required (a) Calculate the break-even point. (b) Calculate the number of pairs that must be sold to achieve a profit of $63 000. What is the margin for safety at this sales level? (c) Would it be better to sell 16 000 pairs at a selling price of $180 each or 19 000 pairs at a selling price of $160? (d) If an additional $63 270 is spent on fixed advertising costs, what level of dollar sales must be attained to earn a new profit of $36 000? Assume that there has been no change in the sales price. (e) Assume an income tax rate of 30%. Using the given information, how many pairs of shoes need to be sold to earn an after-tax profit of $37 800? (LO4 and LO5) (a) CM = $180 – (22 + 35 + 15 + 18) = $90 or 50% Break-even point (units) = $1 125 000/90 = 12 500 units Break-even point (dollars) = $1 125 000/0.50 = $2 250 000 Check: 12 500 units $180 = $2 250 000 (b) Break-even point + DNP (units) = ($1 125 000 + $63 000)/$90 = 13 200 units Margin of safety = 13 200 – 12 500 = 700 units (c) Total CM 16 000 ($180 – 22 – 35 – 15 – 18) = $1 440 000 Total CM 19 000 ($160 – 22 – 35 – 15 – 16) = 1 368 000 Advantage from 16 000 @ $180 $ 72 000 (d) Fixed costs = $1 125 000 + $63 270 = $1 188 270 Break even + DNP = ($1 188 270 + $36 000)/0.50 Sales to earn new profit = $2 448 540 $2 448 540/$180 = 13 603 units (e) Before-tax profit: $37 800/(1 – 0.30) = $54 000 $180 x = $90 x + $1 125 000 + $54 000 $90 x = $1 179 000 X = 13 100 pairs of shoes Problem 22.18 CVP Analysis of Profitability Move On Marketing (MOM) Pty Ltd produces television advertisements for local businesses. The contribution margin income statement for the company is as follows. The company is supposed to achieve a 15% profit margin (profit ÷ marketing fees) and as the CEO of the company you have to sign off on any actions taken to meet this target. This requires you to understand each of the possible alternative actions. Required (a) With the current level of fees, what is the required profit to achieve the target profit margin? (b) What is the CVP equation for MOM Pty Ltd and the break-even number of television advertisements per year? (c) With the current pricing and variable cost structure, what level of sales are required to meet the company’s profit target? (LO5) (a) $624 000 15% = $93 600 required profit margin (b) The CVP equation for MOM Pty Ltd is: $12 000 x = $4 800 x + $324 000 $624 000 / 52 = $12 000 marketing fee per television advertisements $249 600 / 52 = $4 800 variable expenses per advertisement 12 000 x = 4 800 x + 324 000 (12 000 – 4 800) x = 324 000 x = 324 000 / 7 200 x = 45 television advertisements (c) $12 000 x = $4 800 x + $324 000 + 15% ($12 000 x) ($12 000 – $4 800 – $1 800) x = $324 000 $5 400 x = $324 000 x = 60 television advertisements are required to meet the required profit target Problem 22.19 CVP analysis with changes AEK Ltd has prepared its income statement, summarised below, for the year ended 30 June 2019. The company is evaluating three independent situations and has asked for your assistance. Required (a) If the company hires a new salesperson at a salary of $36 000, how much must sales increase in terms of dollars to maintain the company’s current profit. (b) If sales units increase 25% in the next year and profit increases 50%, would management perform better or worse than expected in terms of profit? Assume that there would be adequate capacity to meet the increased volume without increasing fixed costs. Comment on the variable cost per unit. (c) If a new marketing method would increase variable expenses (by an amount you should calculate), increase sales units 10%, decrease fixed costs 10%, and increase profit by 20%, what would be the company’s break-even point in terms of dollar sales if it adopts this new method? Assume that the sales price per unit would not be changed. Round your answer to the nearest whole number. (LO6) (a) Required increase in sales $36 000/0.25(1) = $144 000 (1) Contribution margin/sales 64 000/256 000 = 0.25 (b) Sales units 1.25 (40 000) = 50 000 units SP $ 6.40 Sales revenue $320 000 Variable expense (work back from profit) 244 000 Contribution margin 76 000 Fixed costs 40 000 Profit 1.5 ($24 000) $36 000 Profit should be: 50 000 (6.40)(0.25) – 40 000 = $40 000 (Management performance is worse by $4 000). This is accounted for in the increased VC per unit $4.88 – $4.80 = $0.08, e.g. $0.08 50 000 = $4 000. (c) Adjusted income statement SP $256 000/40 000 = $6.40 per unit Sales (44 000 $6.40) 281 600 Variable expenses (work back from profit) 216 800 