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 Petrox Oil Co$.$:

Petrox Oil Co$.$ is considering a project that will have fixed costs of $$15,000,000.$ The product will be sold for $$41\mathrm{.}50$ per unit, and will

incur a variable cost of $$10\mathrm{.}75$ per unit.

Given Petrox's cost structure, it will have to sell

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

Petrox Oil Co$.\text{'}$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 $$20,000,000.$ In fact, she believes that the firm will be able to sell only about $200,000$ units. However, she also thinks the

demand for Petrox Oil Co$.\text{'}$s product is relatively inelastic, so the firm can increase the sale price. Assuming that the firm can sell $200,000$ units, what

price must it set to meet the CFO's EBIT goal of $$20,000,000?$

$$213\mathrm{.}61$ per unit

$$195\mathrm{.}04$ per unit

$$185\mathrm{.}75$ per unit

$$232\mathrm{.}19$ per unit