Reading 28: Capital Structure and Leverage-LOS b 习题精选 capital, structure, interpret, class

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Session 8: Corporate Finance
Reading 28: Capital Structure and Leverage

LOS b: Calculate and interpret the degree of operating leverage, the degree of financial leverage, and the degree of total leverage.

 

 

 

FCO, Inc. (FCO) is using EBIT forecasts to help plan its capital structure.

	Expected EBIT	EBIT + 10%
EBIT	$80,000	$88,000
Interest expense	15,000	15,000
EBT	65,000	73,000
Taxes	26,000	29,200
Net income	39,000	43,800

Liabilities	200,000
Shareholder equity	250,000
Return on equity	15.60%

What is FCO’s degree of financial leverage?

A) 0.60.

B) 0.75.

C) 0.80.

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The "degree of leverage" concept is designed to show how changes in sales will affect earnings before interest and taxes (EBIT) and EPS. If a 10% increase in sales causes EPS to increase from $1.00 to $1.50, and if the firm uses no debt, then what is its degree of operating leverage?

A) 4.7.

B) 5.0.

C) 4.2.

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Upon first glance, it appears there is not enough information to complete the problem. However when one realizes DTL = (DOL)(DFL) it is possible to complete this problem. 

DTL = %?EPS/%?Sales = 5

DFL =  EBIT/(EBIT-I) = 1.

(DOL)(1) =5

DOL= 5.

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The management of Strings & All, Inc., a small, highly leveraged, electric guitar manufacturer, wants to reduce the company’s degree of total leverage (DTL) to 2.0. Currently, the company’s expected operating performance is as follows:

• Sales of $500,000.

• Variable Costs at 60% of sales.

• Fixed Costs of $120,000.

• Fixed-Interest Debt with annual interest payments of $25,000.

All else constant, to obtain a DTL of 2.0, management must:

A) reduce variable expenses by 30%.

B) increase variable expenses by 30%.

C) reduce variable expenses by 38.5%.

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To obtain this result, we need to calculate the current variable costs, determine the variable costs that will result in a DTL ratio of 2.00, and calculate the percentage change.

Step 1: Calculate current variable costs (VC): VC = 0.6 × 500,000 = 300,000

Step 2: Calculate Variable costs needed to decrease the DTL to 2.0:

Rearranging the formula for DTL:

(Sales ? Variable Costs) / (Sales ? Variable Costs ? Fixed Costs ? Interest Expense)

results in: 

Variable Costs (VC) = Sales ? (2 × Fixed Costs) ? (2 × Interest Expense)

= 500,000 ? (2 × 120,000) ? (2 × 25,000) = 210,000

Step 3: Calculate percentage change:

DVC = (300,000 ? 210,000) / 300,000 = 0.30, or 30%.

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Which of the following statements about leverage is CORRECT?

A) An increase in fixed costs (holding sales and variable costs constant) will reduce the company's degree of operating leverage.

B) If the company has no debt outstanding, then its degree of total leverage equals its degree of operating leverage.

C) A decrease in interest expense will increase the company's degree of total leverage.

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If debt = 0 then DFL = 1 because DFL = EBIT/(EBIT - I)

If debt = 0 then I = 0 and DFL = EBIT/(EBIT - 0) = EBIT/EBIT = 1

DTL = (DOL)(DFL)

If DFL = 1 then DTL = (DOL)(1) which complies to DTL = DOL

A decrease in interest expense will decrease DFL, which will decrease DTL. An increase in fixed costs will increase the company’s DOL.

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The following information reflects the projected operating results for Opstalan, a catalog printer.

• Sales of $5.0 million.
• Variable Costs at 40% of sales.
• Fixed Costs of $1.0 million.> >
• Debt interest payments on $1.5 million issued with an annual 7.0% coupon (current yield is 8.0%).> >
• Tax Rate of 0.0%.

Opstalan’s degree of total leverage (DTL) is closest to:

A) 2.58.