Contribution margin 64 800 Fixed costs (0.9 $40 000) 36 000 Profit (1.20 $24 000) $28 800 VC per unit $216 800/44 000 = $4.93 (rounded) CM = $6.40 – $4.93 = $1.47 or 23% Break even point = $36 000/0.23 = $156 522 Problem 22.20 CVP analysis in a medical centre The accountant of Pearl Coast Medical Centre is evaluating ways to increase revenues. The financial objective of the centre is to operate at or just above its break-even point. The centre currently refers approximately 8000 patients each year to a nearby laboratory for a standard blood test. The laboratory charges $100 for each test. The equipment needed to perform the test can be leased by the centre for $80 000 per year, and a technician would have to be hired at an annual salary of $60 000. Other fixed annual costs for the tests are expected to be $24 000. The accountant estimates that the direct costs of performing each test (e.g. supplies) would be $20. Required (a) If the centre charges $100 per test, how many tests must be performed each year to break even on the service? (b) Prepare a CVP graph based on a fee of $100 per test. (c) If the centre can perform 8000 tests per year, how much should be charged for each test to break even? (d) Assume that the centre wants to offset losses of $32 000 from another department with profit from the blood tests. If $100 per test is charged, how many patients must be treated annually? (LO6) (a) CM = $100 – $20 = $80 or 80% FC = 80 000 + $60 000 + $24 000 = $164 000 Break-even point = $164 000/$80 = 2 050 tests or = $164 000/0.8 = $205 000 Check: 2 050 $100 = $205 000 (b) (c) 8 000 S = $20 (8 000) + $164 000 S = $324 000/8 000 Charge per test = $40.50 (d) Break-even + loss offset = Check: At CM = $80 $32 000/$80 = 400 tests beyond break-even (A) are required. Problem 22.21 CVP analysis in a service business XYZ Childcare Ltd plans to open a day care centre at the beginning of next year. A building has been leased and the company has estimated that the following annual costs will be required. Based on available space and qualified staff, management believes that the maximum number of children that can be cared for at the day care centre is 120. Required (a) Assume that the day care centre can attract 120 children when it opens. Determine the annual fee per child that must be charged to break even financially. (b) If the company charges $5980 per child annually, how many children must be enrolled to break even? (c) Prepare a CVP graph based on a charge of $5980 per child. (d) If management wants to earn an annual profit of $62 400 from the day care centre and can charge $5980 per child, how many children must be enrolled? (e) If the day care centre can attract 120 children, how much must be charged per child to earn a profit of $60 000? (f) If the day care centre can attract 120 children, how much must be charged per child to earn a profit of $60 000 plus 15% of annual fees? (LO6) (a) Fixed costs: $128 000 + 64 000 + 62 400 + 4 800 + 21 600 = $280 800 Variable costs per child: $780 + 2 080 = $2 860 120F = 120 (2 860) + $280 800 120F = 624 000 F = $5 200 (b) CM = $5 980 – $2 860 = $3 120 Break even (children) = (c) (d) Break even (children) = (e) 120F = 120 ($2 860) + 280 800 + 60 000 F = $684 000/120 = $5 700 per child (f) 120F = 120(2 860) + 280 800 + 60 000 + 0.15 (120F) 102 = 684 000 F = $684 000/$102 = $6706 (rounded) Problem 22.22 CVP analysis with multiple services Copeland Hotels Ltd provide three levels of rooms in their hotels. The following planning data are provided for the year ended 31 December 2020: Fixed hotel overhead costs are $24 360 000 per year, and the annual fixed marketing and administrative costs are $10 200 000. As a graduate of a tourism management course, you are part of the planning process for 2020 and need to understand what is happening in the process. Required (a) Calculate the break-even point for 2019 and 2020 in total room nights and the number of room nights of each type of room that must be sold at the break-even point. (b) Calculate the number of room nights of each type of room that will have to be sold in 2020 to earn an after-tax profit of $19 488 000. Assume a tax rate of 30%. (LO7) (a) Deluxe Suite 120 000 / (120 000 + 72 000 + 48 000) = 50% Superior Suite 72 000 / (120 000 + 72 000 + 48 000) = 30% Presidential Suite 48 000 / (120 000 + 72 000 + 48 000) = 20% Deluxe Suite Superior Suite Presidential Suite Rate per night $480 $720 $1 200 Direct room maintenance costs 160 200 280 Variable hotel overhead 40 60 80 Variable marketing expenses 