Chapter 14 - answer - Lecture notes 1 PDF

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Solutions ManualCHAPTER 14OPERATING AND FINANCIAL LEVERAGESUGGESTED ANSWERS TO THE REVIEW QUESTIONS AND PROBLEMSI. Questions The contribution margin (CM) ratio is the ratio of the total contribution margin to total sales revenue. It can be used in a variety of ways. For example, the change in total ...

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Solutions Manual

CHAPTER 14 OPERATI NG AND FI NANCI ALLEVERAGE SUGGESTED ANSWERS TO THE REVIEW QUESTIONS AND PROBLEMS I. Questions 1. The contribution margin (CM) ratio is the ratio of the total contribution margin to total sales revenue. It can be used in a variety of ways. For example, the change in total contribution margin from a given change in total sales revenue can be estimated by multiplying the change in total sales revenue by the CM ratio. If fixed costs do not change, then a dollar increase in contribution margin results in a dollar increase in net operating income. The CM ratio can also be used in target profit and break-even analysis. 2. Incremental analysis focuses on the changes in revenues and costs that will result from a particular action. 3. Operating leverage measures the impact on net operating income of a given percentage change in sales. The degree of operating leverage at a given level of sales is computed by dividing the contribution margin at that level of sales by the net operating income at that level of sales. 4. The break-even point is the level of sales at which profits are zero. 5. (a) If the selling price decreased, then the total revenue line would rise less steeply, and the break-even point would occur at a higher unit volume. (b) If the fixed cost increased, then both the fixed cost line and the total cost line would shift upward and the break-even point would occur at a higher unit volume. (c) If the variable cost increased, then the total cost line would rise more steeply and the break-even point would occur at a higher unit volume. 6. The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales. It states the amount by which sales can drop before losses begin to be incurred. 7. The sales mix is the relative proportions in which a company’s products are sold. The usual assumption in cost-volume-profit analysis is that the sales mix will not change. 14-1

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Operating and Financial Leverage

8. A higher break-even point and a lower net operating income could result if the sales mix shifted from high contribution margin products to low contribution margin products. Such a shift would cause the average contribution margin ratio in the company to decline, resulting in less total contribution margin for a given amount of sales. Thus, net operating income would decline. With a lower contribution margin ratio, the breakeven point would be higher because more sales would be required to cover the same amount of fixed costs. 9. A utility is in a stable, predictable industry and therefore can afford to use more financial leverage than an automobile company, which is generally subject to the influences of the business cycle. An automobile manufacturer may not be able to service a large amount of debt when there is a downturn in the economy. 10. A labor-intensive company will have low-fixed costs and a correspondingly low break-even point. However, the impact of operating leverage on the firm is small and there will be little magnification of profits as volume increases. A capital-intensive firm, on the other hand, will have a higher break-even point and enjoy the positive influences of operating leverage as volume increases. 11. For break-even analysis based on accounting flows, depreciation is considered part of fixed costs. For cash flow purposes, it is eliminated from fixed costs. The accounting flows perspective is longer-term in nature because we must consider the problems of equipment replacement. 12. Both operating and financial leverage imply that the firm will employ a heavy component of fixed cost resources. This is inherently risky because the obligation to make payments remains regardless of the condition of the company or the economy. 13. Debt can only be used up to a point. Beyond that, financial leverage tends to increase the overall costs of financing to the firm as well as encourage creditors to place restrictions on the firm. The limitations of using financial leverage tend to be the greatest in industries that are highly cyclical in nature. 14. The higher the interest rate on new debt, the less attractive financial leverage is to the firm. 14-2

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15. Operating leverage primarily affects thee operating income of the firm. At this point, financial leverage takes over and determines the overall impact on earnings per share. 16. At progressively higher levels of operation than the break-even point, the percentage change in operating income as a result of a percentage change in unit volume diminishes. The reason is primarily mathematical - as we move to increasingly higher levels of operating income, the percentage change from the higher base is likely to be less. 17. The point of equality only measures indifference based on earnings per share. Since, our ultimate goal is market value maximization; we must also be concerned with how these earnings are valued. Two plans that have the same earnings per share may call for different price-earnings ratios, particularly when there is a differential risk component involved because of debt. II. Multiple Choice Questions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

A A B D B C D C D B

11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

C B B D A B D B A C

21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

B D B B B D A A A D

31. 32. 33. 34. 35. 36. 37. 38. 39.

A B A D B B A D D

III. Problems Problem 1 (Computing and Using the CM Ratio) 1. The company’s contribution margin (CM) ratio is: Total sales.................................................. Total variable expenses.............................. = Total contribution margin....................... ÷ Total sales............................................... = CM ratio................................................. 14-3

₱200,000 120,000 80,000 ₱200,000 40%

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Operating and Financial Leverage

2. The change in net operating income from an increase in total sales of ₱1,000 can be estimated by using the CM ratio as follows: Change in total sales......................................................................... ₱1,000 × CM ratio........................................................................................ 40 % = Estimated change in net operating income.................................... ₱ 400 This computation can be verified as follows: Total sales........................................ ÷ Total units sold.............................. = Selling price per unit.....................

₱200,000 50,000 units ₱4.00 per unit

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

₱1,000 ₱4.00 per unit 250 units 50,000 units 50,250 units

Total unit sales................................. Sales................................................. Variable expenses............................. Contribution margin......................... Fixed expenses................................. Net operating income.......................

Original 50,000 ₱ 200,000 120,000 80,000 65,000 ₱ 15,000

New 50,250 ₱201,000 120,600 80,400 65,000 ₱ 15,400

Problem 2 (Compute the Break-even Point) 1. The equation method yields the break-even point in unit sales, Q, as follows: Profit = Unit CM × Q − Fixed expenses ₱0 = ( ₱15 − ₱12) × Q − ₱4,200 ₱0 = (₱3) × Q − ₱4,200 ₱3Q = ₱4,200 Q = ₱4,200 ÷ ₱3 Q = 1,400 baskets 2. The equation method can be used to compute the break-even point in sales pesos as follows: 14-4

Operating and Financial Leverage

CM =

Unit contribution margin Unit selling price

CM =

₱3/₱15 = 0.20

Profit ₱0 0.20 × Sales Sales Sales

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= CM ratio × Sales − Fixed expenses = 0.20 × Sales − ₱4,200 = ₱4,200 = ₱4,200 ÷ 0.20 = ₱21,000

3. The formula method gives an answer that is identical to the equation method for the break-even point in unit sales: Unit sales to break even =

Fixed expenses Unit CM

Unit sales to break even =

₱4,200/₱3 = 1,400 baskets

4. The formula method also gives an answer that is identical to the equation method for the break-even point in peso sales: Peso sales to break even =

Fixed expenses CM ratio

Peso sales to break even =

₱4,200/0.20 = ₱21,000

Problem 3 (Compute the Margin of Safety) 1. To compute the margin of safety, we must first compute the break-even unit sales. Profit ₱0 ₱0 ₱10Q Q Q

= Unit CM × Q − Fixed expenses = ( ₱30 − ₱20) × Q − ₱7,500 = (₱10) × Q − ₱7,500 = ₱7,500 = ₱7,500 ÷ ₱10 = 750 units

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Operating and Financial Leverage

Sales (at the budgeted volume of 1,000 units)............ Less break-even sales (at 750 units)........................... Margin of safety (in pesos)........................................

₱30,000 22,500 ₱ 7,500

2. The margin of safety as a percentage of sales is as follows: Margin of safety (in pesos)........................................ ÷ Sales....................................................................... Margin of safety percentage.......................................

₱ 7,500 ₱30,000 25%

Problem 4 (Compute and Use the Degree of Operating Leverage) 1. The company’s degree of operating leverage would be computed as follows: Contribution margin................................................... ÷ Net operating income.............................................. Degree of operating leverage.....................................

₱48,000 ₱10,000 4.8

2. A 5% increase in sales should result in a 24% increase in net operating income, computed as follows: Degree of operating leverage..................................... × Percent increase in sales......................................... Estimated percent increase in net operating income...

4.8 5% 24%

3. The new income statement reflecting the change in sales is: Amount Sales............................................. ₱84,000 Variable expenses......................... 33,600 Contribution margin...................... 50,400 Fixed expenses.............................. 38,000 Net operating income.................... ₱12,400

Percent of Sales 100% 40% 60%

Net operating income reflecting change in sales........ Original net operating income.................................... Percent change in net operating income.....................

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₱12,400 ₱10,000 24%

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Problem 5 (Target Profit and Break-Even Analysis; Margin of Safety; CM Ratio) 1. Profit ₱0 ₱0 ₱18Q Q Q

= Unit CM × Q − Fixed expenses = ( ₱30 − ₱12) × Q − $216,000 = (₱18) × Q − ₱216,000 = ₱216,000 = ₱216,000 ÷ ₱18 = 12,000 units, or at ₱30 per unit, ₱360,000

Alternative solution: Unit sales to break even =

Fixed expenses Unit CM

Unit sales to break even =

₱216,000/₱18 = 12,000 units or at ₱30 per unit, ₱360,000

2. The contribution margin is ₱216,000 because the contribution margin is equal to the fixed expenses at the break-even point. Unit sold to attain target profit =

Target profit + Fixed expenses Unit CM

Unit sold to attain target profit =

₱90,000 + ₱216,000 ₱18

Unit sold to attain target profit =

17,000 units

3. Sales (17,000 units × ₱30 per unit)............ Variable expenses (17,000 units × ₱12 per unit)................. 14-7

Total ₱510,000

Unit ₱30

204,000

12

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Operating and Financial Leverage

Contribution margin................................... Fixed expenses........................................... Net operating income.................................

306,000 216,000 ₱ 90,000

₱18

4. Margin of safety in peso terms: Margin of safety in pesos =

Total sales − Break even sales

Margin of safety in pesos =

₱450,000 − ₱360,000 = ₱ 90,000

Margin of safety in percentage terms: Margin of safety percentage =

Margin of safety in pesos Total sales

Margin of safety percentage =

₱90,000/₱450,000 = 20%

5. The CM ratio is 60%. Expected total contribution margin: ( ₱500,000 × 60%)... Present total contribution margin: (₱450,000 × 60%)...... Increased contribution margin..........................................

₱300,000 270,000 ₱ 30,000

Alternative solution: ₱50,000 incremental sales × 60% CM ratio = ₱30,000 Given that the company’s fixed expenses will not change, monthly net operating income will also increase by ₱30,000.

Problem 6 (Operating Leverage) 1. Sales (15,000 games)................. 14-8

Total Per Unit ₱3,000,000 ₱200

Operating and Financial Leverage

Variable expenses....................... Contribution margin.............................. Fixed expenses...................................... Net operating income............................

900,000 2,100,000 1,820,000 ₱ 280,000

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60 ₱140

The degree of operating leverage is:

2.

Degree of operating leverage =

Contribution margin Net operating income

Degree of operating leverage =

₱2,100,000/₱280,000 = 7.5

a.

Sales of 18,000 games represent a 20% increase over last year’s sales. Because the degree of operating leverage is 7.5, net operating income should increase by 7.5 times as much, or by 150% (7.5 × 20%).

b.

The expected total amount of net operating income for next year would be: ₱280,000

Last year’s net operating income............................. Expected increase in net operating income next year (150% × ₱280,000).............................. Total expected net operating income.......................

420,000 ₱700,000

Problem 7 (Multiproduct Break-even Analysis) 1. Super Fast Dynamic Shot Total Company Amount % Amount % Amount % Sales............................. ₱150,000 100 ₱250,000 100 ₱400,000 100.0 Variable expenses......... 30,000 Contribution margin..... ₱120,000

20 160,000 80 ₱ 90,000

Fixed expenses............. Net operating income.... 2. The break-even point for the company as a whole is: *₱210,000 ÷ ₱400,000 = 52.5%

Peso sales to break even =

Fixed expenses Overall CM ratio 14-9

64 36

190,000 47.5 210,000 52.5* 183,750 ₱ 26,250

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Operating and Financial Leverage

₱183,75 0 0.525

Peso sales to break even =

= ₱350,000

3. The additional contribution margin from the additional sales is computed as follows: ₱100,000 × 52.5% CM ratio = ₱52,500 Assuming no change in fixed expenses, all of this additional contribution margin of ₱52,500 should drop to the bottom line as increased net operating income. This answer assumes no change in selling prices, variable costs per unit, fixed expense, or sales mix. Problem 8 (Break-even Analysis) a. BE =

₱2,000,000 ₱1,200 − ₱700

b Q = .

