Cost Volume Profit Analysis Solutions Part 5

EA 2. None of the alternatives will help Carlisle Engineering achieve its net income objective of $1,200,000. Alternative b, where variable costs are reduced by $300 and selling price is reduced by $400 resulting in 1,750 additional units being sold through the end of the year, yields the highest net income of $1,180,000. Carlisle’s managers should examine how to modify Alternative b to further increase net income. For example, could variable costs be decreased by more than $300 per unit or selling prices decreased by less than $400? Calculations for the three alternatives are shown below. Alternative a Revenues = ($4,000  400) + ($3,400a  2,100) = $8,740,000 Variable costs = $1,000  2,500b = $2,500,000 Operating income = $8,740,000 $2,500,000  $4,800,000 = $1,440,000 Net income = $1,440,000  (1  0.20) = $1,152,000 a $4,000 – ($4,000 × 0.15) ; b400 units + 2,100 units. Alternative b Revenues = ($4,000  400) + ($3,600a  1,750) = $7,900,000 Variable costs = ($1,000  400) + (700b  1,750) = $1,625,000 Operating income = $7,900,000  $1,625,000  $4,800,000 = $1,475,000 Net income = $1,475,000  (1  0.20) = $1,180,000 a $4,000 – 400 ; b$1,000 – $300. Alternative c Revenues = ($4,000  400) + ($2,800a  2,200) = $7,760,000 Variable costs = $1,000  2,600b = $2,600,000 Operating income = $7,760,000 $2,600,000  $4,320,000c = 840,000 Net income = $840,000  (1  0.20) = $672,000 a $4,000 – ($4,000 0.30); b400 units + 2,200nits; c$4,800,000 – ($4,800,000  0.10) 3-48 Choosing between compensation plans, operating leverage. CMA, adapted) AgroPharm Corporation manufactures pharmaceutical products that are sold through a network of external sales agents. The agents are paid a commission of 18% of revenues. AgroPharm is considering replacing the sales agents with its own salespeople, who would be paid a commission of 12% of revenues and total salaries of $7,950,000. The income statement for the year ending December 31, 2017, under the two scenarios is shown here. 3-51 EA Required: 1. Calculate AgroPharm’s 2017 contribution margin percentage, breakeven revenues, and degree of operating leverage under the two scenarios. 2. Describe the advantages and disadvantages of each type of sales alternative. 3. In 2018, AgroPharm uses its own salespeople, who demand a 14% commission. If all other cost-behavior patterns are unchanged, how much revenue must the salespeople generate in order to earn the same operating income as in 2017? SOLUTION (30 min.) Choosing between compensation plans, operating leverage. 1. We can recast AgroPharm’s income statement to emphasize contribution margin, and then use it to compute the required CVP parameters. AgroPharm Corporation Income Statement for the Year Ended Decemeber 31, 2017 Revenues Variable Costs Cost of goods sold − variable Marketing commissions Contribution margin Fixed costs Cost of goods sold − fixed Using Sales Agents Using Own Sales Force $45,000,000 $45,000,000 $15,750,000 8,100,00 0 $15,750,000 23,850,000 $21,150,000 $5,425,000 5,400,00 0 $5,425,000 3-52 21,150,000 $23,850,000 EA Marketing fixed Operating income 5,250,00 0 10,675,000 $10,475,000 7,950,00 0 13,375,000 $10,475,000 Contribution margin percentage ($21,150,000-:-$45,000,000; $23,850,000÷$45,000,000) 47.00% 53.00% Breakeven revenues ($10,675,000 ÷ 0.47; $13,375,000 ÷ 0.53) $22,712,766 $25,235,849 Degree of operating leverage ($21,150,000 ÷ $10,475,000; $23,850,000 ÷ $10,475,000) 2.02 2.28 2. The calculations indicate that at sales of $45,000,000, a percentage change in sales and contribution margin will result in 2.02 times that percentage change in operating income if AgroPharm continues to use sales agents and 2.28 times that percentage change in operating income if AgroPharm employs its own sales staff. The higher contribution margin per dollar of sales and higher fixed costs gives AgroPharm more operating leverage, that is, greater benefits (increases in operating income) if revenues increase but greater risks (decreases in operating income) if revenues decrease. AgroPharm also needs to consider the skill levels and incentives under the two alternatives. Sales agents have more incentive compensation and, hence, may be more motivated to increase sales. On the other hand, AgroPharm’s own sales force may be more knowledgeable and skilled in selling the company’s products. That is, the sales volume itself will be affected by who sells and by the nature of the compensation plan. 3. Variable costs of marketing = 14% of Revenues Fixed marketing costs = $7,950,000 Variable Fixed marketing marketing Variable Fixed Operating income = Revenues  manuf. costs  manuf. costs  costs  costs Denote the revenues required to earn $10,475,000 of operating income by R, then R  0.35R  $5,425,000  0.14R  $7,950,000 = $10,475,000 R  0.35R  0.14R = $5,425,000 + $7,950,000 + $10,475,000 0.51R = $23,850,000 R = $$23,850,000  0.51 = $46,764,706 3-49 Sales mix, three products. The Matrix Company has three product lines of belts—A, B, and C—with contribution margins of $7, $5, and $4, respectively. The president foresees sales of 3-53 EA 400,000 units in the coming period, consisting of 40,000 units of A, 200,000 units of B, and 160,000 units of C. The company’s fixed costs for the period are $1,020,000. Required: 1. What is the company’s breakeven point in units, assuming that the given sales mix is maintained? 2. If the sales mix is maintained, what is the total contribution margin when 400,000 units are sold? What is the operating income? 3. What would operating income be if 40,000 units of A, 160,000 units of B, and 200,000 units of C were sold? What is the new breakeven point in units if these relationships persist in the next period? SOLUTION (15–25 min.) Sales mix, three products. 1. Sales of A, B, and C are in ratio 40,000 : 200,000 : 160,000. So for every 1 unit of A, 5 (200,000 ÷ 40,000) units of B are sold, and 4 (160,000 ÷ 40,000) units of C are sold. Contribution margin of the bundle = 1  $7 + 5  $5 + 4  $4 = $7 + $25 + $16 = $48 $1, 020, 000 $48 Breakeven point in bundles = = 21,250 bundles Breakeven point in units is: Product A: 21,250 bundles × 1 unit per bundle 21,250 units Product B: 21,250 bundles × 5 units per bundle 106,250 units Product C: 21,250 bundles × 4 units per bundle 85,000 units Total number of units to breakeven 212,500 units Alternatively, Let Q = Number of units of A to break even 5Q = Number of units of B to break even 4Q = Number of units of C to break even Contribution margin – Fixed costs = Zero operating income $7Q + $5(5Q) + $4(4Q) – $1,020,000 = $48Q = Q= A 5Q = 4Q = Total = 0 $1,020,000 21,250 ($1,020,000 ÷ $48) units of 106,250 units of B 85,000 units of C 212,500 units 2. Contribution margin: A: B: 40,000  $7 $ 280,000 200,000  $5 1,000,000 3-54 EA C: Contribution margin Fixed costs Operating income 3. Contribution margin A: 40,000  $7 B: 160,000  $5 C: 200,000  $4 Contribution margin Fixed costs Operating income $ 860,000 160,000  $4 640,000 $1,920,000 1,020,000 $ 900,000 $ 280,000 800,000 800,000 $1,880,000 1,020,000 Sales of A, B, and C are in ratio 40,000 : 160,000 : 200,000. So for every 1 unit of A, 4 (160,000 ÷ 40,000) units of B and 5 (200,000 ÷ 40,000) units of C are sold. Contribution margin of the bundle = 1  $7 + 4  $5 + 5  $4 = $7 + $20 + $20 = $47 $1, 020, 000 $47 Breakeven point in bundles = = 21,703 bundles (rounded up) Breakeven point in units is: Product A: 21,703 bundles × 1 unit per bundle 21,703 units Product B: 21,703 bundles × 4 units per bundle 86,812 units Product C: 21,703 bundles × 5 units per bundle 108,515 units Total number of units to breakeven 217,030 units Alternatively, Let Q = 4Q = 5Q = Number of units of A to break even Number of units of B to break even Number of units of C to break even Contribution margin – Fixed costs = Breakeven point $7Q + $5(4Q) + $4(5Q) – $1,020,000 = 0 $47Q = $1,020,000 Q = 21,703 ($1,020,000 ÷ $47) units of A (rounded up) 4Q = 86,812 units of B 5Q = 108,515 units of C Total = 217,030 units Breakeven point increases because the new mix contains less of the higher contribution margin per unit, product B, and more of the lower contribution margin per unit, product C. 3-50 Multiproduct CVP and decision making. Romi Filters produces two types of water filters. One attaches to the faucet and cleans all water that passes through the faucet; the other is a pitcher-cum-filter that only purifies water meant for drinking. The unit that attaches to the faucet is sold for $150 and has variable costs of $90. 