40 60 120 Contribution margin $240 $400 $720 Total contribution margin for 10 rooms: ($240 5) + ($400 3) + ($720 2) = $3840 Divided by number of rooms 10 Average contribution margin per room $384 Alternatively, it can be calculated using the assumed mix of 5:3:2 5/10($240) + 3/10($400) + 2/10($720) = $384 Therefore break-even number of rooms is: S = Break-even sales S = Fixed costs Weighted average contribution margin per room S = $24 360 000 + $10 200 000 $384 S = 90 000 room nights Deluxe Suites 90 000 50% = 45 000 room nights Superior Suites 90 000 30% = 27 000 room nights Presidential Suites 90 000 20% = 18 000 room nights (b) Deluxe Suite 128 000 / (128 000 + 112 000 + 80 000) = 40% Superior Suite 112 000 / (128 000 + 112 000 + 80 000) = 35% Presidential Suite 80 000 / (128 000 + 112 000 + 80 000) = 25% Assume the sales mix is 40:35:25 40/100($240) + 35/100($400) + 25/100($720) = $416 If the after tax profit is $19 488 000 and the tax rate is 30% then the before tax profit is: $19 488 000 / (1 – 0.3) = $27 840 000 S = Sales to make an after tax profit of $19 488 000 S = Fixed costs + Profit Weighted average contribution margin per room S = $24 360 000 + $10 200 000 + 27 840 000 $416 S = 150 000 room nights Deluxe Suites 150 000 40% = 60 000 room nights Superior Suites 150 000 35% = 52 500 room nights Presidential Suites 150 000 25% = 37 500 room nights Deluxe Superior Presidential Suite Total Suite Suite Sales – rooms 60000 52500 37500 150000 Sales revenue – dollars $28 800 000 $37 800 000 $45 000 000 $111600 000 Variable expenses 14 400 000 16 800 000 18 000 000 49 200 000 Contribution margin $14 400 000 $21 000 000 $27 000 000 62 400 000 Fixed expenses 34 560 000 Profit before tax 27 840 000 Tax 8 352 000 Profit $19 488 000 Problem 22.23 CVP analysis with multiple products A to Z Pty Ltd has provided the following planned per-unit cost and sales data for the year ended 30 June 2020. Fixed factory overhead costs are $1 056 000 per year, and the annual fixed selling and administrative costs are $352 000. Required (a) Calculate the break-even point for 2019 and 2020 in total units and the number of units of each product that must be sold at the break-even point. (b) Calculate the number of units of each product that would have had to be sold in 2019 to earn an after-tax profit of $246 400. Assume a tax rate of 30%. (c) Calculate the number of units of each product that would have to be sold in 2020 to earn an after-tax profit of $255 640. (LO7) (a) Product A B C CM $30 $34 $40 2019 proportion of sales 30% 30% 40% 2020 proportion of sales 35% 40% 25% Weighted Average CM 2015 0.3(30) + 0.3(34) + 0.4(40) = $35.20 Weighted Average CM 2016 0.35(30) + 0.40(34) + 0.25(40) = $34.10 Break-even 2019: $1 408 000/$35.20 = 40 000 units Units A: 0.30 (40 000) = 12 000 units Units B: 0.30 (40 000) = 12 000 units Units C: 0.40 (40 000) = 16 000 units 40 000 units Break-even 2020: $1 408 000/$34.10 = 41 290 units Units A: 0.35 (41 290) = 14 452 units Units B: 0.40 (41 290) = 16 516 units Units C: 0.25 (41 290) = 10 322 units = 41 290 units (Calculations rounded.) (b) 2019 Break even + NPAT = [$1 408 000 + (246 400/(1 – 0.30))]/$35.20 = $1 760 000/$35.20 = 50 000 units Units A: 0.30 (50 000) = 15 000 units Units B: 0.30 (50 000) 15 000 units Units C: 0.40 (50 000) 20 000 units 50 000 units (c) 2020 Break even + NPAT = [$1 408 000 + (255 640/(1 – 0.30))]/$34.10 = $1 773 200/$34.10 = 52 000 units Units A: 0.35 (52 000) = 18 200 units Units B: 0.40 (52 000) 20 800 units Units C: 0.25 (52 000) 13 000 units 52 000 units Problem 22.24 Break-even analysis Long Weekend Ltd suffered a severe drop in sales and profit performance for the year ended 30 June 2019. The income statement revealed that net sales were $1 500 000 with a profit of $310 000. Unit sales were 300 000, and total costs were $1 190 000. A breakdown of costs and expenses is presented below. In response to the bad result, management is considering a number of options for the year ending 30 June 2020 to try to improve performance. Independent policy options being considered are set out below. 1. Update factory machinery and production methods to adjust the mix of fixed and variable cost of sales (which includes manufacturing costs) to 40% fixed and 60% variable. 2. Increase the selling price by 15%, with no changes to costs and expenses but unit sales will decrease 10%. 