OM FINAL

LEVERAGE DOL, DFL AND DTL

THE BREAKEVEN POINTS, QBE AND QOBE

CHAPTER FOUR: MEASURES OF LEVERAGE

Yi Zhou

Associate Professor Department of Finance

College of Business San Francisco State University

YI ZHOU CHAPTER FOUR: MEASURES OF LEVERAGE

LEVERAGE DOL, DFL AND DTL

THE BREAKEVEN POINTS, QBE AND QOBE

LEVERAGE BUSINESS RISK & FINANCIAL RISK DEFINITIONS

LEVERAGE

Leverage is the use of fixed costs in a company’s cost structure. A company’s use of leverage affects its risk and return.

Operating leverage relates to the company’s operating cost structure. Financial leverage relates to the company’s capital structure.

Leverage helps us understand a company’s future cash flows and the risk associated with those cash flows and, hence, its valuation.

Leverage increases the volatility of earnings and cash flows. Hence, it increases risk to suppliers of capital (creditors and owners).

Total leverage is the combined effect of operating leverage and financial leverage.

YI ZHOU CHAPTER FOUR: MEASURES OF LEVERAGE

LEVERAGE DOL, DFL AND DTL

THE BREAKEVEN POINTS, QBE AND QOBE

LEVERAGE BUSINESS RISK & FINANCIAL RISK DEFINITIONS

BUSINESS RISK & FINANCIAL RISK

Business risk is the risk associated with operating earnings and reflects both sales risk (uncertainty with respect to the price and quantity of sales) and operating risk (the risk related to the use of fixed costs in operations). It is affected by demand uncertainty, output price uncertainty, and cost uncertainty.

Financial risk is the risk associated with how a company finances its operations (i.e., the split between equity and debt financing of the business).

In the event that creditor claims cannot be satisfied, there may be legal statuses that help sort out the claims: –Reorganization is the restructuring of claims, with the expectation that the company will be able to continue, in some form, as a going concern. –Liquidation is the situation in which assets are sold and then the proceeds distributed to claimants.

YI ZHOU CHAPTER FOUR: MEASURES OF LEVERAGE

LEVERAGE DOL, DFL AND DTL

THE BREAKEVEN POINTS, QBE AND QOBE

LEVERAGE BUSINESS RISK & FINANCIAL RISK DEFINITIONS

DEFINITIONS

The degree of operating leverage (DOL) is the sensitivity of operating earnings to changes in units produced and sold. It is the ratio of the percentage change in operating income to the percentage change in units sold.

The degree of financial leverage (DFL) is the sensitivity of cash flows to owners to changes in operating earnings. It is the ratio of the percentage change in net income to the percentage change in operating income.

The degree of total leverage (DTL) is the sensitivity of the cash flows to owners to changes in unit sales.

The breakeven point, QBE , is the number of units produced and sold at which the company’s net income is zero.

The operating breakeven point, QOBE , is the number of units produced and sold at which the company’s operating income is zero.

YI ZHOU CHAPTER FOUR: MEASURES OF LEVERAGE

LEVERAGE DOL, DFL AND DTL

THE BREAKEVEN POINTS, QBE AND QOBE

DOL, DFL AND DTL EXAMPLE OF DOL, DFL AND DTL

DOL, DFL AND DTL

The degree of operating leverage (DOL) (operating income): DOL = Q(P−V)Q(P−V)−F The degree of financial leverage (DFL) (net income): DFL = Q(P−V)−FQ(P−V)−F−C The degree of total leverage (DTL) (cash flow): DTL = DOL × DFL.

Q: Number of units sold.

P: Price per unit.

V : Variable operating cost per unit.

F: Fixed operating cost.

C: Fixed financing expense.

YI ZHOU CHAPTER FOUR: MEASURES OF LEVERAGE

LEVERAGE DOL, DFL AND DTL

THE BREAKEVEN POINTS, QBE AND QOBE

DOL, DFL AND DTL EXAMPLE OF DOL, DFL AND DTL

EXAMPLE OF DOL, DFL AND DTL

DOL1 = Q(P − V)

Q(P − V) − F =

1, 000(250 − 125) 1, 000(250 − 125) − 50, 000

= 1.67 (1)

DOL2 = Q(P − V)

Q(P − V) − F =

1, 000(250 − 25) 1, 000(250 − 25) − 100, 000

= 1.80

DFL1 = Q(P − V) − F

Q(P − V) − F − C =

1, 000(250 − 125) − 50, 000 1, 000(250 − 125) − 50, 000 − 5, 000

= 1.07

DFL2 = Q(P − V) − F

Q(P − V) − F − C =

1, 000(250 − 25) − 100, 000 1, 000(250 − 25) − 100, 000 − 55, 000

= 1.79

DTL1 = DOL1 × DFL1 = 1.67 × 1.07 = 1.79 DTL2 = DOL1 × DFL1 = 1.80 × 1.79 = 3.22

YI ZHOU CHAPTER FOUR: MEASURES OF LEVERAGE

LEVERAGE DOL, DFL AND DTL

THE BREAKEVEN POINTS, QBE AND QOBE

THE BREAKEVEN POINTS, QBE AND QOBE EXAMPLE OF QBE AND QOBE

THE BREAKEVEN POINTS, QBE AND QOBE

The financial breakeven point, QBE, is the number of units produced and sold at which the company’s net income is zero, QBE =

F+C P−V .

The operating breakeven point, QOBE, is the number of units produced and sold at which the company’s operating income is zero, QOBE =

F P−V .

YI ZHOU CHAPTER FOUR: MEASURES OF LEVERAGE

LEVERAGE DOL, DFL AND DTL

THE BREAKEVEN POINTS, QBE AND QOBE

THE BREAKEVEN POINTS, QBE AND QOBE EXAMPLE OF QBE AND QOBE

EXAMPLE OF QBE AND QOBE

QBE,1 = F + C P − V

= 50, 000 + 5, 000

250 − 125 = 440 (2)

QOBE,1 = F

P − V =

50, 000 250 − 125

= 400

QBE,2 = F + C P − V

= 100, 000 + 55, 000

250 − 25 = 689

QOBE,2 = F

P − V =

100, 000 250 − 25

= 444

YI ZHOU CHAPTER FOUR: MEASURES OF LEVERAGE