B) 1.41.

C) 1.59.

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First, calculate the operating results:

Opstalan Annual Operating Results
Sales	$5,000,000
Variable Costs1	2,000,000
	3,000,000
Fixed Costs	1,000,000
EBIT	2,000,000
Interest Expense2	105,000
	1,895,000

¹Variable costs = 0.40 × 5,000,000
²Interest Expense = 0.07 × 1,500,000

Second, calculate DOL = (Sales ? Variable Costs) / (Sales ? Variable Costs ? Fixed Costs) = 3,000,000 / 2,000,000 = 1.50

Third, calculate DFL = EBIT / (EBIT ? I) = 2,000,000 / 1,895,000 = 1.06.

Finally, calculate DTL = DOL × DFL = 1.50 × 1.06 = 1.59.

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Stromburg Corporation's sales are $75,000,000. Fixed costs, including research and development, are $40,000,000, while variable costs amount to 30% of sales. Stromburg plans an expansion which will generate additional fixed costs of $15,000,000, decrease variable costs to 25% of sales, and permit sales to increase to $100,000,000. What is Stromburg's degree of operating leverage at the new projected sales level?

A) 4.20.

B) 3.50.

C) 3.75.

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Sales = $100,000,000

VC of 25% of sales = 25,000,000

FC of 40,000,000 + 15,000,000 = 55,000,000

DOL= [100,000,000 – 25,000,000] / [100,000,000 – 25,000,000 – 55,000,000] = 3.75

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Given the following information on the annual operating results for ArtFrames, a producer of quality metal picture frames, what is the degree of operating leverage (DOL) and the degree of financial leverage (DFL)?

• Sales of $3.5 million
• Variable Costs at 45% of sales
• Fixed Costs of $1.05 million
• Debt interest payments on $750,000 issued with an annual 9.0% coupon (current yield is 7.0%)

Which of the following choices is closest to the correct answer? ArtFrame’s DOL and DFL are:

DOL

DFL

A) 3.00 1.50

B) 2.20 1.50

C) 2.20 1.08

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The calculations are as follows:

First, calculate the operating results:

ArtFrames Annual Operating Results
Sales	$3,500,000
Variable Costs1	1,575,000
	1,925,000
Fixed Costs	1,050,000
Earnings before interest and taxes (EBIT)	875,000
Interest Expense2	67,500
	807,500
1Variable costs = 0.45 × 3,500,000
2Interest Expense = 0.09 × 750,000

Second, calculate DOL:

DOL = (Sales – Variable Costs) / (Sales – Variable Costs – Fixed Costs)

= (3,500,000 – 1,575,000) / (3,500,000 – 1,575,000 – 1,050,000) = 2.20

Third, calculate DFL:

DFL = EBIT / (EBIT – I) = 875,000 / 807,500 = 1.08

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Which of the following statements regarding leverage is TRUE?

A) A firm with high business risk is more likely to increase its use of financial leverage than a firm with low business risk.

B) High levels of financial leverage increase business risk while high levels of operating leverage will decrease business risk.

C) A firm with low operating leverage has a small proportion of its total costs in fixed costs.

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A firm with high operating leverage has a high percentage of its total costs in fixed costs.

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Financial leverage magnifies:

A) taxes.

B) earnings per share variability.

C) operating income variability.

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Financial leverage results in the existence of required interest payments and, hence, increased earnings per share variability. Higher debt ratios, given a fixed asset base, result in a greater earnings per share variability. Operating income is based on the products and assets of the firm and not on the firm’s financing and, hence, has no impact on financial leverage. Greater financial leverage is likely to reduce taxes due to the tax deductibility of interest payments.

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Which of the following is a key determinant of operating leverage?

A) The competitive nature of the business.

B) Level and cost of debt.

C) The tradeoff between fixed and variable costs.

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Operating leverage can be defined as the trade off between variable and fixed costs.