3. Change the manner in which sales staff are remunerated. It is proposed to pay sales staff on the basis of a base salary of $32 000 plus a 5% commission on net sales. The current policy is to pay fixed total salaries of $105 000. Required (a) Calculate the break-even point in dollars of sales for the year ended 30 June 2019. (b) Calculate the break-even point and profit for each of the options being considered by management. (c) What action should be recommended to management? Explain why. (LO4, LO5 and LO6) (a) P = S x – V x – FC 0 = $5 x – $2.20 x – $530 000 2.8 x = $530 000 x = 189 286 units (rounded up) 189 286 $5 = $946 430 (b) Original Profit = $1 500 000 – 660 000 – 530 000 = $310 000 1. P = S x – V x – FC 0 = $5 x – $2.10 x – $560 000 2.90 x = $560 000 x = 193 103 units (rounded up) 193 104 $5 = $965 520 FC change to $950 000 0.4 + $108 000 + $72 000 = $560 000 VC per unit change to ($950 000 0.6 + $36 000 + $24 000)/300 000 = $2.10 Profit = $5(300 000) – $2.10 (300 000) – $560 000 = $310 000 This policy increased the B/E level of sales which worsens the original position, and profit is the same if sales remain at 300 000 units. 2. P = Sx – Vx – FC 0 = $5(1.15) x – $2.44 x – 530 000 3.31 x = $530 000 x = 160 121 units (rounded up) 160 121 $5.75 = $920 695.75 Profit = $5.75 (300 000 0.9) – $2.44 (300 000 0.9) – 530 000 = $363 700 This reduces B/E level of sales and is an improvement on the original position as the increase in price more than makes up for the decrease in sales. Profit increases significantly. 3. P = S x – V x – FC 0 = $5 x – $2.45 x – $457 000 2.55 x = $457 000 x = 179 216 units(rounded up) FC = $530 000 – 73 000 = $457 000 VC = $2.20 + 5% ($5) = $2.45 B/E point is reduced. Profit = $1 500 000 – $735 000 – $457 000 = $308 000 (c) Option 2 is recommended since the highest profit will result. In option 1, B/E sales increase worsening the original position, while option 3 reduces the B/E point, but the profit is less than in Option 2. Option 2 allows an increase in sales without any change in costs. Problem 22.25 Alternatives with CVP analysis Details of BJM Pty Ltd’s income statement for the past year are as follows. Required Consider each of the following independent situations. (a) Determine the company’s break-even point in units and sales dollars. What is the margin of safety? (b) If the company wants to make an after-tax profit of $109 200, what is the dollar level of sales necessary to reach its goal? (c) If the sales volume is 15 000 units, what is the selling price needed to achieve an after-tax profit of $109 200 (d) If the company’s sales volume increases by 10% as a result of increasing fixed selling expenses by $30 000 and variable selling expenses by $0.60 per unit, what is the company’s after-tax profit? (e) If direct material costs increase 10%, direct labour costs increase 15%, variable overhead costs increase 10%, and fixed overhead increases by $10 000, how many units must be sold to earn an after-tax profit of $89 600? Round your calculations to the next highest unit. (LO6) (a) Sales price = $1 320 000 / 22 000 = $60 / unit Variable costs = ($440 000 + $396 000 + $88 000 + $132 000) / 22 000 = $48 / unit Fixed costs = $60 000 + $30 000 = $90 000 Break-even: $60 x = $48 x + $90 000 $12 x = $90 000 x = $90 000 / $12 = 7 500 units at breakeven The firm’s margin of safety is 14 500 (22 000 – 7 500) units. (b) BTP = $109 200 / (1 – 0.3) = $156 000 $60 x = $48 x + $90 000 + $156 000 $12 x = $246 000 x = 20 500 units = $1 230 000 (c) S (15 000) = $48 (15 000) + $90 000 + $156 000 S (15 000) = $966 000 S = $64.40 (d) $60 (22 000 1.1) = $48.60 (22 000 1.1) + $90 000 + $30 000 + P $1 452 000 = $1 176 120 + $120 000 + P P = $155 880 Therefore after tax profit is: ATP = $155 880 0.7 = $109 116 As this is less than the initial after tax profit of $121 800 this would not be a worthwhile strategy. (e) DM / unit = $440 000 / 22 000 = $20 DL / unit = $396 000 / 22 000 = $18 VOH / unit = $88 000 / 22 000 = $4 VSE / unit = $132 000 / 22 000 = $6 Unit costs after increases: DM / unit = $20 1.1 = $22.00 DL / unit = $18 1.15 = $20.70 VOH / unit = $4 1.1 = $ 4.40 VSE / unit = $ 6.00 $53.10 BTP = $89 600 / (1 – 0.3) = $128 000 $60 x = $53.10 x + $90 000 + $10 000 + $128 000 $6.90 x = $228 000 x = 33 044 units Problem 22.26 Impact of change with CVP analysis TMP Human Resource Consulting had the following contribution margin income statement for the year ended 2019. Required Answer each of the following independent situations. (a) Explain how an understanding of CVP analysis would improve the performance of the manager of a human resource consulting firm like TMP Human Resources Consulting. (b) As a graduate