Chap 4-1 - Summary Managerial Accounting PDF

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Chapter 4 Cost Cost--Volume-Profit R Rela ela elationships tionships Discussion Case 4-1 The point of this case is to illustrate that even when competition is high, CVP analysis can easily cope with changing assumptions and estimates. Some possible reasons for disagreeing:  Even when competition is high, selling prices, unit costs and cost behavior patterns are unlikely to change by large amounts in the short-run or to change so quickly that CVP analysis will be of limited use.  When completion is high, some values used in CVP analysis such as selling prices will likely be based on the current price offerings by key competitors. This will make these estimates quite accurate since selling prices that customers are willing to pay are easily observable and given their importance to CVP analysis, will make the resultant estimates (e.g., break-even points) more reliable.  Managers can use sensitivity analysis to improve their decisionmaking when competition is high. For example, break-even levels, targeted profit levels, and so on can all be calculated under differing assumptions about selling prices and unit costs. Indeed this is one of the strengths of CVP analysis is that it allows for the use of “what if” assumptions to produce estimates of key metrics such as the breakeven point. This idea is noted in the chapter. So, for example, even if prices do change quickly in the short-run CVP analysis can easily be updated to reflect any estimated or actual changes. Some possible reasons for agreeing:  If competition causes selling prices, unit costs or cost behavior to change by large amounts over the short-run then CVP analysis may have limited value.  Sales mix may change quickly as the result of competitors’ actions such as price changes or the introduction of new models. To the extent these actions are unforeseen, the sales mix assumption used in multi-product CVP analysis may inaccurate. © McGraw-Hill Education Ltd., 2018. All rights reserved. Solutions Manual, Chapter 4 1

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4-1 The contribution margin per unit is the difference between the sales price per unit and the variable costs per unit. It can be used in a variety of ways. For example a change in the number of units a company expects to sell can be multiplied by the contribution margin per unit to estimate the impact on the contribution margin in dollars. If fixed costs do not change, then a dollar increase in contribution margin will result in a dollar increase in operating income. The CM per unit can also be used in break-even analysis in determining the number of units that must be sold to earn $0 in operating income. Therefore, knowledge of a product’s CM per unit is extremely helpful in forecasting contribution margin and operating income. 4-2 The slope of a profit graph is determined by the contribution margin per unit. The higher the contribution margin per unit, the steeper the slope. 4-3 Incremental analysis focuses on the changes in revenues, costs and volumes that will result from a particular decision. 4-4 All other things equal, Company B, with its higher fixed costs and lower variable costs, will have a higher contribution margin ratio than Company A. Therefore, it will tend to realize a larger increase in contribution margin and in profits when sales increase. 4-5 The margin of safety is the amount by which budgeted or actual sales exceed the break-even level of sales.

break-even level of sales will increase, assuming no change to fixed expenses. A decrease in the CM ratio means that each dollar of sales revenue is generating less contribution margin to cover fixed expenses. As a result, the level of sales required to break-even will increase. 4-7 Two approaches to breakeven analysis are (a) the graphical method and (b) the formula method. In the graphical method, total cost and total revenue data are plotted on a graph. The intersection of the total cost and the total revenue lines indicates the break-even point. The graph shows the break-even point in both units and dollars of sales. Derived from the contribution format profit equation, the formula method, total fixed cost is divided by the contribution margin per unit to obtain the break-even point in units. Alternatively, total fixed cost can be divided by the contribution margin ratio to obtain the break-even point in sales dollars.

4-8 If the slope of the total revenue line gets steeper, that means selling price per unit has increased. Assuming no changes to variable expenses per unit or fixed expenses in total, this will result in a decrease to the breakeven level of sales because the contribution margin per unit has increased. If the slope of the total expenses line gets steeper, that means variable expenses per unit have increased. Assuming no changes to the selling price per unit or fixed expenses in total, this will result in an increase to the break-even level of sales because the contribution margin per unit has decreased.

4-9 A 5% increase in the income 4-6 If a company’s contribution tax rate would have no impact on margin ratio decreases, then its the break-even point since at a $0 © McGraw-Hill Education Ltd., All rights reserved. 2 Managerial Accounting, 11th Edition

level of profit, there is no income tax. 4-10 Cost structure represents the relative proportion of fixed and variable costs in an organization. 4-11 Because Company X is highly automated it, will likely have higher fixed costs and lower variable costs, and thus have a higher break-even point than Company Y. Hence, Company X would also have the lower margin of safety.

4-12 The weighted average contribution margin per unit is calculated as follows: (1) Calculate the percentage sales mix of each product, e.g., Product A unit sales ÷ Total unit sales all products. (2) Multiply the percentage from (1) by the contribution margin for the product. (3) Sum the individual weighted contribution margins. 4-13 A lower break-even point would result if the sales mix shifted from the low contribution margin product to the high contribution margin product. Such a shift would cause the overall contribution margin ratio in the company to increase, resulting in a higher total contribution margin for a given amount of sales. With a higher overall contribution margin ratio, the break-even point would be lower because less sales would be required to cover the same amount of fixed costs.

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Foundational Ex Exercises ercises 1. The contribution margin per unit is calculated as follows: Total contribution margin (a)................ Total units sold (b)............................. Contribution margin per unit (a) ÷ (b). .

$8,000 1,000 units $8.00 per unit

The contribution margin per unit ($8) can also be derived by calculating the selling price per unit of $20 ($20,000 ÷ 1,000 units) and deducting the variable expense per unit of $12 ($12,000 ÷ 1,000 units). 2. The contribution margin ratio is calculated as follows: Total contribution margin (a)................ Total sales (b).................................... Contribution margin ratio (a) ÷ (b).......

$8,000 $20,000 40%

3. The variable expense ratio is calculated as follows: Total variable expenses (a).................. Total sales (b).................................... Variable expense ratio (a) ÷ (b)...........

$12,000 $20,000 60%

4. The increase in net operating is calculated as follows: Contribution margin per unit (a)..................... $8.00 per unit Increase in unit sales (b) unit 1 Increase in net operating income (a) × (b) $8.00 5. If sales decline to 900 units, the net operating would be computed as follows: Sales (900 units)........... Variable expenses......... Contribution margin...... Fixed expenses............. Net operating income....

Total Per Unit $18,000 $20.00 10,800 12.00 7,200 $ 8.00 6,000 $ 1,200

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Foundational Ex Exercises ercises (continued) 6. The new net operating income would be computed as follows: Sales (900 units)........... Variable expenses......... Contribution margin...... Fixed expenses............. Net operating income....

Total Per Unit $19,800 $22.00 10,800 12.00 9,000 $10.00 6,000 $ 3,000

7. The new net operating income would be computed as follows: Sales (1,250 units)........ Variable expenses......... Contribution margin...... Fixed expenses............. Net operating income....

Total Per Unit $25,000 $20.00 16,250 13.00 8,750 $ 7.00 7,500 $ 1,250

8. The break-even point in unit sales is as follows: ¿ expenses $ 6,000 = =750 units CM per unit $8

9. The dollar sales to break-even is as follows: ¿ expenses $ 6,000 =$ 15,000 = .4 CM ratio

The dollar sales to break-even ($15,000) can also be computed by multiplying the selling price per unit ($20) by the unit sales to breakeven (750 units).

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Foundational Ex Exercises ercises (continued) 10. The number of units that must be sold to achieve the target profit of $5,000 is as follows: ¿ expenses+Target profit $ 6,000 + $ 5,000 =1,375 = $8 CM per unit

11. The margin of safety in dollars is calculated as follows: Sales.............................................................. Break-even sales (at 750 units)........................ Margin of safety (in dollars).............................

$20,000 15,000 $ 5,000

The margin of safety as a percentage of sales is calculated as follows: Margin of safety (in dollars) (a).................. Sales (b).................................................. Margin of safety percentage (a) ÷ (b)........

$5,000 $20,000 25%

12. The degree of operating leverage is calculated as follows: Contribution margin (a). Net operating income (b)...................... Degree of operating leverage (a) ÷ (b). .

