CFA® Program Curriculum, Volume 4, page 143 The level of sales that a firm must generate to cover all of its fixed and variable costs is called the breakeven quantity. The breakeven quantity of sales is the quantity of sales for which revenues equal total costs, so that net income is zero. We can calculate the breakeven quantity by simply determining how many units must be sold to just cover total fixed costs.
For each unit sold, the contribution margin, which is the difference between price and variable cost per unit, is available to help cover fixed costs. We can thus describe the breakeven quantity of sales, QBE, as:
EXAMPLE: Breakeven quantity of sales
Consider the prices and costs for Atom Company and Beta Company shown in the following table.
Compute and illustrate the breakeven quantity of sales for each company.
Operating Costs for Atom Company and Beta Company
Atom Company Beta Company
Price $4.00 $4.00
Variable costs $3.00 $2.00
Fixed operating costs $10,000 $80,000 Fixed financing costs $30,000 $40,000
Answer:
For Atom Company, the breakeven quantity is:
Similarly, for Beta Company, the breakeven quantity is:
The breakeven quantity and the relationship between sales revenue, total costs, net income, and net loss are illustrated in Figure 36.1 and Figure 36.2.
Figure 36.1: Breakeven Analysis for Atom Company
Figure 36.2: Breakeven Analysis for Beta Company
We can also calculate an operating breakeven quantity of sales. In this case, we consider only fixed operating costs and ignore fixed financing costs. The calculation is simply:
EXAMPLE: Operating breakeven quantity of sales
Calculate the operating breakeven quantity of sales for Atom and Beta, using the same data from the previous example.
Answer:
For Atom, the operating breakeven quantity of sales is:
$10,000 / ($4.00 − $3.00) = 10,000 units For Beta, the operating breakeven quantity of sales is:
$80,000 / ($4.00 − $2.00) = 40,000 units
We can summarize the effects of leverage on net income through an examination of Figure 36.1 and Figure 36.2. Other things equal, a firm that chooses operating and financial structures that result in greater total fixed costs will have a higher breakeven quantity of sales. Leverage of either type magnifies the effects of changes in sales on net income. The further a firm’s sales are from its breakeven level of sales, the greater the magnifying effects of leverage on net income.
These same conclusions apply to operating leverage and the operating breakeven
quantity of sales. One company may choose a larger scale of operations (larger factory), resulting in a greater operating breakeven quantity of sales and greater leverage, other things equal.
Note that the degree of total leverage is calculated for a particular level of sales. The slope of the net income line in Figure 36.1 and Figure 36.2 is related to total leverage but is not the same thing. The degree of total leverage is different for every level of sales.
MODULE QUIZ 36.1
To best evaluate your performance, enter your quiz answers online.
1. Business risk is the combination of:
A. operating risk and financial risk.
B. sales risk and financial risk.
C. operating risk and sales risk.
2. Which of the following is a key determinant of operating leverage?
A. Level and cost of debt.
B. The competitive nature of the business.
C. The trade-off between fixed and variable costs.
3. Which of the following statements about capital structure and leverage is most accurate?
A. Financial leverage is directly related to operating leverage.
B. Increasing the corporate tax rate will not affect capital structure decisions.
C. A firm with low operating leverage has a small proportion of its total costs in fixed costs.
4. Jayco, Inc., sells blue ink for $4 a bottle. The ink’s variable cost per bottle is $2. Ink has fixed operating costs of $4,000 and fixed financing costs of $6,000. What is Jayco’s breakeven quantity of sales, in units?
A. 2,000.
B. 3,000.
C. 5,000.
5. Jayco, Inc., sells blue ink for $4 a bottle. The ink’s variable cost per bottle is $2. Ink has fixed operating costs of $4,000 and fixed financing costs of $6,000. What is Jayco’s operating breakeven quantity of sales, in units?
A. 2,000.
B. 3,000.
C. 5,000.
6. If Jayco’s sales increase by 10%, Jayco’s EBIT increases by 15%. If Jayco’s EBIT increases by 10%, Jayco’s EPS increases by 12%. Jayco’s degree of operating leverage (DOL) and degree of total leverage (DTL) are closest to:
A. 1.2 DOL and 1.5 DTL.
B. 1.2 DOL and 2.7 DTL.
C. 1.5 DOL and 1.8 DTL.
Use the following data to answer Questions 7 and 8.
Jayco, Inc., sells 10,000 units at a price of $5 per unit. Jayco’s fixed costs are $8,000, interest expense is $2,000, variable costs are $3 per unit, and EBIT is $12,000.
7. Jayco’s degree of operating leverage (DOL) and degree of financial leverage (DFL) are closest to:
A. 2.50 DOL and 1.00 DFL.
B. 1.67 DOL and 2.00 DFL.
C. 1.67 DOL and 1.20 DFL.
8. Jayco’s degree of total leverage (DTL) is closest to:
A. 2.00.
B. 1.75.
C. 1.50.
9. Vischer Concrete has $1.2 million in assets that are currently financed with 100%
equity. Vischer’s EBIT is $300,000, and its tax rate is 30%. If Vischer changes its capital structure (recapitalizes) to include 40% debt, what is Vischer’s ROE before and after the change? Assume that the interest rate on debt is 5%.
ROE at 100% equity ROE at 60% equity
A. 17.5% 26.8%
B. 25.0% 26.8%
C. 25.0% 37.5%
KEY CONCEPTS
LOS 36.a
Leverage increases the risk and potential return of a firm’s earnings and cash flows.
Operating leverage increases with fixed operating costs.
Financial leverage increases with fixed financing costs.
Sales risk is uncertainty about the firm’s sales.
Business risk refers to the uncertainty about operating earnings (EBIT) and results from variability in sales and expenses. Business risk is magnified by operating leverage.
Financial risk refers to the additional variability of EPS compared to EBIT. Financial risk increases with greater use of fixed cost financing (debt) in a company’s capital structure.
LOS 36.b
The degree of operating leverage (DOL) is calculated as and is interpreted as
The degree of financial leverage (DFL) is calculated as and is interpreted as The degree of total leverage (DTL) is the combination of operating and financial leverage and is calculated as DOL × DFL and interpreted as
LOS 36.c
Using more debt and less equity in a firm’s capital structure reduces net income through added interest expense but also reduces net equity. The net effect can be to either
increase or decrease ROE.
LOS 36.d
The breakeven quantity of sales is the amount of sales necessary to produce a net income of zero (total revenue just covers total costs) and can be calculated as:
Net income at various sales levels can be calculated as total revenue (i.e., price
× quantity sold) minus total costs (i.e., total fixed costs plus total variable costs).
LOS 36.e
The operating breakeven quantity of sales is the amount of sales necessary to produce an operating income of zero (total revenue just covers total operating costs) and can be calculated as: