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Foundations of Financial Management 15th Edition

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Chapter 5 Operating and Financial Leverage

Discussion Questions

5-1. Discuss the various uses for break-even analysis.

Such analysis allows the firm to determine at what level of operations it will break even (earn zero profit) and to explore the relationship between volume, costs, and profits.

5-2. What factors would cause a difference in the use of financial leverage for a utility company and an automobile company?

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.

5-3. Explain how the break-even point and operating leverage are affected by the choice of manufacturing facilities (labor intensive versus capital intensive).

Chapter 05 - Operating and Financial Leverage 5-1

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.

5-4. What role does depreciation play in break-even analysis based on accounting flows? Based on cash flows? Which perspective is longer term in nature?

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.

Chapter 05 - Operating and Financial Leverage 5-2

5-5. What does risk taking have to do with the use of operating and financial leverage?

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.

5-6. Discuss the limitations of financial leverage.

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 greatest in industries that are highly cyclical in nature.

5-7. How does the interest rate on new debt influence the use of financial leverage?

The higher the interest rate on new debt, the less attractive financial leverage is to the firm.

5-8. Explain how combined leverage brings together operating income and earnings per share.

Operating leverage primarily affects the operating income of the firm. At this point, financial leverage takes over and determines the overall impact on earnings per share. A delineation of the combined effect of operating and financial leverage is presented in Table 5-6 and Figure 5-5.

5-9. Explain why operating leverage decreases as a company increases sales and shifts away from the break-even point.

At progressively higher levels of operations 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.

Chapter 05 - Operating and Financial Leverage

5-3

5-10. When you are considering two different financing plans, does being at the level where earnings per share are equal between the two plans always mean you are indifferent as to which plan is selected?

The point of equalityonly 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 maycall for different price-earnings ratios, particularly when there is a differential risk component involved because of debt.

Chapter 5 Problems

1. Break-even analysis (LO2) Shock Electronics sells portable heaters for $35 per unit, and the variable cost to produce them is $22. Mr. Amps estimates that the fixed costs are $97,500.

a. Compute the break-even point in units.

b Fill in the following table (in dollars) to illustrate that the break-even point has been achieved.

Sales………………….

– Fixed costs………….

– Total variable costs…

Net profit (loss)

Shock Electronics

a. Fixed costs BE Price-variable cost per unit

$97,500$97,500 7,500 units $35$22$13

Chapter 05 - Operating and Financial Leverage 5-4

5-1. Solution:





b. Sales $262,500 (7,500 units × $35)

– Fixed costs 97,500

– Total variable costs 165,000 (7,500 units × $22) Net profit (loss) $ 0

2. Break-even analysis (LO2) The Hartnett Corporation manufactures baseball bats with Pudge Rodriguez’s autograph stamped on them. Each bat sells for $35 and has a variable cost of $22. There are $97,500 in fixed costs involved in the production process.

a. Compute the break-even point in units.

b. Find the sales (in units) needed to earn a profit of $262,500.

5-2. Solution: Hartnett Corporation

a. $97,500 BE7,500 units $35$22

Factory labor $4.00 per unit

Executives under contract $186,500

Raw material .............................. $1.20 per unit

Chapter 05 - Operating and Financial Leverage

5-5



b. ProfitFC$262,500$97,500 (VC) $35$22 $360,000 27,692 units $13   

3. Break-even analysis (LO2) Therapeutic Systems sells its products for $13 per unit. It has the following costs: Rent............................................ $145,000

Separate the expenses between fixed and variable costs per unit. Using this information and the sales price per unit of $13, compute the break-even point.

5-3. Solution:

4. Break-even analysis (LO2) Draw two break-even graphs one for a conservative firm using labor-intensive production and another for a capital-intensive firm. Assuming these companies compete within the same industry and have identical sales, explain the impact of changes in sales volume on both firms’ profits.

5-4. Solution:

Labor-Intensive and Capital-Intensive Break-Even Graphs

Chapter 05 - Operating and Financial Leverage 5-6

Therapeutic Systems Fixed Costs Variable Costs (per unit) Rent $145,000 Factory labor $4.00 Executive under contract $186,500 Raw materials 1.20 $331,500 $5.20 FC$331,500$331,500 BE42,500 units VC$13$5.20$7.80 P 

The company having the higher fixed costs will have lower variable costs than its competitor since it has substituted capital for labor. With a lower variable cost, the high-fixed-cost company will have a larger contribution margin. Therefore, when sales rise, its profits will increase faster than the lowfixed-cost firm, and when the sales decline, the reverse will be true.

5. Break-even analysis (LO2) Eaton Tool Company has fixed costs of $255,000, sells its units for $66, and has variable costs of $36 per unit.

a. Compute the break-even point.

b. Ms. Eaton comes up with a new plan to cut fixed costs to $200,000. However, more labor will now be required, which will increase variable costs per unit to $39. The sales price will remain at $66. What is the new break-even point?

c. Under the new plan, what is likely to happen to profitability at very high volume levels (compared to the old plan)?

5-5. Solution:

Chapter 05 - Operating and Financial Leverage 5-7 Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Unitsproducedandsold Revenueandcosts Totalrevenue Total costs Variable Cost Profits BE Fixed costs Labor-Intensive Capital-Intensive Unitsproducedandsold Revenueandcosts Totalrevenue Total costs Variable Cost Profits BE Fixed costs

Eaton Tool Company

The break-even level decreases.

c. With less operating leverage and a smaller contribution margin, profitability is likely to be less than it would have been at very high volume levels.

6. Break-even analysis (LO2) Shawn Pen & Pencil Sets Inc. has fixed costs of$80,000. Its product currentlysells for $5 per unit and has variable costs of $2.50 per unit. Mr. Bic, the head of manufacturing, proposes to buynew equipment that will cost $400,000 and drive up fixed costs to $120,000. Although the price will remain at $5 per unit, the increased automation will reduce costs per unit to $2.00.

As a result of Bic’s suggestion, will the break-even point go up or down? Compute the necessary numbers.

5-6. Solution:

Chapter 05 - Operating and Financial Leverage 5-8

the prior written

consent of McGraw-Hill Education.

Fixed costs BE PriceVariable cost per unit $255,000$255,000 8,500 units $66$36$30  

Fixed costs BE PriceVariable cost per unit $200,000$200,000 7,407 units $66$39$27  

Shawn Pen & Pencil Sets Inc. $80,000$80,000 BE(before)32,000 units $5.00$2.50$2.50 

$120,000$120,000 BE (after)40,000 units $5.00$2.00$3.00

The break-even point will go up.

7. Cash break-even analysis (LO2) Calloway Cab Company determines its break-even strictly on the basis of cash expenditures related to fixed costs. Its total fixed costs are $450,000, but 5 percent of this value is represented by depreciation. Its contribution margin (price minus variable cost) for each unit is $4.10. How many units does the firm need to sell to reach the cash break-even point?

5-7. Solution: Calloway Cab Company

Cash-related fixed costs = Total fixed costs – Depreciation = $450,000 – 5% ($450,000) = $450,000 – $22,500 = $427,500 $427,500 Cash BE104,268 $4.10

8. Cash break-even analysis (LO2) Air Purifier Inc. computes its break-even point strictly on the basis of cash expenditures related to fixed costs. Its total fixed costs are $2,450,000, but 15 percent of this value is represented by depreciation. Its contribution margin (price minus variable cost) for each unit is $40. How many units does the firm need to sell to reach the cash break-even point?

5-8. Solution: Air Purifier Inc.

Cash-related fixed costs = Total fixed costs – Depreciation

Chapter 05 - Operating and Financial Leverage 5-9

or distribution without the prior written

consent of McGraw-Hill Education.





= $2,450,000 – 15% (2,450,000) = $2,450,000 – $367,500 = $2,082,500

2,082,500

BE52,063 units

$40

9. Cash break-even analysis (LO2) Boise Timber Co. computes its break-even point strictly on the basis of cash expenditures related to fixed costs. Its total fixed costs are $6,500,000, but 10 percent of this value is represented by depreciation. Its contribution margin (price minus variable cost) for each unit is $9. How many units does the firm need to sell to reach the cash break-even point?

5-9. Solution: Boise Timber Co.

Cash-related fixed costs = Total fixed costs – Depreciation = $6,500,000 – 10% ($6,500,000) = $6,500,000 – $650,000 = $5,850,000 $5,850,000

without the prior written consent of McGraw-Hill Education.

Chapter 05 - Operating and Financial Leverage 5-10

or distribution



$9 

BE650,000units

10 Degree of leverage (LO2 and 5) The Sterling Tire Company’s income statement for 2013 is as follows:

STERLING TIRE COMPANY

For the Year Ended December 31, 2013

tires at $60 each)...................................

Given this income statement, compute the following:

a. Degree of operating leverage.

b Degree of financial leverage.

c. Degree of combined leverage.

d Break-even point in units.

Chapter 05 - Operating and Financial Leverage 5-11

Income Statement

Sales

$1,200,000 Less: Variable costs (20,000 tires

$30) 600,000 Fixed costs.............................................................. 400,000 Earnings before interest and taxes (EBIT) 200,000 Interest expense........................................................... 50,000 Earnings before taxes (EBT) 150,000 Income tax expense (30%).......................................... 45,000 Earnings after taxes (EAT).......................................... $ 105,000

(20,000

Sterling

Q = 20,000, P = $60, VC = $30, FC = $400,000, I = $50,000

5-10. Solution:

Tire Company

Chapter 05 - Operating and Financial Leverage 5-12 Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

(VC) DOL (VC)FC 20,000($60$30) 20,000($60$30)$400,000 20,000($30) 20,000($30)$40,000 $600,000$600,000 3.00x $600,000$400,000$200,000 QP QP    

(Continued)

EBIT$200,000 DFL EBIT$200,000$50,000 $200,000 1.33x $150,000 I  

(VC) DCL (VC)FC 20,000($60$30) 20,000($60$30)$400,000$50,000 $600,000$600,000 4x $600,000$400,000$50,000$150,000 QP QPI   

$400,000$400,000 BE13,333 units $60$30$30 

5-10.

11. Degree of leverage (LO2 and 5) The Harding Company manufactures skates. The company’s income statement for 2013 is as follows:

Given this income statement, compute the following:

a. Degree of operating leverage.

b. Degree of financial leverage.

c. Degree of combined leverage.

d. Break-even point in units (number of skates).

Chapter 05 - Operating and Financial Leverage 5-13

HARDING

Income Statement For the Year Ended December 31, 2013 Sales (10,500 skates @ $60 each)................................. $630,000 Less: Variable costs (10,500 skates at $25) 262,500 Fixed costs................................................................. 200,000 Earnings before interest and taxes (EBIT) .................... 167,500 Interest expense............................................................. 62,500 Earnings before taxes (EBT)......................................... 105,000 Income tax expense (30%) 31,500 Earnings after taxes (EAT)............................................ $ 73,500

COMPANY

5-11. Solution: Harding Company Q = 10,500, P = $60, VC = $25, FC = $200,000, I = $62,500 a. (VC) DOL (VC)FC 10,500($60$25) 10,500($60$25)$200,000 10,500($35) 10,500($35)$200,000 $367,500$367,500 2.19x $367,500$200,000$167,500 QP QP     

5-11. (Continued)

12. Break-even point and degree of leverage (LO2 and 5) Healthy Foods Inc. sells 50-pound bags of grapes to the military for $10 a bag. The fixed costs of this operation are $80,000, while the variable costs of grapes are $.10 per pound.

a What is the break-even point in bags?

b. Calculate the profit or loss on 12,000 bags and on 25,000 bags.

c. What is the degree of operating leverage at 20,000 bags and at 25,000 bags? Why does the degree of operating leverage change as the quantity sold increases?

d. If Healthy Foods has an annual interest expense of $10,000, calculate the degree of financial leverage at both 20,000 and 25,000 bags.

e. What is the degree of combined leverage at both sales levels?

