Break$-$even analysis

To be profitable, a firm has 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 $$12\mathrm{.}80$ per unit.

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

units to break even on this project $($QBE$).$

Petrox's marketing and sales director doesn't think that the firm's market is big enough for the firm to break even. In fact, she believes that the firm

will be able to sell only about $175,000$ units. However, she also thinks that the demand for Petrox's product is relatively inelastic $($so the firm can

increase the sales price without significantly decreasing the volume of product sold$).$ Assuming that the firm can sell $175,000$ units, what price must it

set to break even?

$$98\mathrm{.}51$ per unit

$$93\mathrm{.}58$ per unit

$$118\mathrm{.}21$ per unit

$$108\mathrm{.}36$ per unit

What affects the firm's operating break$-$even point?

Several factors affect a firm's operating break$-$even point. Based on the scenarios described in the following table, indicate whether these factors

would increase, decrease, or leave unchanged a firm's break$-$even quantity$-$assuming that only the listed factor changes and all other relevant factors

remain constant.

The firm depreciates its fixed assets more quickly over a shorter life.

The variable cost per unit decreases.

The amount of debt increases, causing the firm's total interest expense to increase.