of a human resource management course you have finally become the manager of TMP Human Resource Consulting. In setting your salary at $500 000, you need to calculate what the service fees need to increase by to maintain the company’s profit equal to at least 25% of total service fees. (c) You employ a friend who graduated with a degree in marketing and she believes that by increasing variable expenses by $1 200 per client and fixed advertising expenses by $300 000 the firm will increase the number of clients by 100 per year. Would your marketing friend’s suggestions improve profitability? Explain why or why not. (LO6) (a) An understanding of CVP analysis would improve the performance of the manager of a human resource consulting firm like TMP Human Resources Consulting by: • before a cost can be controlled a manager needs to understand what causes it to be incurred and what causes it to change • helping them to understand the variable costs of employing staff so that they can determine the appropriate fees to achieve a contribution margin that would help them to maximise profit • understanding what costs are incurred in employing staff for others and how these costs vary with the number of people employed is necessary to be able to control these costs so that the firm can maximise its profits. • understanding the fixed costs that don’t vary with the level of people employed would provide the manager with an understanding of the costs that will be incurred regardless of the number of customers. (b) Fee per job = $36 000 000 / 1500 = $24 000 Variable expenses = $14 400 000 / 1500 = $9600 / job $24 000 x = $9600 x + $12 240 000 + $500 000 (salary) + 25% ($24 000 x) $8400 x = $12 740 000 x = 1517 jobs = 1517 $24 000 = $36 408 000 (c) P = $24 000 (1600) – $10 800 (1600) – 12 540 000 = $38 400 000 – $17 280 000 – $12 540 000 = $8 580 000 As the profit would fall, the suggestion is not a good idea. Problem 22.27 Impact of change with CVP analysis and tax Kids Sports Consulting Pty Ltd is a company set up by sports and recreation management students to gain experience in running their own business. It had the following contribution margin income statement data for the year ended 2019. Required Answer each of the following independent situations. (a) Explain how an understanding of CVP analysis would improve the performance of the manager of a sports and recreation firm like Kids Sports Consulting Pty Ltd. (b) As a student in a sports and recreation management degree you are required to act as the manager of Kids Sports Consulting Pty Ltd. In setting your salary at $20 000, calculate the increase in service fees to maintain the company’s profit after tax equal to at least 25% of total service fees. (c) You employ a friend who is studying for a marketing degree. She believes that by increasing variable expenses by $100 per client and fixed advertising expenses by $3000 the company will increase the number of clients by 20 per year. Would your marketing friend’s suggestions improve profitability after tax? Explain why the suggestions will, or will not, increase the company’s profit. (LO6) (a) An understanding of CVP analysis would improve the performance of the manager of a sports and recreation consulting firm like Kids Sports Consulting Pty Ltd by: • before a cost can be controlled a manager needs to understand what causes it to be incurred and what causes it to change • helping them to understand the variable costs of running a sporting event so that they can determine the appropriate fees to achieve a contribution margin that would help them to maximise profit • understanding what costs are incurred in running a sporting event for others and how these costs vary with the number of events is necessary to be able to control these costs so that the firm can maximise its profits. • understanding the fixed costs that don’t vary with the level of events organised would provide the manager with an understanding of the costs that will be incurred regardless of the number of customers. (b) Fee per job = $48 000 / 96 = $500 Variable expenses = $19 200 / 96 = $200 / job Profit after tax = 25% $48 000 = $12 000 Profit before tax = $12 000 / (1 – 0.3) = $17 143 (rounded up) $500 x = $200 x + $16 320 + $20 000 (salary) + $17 143 $300 x = $53 463 x = 178 events = 178 $500 = $89 000 (c) P = $500 (116) – $300 (116) – 16 320 – 3 000 = $3 880 PAT = $3 880 0.7 = $2 716 As the profit would fall, the suggestion is not a good idea. Problem 22.28 Impact of change with CVP analysis Lawsistan Ltd