ACCT 215 Problems Solutions, Fall 2011

Chapter 5 Cost-Volume-Profit Relationships Chapter 5 Cost-Volume-Profit Relationships Exercise 5-9 (20 minutes) 1. The company’s degree of operating leverage would be computed as follows: Contribution margin.............. $36,000 ÷ Net operating income........ $12,000 Degree of operating leverage................................ 3.0 2. A 10% increase in sales should result in a 30% increase in net operating income, computed as follows: Degree of operating leverage.................................... 3.0 × Percent increase in sales.......................................... 10 % Estimated percent increase in net operating income........................................................................ 30 % 3. The new income statement reflecting the change in sales is: Amount Percent of Sales Sales............................... $132,000 100% Variable expenses........ 92,400 70 % Contribution margin.... 39,600 30 % Fixed expenses............. 24,000 Net operating income.. $   15,600 Net operating income reflecting change in sales.. $15,600 Original net operating income (a)........................... 12,000 Change in net operating income (b)........................ $   3,600 Percent change in net operating income (b ÷ a).... 30% 5-1 Chapter 5 Cost-Volume-Profit Relationships Exercise 5-10 (20 minutes) 1. The overall contribution margin ratio can be computed as follows: 2. The overall break-even point in sales dollars can be computed as follows: 3. To construct the required income statement, we must first determine the relative sales mix for the two products: Predator Runway Total Original dollar sales..... $100,000 $50,000 $150,000 Percent of total............. 67% 33% 100% Sales at break-even...... $75,000 $37,500 $112,500 Predator Runway Total Sales............................... $75,000 $37,500 $112,500 Variable expenses*...... 18,750 3,750 22,500 Contribution margin.... $56,250 $33,750 90,000 Fixed expenses............. 90,000 Net operating income.. $                 0 *Predator variable expenses: ($75,000/$100,000) × $25,000 = $18,750 Runway variable expenses: ($37,500/$50,000) × $5,000 = $3,750 5-2 Chapter 5 Cost-Volume-Profit Relationships Exercise 5-11 (30 minutes) 1. Profit = Unit CM × Q Fixed expenses − $0 = ($40 $28) × Q $150,000 − − $0 = ($12) × Q $150,000 − $12Q = $150,000 Q = $150,000 ÷ $12 per unit Q = 12,500 units, or at $40 per unit, $500,000 Alternatively: or, at $40 per unit, $500,000. 2. The contribution margin at the break-even point is $150,000 because at that point it must equal the fixed expenses. Total Unit Sales (14,000 units × $40 per unit)................ $560,000 $40 Variable expenses (14,000 units × $28 per unit)....................... 392,000 28 Contribution margin (14,000 units × $12 per unit)....................... 168,000 $12 Fixed expenses................................................ 150,000 Net operating income.................................... $ 18,000 5-3 Chapter 5 Cost-Volume-Profit Relationships Exercise 5-11 (continued) 4. Margin of safety in dollar terms: Margin of safety in percentage terms: 5. The CM ratio is 30%. Expected total contribution margin: $680,000 × 30%.................................................................................. $204,000 Present total contribution margin: $600,000 × 30%.... 180,000 Increased contribution margin...................................... $ 24,000 Alternative solution: $80,000 incremental sales × 30% CM ratio = $24,000 Given that the company’s fixed expenses will not change, monthly net operating income will increase by the amount of the increased contribution margin, $24,000. 5-4 Chapter 5 Cost-Volume-Profit Relationships Exercise 5-12 (30 minutes) 1. Profit = Unit CM × Q Fixed expenses − $0 = ($90 $63) × Q $135,000 − − $0 = ($27) × Q $135,000 − $27Q = $135,000 Q = $135,000 ÷ $27 per lantern Q = 5,000 lanterns, or at $90 per lantern, $450,000 in sales Alternative solution: or at $90 per lantern, $450,000 in sales 2. An increase in variable expenses as a percentage of the selling price would result in a higher break-even point. If variable expenses increase as a percentage of sales, then the contribution margin will decrease as a percentage of sales. With a lower CM ratio, more lanterns would have to be sold to generate enough contribution margin to cover the fixed costs. 