Profit and Break-Even

We begin with the basics. Later in this chapter, we will use an income statement to illustrate the calculations.

Revenues, Costs, and Profit The basic relationship for profit is expressed by the well-known equation:

(10.1) Revenues, or income, depend on both the unit selling price of a company’s products and the number

Profit = Revenues – Costs

of units sold. Costs include both the fixed and variable costs of producing goods or providing services. Examples of variable costs are: (1) the cost of raw materials used in factory production; (2) the

Profit, Break-Even, and Leverage ❧ 319 workers; (4) the cost of fuel to operate planes and other transportation equipment; and, (5) sales commis-

sions for selling a firm’s products. Variable costs are directly related to a firm’s level of sales; that is, they are expected to increase or decrease in proportion to any increase or decrease in the number of units of product sold.

Examples of fixed costs are: (1) rent and lease payments; (2) the salaries of supervisors, managers, executives, and other administrators; and (3) the depreciation of equipment. Fixed costs are constant, regardless of the level of production or sales.

In a strict sense, variable costs may not be exactly proportional to the level of production or sales. Nor are fixed costs precisely constant, regardless of the level of production or sales. However, treating variable costs as proportional to production or sales and fixed costs as fixed provides satisfactory approximations for computing profit over some relevant range of operation.

Accordingly, the model of equation 10.1 can be rewritten in the following form, which identifies the effects of fixed and variable cost on the earnings before interest and taxes:

EBIT =× N SP − ( FC N VC +× ) (10.2) where EBIT = Earnings before interest and taxes (EBIT is a measure of what we can call net operating

income before considering taxes and the interest paid or received from short-term bor- rowing and lending.)

N = Number of units produced and sold (As a simplification, all units produced are assumed to be sold.) SP = Unit selling price, or the selling price per unit FC = Fixed operating cost VC = Unit variable cost, or the variable cost per unit produced and sold (e.g., the cost of the

direct labor and materials to make and sell one unit of the product) Equation 10.2 expresses very succinctly the dependence of EBIT on unit selling price, number of

units made and sold, fixed cost, and unit variable cost. In this form, EBIT is said to be the dependent variable. Its value depends on the values of the variables on the right side of the equal sign, which are called the independent variables.

When values are assigned to the independent variables on the right side of equation 10.2, the value of the dependent variable on the left side can be calculated. For example, if FC is $100,000, VC is $8/unit, SP is $12/unit, and N is 50,000 units,

EBIT = (50,000 units)($12/unit) – [$100,000 + (50,000 units)($7/unit)] = $600,000 – $100,000 – $350,000 = $150,000

Figure 10-1 shows a spreadsheet solution. Data values have been inserted into cells B2, B3, B4, and B5. The calculation of profit has been programmed in cell B6 by the entry =B5*B4-(B2+B5*B3). An important assumption made in this profit model is that the company can sell 50,000 units at a selling price of $12/unit. Later we will examine the effect of selling price on the number of units that can

320 ❧ Corporate Financial Analysis with Microsoft Excel ® Figure 10-1

Profit as a Function of Fixed Cost, Unit Variable Cost, Unit Selling Price, and Number of Units Sold

1 PROFIT MODEL: Profit for Producing and Selling 50,000 Units

2 Fixed cost

Entry in B2 is data value.

3 Unit variable cost

Entry in B3 is data value.

4 Unit selling price

Entry in B4 is data value.

5 Units sold

Entry in B5 is data value.

6 Profit

Entry in B6 is =B5*B4–(B2+B5*B3).

Break-Even Point The break-even point of the profit model is the number of units at which EBIT is zero. Companies use

this number to determine the level of sales needed to recoup their fixed costs. Equation 10.2 can be used in several ways to determine the break-even point. The algebraic method would be to set the right side of equation 10.2 equal to zero and solve for N. The result is

N is written with a subscript zero in equation 10.3 to indicate it is the special value for which EBIT is zero. Equation 10.3 treats the break-even point as the dependent variable and defines its dependence

on the fixed cost, selling price, and unit variable cost. The break-even point defined by equation 10.3 is sometimes referred to as the operating break-even point.

For the same values of FC, SP and VC as before, the break-even point can be calculated as

$/ 12 unit − $/ 7 unit $/ 5 unit

The expression in the denominator (i.e., the difference between the unit selling price and the unit variable cost) is known as the marginal profitability or the marginal contribution to profit. The company must make and sell 20,000 units, each with a marginal profitability of $5, to recover an investment of $100,000 in facilities, equipment, and any other fixed costs.

With a spreadsheet, the break-even point can be determined without performing the algebraic manipulations to rearrange equation 10.2 into the form of equation 9.3. Figure 10-2 shows the results by using Excel’s Solver tool with the spreadsheet shown as Figure 10-1. As with the algebraic solution, the break-even point is found to be 20,000 units.

Figure 10-3 shows the dialog box for using Excel’s Solver tool. To access the tool, pull down the Tools menu and click on the Solver box. Cell B6 (the value of profit) is designated as the target cell and its target value is set equal to zero. Cell B5 is allowed to change from the value on the spreadsheet to whatever value will make B6 equal to its target value. To execute Solver, click on Solve or press Enter.

Profit, Break-Even, and Leverage ❧ 321 Figure 10-2

Determining the Break-Even Point with Excel’s Solver Tool

1 PROFIT MODEL: Break-Even Analysis with Solver Tool

2 Fixed cost

3 Unit variable cost

4 Unit selling price

5 Units sold

Cell B5 gives break-even point for zero profit.

6 Profit

Entry in B6 is =B5*B4–(B2+B5*B3). 7 B6 is the target cell, with a target value of zero.

8 Value of B5 is allowed to vary to hit target (i.e., B6 = 0).

Figure 10-3

“Solver Parameters” Dialog Box with Settings for Break-Even Point

The break-even point in dollars ($BEP) equals the break-even point in units multiplied by the unit selling price; that is,

$BEP N = 0 × SP (10.4) For a break-even point of 20,000 units and a selling price of $12/unit, the break-even point in dollars

of sales is calculated by equation 9.4 as

$ BEP = , 20 000 units × $/ 12 unit = $ 240 000 ,

Substituting equation 10.3 into equation 10.4 gives

FC $BEP  = × SP (10.5)

 SP VC − 

which can be rearranged in the form

$ BEP =

( SP VC SP − )

322 ❧ Corporate Financial Analysis with Microsoft Excel ®

The ratio (SP – VC)/SP is the ratio of the marginal profitability to the selling price that is, it meas- ures marginal profitability as a fraction or percentage of the price. For a price of $12/unit and a variable cost of $7/unit, the marginal profitability is 41.67 percent (calculated as (12 – 7)/12 = 5/12 = 0.4167 = 41.67%). For a fixed cost of $100,000, the break-even point in dollars is calculated by equation 10.6 as

which is the same value, by multiplying the number of units at the break-even point by the selling price.

Profit and Break-Even