Q=

Profit + FC

=

4,000 units ₱1,500,000 + ₱2,000,000 ₱1,200 − ₱700

=

(P − VC) ₱3,500,000 ₱500

=

7,000 units

Problem 9 (Break-even Analysis) BE (before) =

₱70,000 ₱4.00 − ₱2.60

=

₱70,000 ₱1.40

= 50,000 units

BE (after) =

₱105,000 ₱4.00 − ₱2.25

=

₱105,000 ₱1.75

= 60,000 units

The break-even point will go up. Problem 10 (Degree of Leverage) Q = 20,000, P = ₱60, VC = ₱30, FC = ₱400,000, I = ₱50,000 14-10

Operating and Financial Leverage

20,000 (₱60 − ₱30) 20,000 (₱60 − ₱30) − ₱400,000

Q (P − VC) a. DOL =

=

=

Q (P − VC) − FC

20,000 (₱30) 20,000 (₱30) − ₱400,000

₱600,000 =

₱600,000 − ₱400,000

₱600,00 0 ₱200,00 0

=

3x

b. DFL =

EBIT EBIT − I

=

₱200,000 ₱200,000 − ₱50,000

DFL =

₱200,00 0 ₱150,00 0

=

1.33x

DOL =

c. DCL =

=

20,000 (₱60 − ₱30) 20,000 (₱60 − ₱30) − ₱400,000 − ₱50,000

=

₱600,000 ₱600,000 − ₱400,000 − ₱50,000

DCL =

d. BE =

Q (P − VC) Q (P − VC) − FC − I

₱600,00 0 ₱150,00 0 ₱400,000 ₱60 − ₱30

=

4x

=

₱400,00 0 ₱30

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=

13,333 units

Chapter 14

Operating and Financial Leverage

Problem 11 (Break-even Point and Degree of Leverage) a. BE =

₱ 80,000 ₱15 − ₱10

=

₱80,000 ₱5

b.

16,000 pieces

15,000 pieces ₱225,000 (150,000) (80,000) ( ₱5,000)

Sales @ ₱15 per piece Less: Variable costs (₱10) Fixed costs Profit or Loss c. DOL =

=

30,000 pieces ₱450,000 (300,000) (80,000) (₱70,000)

Q (P − VC) Q (P − VC) − FC

DOL at 20,000 =

20,000 (₱15 – ₱10) 20,000 (₱15 − ₱10) − ₱80,000

DOL at 20,000 =

₱100,00 0 ₱20,000

DOL at 30,000 =

30,000 (₱15 – ₱10) 30,000 (₱15 − ₱10) − ₱80,000

DOL at 30,000 =

₱150,00 0 ₱70,000

= 5x

= 2.14x

Leverage goes down because we are further away from the break-even point, thus the firm is operating on a larger profit base and leverage is reduced. EBIT d DFL = . EBIT − I

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First, determine the profit or loss (EBIT) at 20,000 pieces. As indicated in part (b), the profit (EBIT) at 30,000 pieces is ₱70,000. 20,000 pieces ₱300,000 (200,000) (80,000) (₱20,000)

Sales @ ₱15 per piece Less: Variable costs (₱10) Fixed costs Profit or Loss

DFL at 20,000 =

DFL at 20,000 = DFL at 30,000 =

DFL at 30,000 =

e. DCL =

₱20,000 ₱20,000 − ₱10,000 ₱20,000 = 2x ₱10,000 ₱70,000 ₱70,000 − ₱10,000 ₱70,000 ₱60,000

= 1.17x

Q (P − VC) Q (P − VC) − FC − I

DCL at 20,000 =

DCL at 20,000 =

DCL at 30,000 =

DCL at 30,000 =

20,000 (₱15 − ₱10) 20,000 (₱15 − ₱10) − ₱80,000 − ₱10,000 ₱100,00 0 ₱10,000

=

10x

30,000 (₱15 − ₱10) 30,000 (₱15 − ₱10) − ₱80,000 − ₱10,000 ₱150,00 0 ₱60,000

=

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2.50x

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Operating and Financial Leverage

Problem 12 (Japanese Firm and Combined Leverage) Q (P − VC) Q (P − VC) − FC − I

DCL =

=

125,000 (₱25 − ₱5) 125,000 (₱25 − ₱5) − ₱1,800,000 − ₱400,000

=

125,000 (₱20) 125,000 (₱20) − ₱2,200,000

DCL =

₱2,500,000 ₱2,500,000 − ₱2,200,000

= 8.33x

Problem 13 (Leverage and Sensitivity Analysis) Income Statements a. Return on assets = 10%

EBIT Le...