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 $$10,000,000.$ The product will be sold for $$32\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 $($QBE

$).$

Petrox$$s marketing and sales director doesn$$t think that the firm$$s market is big enough for the firm to break even. In fact, she believes that the firm will be able to sell only about $150,000$ units. However, she also thinks that the demand for Petrox$$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 $150,000$ units, what price must it set to break even?

$$77\mathrm{.}42$ per unit

$$92\mathrm{.}90$ per unit

$$73\mathrm{.}55$ per unit

$$85\mathrm{.}16$ 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.

Increase

Decrease

No Change

The firm$$s fixed costs increase.

The variable cost per unit decreases.

The firm$$s tax rate increases.

When fixed costs are high, a small decline in sales can lead to a decline in return on invested capital $($ROI$).$