2014

b. EBIT$167,500 DFL EBIT$167,500$62,500 $167,500 1.60x $105,000 I    c. (VC) DCL (VC)FC 10,500($60$25) 10,500($60$25)$200,000$62,500 $10,500($35)$367,500 3.50x $10,500($35)$262,500$105,000 QP QPI     d. $200,000$200,000 BE5,714 skates $60$25$35 

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.

Chapter 05 - Operating and Financial Leverage 5-15 Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5-12. Solution: Healthy Foods Inc. a. $80,000$80,000 BE16,000$10($.1050)$5bags   b. 12,000 bags 25,000 bags Sales @ $10 per bag $120,000 $250,000 Less: Variables costs ($5) (60,000) (125,000) Fixed costs (80,000) (80,000) Profit or loss ($ 20,000) $ 45,000 c. (VC) DOL (VC)FC 20,000($10$5) DOL at 20,000 20,000 ($10$5)$80,000 $100,000 5.00x $20,00 QP QP     25,000($10$5) DOLat25,000 25,000($10$5)$80,000 $125,000 2.78x $45,000  

5-12. (Continued)

d. EBIT DFL EBIT I

First determine the profit or loss (EBIT) at 20,000 bags. As indicated in part b, the profit (EBIT) at 25,000 bags is

Chapter 05 - Operating and Financial Leverage 5-16



20,000 bags Sales @ $10 per bag $200,000 Less: Variable costs ($5) 100,000 Fixed costs 80,000 Profit or loss $ 20,000 $20,000 DFL at 20,000 $20,000$10,000 2.0x    $45,000 DFL at 25,000 $45,000$10,000 1.29x   e. DCL(VC) (VC)FC QP QPI   20,000 ($10$5) DCLat 20,000 20,000($10$5)$80,000$10,000 $100,000 10.0x $10,000  

$45,000:

13. Break-even point and degree of leverage (LO2 and 5) United Snack Company sells 50-pound bags of peanuts to university dormitories for $20 a bag. The fixed costs of this operation are $176,250, while the variable costs of peanuts are $.15 per pound.

a. What is the break-even point in bags?

b. Calculate the profit or loss on 7,000 bags and on 20,000 bags.

c. What is the degree of operating leverage at 19,000 bags and at 24,000 bags? Why does the degree of operating leverage change as the quantity sold increases?

d. If United Snack Company has an annual interest expense of $15,000, calculate the degree of financial leverage at both 19,000 and 24,000 bags.

e. What is the degree of combined leverage at both sales levels?

Solution:

Chapter 05 - Operating and Financial Leverage 5-17 Copyright

Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 25,000 ($10$5) DCL at 25,000 25,000($10$5)$80,000$10,000 $125,000 3.57x $35,000  

United Snack Company a. $176,250$176,250 BE14,100$20($.1550)$12.50bags   b. 7,000 bags 20,000 bags Sales @ $20 per bag $140,000 $400,000 Less: Variables costs ($7.50) (52,500) (150,000) Fixed costs (176,250) (176,250) Profit or loss (EBIT) ($ 88,750) $ 73,750

5-13.

(Continued)

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.

5-13. (Continued)

First determine the profit or loss (EBIT) at 19,000 bags and at 24,000 bag: 19,000 bags 24,000 bags

Chapter 05 - Operating and Financial Leverage 5-18

distribution without the prior written

(VC) DOL (VC)FC 19,000($20$7.50) DOL at 19,000 19,000 ($20$7.50)$176,250 $237,500 3.88x $61,250 QP QP    24,000($20$7.50) DOLat24,000 24,000($20$7.50)$176,250 $300,000 2.42x $123,750  

consent

McGraw-Hill Education. 5-13.

EBIT DFL EBIT I  

@ $20 per

$380,000 $480,000 Less: Variable costs ($7.50) 142,500 180,000 Fixed costs 176,250 176,250 Profit or loss (EBIT) $ 61,250 $ 123,750

Sales

bag

14. Nonlinear breakeven analysis (LO2) International Data Systems information on revenue and costs is only relevant up to a sales volume of 105,000 units. After 105,000 units, the market becomes saturated and the price per unit falls from $14.00 to $8.80. Also, there are cost overruns at a production volume of over 105,000 units, and variable cost per unit goes up from $7.00 to $8.00. Fixed costs remain the same at $55,000.

a. Compute operating income at 105,000 units.

b. Compute operating income at 205,000 units.

Chapter 05 - Operating and Financial Leverage 5-19 Copyright

Education. All

reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. $61,250 DFL at 19,000 $61,250$15,000 1.32x   $123,750 DFL at 24,000 $123,750$15,000 1.14x   e. DCL(VC) (VC)FC QP QPI  19,000 ($20$7.50) DCLat 19,000 19,000($20$7.50)$176,250$15,000 $237,500 5.14x $46,250   24,000 ($20$7.50) DCL at 24,000 24,000($20$7.50)$176,250$15,000 $300,000 2.76x $108,750  

rights

Chapter 05 - Operating and Financial Leverage 5-20 Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5-14. Solution: International Data Systems a. Sales (105,000  $14)....................................... $1,470,000 Total variable costs (105,000  $7).................. 735,000 Fixed costs......................................................... 55,000 Operating income.............................................. $680,000 b. Sales (205,000  $8.80).................................... $1,804,000 Total variable costs (205,000  $8.00)............. 1,640,000 Fixed costs......................................................... 55,000 Operating income.............................................. $109,000

15. Use of different formulas for operating leverage (LO3) U.S. Steal has the following income statement data:

a. Compute DOL based on the following formula:

b. Confirm that your answer to part a is correct by recomputing DOL using Formula 5–

3. There may be a slight difference due to rounding.

Q represents beginning units sold (all calculations should be done at this level). P can be found by dividing total revenue by units sold. VC can be found by dividing total variable costs by units sold.