$8,000 $2,000 4.0

13. A 5% increase in sales should result in a 20% increase in net operating income, computed as follows: Degree of operating leverage (a).............................. Percent increase in sales (b)..................................... Percent increase in net operating income (a) × (b)....

4.0 5% 20%

14. The degree of operating leverage is calculated as follows: Contribution margin (a). Net operating income (b)...................... Degree of operating leverage (a) ÷ (b). .

$14,000 $2,000 7.0

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Foundational Ex Exercises ercises (continued) 15. A 5% increase in sales should result in 35% increase in net operating income, computed as follows: Degree of operating leverage (a).............................. Percent increase in sales (b)..................................... Percent increase in net operating income (a) × (b)....

7.0 5% 35%

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Exerc Exercise ise 4-1 (20 minutes) 1. The new income statement would be: Sales (6,200 units)...... Variable expenses....... Contribution margin.... Fixed expenses........... Operating income........

Total Per Unit $322,400 $52.00 223,200 36.00 99,200 $16.00 84,000 $ 15,200

You can get the same operating income using the following approach. Original operating income......... $12,000 Change in contribution margin (200 units × $16.00 per unit). 3,200 New operating income............. $15,200 2. The new income statement would be: Sales (5,800 units)............ Variable expenses.............. Contribution margin........... Fixed expenses.................. Operating income..............

Total Per Unit $301,600 $52.00 208,800 36.00 92,800 $16.00 84,000 $ 8,800

You can get the same operating income using the following approach. Original operating income................... Change in contribution margin (-200 units × $16.00 per unit).......... New operating income........................

$12,000 (3,200 ) $ 8,800

3. The new income statement would be: Sales (5,250 units)........ Variable expenses......... Contribution margin...... Fixed expenses............. Operating income..........

Total Per Unit $273,000 $52.00 189,000 36.00 84,000 $16.00 84,000 $ 0

Note: This is the company's break-even point. McGraw-Hill Education Ltd., 2018. All rights reserved. Solutions Manual, Chapter 4 9

Exerc Exercise ise 4-2 (20 minutes) 1. The profit graph is based on the following simple equation: Profit = Unit CM × Q − Fixed expenses Profit = ($19 − $15) × Q − $12,000 Profit = $4 × Q − $12,000 To plot the graph, select two different levels of sales such as Q=0 and Q=4,000. The profit at these two levels of sales are -$12,000 (= $4 × 0 − $12,000) and $4,000 (= $4 × 4,000 − $12,000). Profit Graph $5,000

$0

Profit

-$5,000

-$10,000

-$15,000

-$20,000 0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

Sales Volume in Units

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Exerc Exercise ise 4-2 (continued) 2. Looking at the graph, the break-even point appears to be 3,000 units. This can be verified as follows: Profit = = = =

Unit CM × Q − Fixed expenses $4 × Q − $12,000 $4 × 3,000 − $12,000 $12,000 − $12,000 = $0

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Exerc Exercise ise 4-3 (10 minutes) 1. The company’s contribution margin (CM) ratio is: Total sales............................. Total variable expenses.......... = Total contribution margin.... ÷ Total sales......................... = CM ratio.............................

$250,000 190,000 $ 60,000 $250,000 24%

2. The break-even level of sales dollars is: Fixed expenses $ 36,000 =$ 150,000 = .24 CM ratio

3. The change in operating income from an increase in total sales of $20,000 can be estimated by using the CM ratio as follows: Change in total sales...................... × CM ratio..................................... = Estimated change in operating income........................................

$20,000 24% $ 4,800

This computation can be verified as follows: Total sales.................... ÷ Total units sold.......... = Selling price per unit. .

$250,000 50,000 units $5.00 per unit

Increase in total sales.... ÷ Selling price per unit. . = Increase in unit sales. Original total unit sales. . New total unit sales.......

$20,000 $5.00 per unit 4,000 units 50,000 units 54,000 units

Total unit sales.............. Sales............................ Variable expenses......... Contribution margin...... Fixed expenses............. Operating income..........