3. Present: 8,000 Lanterns Proposed: 10,000 Lanterns* Total Per Unit Total Per Unit Sales................................. $720,000 $90 $810,000 $81 ** Variable expenses........... 504,000 63 630,000 63 Contribution margin...... 216,000 $27 180,000 $18 Fixed expenses................ 135,000 135,000 Net operating income.... $ 81,000 $ 45,000 * 8,000 lanterns × 1.25 = 10,000 lanterns ** $90 per lantern × 0.9 = $81 per lantern As shown above, a 25% increase in volume is not enough to offset a 10% reduction in the selling price; thus, net operating income 5-5 Chapter 5 Cost-Volume-Profit Relationships decreases. 5-6 Chapter 5 Cost-Volume-Profit Relationships Exercise 5-12 (continued) 4. Profit = Unit CM × Q Fixed expenses − $72,000 = ($81 $63) × Q $135,000 − − $72,000 = ($18) × Q $135,000 − $18Q = $207,000 Q = $207,000 ÷ $18 per lantern Q = 11,500 lanterns Alternative solution: 5-7 Chapter 5 Cost-Volume-Profit Relationships Exercise 5-14 (30 minutes) 1. Model A100 Model B900 Total Company Amount % Amount % Amount % Sales................. $700,000 100 $300,000 100 $1,000,000 100 Variable expenses...... 280,000 40 90,000 30 370,000 37 Contribution margin.......... $420,000 60 $210,000 70 630,000 63 * Fixed expenses...... 598,500 Net operating income.......... $         31,500 *630,000 ÷ $1,000,000 = 63%. 2. The break-even point for the company as a whole is: 3. The additional contribution margin from the additional sales is computed as follows: $50,000 × 63% CM ratio = $31,500 Assuming no change in fixed expenses, all of this additional contribution margin should drop to the bottom line as increased net operating income. This answer assumes no change in selling prices, variable costs per unit, fixed expenses, or sales mix. 5-8 Chapter 5 Cost-Volume-Profit Relationships Exercise 5-17 (20 minutes) Total Per Unit 1. Sales (30,000 units × 1.15 = 34,500 units)... $172,500 $5.00 Variable expenses.......................................... 103,500 3.00 Contribution margin...................................... 69,000 $2.00 Fixed expenses............................................... 50,000 Net operating income................................... $ 19,000 2. Sales (30,000 units × 1.20 = 36,000 units)... $162,000 $4.50 Variable expenses.......................................... 108,000 3.00 Contribution margin...................................... 54,000 $1.50 Fixed expenses............................................... 50,000 Net operating income................................... $  4,000 3. Sales (30,000 units × 0.95 = 28,500 units)... $156,750 $5.50 Variable expenses.......................................... 85,500 3.00 Contribution margin...................................... 71,250 $2.50 Fixed expenses ($50,000 + $10,000)............ 60,000 Net operating income................................... $ 11,250 4. Sales (30,000 units × 0.90 = 27,000 units)... $151,200 $5.60 Variable expenses.......................................... 86,400 3.20 Contribution margin...................................... 64,800 $2.40 Fixed expenses............................................... 50,000 Net operating income................................... $ 14,800 5-9 Chapter 5 Cost-Volume-Profit Relationships Exercise 5-18 (20 minutes) a. Case #1 Case #2 Number of units sold... 9,000 * 14,000 Sales............................... $270,000 * $30 $350,000 * $25 Variable expenses........ 162,000 * 18 140,000 10 Contribution margin.... 108,000 $12 210,000 $15 * Fixed expenses............. 90,000 * 170,000 * Net operating income.. $ 18,000 $ 40,000 * Case #3 Case #4 Number of units sold... 20,000 * 5,000 * Sales............................... $400,000 $20 $160,000 * $32 Variable expenses....... 280,000 * 14 90,000 18 Contribution margin.... 120,000 $   6 * 70,000 $14 Fixed expenses............. 85,000 82,000 * Net operating income.. $ 35,000 * $(12,000) * b. Case #1 Case #2 Sales............................... $450,000 * 100% $200,000 * 100 % Variable expenses........ 270,000 60 130,000 * 65 Contribution margin.... 180,000 40 %* 70,000 35 % Fixed expenses............. 115,000 60,000 * Net operating income.. $ 65,000 * $ 10,000 Case #3 Case #4 Sales............................... $700,000 100% $300,000 * 100 % Variable expenses........ 