Chapter 05 - Operating and Financial Leverage 5-21

Units Sold Total Variable Costs Fixed Costs Total Costs Total Revenue Operating Income (Loss) 60,000 $ 120,000 $50,000 $170,000 $360,000 $190,000 80,000 160,000 50,000 210,000 480,000 270,000

Percent change in operating DOLincome Percent change in units sold 

(VC)FC



DOL(VC)

QP QP

5-15. Solution: U.S. Steal a. Percent change in operating income DOL Percent change in units sold $80,000 42% 190,000 1.27 20,000 33% 60,000   b. DOL(VC) (VC)FC QP QP  

16. Earnings per share and financial leverage (LO4) Lenow’s Drug Stores and Hall’s Pharmaceuticals are competitors in the discount drug chain store business. The separate capital structures for Lenow and Hall are presented next.

a. Compute earnings per share if earnings before interest and taxes are $20,000, $30,000, and $120,000 (assume a 30 percent tax rate).

b. Explain the relationship between earnings per share and the level of EBIT.

c. If the cost of debt went up to 12 percent and all other factors remained equal, what would be the break-even level for EBIT?

Chapter 05 - Operating and Financial Leverage 5-22 Copyright

Education. All

reserved. No reproduction or distribution without the prior written consent of

Education. 60,000 Total revenue$360,000 $6 Units sold60,000 Total

costs$120,000 VC$2 Units sold60,000 FC$50,000 60,000 ($6$2)$240,000 DOL 60,000($6$2)$50,000$240,000$50,000 $240,000 1.26 $190,000 Q P      

rights

McGraw-Hill

variable

Lenow Hall Debt @ 10%......................... $100,000 Debt @ 10%.......................... $200,000 Common stock, $10 par 200,000 Common stock, $10 par 100,000 Total..................................... $300,000 Total ...................................... $300,000 Shares 20,000 Common shares 10,000

Chapter 05 - Operating and Financial Leverage 5-23 Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5-16. Solution: a. Lenow Drug Stores and Hall Pharmaceuticals Lenow Hall EBIT $ 20,000 $ 20,000 Less: Interest 10,000 20,000 EBT 10,000 0 Less: Taxes @ 30% 3,000 0 EAT 7,000 0 Shares 20,000 10,000 EPS $ .35 0 EBIT $ 30,000 $ 30,000 Less: Interest 10,000 20,000 EBT 20,000 10,000 Less: Taxes @ 30% 6,000 3,000 EAT 14,000 7,000 Shares 20,000 10,000 EPS $ .70 $ .70 EBIT $120,000 $120,000 Less: Interest 10,000 20,000 EBT 110,000 100,000 Less: Taxes @ 30% 33,000 30,000 EAT 77,000 70,000 Shares 20,000 10,000 EPS $ 3.85 $ 7.00

5-16. (Continued)

b. Before-tax return on assets = 6.67 percent, 10 percent, and 40 percent at the respective levels of EBIT. When the before-tax return on assets (EBIT/Total assets) is less than the cost of debt (10 percent), Lenow does better with less debt than Hall. When before-tax return on assets is equal to the cost of debt, both firms have equal EPS. This would be where the method of financing has a neutral effect on EPS. As return on assets becomes greater than the interest rate, financial leverage becomes more favorable for Hall.

c. 12%  $300,000 = $36,000 break-even level for EBIT.

17. P/E ratio (LO6) The capital structure for Cain Supplies is presented next. Compute the stock price for Cain if it sells at 19 times earnings per share and EBIT is $50,000. The tax rate is 20 percent.

Chapter 05 - Operating and Financial Leverage

5-24

Cain Debt @ 9%.......................... $100,000 Common stock, $10 par...... 200,000 Total................................ $300,000 Common shares................... 20,000

18. Leverage and stockholder wealth (LO4) Sterling Optical and Royal Optical both make glass frames and each is able to generate earnings before interest and taxes of $132,000. The separate capital structures for Sterling and Royal are shown next:

a. Compute earnings per share for both firms. Assume a 25 percent tax rate.

b. In part a, you should have gotten the same answer for both companies’ earnings per share. Assuming a P/E ratio of 22 for each company, what would its stock price be?

c. Now as part of your analysis, assume the P/E ratio would be 16 for the riskier company in terms of heavy debt utilization in the capital structure and 24 for the less risky company. What would the stock prices for the two firms be under these assumptions? (Note: Although interest rates also would likely be different based on risk, we will hold them constant for ease of analysis.)

d. Based on the evidence in part c, should management only be concerned about the impact of financing plans on earnings per share or should stockholders’ wealth maximization (stock price) be considered as well?

Cain Supplies Cain EBIT $50,000 Less: Interest 9,000 EBT $41,000 Less: Taxes @ 20% 8,200 EAT $32,800 Shares 20,000 EPS $1.64 P/E 19x Stock price $ 31.16

2014 McGraw-Hill

5-17. Solution:

Sterling Royal Debt @ 12%……………… $ 660,000 Debt @ 12%…………… $ 220,000 Common stock, $5 par…… 440,000 Common stock, $5 par 880,000 Total……………………… $1,100,000 Total…………………… $1,100,000 Common shares………….. 88,000 Common shares………... 176,000

5-18. Solution: Sterling Optical and Royal Optical

b. Stock price = P/E ×EPS 22 × $.45 = $9.90

c. Sterling Royal 16 × $.45 = $7.20 24 × $.45 = $10.80

d. Clearly, the ultimate objective should be to maximize the stock price. While management would be indifferent between the two plans based on earnings per share, Royal Optical, with the less risky plan, has a higher stock price.

19. Japanese firm and combined leverage (LO5) Firms in Japan often employ both high operating and financial leverage because of the use of modern technology and close borrower–lender relationships. Assume the Mitaka Company has a sales volume of 130,000 units at a price of $30 per unit; variable costs are $10 per unit and fixed costs are $1,850,000. Interest expense is $405,000. What is the degree of combined leverage for this Japanese firm?

