Reading 46: Measures of Leverage-LOS b 习题精选 2011, interpret, period, center, style

1215

Session 11: Corporate Finance
Reading 46: Measures of Leverage

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

 

 

During a period of expansion in the economy compared to firms with lower operating expense levels, the earnings growth for firms with high operating leverage will be:

A) higher.

B) lower.

C) not enough information.

---

 

If a high percentage of a firm's total costs are fixed, the firm is said to have high operating leverage. High operating leverage, other things held constant, means that a relatively small change in sales will result in a large change in operating income. Therefore, during an expansionary phase in the economy a highly leveraged firm will have higher earnings growth than a lesser leveraged firm. The opposite will happen during an economic contraction.

1215

As financial leverage increases, what will be the impact on the expected rate of return and financial risk?

A) Both will rise.

B) Both will fall.

C) One will rise while the other falls.

---

A higher breakeven point resulting from increased interest costs associated with debt financing increases the risk of the company. Since the risk is tied to firm financing, it is referred to as financial risk. Given the positive risk-return relationship, the expected return of the company’s common stock also rises.

1215

 

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%.

---

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%.

1215

Which of the following statements about leverage is most accurate?

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.

---

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.

1215

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) 1.59.

C) 1.41.

---

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.

1215

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.

---

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

1215

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 1.08

C) 2.20 1.50

---

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

1215

Which of the following statements regarding leverage is most accurate?

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

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

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

---

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

1215

A firm expects to produce 200,000 units of flour that can be sold for $3.00 per bag. The variable costs per unit are $2.00, the fixed costs are $75,000, and interest expense is $25,000. The degree of operating leverage (DOL) and the degree of total leverage (DTL) is closest to:

DOL

DTL

A) 1.6 2.0

B) 1.3 1.3

C) 1.6 1.3

---

DOL = Q(P – V) / [Q(P – V) – F]
DOL = 200,000 (3 – 2) / [200,000(3 – 2) – 75,000] = 1.6

DTL = [Q(P - V) / Q(P - V) - F - I]
DTL = 200,000 (3 - 2) / [200,000 (3 - 2) - 75,000 - 25,000] = 2

1215

All else equal, which of the following statements about operating leverage is least accurate?

A) Operating leverage reflects the tradeoff between variable costs and fixed costs.

B) Lower operating leverage generally results in a higher expected rate of return.

C) Firms with high operating leverage experience greater variance in operating income.

---

Operating leverage is the trade off between fixed and variable costs. Higher operating leverage typically is indicative of a firm with higher levels of risk (greater income variance). Given the positive risk/return relationship, higher operating leverage firms are expected to have a higher rate of return. And, lower operating leverage firms are expected to have a lower rate of return.