# Break-Even Analysis

### Break-Even Point

The break-even point is a factor in deciding whether to invest in a new capital project.

At some time in any profitable capital investment, there will be a point at which loss becomes gain. This point is the break-even point. In the normal operations of a business, breakeven is the number of units that need to be sold to cover all of the expenses. The simplest examples come from the manufacturing industry. When an item is produced, there are costs for the materials and direct labor. These are variable costs, since they will change with the number of items produced. There are also costs that are not dependent on the number of units, called fixed costs. A typical fixed cost is rent. Breakeven calculates the number of units that need to be produced so that both the fixed and variable costs are overcome. This amount is expressed as units and as a currency amount.

For capital decisions, the break-even point is the point in time when the investment begins to pay off—that is, the investment begins to generate positive cash flow. These two analytical definitions are not exclusive. The break-even point for a capital investment dictates the income that must be generated, which, in turn, gives the number of units that would be produced (in a manufacturing scenario). This number of units generates capacity requirements for the machinery, which is a factor in the price of the asset. The number of units required and the total cost will be significant factors in setting the price of the item. Compared to net present value and similar measures, breakeven is a robust analysis that is considered in the overall sales strategy and is associated with the capital venture. It is an especially useful analysis for start-up ventures that must show an early break-even point in order to attract serious investors.

### Break-Even Calculations

The break-even point of an investment is calculated by dividing fixed costs by the sales price per unit minus the variable costs.
Breakeven is the number of units that need to be sold to cover all of the expenses. Compared to the other capital investment calculations, the break-even formula is relatively simple.
$\text{Break-even Units}=\frac{\text{Fixed Costs}}{\text{Sales per Unit}-{\text {Variable Costs}}}$
For manufacturing calculations, the sales price per unit is the sales price. For capital investment analysis, the sales price per unit is the increase in revenue from the new venture or the associated savings. Vision Inc. is considering purchasing a machine for $500,000 to make a new product. The labor cost is$12 per hour, and each unit takes four hours to produce. The materials cost $7 per unit. Each unit of the new product will sell for$100. The variable costs are the direct costs associated with making one unit. In this case, 4 hours of labor at $12 per hour is added to materials of$7 per unit. Using this information, the breakeven for the units made is calculated, showing how many units need to be manufactured to cover manufacturing expenses. The break-even sales is the dollar amount that correspond to the units being sold, and the break-even point is the point in time when this happens.
\begin{aligned}\text{Variable Costs}&=(\12.00\times4)+\7\\\\&=\55\;\text{per unit}\end{aligned}
Break-even units can be calculated.
\begin{aligned}{\text{Break-even Units}}&=\frac{\500,000}{\100-\55}\\\\&=11{,}111\;\text{units}\end{aligned}
At $100 per unit, the break-even sales are$1,111,100. If the new machine can produce 500 units per month, the break-even point for this investment can be calculated. This is the point in time when the investment begins to pay off by generating positive cash flow.
\begin{aligned}\text{Break-even Point}&=\frac{\500,000}{500\;\times\;(\100-\55)}\\\\&=22\;\text{months (or 1 year 10 months})\end{aligned}
Graphically, breakeven is the intersection of the total costs line and the total income line. Marginal costs (MC), average total costs (ATC), and average variable costs (AVC) are all associated with the production process. Marginal costs of production include all of the costs that vary with the level of production. Average total costs are unit costs that include all fixed costs and all variable costs. Knowing the average total cost is critical in making pricing decisions, as any price below average total cost will result in a financial loss. Finally, average variable costs represent the total variable cost per unit, including materials and labor, in short-term production calculated by dividing total variable costs by total output. A shutdown point is a level of operations at which a company experiences no benefit for continuing operations and therefore decides to shut down temporarily, or in some cases, permanently. It results from the combination of output and price where the company earns just enough revenue to cover its total variable costs. The shutdown point denotes the exact moment when a company's marginal revenue is equal to its variable marginal costs. In other words, it occurs when the marginal profit becomes negative.

#### Graphical Representation of Breakeven

Breakeven analysis can be used in conjunction with discounted cash flow to give an accurate representation of actual cash flow. Both discounted cash flow, a system of calculating the present value of forecasted future cash flows, and internal rate of return, the measure of an investment's rate of return, assume that the income will be reinvested. This is true up to the break-even date. After that date, the cash flow may be invested in other projects, as it is profit after that time. These other investments may have different return rates and cash flows, leading to a new or more robust capital structure analysis.