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Lim,%2014% Lesson 1 and 2: Cost-Volume-Profit Analysis and Other Related Topics For those who are not familiar with my types of exercises, they are broken down into theoretical, simple solving, and moderate solving / case type questions. The answer keys are at the end. Warm-Up 1)

Explain why the break-even point changes when there is a change in sales mix.

2) Define the term ‘operating leverage’ and explain how the degree of operating leverage can influence future profits. 3) How can sensitivity analysis be used in conjunction with cost–volume–profit analysis? 4) A company has established a budgeted sales revenue for the forthcoming period of £500 000 with an associated contribution of £275 000. Fixed production costs are £137 500 and fixed selling costs are £27 500. What is the break-even sales revenue? (a) £75,625 (b) £90,750 (c) £250,000 (d) £300,000 5) Z plc currently sells products Aye, Bee and Cee in equal quantities and at the same selling price per unit. The contribution to sales ratio for product Aye is 40 per cent; for product Bee it is 50 per cent and the total is 48 per cent. If fixed costs are unaffected by mix and are currently 20 per cent of sales, the effect of changing the product mix to: Aye 40%, Bee 25%, Cee 35% s that the total contribution/total sales ratio changes to: (a) 27.4% (b) 45.3% (c) 47.4% (d) 48.4% (e) 68.4% 6) The following information is required for sub-questions (a) and (b). W Ltd makes leather purses. It has drawn up the following budget for its next financial period:

Selling price per unit Variable production cost per unit Sales commission Fixed production costs Fixed selling and administration costs Sales

$11.60 $3.40 5% of selling price $430 500 $198 150 90 000 units

6a) The margin of safety represents: (i) 5.6% of budgeted sales (ii) 8.3% of budgeted sales (iii) 11.6% of budgeted sales (iv) 14.8% of budgeted sales 6b) The marketing manager has indicated that an increase in the selling price to $12.25 per unit would not affect the number of units sold, provided that the sales commission is increased to 8 per cent of the selling price.

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These changes will cause the break-even point (to the nearest whole number) to be: (i) 71,033 units (ii) 76,016 units (iii) 79,879 units (iv) 87,070 units 7) RT plc sells three products. Product R has a contribution margin of $30. Product S has a contribution margin of $20. Product T has a contribution margin of $25. Assume they all sell for $100 each. Monthly fixed costs are $100,000. If the products are sold in the ratio: R:2 S:5 T:3 The monthly break-even sales revenue, to the nearest $1, is: a) £400 000 (b) £411 107 (c) £425 532 (d) impossible to calculate without further 8) S plc produces and sells three products, X, Y and Z. It has contracts to supply products X and Y, which will utilize all of the specific materials that are available to make these two products during the next period. The revenue these contracts will generate and the information of products X and Y are as follows: Product X = $10,000,000 in revenue, 85% of revenue are variable costs Product Y = $20,000,000 in revenue, 10% of revenue are variable costs Product Z’s variable costs are 75% of total revenues. The total fixed costs of S plc are £5.5 million during the next period and management have budgeted to earn a profit of £1 million. Calculate the revenue that needs to be generated by Product Z for S plc to achieve the budgeted profit. 9) XYZ Ltd produces two products and the following budget applies: Product X Product Y (£) (£) Selling price Variable costs Contribution margin Fixed costs apportioned Units sold

6 2 4 100 000 70 000

12 4 8 200 000 30 000

You are required to calculate the break-even points for each product and the company as a whole and comment on your findings. 10) Toowomba manufactures various products and uses CVP analysis to establish the minimum level of production to ensure profitability. Fixed costs of £50 000 have been allocated to a specific product but are expected to increase to £100 000 once production exceeds 30 000 units, as a new factory will need to be rented in order to produce the extra units. Variable costs per unit are stable at £5 per unit over all levels of activity. Revenue from this product will be £7.50 per unit.

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Lim,%2014% a) Formulate the equations for the total cost at: (i) less than or equal to 30 000 units; (ii) more than 30 000 units. b) Prepare a break-even chart and clearly identify the break- even point or points. (c) Discuss the implications of the results from your graph in (b) with regard to Toowomba’s production plans. Getting Serious: 11) Tweed Ltd is a company engaged solely in the manufacture of sweaters, which are bought mainly for sporting activities. Present sales are direct to retailers, but in recent years there has been a steady decline in output because of increased foreign competition. In the last trading year (2011) the accounting report indicated that the company produced the lowest profit for 10 years. The forecast for 2012 indicates that the present deterioration in profits is likely to continue. The company considers that a profit of £80 000 should be achieved to provide an adequate return on capital. The managing director has asked that a review be made of the present pricing and marketing policies. The marketing director has completed this review, and passes the proposals on to you for evaluation and recommendation, together with the profit and loss account for year ending 31 December 2011.