has prepared the following draft profit analysis for the current year. Required Answer each of the following four independent situations. (a) If the company’s manager is considering increasing his salary by $42 500, how much must dollar sales increase to maintain the company’s current profit? (b) If the company changes its marketing approach, it is expected that variable expenses will increase 10%, fixed expenses will decrease 15% and sales units and dollars will increase 20%. Calculate the company’ break-even point in terms of sales dollars if the new strategy is adopted. Assume that the sales price per unit would not be changed. Round your answer to the nearest dollar. (c) If the company decreases sales commissions, variable expenses will decrease by 10%. The company believes that unit sales will decrease 5% because of a loss of sales representatives, even though the company plans to increase its advertising budget by $25 000. Should the company decrease the sales commissions? (d) If the company’s profit increases 100% next year because of a 35% increase in sales, will performance be better or worse than expected? Assume adequate capacity exists to meet the increased volume without increasing fixed costs. (LO6) (a) SP per unit $ 1200 000/150 000 = $8.00 per unit Variable expenses pr. unit $690 000/150 000 = 4.60 per unit CM per unit $3.40 CM ratio $3.4/$8 42.5% Dollar sales to absorb increase in company manager’s salary. $42 500/0.425 = $100 000 OR $8 S = $4.60 S + $217 600 + $42 500 + $292 400 $3.40 S = $552 500 S = 162 500 Increase of 12 500 units @ $8 = $100 000 (b) Variable expenses 1.10 ($4.60) = $5.06 Fixed expenses 0.85 ($217 600) = 184 960 CM ratio ($8.00 – $5.06)/$8 = 36.75% Break even $ = $184 960/0.3675 = $503 293 OR $8 S = $5.06 S + $184 960 $2.94 S = $184 960 S = 62 912 units 62 912 @ $8 = $503 296 (c) Variable expenses per unit: 0.9 ($4.60) = $4.14 CM: $8 – $4.14 = $3.86 Unit sales 0.95 (150 000) = 142 500 Total CM (new) ($3.86 142 500) $550 050 Prior total CM $3.40 (150 000) 510 000 Incremental CM 40 050 Incremental advertising expense 25 000 Differential gain 15 050 The company should decrease sales commissions. OR $8 (0.95 150 000) = $4.14 (0.95 150 000) + $217 600 + 25 000 + P P = $307 450 $307 450 – $292 400 = $15 050 increase in profit. (d) Profit next year 2.00 ($292 400) $584 800 Sales next year 1.35 ($1 200 000) = 1 620 000 Profit % of sales 36.1% This year: Profit % $292 400/$1 200 000 24.37% Performance would be considerably better next year. Problem 22.29 Impact of change with CVP analysis and tax Richards Ltd has prepared the following draft profit analysis for the current year. Required Answer each of the following four independent situations. (a) If the company’s manager is considering increasing his salary by $34 000, how much must dollar sales increase to maintain the company’s current after-tax profit? (b) If the company changes its marketing approach, it is expected that variable expenses will increase 10%, fixed expenses will decrease 15%, and sales units and dollars will increase 20%. Calculate the company’ break-even point in terms of sales dollars if the new strategy is adopted. Assume that the sales price per unit will not change. Round your answer to the nearest dollar. (c) If the company decreases sales commissions, variable expenses would decrease by 10%. The company believes that unit sales would decrease 5% due to the loss of sales representatives, even though the company plans to increase its advertising budget by $25 000. Should the company decrease sales commissions? (LO6) (a) SP per unit $ 600 000/15 000 = $40.00 per unit Variable expenses per unit $345 000/15 000 = 23.00 per unit CM per unit $17.00 CM ratio $17/$40 42.5% $40 S = $23 S + $108 800 + $34 000 + $146 200 $17 S = $289 000 S = 17 000 Increase of 17 000 units @ $40 = $680 000 $680 000 – $600 000 = $80 000 increase in sales. (b) Variable expenses 1.10 ($23) = $25.30 Fixed expenses 0.85 ($108 800) = 92 480 CM ratio ($40.00 – $25.30)/$40 = 36.75% Break even $ = $92 480/0.3675 = $251 646 OR $40 S = $25.30 S + $92 480 $14.7 S = $92 480 S = 6 291 units 6 291 @ $40 = $251 640 (c) Variable expenses per unit: 0.9 ($23) = $20.70 CM: $40 – $20.70 = $19.30 Unit sales 0.95 (15 000) = 14 250 Total CM (new) ($19.30 14 250) $275 025 Prior total CM $17 (15 000) 255 000 Incremental CM 20 025 Incremental advertising expense 25 000 Differential loss (4 975) The company should not decrease sales commissions. OR $40 (0.95 15 000) = $20.70 (0.95 15 000) + $108 800 + 25 000 + P P = $141 