Original New 50,000 54,000 $250,000 $270,000 190,000 205,200 60,000 64,800 36,000 36,000 $ 24,000 $ 28,800

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Exerc Exercise ise 4-4 (20 minutes) 1. The following table shows the effect of the proposed change in monthly advertising budget: Sales With Additional Current Webinar Sales Budget Difference Unit sales 1,000 1,050 50 Sales............................ $1,000,000 $1,050,000 $50,000 Variable expenses......... 800,000 840,000 40,000 Contribution margin...... 200,000 210,000 10,000 Fixed expenses............. 100,000 105,000 5,000 Operating income.......... $ 100,000 $ 105,000 $5,000 Assuming that there are no other important factors to be considered, the increase in the webinar budget should be approved since it would lead to an increase in operating income of $5,000. Alternative Solution 1 Expected total contribution margin: $200 × 1,050..................................... Present total contribution margin: $200 × 1,000..................................... Incremental contribution margin............ Change in fixed expenses: Less incremental advertising expense. . Change in operating income..................

$210,000 200,000 10,000 5,000 $5,000

Alternative Solution 2 Incremental contribution margin: $200 × 50 units................................ Less incremental advertising expense.. .. Change in operating income..................

$ 10,000 5,000 $5,000

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Exerc Exercise ise 4-4 (continued) 2. The $80 increase in variable costs will cause the unit contribution margin to decrease from $200 to $120 with the following impact on operating income: Expected total contribution margin with the higher-quality components: 1,150* units × $120 per unit........................... $138,000 Present total contribution margin: 1,000 units × $200 per unit............................. 200,000 Change in total contribution margin.................... $ (62,000) *1,000 x 115% Assuming no change in fixed costs and all other factors remain the same, the higher-quality components should not be used.

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Exerc Exercise ise 4-5 (10 minutes) 1. Using the formula method: Break-even point in units sold = Fixed expenses ÷ Unit CM = $4,200 ÷ $3 per scarf = 1,400 scarfs 2. Using the formula method: Break-even point in sales dollars = Fixed expenses ÷ CM ratio = $4,200 ÷ 0.20 =$21,000 3. Break-even point in units sold = Fixed expenses ÷ Unit CM = $4,200 ÷ $2 per scarf = 2,100 scarfs

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Exerc Exercise ise 4-6 (10 minutes) 1. Unit sales required to earn before-tax target profit of $3,000: Fixed expenses + Target profit $ 20,000 + 3,000 =1,150 units = $ 20 CM per unit

2. The formula approach yields the dollar sales required to attain a target profit of $4,000 (before tax) as follows: Fixed expenses + Target profit $ 20,000 + 4,000 =$ 120,000 = .20 CM ratio

3. Unit sales required to earn target after-tax income of $6,000 given a tax rate of 25%. Target after−tax profit 1−Tax Rate Unit Contribution Margin $ 6,000 $ 20,000+ 1−.25 ¿ $ 20 $ 20,000 +$ 8,000 ¿ $ 20

¿ expenses+ ¿

¿ 1,400units

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Exerc Exercise ise 4-7 (15 minutes) 1. The indifference point in hours can be calculated using the following formula: (Residential CM per hour x Q) - $500 = (Commercial CM per hour) $750 Where Q = the number of hours. ($25-$15)Q - $500 = ($35-$20)Q - $825 10Q - $500 = $15Q - 825 Q = 65 hours James will be indifferent between choosing to focus on residential versus commercial clients at a volume of 65 hours per month. 2. Break-even hours for residential clients: Fixed expenses $ 500 =50 hours = $ 10 CM per unit

Break-even hours for commercial clients: Fixed expenses $ 825 =55 hours = $ 15 CM per unit

3. Revenue at 120 hours per month*.................... $4,200 Break-even revenue (at 55 hours)**................. 1,925 Margin of safety (in dollars)............................. $ 2,275 *$35 x 120; **$35 x 55 The margin of safety as a percentage of sales is as follows: Margin of safety (in dollars)....................... ÷ Sales.........................................