3-55 EA The pitcher-cum-filter sells for $160 and has variable costs of $80. Romi Filters sells two faucet models for every three pitchers sold. Fixed costs equal $1,260,000. Required: 1. What is the breakeven point in unit sales and dollars for each type of filter at the current sales mix? 2. Romi Filters is considering buying new production equipment. The new equipment will increase fixed cost by $240,000 per year and will decrease the variable cost of the faucet and the pitcher units by $5 and $10, respectively. Assuming the same sales mix, how many of each type of filter does Romi Filters need to sell to break even? 3. Assuming the same sales mix, at what total sales level would Romi Filters be indifferent between using the old equipment and buying the new production equipment? If total sales are expected to be 28,000 units, should Romi Filters buy the new production equipment? SOLUTION (40 min.) Multi-product CVP and decision making. 1. Faucet filter: Selling price $150 Variable cost per unit 90 Contribution margin per unit $60 Pitcher-cum-filter: Selling price $160 Variable cost per unit 80 Contribution margin per unit $ 80 Each bundle contains two faucet models and three pitcher models. So contribution margin of a bundle = 2 $60 + 3 $80 = $360 Breakeven Fixed costs $1, 260,000  3,500 bundles point in = Contribution margin per bundle $360 bundles Breakeven point in units of faucet models and pitcher models is: Faucet models: 3,500 bundles 2 units per bundle = 7,000 units Pitcher models: 3,500 bundles 3 units per bundle =10,500 units Total number of units to breakeven 17,500 units Breakeven point in dollars for faucet models and pitcher models is: Faucet models: 7,000 units $150 per unit = $1,050,000 Pitcher models: 10,500 units  $160 per unit = 1,680,000 Breakeven revenues = $2,730,000 3-56 EA Alternatively, weighted average contribution margin per unit = Breakeven point = $1,260,000 17,500 units $72 (2$60) + (3 $80) = $72 5 2  17,500 units = 7,000 units 5 3 Pitcher-cum-filter: 17,500 units 10,500 units 5 Breakeven point in dollars Faucet filter: 7,000 units $150 per unit = $1,050,000 Pitcher-cum-filter: 10,500 units  $160 per unit = $1,680,000 Faucet filter: 2. Faucet filter: Selling price Variable cost per unit 85 Contribution margin per unit Pitcher-cum-filter: Selling price Variable cost per unit Contribution margin per unit $150 $ 65 $160 70 $ 90 Each bundle contains two faucet models and three pitcher models. So contribution margin of a bundle = 2 $65 + 3 $90 = $400 Breakeven Fixed costs $1, 260, 000 $240,000  3, 750 bundles point in = Contribution margin per bundle $400 bundles Breakeven point in units of faucet models and pitcher models is: Faucet models: 3,750 bundles 2 units per bundle = 7,500 units Pitcher models: 3,750 bundles 3 units per bundle = 11,250 units Total number of units to breakeven: 18,750 units Breakeven point in dollars for faucet models and pitcher models is: Faucet models: 7,500 bundles $150 per unit = $ 1125,000 Pitcher models: 11,250 bundles $160 per unit = 1,800,000 Breakeven revenues: $2,925,000 Alternatively, weighted average contribution margin per unit = $1,260,000 + $240,000 18, 750 units Breakeven point = $80 2  18, 750 units = 7,500 units Faucet filter: 5 3 Pitcher-cum-filter: 18, 750 units 11, 250 units 5 Breakeven point in dollars: 3-57 (2$65) + (3 $90) = $80 5 EA Faucet filter: 7,500 units $150 per unit = $1,125,000 Pitcher-cum-filter: 11,250 units $160 per unit = $1,800,000 3. Let x be the number of bundles for Romi Filters to be indifferent between the old and new production equipment. Operating income using old equipment = $360 x – $1,260,000 Operating income using new equipment = $400 x – $1,260,000 – $240,000 At point of indifference: $360 x – $1,260,000= $400 x – $1,500,000 $400 x – $360 x = $1,500,000 – $1,260,000 $40 x = $240,000 x = $240,000 ÷ $40 = 6,000 bundles Faucet models = 6,000 bundles 2 units per bundle = 12,000 units Pitcher models = 6,000 bundles 3 units per bundle = 18,000 units Total number of units: 30,000 units Let x be the number of bundles; When total sales are less than 30,000 units (6,000 bundles) Romi Filters is better off with the old equipment. When total sales are greater than 30,000 units (6,000 bundles) Romi Filters is better off buying the new equipment. At total sales of 28,000 units (5,600 bundles), Romi Filters should keep the old production equipment. Check $360 5,600 – $1,260,000 = $756,000 is greater than $400 5,600 –$1,500,000 = $740,000. 