Chapter 05 - Operating and Financial Leverage 5-26

Sterling Royal EBIT $132,000 $132,000 Less: Interest 79,200 26,400 EBT 52,800 105,600 Less: Taxes

13,200 26,400 EAT 39,600 79,200 Shares 88,000 176,000 EPS $.45 $.45

@ 25%

20. Combining operating and financial leverage (LO5) Sinclair Manufacturing and Boswell Brothers Inc. are both involved in the production of brick for the homebuilding industry. Their financial information is as follows:

a. If you combine Sinclair’s capital structure with Boswell’s operating plan, what is the degree of combined leverage? (Round to two places to the right of the decimal point.)

b. If you combine Boswell’s capital structure with Sinclair’s operating plan, what is the degree of combined leverage?

McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5-19. Solution: Mitaka Company (VC) DCL (VC)FC 130,000 ($30$10) 130,000 ($30$10)$1,850,000$405,000 130,000 ($20) 130,000 ($20)$2,255,000 $2,600,000 $2,600,000$2,255,000 7.54x QP QPI     

2014

Capital Structure Sinclair Boswell Debt @ 11%...... $ 900,000 0 Common stock, $10 per share................................ 600,000 $ 1,5000,000 Total....... $ 1,500,000 $ 1,500,000 Common shares....................................................... 60,000 150,000 Operating Plan Sales (55,000 units at $20 each).............................. $ 1,100,000 $ 1,100,000 Less: Variable costs............................................. 880,000 550,000 ($16 per unit) ($10 per unit) Fixed costs....... 0 305,000 Earnings before interest and taxes (EBIT)....... $ 220,000 $ 245,000

c. Explain why you got the results you did in part b.

d. In part b, if sales double, by what percentage will EPS increase?

Chapter 05 - Operating and Financial Leverage 5-28

5-20. Solution: Sinclair Manufacturing and Boswell Brothers a. (VC) DCL (VC)FC 55,000 ($20$10) 55,000 ($20$10)$305,000$99,000 550,000 550,000 $305,000$99,000 $550,000 $146,000 3.77x QP QPI     

5-20. (Continued)

c. The leverage factor is only lx because Boswell has no financial leverage and Sinclair has no operating leverage.

d. EPS will increase by 100 percent. However, there is no leverage involved. EPS merely grows at the same rate as sales.

Chapter 05 - Operating and Financial Leverage 5-29 Copyright

Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. b. (VC) DCL (VC)FC 55,000($20$16) 55,000($20$16)00 55,000($4) 55,000($4) $220,000 $220,000 1x QP QPI     

21 Expansion and leverage (LO5) DeSoto Tools Inc. is planning to expand production. The expansion will cost $300,000, which can be financed either by bonds at an interest rate of 14 percent or by selling 10,000 shares of common stock at $30 per share. The current income statement before expansion is as follows:

DESOTO TOOLS Inc.

After the expansion, sales are expected to increase by $1,000,000. Variable costs will remain at 30 percent of sales, and fixed costs will increase to $800,000. The tax rate is 34 percent.

a. Calculate the degree of operating leverage, the degree of financial leverage, and the degree of combined leverage before expansion. (For the degree of operating leverage, use the formula developed in footnote 2. For the degree of combined leverage, use the formula developed in footnote 3. These instructions apply throughout this problem.)

b Construct the income statement for the two alternative financing plans.

c. Calculate the degree of operating leverage, the degree of financial leverage, and the degree of combined leverage, after expansion.

d. Explain which financing plan you favor and the risks involved with each plan.

Chapter 05 - Operating and Financial Leverage 5-30

Income Statement 200X Sales $1,500,000 Less: Variable costs..................................................... $450,000 Fixed costs 550,000 1,000,000 Earnings before interest and taxes.................................. 500,000 Less: Interest expense 100,000 Earnings before taxes..................................................... 400,000 Less: Taxes @ 34%..................................................... 136,000 Earnings after taxes $ 264,000 Shares............................................................................. 100,000 Earnings per share $ 2.64

Chapter 05 - Operating and Financial Leverage 5-31 Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 5-21. Solution: DeSoto Tools Inc. a. VC DOL TVCFC S S  $1,500,000$450,000 2.1x $1,500,000$450,000$550,000 EBIT DFL EBIT $500,000 $500,000$100,000 $500,000 1.25x $400,000 I     TVC DCL TVCFC $1,500,000$450,000 $1,500,000$450,000$550,000$100,000 $1,050,000 2.63x $400,000 S SI   

5-21. (Continued)

b. Income Statement after Expansion

1 New interest expense level if expansion is financed with debt.

$100,000 + 14% ($300,000) = $142,000

2 Number of common shares outstanding if expansion is financed with equity.

100,000 + 10,000 = 110,000

Chapter 05 - Operating and Financial Leverage 5-32

Debt Equity Sales $2,500,000 $2,500,000 Less: Variable costs (30%) 750,000 750,000 Fixed costs 800,000 800,000 EBIT 950,000 950,000 Less: Interest 142,0001 100,000 EBT 808,000 850,000 Less: Taxes @ 34% 274,720 289,000 EAT (Net income) 533,280 561,000 Common shares 100,000 110,0002 EPS $ 5.33 $ 5.10

$2,500,000$750,000 DOL (Debt/Equity) $2,500,000$750,000$800,000 $1,750,000 1.84x $950,000 S S   

c. TVC DOL TVCFC

d. The debt financing plan provides a greater earnings per share at the new sales level, but provides more risk because of the increased use of debt. However, the interest coverage ratio in both cases is certainly satisfactory and interest expense is well protected. The crucial point is expectations for future sales. If sales are expected to decline, the debt plan will not provide higher EPS at sales of less than about $2 million, so cyclical swings in sales, earnings, and profit margins need to be considered in choosing the financing plan.