140,000 20 90,000 * 30 Contribution margin.... 560,000 80 %* 210,000 70 % Fixed expenses............. 470,000 * 225,000 Net operating income.. $ 90,000 * $(15,000) * *Given 5-10 Chapter 5 Cost-Volume-Profit Relationships Problem 5-20 (60 minutes) 1. The CM ratio is 30%. Total Per Unit Percentage Sales (13,500 units)......... $270,000 $20 100% Variable expenses........... 189,000 14 70% Contribution margin....... $ 81,000 $ 6 30% The break-even point is: Profit = Unit CM × Q Fixed expenses − $0 = ($20 $14) × Q $90,000 − − $0 = ($6) × Q − $90,000 $6Q = $90,000 Q = $90,000 ÷ $6 per unit Q = 15,000 units 15,000 units × $20 per unit = $300,000 in sales Alternative solution: 2. Incremental contribution margin: $70,000 increased sales × 30% CM ratio............ $21,000 Less increased fixed costs: Increased advertising cost.................................. 8,000 Increase in monthly net operating income.......... $13,000 Since the company presently has a loss of $9,000 per month, if the 5-11 Chapter 5 Cost-Volume-Profit Relationships changes are adopted, the loss will turn into a profit of $4,000 per month. 5-12 Chapter 5 Cost-Volume-Profit Relationships Problem 5-20 (continued) 3. Sales (27,000 units × $18 per unit*)............... $486,000 Variable expenses (27,000 units × $14 per unit)........................ 378,000 Contribution margin........................................ 108,000 Fixed expenses ($90,000 + $35,000).............. 125,000 Net operating loss............................................ $(17,000) *$20 – ($20 × 0.10) = $18 4. Profit = Unit CM × Q Fixed expenses − $4,500 = ($20.00 $14.60*) × Q $90,000 − − $4,500 = ($5.40) × Q $90,000 − $5.40Q = $94,500 Q = $94,500 ÷ $5.40 per unit Q = 17,500 units *$14.00 + $0.60 = $14.60. Alternative solution: **$6.00 – $0.60 = $5.40. 5. a. The new CM ratio would be: Per Unit Percentage Sales................................................ $20 100% Variable expenses......................... 7 35% Contribution margin..................... $13 65% 5-13 Chapter 5 Cost-Volume-Profit Relationships Problem 5-20 (continued) The new break-even point would be: b. Comparative income statements follow: Not Automated Automated Total Per Unit % Total Per Unit % Sales (20,000 units).... $400,000 $20 100 $400,000 $20 100 Variable expenses...... 280,000 14 70 140,000 7 35 Contribution margin.. 120,000 $   6 30 260,000 $13 65 Fixed expenses........... 90,000 208,000 Net operating income $ 30,000 $ 52,000 5-14 Chapter 5 Cost-Volume-Profit Relationships Problem 5-20 (continued) c. Whether or not one would recommend that the company automate its operations depends on how much risk he or she is willing to take, and depends heavily on prospects for future sales. The proposed changes would increase the company’s fixed costs and its break-even point. However, the changes would also increase the company’s CM ratio (from 30% to 65%). The higher CM ratio means that once the break-even point is reached, profits will increase more rapidly than at present. If 20,000 units are sold next month, for example, the higher CM ratio will generate $22,000 more in profits than if no changes are made. The greatest risk of automating is that future sales may drop back down to present levels (only 13,500 units per month), and as a result, losses will be even larger than at present due to the company’s greater fixed costs. (Note the problem states that sales are erratic from month to month.) In sum, the proposed changes will help the company if sales continue to trend upward in future months; the changes will hurt the company if sales drop back down to or near present levels. Note to the Instructor: Although it is not asked for in the problem, if time permits you may want to compute the point of indifference between the two alternatives in terms of units sold; i.e., the point where profits will be the same under either alternative. At this point, total revenue will be the same; hence, we include only costs in our equation: Let Q = Point of indifference in units sold $14Q + $90,000 = $7Q + $208,000 $7Q = $118,000 Q = $118,000 ÷ $7 per unit Q = 16,857 units (rounded) If more than 16,857 units are sold, the proposed plan will yield the greatest profit; if less than 16,857 units are sold, the present plan will yield the greatest profit (or the least loss). 