Tweed Ltd profit and loss account for year ending 31 December 2011 (£)

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Sales revenue (100 000 sweaters at 1 000 000 £10) Factory cost of goods sold: Direct materials 100 000 Direct labour 350 000 Variable factory overheads 60 000 Fixed factory overheads 220 000 730 000 Administration overhead 140 000 Selling and distribution overhead Sales commission (2% of 20 000 sales) Delivery costs (variable 50 000 per unit sold) Fixed costs 40 000 110 000 980 000 Profit 20 000 The information to be submitted to the managing director includes the following three proposals: (i) To proceed on the basis of analyses of market research studies which indicate that the demand for the sweaters is such that a 10 per cent reduction in selling price would increase demand by 40 per cent. (ii) To proceed with an enquiry that the marketing director has had from a mail order company about the possibility of purchasing 50 000 units annually if the selling price is right. The mail order company would transport the sweaters from Tweed Ltd to its own warehouse, and no sales commission would be paid on these sales by Tweed Ltd. However, if an acceptable price can be negotiated, Tweed Ltd would be expected to contribute £60 000 per annum towards the cost of

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Lim,%2014% producing the mail order catalogue. It would also be necessary for Tweed Ltd to provide special additional packaging at a cost of £0.50 per sweater. The marketing director considers that in 2012 the sales from existing business would remain unchanged at 100 000 units, based on a selling price of £10 if the mail order contract is undertaken. (iii) To proceed on the basis of a view by the marketing director that a 10 per cent price reduction, together with a national advertising campaign costing £30 000 may increase sales to the maximum capacity of 160 000 sweaters. Required: (a) The calculation of break-even sales value based on the 2011 accounts. (b) A financial evaluation of proposal (i) and a calculation of the number of units Tweed Ltd would require to sell at £9 each to earn the target profit of £80 000. (c) A calculation of the minimum prices that would have to be quoted to the mail order company, first, to ensure that Tweed Ltd would, at least, break-even on the mail order contract, second, to ensure that the same overall profit is earned as proposal (i) and, third, to ensure that the overall target profit is earned. (d) A financial evaluation of proposal (iii). 12) A local government authority owns and operates a leisure centre with numerous sporting facilities, residential accommodation, a cafeteria and a sports shop. The summer season lasts for 20 weeks including a peak period of six weeks corresponding to the school holidays. The following budgets have been prepared for the next summer season: Accommodation 60 single rooms let on a daily basis. 35 double rooms let on a daily basis at 160 per cent of the single room rate. Fixed costs £29 900. Variable costs £4 per single room per day and £6.40 per double room per day. Sports Centre Residential guests each pay £2 per day and casual visitors £3 per day for the use of facilities. Fixed costs £15 500 Sports Shop Estimated contribution £1 per person per day. Fixed costs £8250 Cafeteria Estimated contribution £1.50 per person per day. Fixed costs £12 750 During the summer season the centre is open seven days a week and the following activity levels are anticipated: Double rooms fully booked for the whole season. Single rooms fully booked for the peak period but at only 80 per cent of capacity during the rest of the season. 30 casual visitors per day on average. You are required to: (a) calculate the charges for single and double rooms assuming that the authority wishes to make a £10 000 profit on accommodation; (b) calculate the anticipated total profit for the leisure centre as a whole for the season; (c) advise the authority whether an offer of £250 000 from a private leisure company to operate the centre for five years is worthwhile, assuming that the authority uses a 10 per cent cost of capital and operations continue as outlined above.

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Lim,%2014% 13) Walt’s Woodwork Company makes and sells wooden shelves. Walt’s carpenters make the shelves in the company’s rented building. Walt has a separate office at another location that also includes a showroom where customers can view sample shelves and ask questions of salespeople. The company sells all the shelves it produces each year and keeps no inventories. The following information pertains to Walt’s Woodwork Company for the past year:

a. b. c. d. e. f. g. h. i. j. k. l. m.

Units produced and sold Sales price per unit Carpenter labor to make shelves Wood to make the shelves Sales staff salaries Office and showroom rental expenses Depreciation on carpentry equipment Advertising Sales commissions based on number of units sold Miscellaneous fixed manufacturing overhead Rent for the building where the shelves are made Miscellaneous variable manufacturing overhead Depreciation for office equipment

50,000 $70 600,000 450,000 80,000 150,000 50,000 200,000 180,000 150,000 300,000 350,000 10,000

Make appropriate assumptions about cost behavior and assume that direct labor costs vary directly with the number of units produced. How many units must the company sell in order to earn a pre- tax profit of $500,000? 14) Johnson Company and Smith Company are competing firms that offer limousine service from the Charlesburg airport. While Johnson pays most of its employees on a per-ride basis, Smith prefers to pay its employees fixed salaries. Information about the selling prices per ride and cost structures of the two firms is given below.

COST CATEGORY Selling price per ride Variable cost per ride Contribution margin per ride Fixed costs per year

JOHNSON COMPANY $30 24 6 $300,000

SMITH COMPANY $30 15 15 $1,500,000

(a) Calculate the breakeven point in the number of rides for both firms. (b) Draw two graphs plotting profit as a function of the number of rides for the two firms. (c) Explain which firm’s cost structure is more profitable. (d) Explain which firm’s cost structure is riskier. (e) What is the indifference point? Answer Key: 1)

The break-even point changes when the sales mix changes because there is a change in the weighted average contribution margin. You may be able to sell products with higher or lower contribution margins, which lessens/ increases the units needed to breakeven.

2) Operating leverage is the sensitivity of profits relative to growth in sales, and can be measured via the proportion of fixed costs relative to variable costs. It enhances profits significantly like a multiplier because high operating leverage has high fixed costs, so profits go up faster relative to revenues. However, it has a downside of multiplying losses as well.

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Lim,%2014% 3) Sensitivity analysis can be used with CVP analysis to measure changes in margin of safety, breakeven, profit, and the like relative to changes in contribution margins and fixed costs. 4) D. Remember that for CVP analysis, it does not matter if a cost is COGS or in operating expenses under the formal income statement, only that it is variable or fixed. In this particular problem, the per unit variable cost is not given, so you may be surprised. However, note that the question is asking breakeven on a monetary measure. Breakeven in Sales in Volume = (137,500 + 27,500) / Contribution Margin Per Unit Breakeven Sales in Dollar = (165,000 / Contribution Margin Per Unit) x Selling Price Per Unit Breakeven Sales in Dollar = 165,000/ (Contribution Margin Per Unit/ Selling Price Per Unit Contribution Margin Ratio = Proportion contributed to paying for fixed costs relative to $1 earnings, or contribution margin per unit / selling price per unit. Since this is a ratio, it’s the same if we use total contribution margin / total revnue Contribution Margin Ratio = 275,000 / 500,000 = 55% Each $1 gives 0.55 in contribution. Breakeven Sales in Dollar = 165,000 / 55% = $300,000 5) B. This is a classic of encountering an unfamiliar term, but the solution is similar to other problems. Contribution to sales ratio is basically contribution margin ratio, and all it is asking you for is getting the weighted average contribution margin ratio, similar to multiple product CVP analysis. 40% x 40% + 25% x 50 % + 35% x 48% = 45.3% 6) 6a) III. The margin of safety requires both budgeted sales and breakeven sales in terms of units. Breakeven sales in units is computed as Fixed Costs / Contribution Margin Per Unit Be warned that sales commission is a variable cost, which we can convert into a per unit basis. Sales Commission = 5% of Selling Price Sales Commission per unit = 5% x 11.60 = .58 Breakeven Sales = ($430,500 + 198,150) / (11.60 – 0.58 – 3.40) Breakeven Sales = 628,650 / 7.62 = 82,500 Margin of Safety = 90,000 – 82,500 = 7,500 As % of Budget = 7,500 / 90,000 =8.3% Be careful to read what the problem is asking for! 6b) III. Recompute but changing the CM. Remember to use the new inputs forcommission and selling price! Sales Commission = 8% of Selling Price Sales Commission per unit = 8% x 12.25 = .98 Breakeven Sales = ($430,500 + 198,150) / (12.25– 0.58 – 3.40) Breakeven Sales = 628,650 / 7.87 = 79,879 7) C. First do the weighted average contribution margin: 20% x 30 + 50% x 20 + 30% x 25 = 23.5 Breakeven in units = 100000 / 23.5 = 4,255.32

