Break$-$even analysis

To be profitable, a firm must recover its costs. These costs include both its fixed and its variable costs. One way that a firm evaluates at what stage it

would recover the invested costs is to calculate how many units or how much in dollar sales is necessary for the firm to earn a profit.

Consider the case of Dynamic Defenses Corporation:

Dynamic Defenses Corporation is considering a project that will have fixed costs of $$15,000,000.$ The product will be sold for $$32\mathrm{.}50$ per

unit, and will incur a variable cost of $$12\mathrm{.}80$ per unit.

Given Dynamic Defenses's cost structure, it will have to sell

units to break even on this project $(Q_{BE}).$

Dynamic Defenses Corporation's marketing sales director doesn't think that the market for the firm's goods is big enough to sell enough units to make

the company's target operating profit of $$15,000,000.$ In fact, she believes that the firm will be able to sell only about $175,000$ units. However, she

also thinks the demand for Dynamic Defenses Corporation's product is relatively inelastic, so the firm can increase the sale price. Assuming that the

firm can sell $175,000$ units, what price must it set to meet the CFO's EBIT goal of $$15,000,000?$

$$184\mathrm{.}23$ per unit

$$211\mathrm{.}86$ per unit

$$193\mathrm{.}44$ per unit

$$230\mathrm{.}29$ per unit