225 $141 225 – $146 200 = $(4 975) decrease in profit before tax. Problem 22.30 Contribution margin variance analysis The manager of Fritz Fabricators Ltd has just reviewed the income statement for the previous quarter and is concerned by the profit earned. Her main concern is the significant difference between the planned contribution margin and the one actually achieved. The company sells only one product. A summary of contribution margins is shown below. Required (a) Calculate the sales price, sales volume and variable expense variances for the quarter. Explain the variation in contribution margin to the manager. (LO8) (a) Sales price variance: Actual unit sales selling price differential per unit 32 000 ($0.10) = $3 200 favourable Sales volume variance: Budgeted CM unit sales differential $2.75 1000 = $2 750 unfavourable Variable cost variance: Actual unit sales variable cost differential 32 000 ($0.15) = $4 800 favourable Unfavourable CM variance ($90 750 – 96 000) $5 250 F Variances Sales price $3 200 F Sales volume $2 750 U V Cost $4 800 F $5 250 F Calculations: Budget Actual Differential Sales units 33 000 32 000 1 000 U Selling price $6.70 $6.80 $0.10 F VC per unit 3.95 3.80 0.15 F CM per unit $2.75 $3.00 $0.25 F While sale volume was less than budget, actual selling price percent exceeded budgeted selling price, and variable cost also decreased, providing a favourable CM variance. Case studies Critical thinking Costing backpacks Jemma Simpkins began her own business manufacturing backpacks 10 years ago under the brand name Drop Dead. These are popular with secondary school and university students as they have a secure pocket for mobile phones and a hidden compartment that parents can’t find. As Jemma’s accountant, you have been responsible for determining the cost of the backpacks. Demand has been so great that Jemma has not worried about the accounting side of the business and has focused on the creative and marketing aspects. But fashions change, and students are no longer happy with floppy backpacks and now want neon-coloured briefcases with designer graffiti printed all over them. Jemma has been wondering whether she could compete by reducing the price of the Drop Dead backpacks. Jemma decided to look through your accounting files to see what she could work out for herself, but she was confused. She can’t understand why you have been telling her that the backpacks cost $30 to make when the cost of direct material is only $8 and the cost of direct labour is $7. ‘Where did the other $15 come from and why can’t I reduce the price of the bags by $15?’ she asks. Required (a) Explain, in non-accounting terms, about the nature of manufacturing costs and costing products. (b) Why can’t Jemma simply reduce her price by $15 and cover only the variable costs of production? What would you suggest Jemma should do to combat the new competition? (a) The issues students need to cover: • The direct costs of $15 only cover the material and labour for producing the backpacks. What about all of the other costs involved in running the business and also a margin for profit? The rent or cost of the premises that the business uses, any rates and taxes, administration costs and wages and salaries are not included in the $7 direct labour because people, like the accountant and Jemma, do not actually make the backpacks. • The extra $15 covers all of these extra costs that are not directly involved in the production of the backpacks, but without which the backpacks cannot be made. • As well as covering the extra costs, part of the $30 price has to provide the profit for the business. (b) Jemma can’t simply reduce her price to $15 because then she won’t be able to pay her rent, rates and taxes and other general expenses, or pay her accountant or herself. She will also make no profit. To combat the new competition, Jemma could redesign the backpacks so that they are more rigid and offer them in a new range of colours with appropriately abusive graffiti all over them. Alternatively, Jemma could offer her own design of briefcase that includes the features that were popular with her backpacks such as a mobile phone compartment easily accessible from the outside of the briefcase and a hidden compartment inside. Ethics and governance Using CVP analysis when applying for a loan Jill owns and operates a business that makes hand-crafted rocking chairs. The business is expanding but the increasing costs of raw materials and labour, and the GST, have badly affected profitability. Jill believes