Chapter 05 - Operating and Financial Leverage 5-33 Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

EBIT DFL EBIT $950,000$950,000 DFL (Debt)1.18x $950,000-$142,000$808,000 $950,000$950,000 DFL (Equity)1.12x $950,000-$100,000$850,000 $2,500,000$750,000 DCL (Debt) $2,500,000$750,000$800,000$142,00 I     0 $1,750,000 2.17x $808,000  $2,500,000$750,000 DCL (Equity) $2,500,000$750,000$800,000$100,000 $1,750,000 2.06x $850,000  

5-21. (Continued)

22. Leverage analysis with actual companies (LO6) Using Standard & Poor’s data or annual reports, compare the financial and operating leverage of Chevron, Eastman Kodak, and Delta Airlines for the most current year. Explain the relationship between operating and financial leverage for each company and the resultant combined leverage. What accounts for the differences in leverage of these companies?

5-22. Solution:

23 Leverage and sensitivity analysis (LO6) Dickinson Company has $12 million in assets. Currently half of these assets are financed with long-term debt at 10 percent and half with common stock having a par value of $8. Ms. Smith, vice-president of finance, wishes to analyze two refinancing plans, one with more debt (D) and one with more equity (E). The company earns a return on assets before interest and taxes of 10 percent. The tax rate is 45 percent.

Under Plan D, a $3 million long-term bond would be sold at an interest rate of 12 percent and 375,000 shares of stock would be purchased in the market at $8 per share and retired.

Under Plan E, 375,000 shares of stock would be sold at $8 per share and the $3,000,000 in proceeds would be used to reduce long-term debt.

a How would each of these plans affect earnings per share? Consider the current plan and the two new plans.

b Which plan would be most favorable if return on assets fell to 5 percent? Increased to 15 percent? Consider the current plan and the two new plans.

c. If the market price for common stock rose to $12 before the restructuring, which plan would then be most attractive? Continue to assume that $3 million in debt will be used to retire stock in Plan D and $3 million of new equity will be sold to retire debt in Plan E. Also assume for calculations in part c that return on assets is 10 percent.

Chapter 05 - Operating and Financial Leverage 5-34

The results for this problem change every year. This is primarily an Internet/library assignment to facilitate class discussion.

5-23. Solution: Dickinson Company Income Statements

a. Return on assets = 10% EBIT = $ 1,200,000

1 $6,000,000 debt @ 10%

2 $600,000 interest + ($3,000,000 debt @ 12%)

3 ($6,000,000 – $3,000,000 debt retired)  10%

4 ($6,000,000 common equity)/($8 par value) = 750,000 shares

Plan E and the original plan provide the same earnings per share because the cost of debt at 10 percent is equal to the operating return on assets of 10 percent. With Plan D, the cost of increased debt rises to 12 percent, and the firm incurs negative leverage reducing EPS and also increasing the financial risk to Dickinson.

Chapter 05 - Operating and Financial Leverage 5-35

the prior written consent of McGraw-Hill Education.

Current Plan D Plan E EBIT $1,200,000 $1,200,000 $1,200,000 Less: Interest 600,0001 960,0002 300,0003 EBT 600,000 240,000 900,000 Less: Taxes (45%) 270,000 108,000 405,000 EAT 330,000 132,000 495,000 Common shares 750,0004 375,000 1,125,000 EPS $ .44 $ .35 $ .44

5-23. (Continued)

b. Return on assets = 5% EBIT = $600,000

Return on assets = 15% EBIT = $1,800,000

If the return on assets decreases to 5 percent, Plan E provides the best EPS, and at 15 percent return, Plan D provides the best EPS. Plan D is still risky, having an interest coverage ratio of less than 2.0.

Chapter 05 - Operating and Financial Leverage 5-36

Current Plan D Plan E EBIT $600,000 $600,000 $ 600,000 Less: Interest 600,000 960,000 300,000 EBT 0 (360,000) 300,000 Less: Taxes @ 45% --- (162,000) 135,000 EAT 0 $(198,000) $ 165,000 Common shares 750,000 375,000 1,125,000 EPS 0 $ (.53) $ .15

Current Plan D Plan E EBIT $1,800,000 $1,800,000 $1,800,000 Less: Interest 600,000 960,000 300,000 EBT 1,200,000 840,000 1,500,000 Less: Taxes @ 45% 540,000 378,000 675,000 EAT $ 660,000 $ 462,000 $ 825,000 Common shares 750,000 375,000 1,125,000 EPS $ .88 $ 1.23 $ .73

5-23. (Continued)

c. Return on Assets = 10% EBIT = $1,200,000

1 750,000 – ($3,000,000/$12 per share) = 750,000 – 250,000 = 500,000 shares

2 750,000 + ($3,000,000/$12 per share) = 750,000 + 250,000 = 1,000,000 shares

As the price of the common stock increases, Plan E becomes more attractive because fewer shares can be retired under Plan D and, by the same logic, fewer shares need to be sold under Plan E.

24. Leverage and sensitivity analysis (LO6) Edsel Research Labs has $27 million in assets. Currently, half of these assets are financed with long-term debt at 5 percent and half with common stock having a par value of $10. Ms. Edsel, the vice-president of finance, wishes to analyze two refinancing plans, one with more debt (D) and one with more equity (E). The company earns a return on assets before interest and taxes of 5 percent. The tax rate is 30 percent.

Under Plan D, a $6.75 million long-term bond would be sold at an interest rate of 11 percent and 675,000 shares of stock would be purchased in the market at $10 per share and retired. Under Plan E, 675,000 shares of stock would be sold at $10 per share and the $6,750,000 in proceeds would be used to reduce long-term debt.

a. How would each of these plans affect earnings per share? Consider the current plan and the two new plans. Which plan(s) would produce the highest EPS? Note that due to tax loss carry-forwards and carry-backs, taxes can be a negative number.

b. Which plan would be most favorable if return on assets increased to 8 percent? Compare the current plan and the two new plans. What has caused the plans to give different EPS numbers?

c. Assuming return on assets is back to the original 5 percent, but the interest rate on new debt in Plan D is 7 percent, which of the three plans will produce the highest EPS? Why?