5-15 Chapter 5 Cost-Volume-Profit Relationships Problem 5-21 (60 minutes) 1. The CM ratio is 60%: Selling price........................ $15 100% Variable expenses.............. 6 40% Contribution margin......... $   9 60% 2. 3. $45,000 increased sales × 60% CM ratio = $27,000 increase in contribution margin. Since fixed costs will not change, net operating income should also increase by $27,000. 4. a. b. 6 × 15% = 90% increase in net operating income. In dollars, this increase would be 90% × $36,000 = $32,400. 5-16 Chapter 5 Cost-Volume-Profit Relationships Problem 5-21 (continued) 5. Last Year: 28,000 units Proposed: 42,000 units* Total Per Unit Total Per Unit Sales............................... $420,000 $15.00 $567,000 $13.50** Variable expenses........ 168,000 6.00 252,000 6.00 Contribution margin.... 252,000 $ 9.00 315,000 $   7.50 Fixed expenses............. 180,000 250,000 Net operating income.. $ 72,000 $ 65,000 * 28,000 units × 1.5 = 42,000 units ** $15 per unit × 0.90 = $13.50 per unit No, the changes should not be made. 6. Expected total contribution margin: 28,000 units × 200% × $7 per unit*.................... $392,000 Present total contribution margin: 28,000 units × $9 per unit.................................... 252,000 Incremental contribution margin, and the amount by which advertising can be increased with net operating income remaining unchanged......................................... $140,000 *$15 – ($6 + $2) = $7 5-17 Chapter 5 Cost-Volume-Profit Relationships Problem 5-24 (60 minutes) 1. April's Income Statement: Standard Deluxe Pro Total Amount % Amount % Amount % Amount % Sales............................... $80,000 100 $60,000 100 $450,000 100 $590,000 100 Variable expenses: Production.................. 44,000 55 27,000 45 157,500 35 228,500 38.7 Selling.......................... 4,000 5 3,000 5 22,500 5 29,500 5.0 Total variable expenses 48,000 60 30,000 50 180,000 40 258,000 43.7 Contribution margin.... $32,000 40 $30,000 50 $270,000 60 332,000 56.3 Fixed expenses: Production.................. 120,000 Advertising.................. 100,000 Administrative............ 50,000 Total fixed expenses...... 270,000 Net operating income... $ 62,000 5-18 Chapter 5 Cost-Volume-Profit Relationships Problem 5-24 (continued) May's Income Statement: Standard Deluxe Pro Total Amount % Amount % Amount % Amount % Sales.............................. $320,000 100 $60,000 100 $270,000 100 $650,000 100.0 Variable expenses: Production................. 176,000 55 27,000 45 94,500 35 297,500 45.8 Selling......................... 16,000 5 3,000 5 13,500 5 32,500 5.0 Total variable expenses.................... 192,000 60 30,000 50 108,000 40 330,000 50.8 Contribution margin.... $128,000 40 $30,000 50 $162,000 60 320,000 49.2 Fixed expenses: Production................. 120,000 Advertising................. 100,000 Administrative........... 50,000 Total fixed expenses.... 270,000 Net operating income. $ 50,000 5-19 Chapter 5 Cost-Volume-Profit Relationships Problem 5-24 (continued) 2. The sales mix has shifted over the last month from a greater concentration of Pro rackets to a greater concentration of Standard rackets. This shift has caused a decrease in the company’s overall CM ratio from 56.3% in April to only 49.2% in May. For this reason, even though total sales (both in units and in dollars) is greater, net operating income is lower than last month in the division. 3. The break-even in dollar sales can be computed as follows: 4. May’s break-even point has gone up. The reason is that the division’s overall CM ratio has declined for May as stated in (2) above. Unchanged fixed expenses divided by a lower overall CM ratio would yield a higher break-even point in sales dollars. 5. Standard Pro Increase in sales...................................... $20,000 $20,000 Multiply by the CM ratio......................... ×  40% ×  60% Increase in net operating income*...... $ 8,000 $12,000 *Assuming that fixed costs do not change. 5-20 Chapter 5 Cost-Volume-Profit Relationships Problem 5-29 (75 minutes) 1. a. Selling price....................... $37.50 100% Variable expenses............ 22.50 60% Contribution margin........ $15.00 40% Profit = Unit CM × Q − Fixed expenses $0 = $15 × Q − $480,000 $15Q = $480,000 Q = $480,000 ÷ $15 per skateboard Q = 32,000 skateboards Alternative solution: b. The degree of operating leverage would be: 2. The new CM ratio will be: Selling price............................. $37.50 100% Variable expenses.................. 25.50 68% Contribution margin.............. $12.00 32% 5-21 Chapter 5 Cost-Volume-Profit Relationships Problem 5-29 (continued) The new break-even point will be: Profit = Unit CM × Q − Fixed expenses $0 = $12 × Q − $480,000 $12Q = $480,000 Q = $480,000 ÷ $12 per skateboard Q = 40,000 skateboards Alternative solution: 3. Profit = Unit CM × Q − Fixed expenses $120,000 = $12 × Q − $480,000 $12Q = $120,000 + $480,000 Q = $600,000 ÷ $12 per skateboard Q = 50,000 skateboards Alternative solution: 5-22 Chapter 5 Cost-Volume-Profit Relationships Problem 5-29 (continued) Thus, sales will have to increase by 10,000 skateboards (50,000 skateboards, less 40,000 skateboards currently being sold) to earn the same amount of net operating income as earned last year. The computations above and in part (2) show the dramatic effect that increases in variable costs can have on an organization. These effects from a $3 per unit increase in labor costs for Tyrene Company are summarized below: Present Expected Break-even point (in skateboards).......... 32,000 40,000 Sales (in skateboards) needed to earn net operating income of $120,000....... 40,000 50,000 Note that if variable costs do increase next year, then the company will just break even if it sells the same number of skateboards (40,000) as it did last year. 4. The contribution margin ratio last year was 40%. If we let P equal the new selling price, then: P = $25.50 + 0.40P 0.60P = $25.50 P = $25.50 ÷ 0.60 P = $42.50 To verify: Selling price............................... $42.50 100% Variable expenses.................... 25.50 60% Contribution margin................ $17.00 40% Therefore, to maintain a 40% CM ratio, a $3 increase in variable costs would require a $5 increase in the selling price. 5-23 Chapter 5 Cost-Volume-Profit Relationships Problem 5-29 (continued) 5. The new CM ratio would be: Selling price.......................... $37.50 100% Variable expenses................ 13.50 * 36% Contribution margin............ $24.00 64% *$22.50 – ($22.50 × 40%) = $13.50 The new break-even point would be: Profit = Unit CM × Q − Fixed expenses $0 = $24 × Q − $912,000* $24Q = $912,000 Q = $912,000 ÷ $24 per skateboard Q = 38,000 skateboards *$480,000 × 1.9 = $912,000 Alternative solution: Although this break-even figure is greater than the company’s present break-even figure of 32,000 skateboards [see part (1) above], it is less than the break-even point will be if the company does not automate and variable labor costs rise next year [see part (2) above]. 5-24 Chapter 5 Cost-Volume-Profit Relationships Problem 5-29 (continued) 6. a. Profit = Unit CM × Q − Fixed expenses $120,000 = $24 × Q − $912,000* $24Q = $120,000 + $912,000 Q = $1,032,000 ÷ $24.00 per skateboard Q = 43,000 skateboards *480,000 × 1.9 = $912,000 Alternative solution: Thus, the company will have to sell 3,000 more skateboards (43,000 – 40,000 = 3,000) than now being sold to earn a profit of $120,000 each year. However, this is still less than the 50,000 skateboards that would have to be sold to earn a $120,000 profit if the plant is not automated and variable labor costs rise next year [see part (3) above]. 5-25 Chapter 5 Cost-Volume-Profit Relationships Problem 5-29 (continued) b. The contribution income statement would be: Sales (40,000 skateboards × $37.50 per skateboard) $1,500,000 Variable expenses (40,000 skateboards × $13.50 per skateboard) 540,000 Contribution margin............................................... 960,000 Fixed expenses........................................................ 912,000 Net operating income............................................. $         48,000 c. This problem shows the difficulty faced by some companies. When variable labor costs increase, it is often difficult to pass these cost increases along to customers in the form of higher prices. Thus, companies are forced to automate, resulting in higher operating leverage, often a higher break-even point, and greater risk for the company. There is no clear answer as to whether one should have been in favor of constructing the new plant. 5-26