that if she buys some wood-turning equipment that is more modern she could reduce her use of labour and wastage of wood and this would make her business profitable again. The price of the equipment that Jill wishes to install is $15 000, which she will have to borrow from the bank. Jill has done a CVP analysis under her existing structure and also for the new structure if she buys the new wood-turning equipment. Although the new equipment would reduce the direct costs of labour and material, the fixed costs would increase so much that the break-even point of output would still exceed the likely level of rocking chair sales. Jill is passionate about her business and, although the CVP analysis doesn’t support the purchase of the new equipment, she is determined to buy the equipment no matter what. In making her presentation to the bank for the loan of $15 000, Jill uses CVP analysis to show how the new equipment would reduce the direct costs of labour and materials but does not show the fixed manufacturing costs as increasing. Required (a) Who are the stakeholders in this situation? (b) Is there an ethical issue in this situation? If so, explain. (c) What would you have done if you were in Jill’s position? (a) The stakeholders in this situation are: • Jill • the bank and its shareholders and investors. (b) Yes, there is an ethical issue in this situation as Jill is deliberately falsifying her CVP analysis to present a profitable outcome to the bank when she knows that this is more likely not the true scenario. Jill is trying to get a loan of $15 000 from the bank using data that she knows is not a reasonable estimate of the true position. (c) Each student’s answer will depend on their ethical stance and how passionate they would feel about their own small business. Knowing that her business most likely can’t break-even with the new equipment, Jill should not have approached the bank for a loan. Communication and leadership Break-even analysis for a commercial kitchen Phuong Nguyen runs a commercial kitchen that produces a range of bottled Vietnamese cooking sauces that are sold in major retail food stores across the country. Past accounting records show that the business, Phuong’s Fantastic Foods Pty Ltd, has been profitable. The bottles of sauces come in a range of flavours, but they all cost a similar amount to make and are sold for the same price regardless of flavour. The kitchen includes equipment such as ovens, stoves, refrigerators, freezers and automatic chopping and stirring machines, as well as sterilising and bottling equipment. Phuong has been very satisfied with the way the business has grown and the good reputation the sauces enjoy across the country, regularly being featured on television lifestyle shows. However, no records exist to show how many cartons of sauces, each containing 24 bottles, need to be sold so that the business will break even each year. This means Phuong has no idea of his margin of safety. Required (a) As a group, consider how a break-even point based on the number of cartons of sauces could be calculated. Also consider and summarise the typical expenses associated with the running of a commercial kitchen and how they would fluctuate with the level of sales. Consider which types of costs are fixed, variable and mixed and list some of them. (b) As a group, write a letter explaining the procedures Phuong should follow to be able to determine a break-even number of cartons of sauces. (a) and (b) Students need to consider what expenses of running a commercial kitchen are fixed relative to the number of cartons of sauce and what expenses vary with the level of output. Variable costs could include: • sauce ingredients • jars • labelling • packaging • freight • kitchen staff wages. Fixed costs could include: • rates and taxes • financing costs • supervisor’s salary. Mixed costs could include wear and tear on equipment such as ovens, stoves, refrigerators, freezers and automatic chopping and stirring machines and sterilising and bottling equipment. These costs may be simpler to treat as fixed and this may be a reasonable assumption for decision making purposes. Having established variable costs per carton of sauce, fixed costs per year and the price per carton of sauces, it is then possible to estimate the break-even number of cartons of sauces per year. Solution Manual for Accounting John Hoggett, John Medlin, Claire Beattie, Keryn Chalmers, Andreas Hellmann, Jodie Maxfield 9780730344568
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