Chapter 05 - Operating and Financial Leverage 5-37

Current Plan D Plan E EBIT $1,200,000 $1,200,000 $1,200,000 EAT 330,000 132,000 495,000 Common shares 750,000 500,0001 1,000,0002 EPS $ .44 $ .26 $ .50

5-24. Solution:

Edsel Research Labs Income

1 $13,500,000 debt @ 5% = $675,000

2 $675,000 interest + ($6,750,000 new debt @ 11%) = $1,417,500

3 ($13,500,000 $6,750,000 debt retired)  5% = $337,500

4 ($13,500,000 common equity / $10 par value) = 1,350,000 shares

5 ($6,750,000 common equity / $10 par value) = 675,000 shares

6 ($20,250,000 common equity / $10 par value) = 2,025,000 shares

The current plan and Plan E provide the highest return of $0.35.

Chapter 05 - Operating and Financial Leverage 5-38

All rights

No reproduction or distribution without the prior written

Education.

reserved.

consent of McGraw-Hill

Statement

EBIT

Current Plan D Plan E EBIT $1,350,000 $1,350,000 $1,350,000 Less: Interest 675,0001 1,417,5002 337,5003 EBT 675,000 67,500 1,012,500 L Less: Taxes (30%) 202,500 20,250 303,750 EAT 472,500 47,250 708,750 Common shares 1,350,0004 675,0005 2,025,0006 EPS $.35 $ 0.07 $0.35

a. Return on assets = 5%

= $1,350,000

5-25. (Continued)

b. Return on assets = 8%

The current plan and Plan D provides the highest return. The % EBIT (12%) is higher than the interest rate (8% and 10%). Thus, the more debt the firm takes on, the higher the EPS.

c. Return on assets = 5%

= $1,350,000

$675,000 +

 7%) = 1,147,500

The current plan and Plan E provides the highest return. The % EBIT (8%) is higher than the cost of new debt (6%).

Chapter 05 - Operating and Financial Leverage 5-39

distribution

the

without

prior written consent of McGraw-Hill Education.

EBIT

Current PlanD Plan E EBIT $2,160,000 $2,160,000 $2,160,000 Less: Interest 675,000 1,417,500 337,500 EBT 1,485,000 742,500 1,822,500 Less: Taxes (30%) 445,500 222,750 546,750 EAT 1,039,500 519,750 1,275,750 Common shares 1,350,000 675,000 2,025,000 EPS $0.77 $0.77 $0.63

= $2,160,000

EBIT

Current PlanD Plan E EBIT $1,350,000 $1,350,000 $1,350,000 Less: Interest 675,000 1,147,5001 337,500 EBT 675,000 202,500 1,012,500 Less: Taxes (30%) 202,500 60,750 303,750 EAT 472,500 141,750 708,750 Common shares 1,350,000 675,000 2,025,000 EPS $0.35 $0.21 $0.35 1

(6,750,000

25. Leverage and sensitivity analysis (LO6) The Lopez-Portillo Company has $10.6 million in assets, 80 percent financed by debt, and 20 percent financed by common stock. The interest rate on the debt is 9 percent and the par value of the stock is $10 per share.

President Lopez-Portillo is considering two financing plans for an expansion to $18 million in assets.

Under Plan A, the debt-to-total-assets ratio will be maintained, but new debt will cost a whopping 12 percent! Under Plan B, only new common stock at $10 per share will be issued. The tax rate is 40 percent.

a. If EBIT is 9 percent on total assets, compute earnings per share (EPS) before the expansion and under the two alternatives.

b. What is the degree of financial leverage under each of the three plans?

c. If stock could be sold at $20 per share due to increased expectations for the firm’s sales and earnings, what impact would this have on earnings per share for the two expansion alternatives? Compute earnings per share for each.

d. Explain why corporate financial officers are concerned about their stock values.

5-25. Solution: Lopez-Portillo Company

Chapter 05 - Operating and Financial Leverage 5-40

a. Return on Assets = 20% Current Plan A Plan B EBIT $954,000 $1,620,000 $1,620,000 Less: Interest 763,200(a) 1,473,600(c) 763,200(e) EBT 190,800 146,400 856,800 Less: Taxes (40%) 76,320 58,560 342,720 EAT $114,480 $ 87,840 $ 514,080 Common shares 212,000(b) 360,000(d) 952,000(f) EPS $0.54 $0.24 $0.54 (a) (80%  $10,600,000)  9% = $8,480,000  9% = $763,200 (b) (20%  $10,600,000)/$10 = $2,120,000/$10 = 212,000 shares (c) $763,200 (current)  (80%  $7,400,000)  12% = $763,200  $710,400 = $1,473,600 (d) 212,000 shares (current) + (20%  $7,400,000)/$10 = 212,000 + 148,000 = 360,000 shares (e) Unchanged

(f) 212,000 shares (current) + $7,400,000/$10 = 212,000 + 740,000 = 952,000 shares

5-25. (Continued)

b. EBIT DFL EBIT I 

(Plan B)1.89x

1 212,000 shares (current) + (20%  $7,400,000)/$20 = 212,000 + 74,000 = 286,000 shares

2 212,000 shares (current) + $7,400,000/$20 = 212,000 + 370,000 = 582,000 shares

Plan B would continue to provide the higher earnings per share. The difference between plans A and B is even greater than that indicated in part (a).

Chapter 05 - Operating and Financial Leverage 5-41

or distribution without the prior written consent

of McGraw-Hill Education.