3-51 Sales mix, two products. The Stackpole Company retails two products: a standard and a deluxe version of a luggage carrier. The budgeted income statement for next period is as follows: Required: 1. Compute the breakeven point in units, assuming that the company achieves its planned sales mix. 2. Compute the breakeven point in units (a) if only standard carriers are sold and (b) if only 3-58 EA deluxe carriers are sold. 3. Suppose 250,000 units are sold but only 50,000 of them are deluxe. Compute the operating income. Compute the breakeven point in units. Compare your answer with the answer to requirement 1. What is the major lesson of this problem? SOLUTION (20–25 min.) Sales mix, two products. 1. Sales of standard and deluxe carriers are in the ratio of 187,500 : 62,500. So for every 1 unit of deluxe, 3 (187,500 ÷ 62,500) units of standard are sold. Contribution margin of the bundle = 3  $10 + 1  $20 = $30 + $20 = $50 $2, 250, 000 Breakeven point in bundles = = 45,000 bundles $50 Breakeven point in units is: Standard carrier: 45,000 bundles × 3 units per bundle 135,000 units Deluxe carrier: 45,000 bundles × 1 unit per bundle 45,000 units Total number of units to breakeven 180,000 units Alternatively, Let Q = Number of units of Deluxe carrier to break even 3Q = Number of units of Standard carrier to break even Revenues – Variable costs – Fixed costs = Zero operating income $28(3Q) + $50Q – $18(3Q) – $30Q – $2,250,000 = $84Q + $50Q – $54Q – $30Q = $50Q = Q = 3Q = 0 $2,250,000 $2,250,000 45,000 units of Deluxe 135,000 units of Standard The breakeven point is 135,000 Standard units plus 45,000 Deluxe units, a total of 180,000 units. 2a. Unit contribution margins are: Standard: $28 – $18 = $10; Deluxe: $50 – $30 = $20 If only Standard carriers were sold, the breakeven point would be: $2,250,000  $10 = 225,000 units. 2b. If only Deluxe carriers were sold, the breakeven point would be: $2,250,000  $20 = 112,500 units 3. Operating income = Contribution margin of Standard + Contribution margin of Deluxe - Fixed costs = 200,000($10) + 50,000($20) – $2,250,000 = $2,000,000 + $1,000,000 – $2,250,000 = $750,000 3-59 EA Sales of standard and deluxe carriers are in the ratio of 200,000 : 50,000. So for every 1 unit of deluxe, 4 (200,000 ÷ 50,000) units of standard are sold. Contribution margin of the bundle = 4  $10 + 1  $20 = $40 + $20 = $60 $2, 250, 000 Breakeven point in bundles = = 37,500 bundles $60 Breakeven point in units is: Standard carrier: 37,500 bundles × 4 units per bundle 150,000 units Deluxe carrier: 37,500 bundles × 1 unit per bundle 37,500 units Total number of units to breakeven 187,500 units Alternatively, Let Q = Number of units of Deluxe product to break even 4Q = Number of units of Standard product to break even $28(4Q) + $50Q – $18(4Q) – $30Q – $2,250,000 $112Q + $50Q – $72Q – $30Q $60Q Q 4Q = = = = = 0 $2,250,000 $2,250,000 37,500 units of Deluxe 150,000 units of Standard The breakeven point is 150,000 Standard +37,500 Deluxe, a total of 187,500 units. The major lesson of this problem is that changes in the sales mix change breakeven points and operating incomes. In this example, the budgeted and actual total sales in number of units were identical, but the proportion of the product having the higher contribution margin declined. Operating income suffered, falling from $875,000 to $750,000. Moreover, the breakeven point rose from 180,000 to 187,500 units. 3-52 Gross margin and contribution margin. The Garden Club is preparing for its annual meeting in which a magic show will be shown to its contributing members only. Last year, out of 1,500 members, only 600 contributed for the magic show. Tickets for the show were $30 per attendee. The profit report for last year’s show follows. Ticket sales $18,000 Cost of magic show 20,000 Gross margin (2,000) Printing, invitations and paperwork 1,800 Profit / (loss) $(3,800) This year, the club committee does not want to lose money on the magic show due to poor attendance and to achieve this goal, the committee analyzed last year’s costs. It found that of the $20,000 cost of the magic show, 40% was fixed costs and the remaining 60% was variable costs. Of the $1,800 cost of printing, invitations and paperwork, 50% was fixed and 50% variable. Required: 1. Prepare last year’s profit report using the contribution margin format. 3-60