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Lim,%2014% Breakeven in sales = 4,255.32 x 100 = 425,532 Note: If you are given the contribution margin ratio, this can be solved as well. For example, if contribution margin ratio is 30%, 20%, and 25% for A B and C respectively, you can get the weighted average contribution margin ratio and divide the fixed costs with it, without needing to multiply by the selling price. 8) ) You are not given volume, but you do not need it. First solve for the hurdle / target: $5,500,000 + 1,000,000 = 6,500,000 Next, determine the portion already covered by product x and product y. Product X Contribution Margin = 10,000,000 x 15% = 1,500,000 Product Y Contribution Margin = 20,000,000 x 10% = 2,000,000 Fixed Costs and Profit Left to Cover = 6,500,000 – 1,500,000 – 2,000,000 = 3,000,000 Product Z Contribution Margin = 25% of Revenues 3,000,000 = 25% x Product Z Revenues Product Z Revenues = 3,000,000 / 25% = 12,000,000 9) Stand-Alone Breakeven: Product X = 100,000 / 4 = 25,000 units Product Y = 200,000 / 8 = 25,000 units Company Breakeven: Weighted Average Contribution: 1/3 x 4 + 2/3 x 8 = 5.2 Company Breakeven = 300,000 / 5.2 = 57,692 Why the difference? When you do stand-alone breakeven, 1/3 of the fixed costs are allocate to product X, which has a lower margin. When you do combined, 7/10 of the fixed costs are allocated to product X effectively, meaning that it takes more to cover these fixed costs. Which do you use? You have do stand-alone first to see if the products are profitable by itself. The company breakeven is so you have some flexibility to cover for the losses of other products from time-to-time. 10) a) This is a step function / piece-wise cost equation. Where X = Volume If X 30,000: Total Cost = 100,000 + 5X b) Breakeven point is at 20,000 if < 30,000 and at 40,000 for > 30,000

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c) If Toowomba is planning on expansion, then it better makes sure it can sell at least 40,000 to breakeven. Otherwise, it will just lose money. And even then, Toowomba must make sure the profit gained from ramping up capacity is exceeds the profit from not ramping up capacity. At 30,000 units, total profit is 30,000 x 7.5 – 100,000 – 5 x 30,000 = $25,000. So effectively, not only must you produce 40,000 to breakeven, you actually need to produce at this to earn a better return: 7.5 X – 100,000 - 5X > 25,000 X > 50000. In other words, volume must actually be 50,000 for expansion to be worth it. To summarize: If potential sales < 20,000 = Don’t bother producing If potential sales is between 20,000 to 50,000, producing at 30,000 is still better even if you breakeven at 40,000 with the new fixed costs If potential sales is > 50,000, then producing at >50,000 is still better 11) a) Again, we calculate breakeven based on variable and fixed costs (cost behaviors relative to volume) regardless of whether they are COGS, admin, or selling expenses: You can do this directly via sales revenue and contribution margin ratio, or the long cut (less confusing way). First, determine the fixed costs. Total fixed costs include: 1) Fixed Factory Overhead, 2) Administration Overhead, 3) Fixed sales overhead Total fixed costs = 220,000 + 140,000 + 40,000 = 400,000 Total Revenue = 1,000,000 Total Variable Costs = 100,000 + 350,000 +60,000 + 20,000 + 50,000 = 580,000 Contribution Margin Ratio = (1,000,000 – 580,000) / 1,000,000 Contribution Margin Ratio = 42% Breakeven Sales Revenue = 400,000 / 42% = $952,381 If you don’t want to memorize the contribution margin ratio formula (though I encourage you to understand it), here is another way: Unit Selling Price: $10 / sweater Direct Materials: $1 / sweater (100,000 / 100,000) Direct Labour: $3.5 / sweater (350,000 /100,000) Variable Overhead: $0.6 / sweater ( 60,000 / 100,000)

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Lim,%2014% Commission: $0.2 / sweater (2% of $10) Delivery Costs: $0.5 / sweater (50,000 / 100,000) Total Variable Costs Per Unit: $5.8 Total Contribution Margin Per Unit = $10 – 5.8 = $4.2 Breakeven Sales in Units = 400,000 / 4.2 = 95,238 units Breakeven Sales in Dollars = 95,238 units x $10 / sweater = 952,381 b) Proposal (i) asks you do actually do a sensitivity / scenario analysis You can manipulate this on a total revenue or on a per unit basis. Let us say the variable costs remain steady at $5.8, but selling price goes down to $9. Your contribution margin per unit becomes $3.2. Your sales go up by 40%, or by 40,000 sweaters to become 140,000 sweaters. Total Profit = 140,000 x ( 9 – 5.8) – 400,000 Total Profit = $48,000 Better effect than the base case, but ...