$954,000

$954,000$763,200 $1,620,000

$1,620,000$1,473,600 $1,620,000

$1,620,000$763,200   

Plan A Plan B EAT $87,840 $514,080 Common shares 286,0001 582,0002 EPS $ 0.31 $ 0.88

DFL (Current)5.00x

DFL (Plan A)11.07x

DFL

26. Operating leverage and ratios (LO6) Mr. Gold is in the widget business. He currently sells 1.5 million widgets a year at $6 each. His variable cost to produce the widgets is $4 per unit, and he has $1,550,000 in fixed costs. His sales-to-assets ratio is six times, and 30 percent of his assets are financed with 10 percent debt, with the balance financed by common stock at $10 par value per share. The tax rate is 35 percent. His brother-in-law, Mr. Silverman, says he is doing it all wrong. By reducing his price to $5.00 a widget, he could increase his volume of units sold by 60 percent. Fixed costs would remain constant, and variable costs would remain $4 per unit. His sales-to-assets ratio would be 7.5 times. Furthermore, he could increase his debt-to-assets ratio to 50 percent, with the balance in common stock. It is assumed that the interest rate would go up by 1 percent and the price of stock would remain constant.

a. Compute earnings per share under the Gold plan.

b. Compute earnings per share under the Silverman plan.

c. Mr. Gold’s wife, the chief financial officer, does not think that fixed costs would remain constant under the Silverman plan but that they would go up by 15 percent. If this is the case, should Mr. Gold shift to the Silverman plan, based on earnings per share?

Chapter 05 - Operating and Financial Leverage 5-42

d. Not only does the price of the common stock create wealth to the shareholder, which is the major objective of the financial manager, but it greatly influences the ability to finance projects at a high or low cost of capital. Cost of capital will be discussed in Chapter 10, and one will see the impact that the cost of capital has on capital budgeting decisions.

5-26.

Gold-Silverman

Gold Plan Sales ($1,500,000 units  $6)

Fixed costs 1,550,000 Variable costs 6,000,000 Operating income (EBIT) $ 1,450,000  Interest1 45,000 EBT $ 1,405,000 Taxes @ 35% 491,750

Solution:

$9,000,000

1 Debt = 30% of Assets = 30% × $1,500,000 = $450,000

Interest = 10% × $450,000 = $45,000

2 Stock = 70% of $1,500,000 = $1,050,000 Shares = $1,050,000/$10 = 105,000 shares

5-26. (Continued)

b. Silverman Plan

($2,400,000 units at $5.00)

3 Debt = 50% of Assets = 50% × $1,600,000 = $800,000

Interest = 13% × $800,000 = $104,000

4 Stock = 50% of $1,600,000 = $800,000 Shares = $800,000/$10 = 80,000 shares

Chapter 05 - Operating and Financial Leverage 5-43

EAT $ 913,250 Shares2 105,000 Earnings per share $ 8.70 Sales$9,000,000 Assets$1,500,000 Assetturnover6 

Sales

Fixed costs 1,550,000 Variable costs (2,400,000 units  $4) 9,600,000 Operating income (EBIT) $ 850,000 Interest3 104,000 EBT $ 746,000 Taxes @ 35% 261,100 EAT $ 484,900 Shares4 80,000 Earnings per share $ 6.06 Sales$12,000,000 Assets$1,600,000 Assetturnover7.50 

$12,000,000

5-26. (Continued)

c. Silverman Plan (based on Mrs. Gold’s Assumption)

units at $5.00)

27. Expansion, break-even analysis, and leverage (LO2, 3, and 4) Delsing Canning Company is considering an expansion of its facilities. Its current income statement is as follows:

The company is currently financed with 50 percent debt and 50 percent equity (common stock, par value of $10). In order to expand the facilities, Mr. Delsing estimates a need for $2.5 million in additional financing. His investment banker has laid out three plans for him to consider:

1. Sell $2.5 million of debt at 13 percent.

Chapter 05 - Operating and Financial Leverage 5-44

Sales ($2,400,000

$12,000,000 Fixed costs ($1,550,000  1.15) 1,782,500 Variable costs (2,400,000 units  $4) 9,600,000 Operating income (EBIT) $ 617,500 Interest 104,000 EBT $ 513,500 Taxes @ 35% 179,725 EAT $ 333,775 Shares 80,000 Earningspershare $ 4.17

Gold

No!

should not shift to the Silverman Plan if Mrs. Gold’s assumption is correct.

Sales .................................................................. $5,500,000 Less: Variable expense (50% of sales)........... 2,750,000 Fixed expense 1,850,000 Earnings before interest and taxes (EBIT)........ 900,000 Interest (10% cost) 300,000 Earnings before taxes (EBT)............................. 600,000 Tax (40%).......................................................... 240,000 Earnings after taxes (EAT) $ 360,000 Shares of common stock 250,000 .................. Earnings per share $1.44

2. Sell $2.5 million of common stock at $20 per share.

3. Sell $1.25 million of debt at 12 percent and $1.25 million of common stock at $25 per share.

Variable costs are expected to stay at 50 percent of sales, while fixed expenses will increase to $2,350,000 per year. Delsing is not sure how much this expansion will add to sales, but he estimates that sales will rise by $1.25 million per year for the next five years. Delsing is interested in a thorough analysis of his expansion plans and methods of financing. He would like you to analyze the following:

a. The break-even point for operating expenses before and after expansion (in sales dollars).

b. The degree of operating leverage before and after expansion. Assume sales of $5.5 million before expansion and $6.5 million after expansion. Use the formula in footnote 2 of the chapter.

c. The degree of financial leverage before expansion and for all three methods of financing after expansion. Assume sales of $6.5 million for this question.

d. Compute EPS under all three methods of financing the expansion at $6.5 million in sales (first year) and $10.5 million in sales (last year).

e. What can we learn from the answer to part d about the advisability of the three methods of financing the expansion?

Chapter 05 - Operating and Financial Leverage 5-45

5-27. Solution: Delsing Canning Company a. At break-even before expansion: PQFCVC where PQ equals sales volume at break-even point  Sales FixedcostsVariablecosts (Variablecosts50%ofsales) Sales $1,850,000.50Sales .50Sales$1,850,000 Sales $3,700,000      At break-even after expansion: