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 Blue Mouse Manufacturers:

Blue Mouse Manufacturers is considering a project that will have fixed costs of $$12,000,000.$ The product will be sold for $$32\mathrm{.}50$ per unit, and will incur a variable cost of $$12\mathrm{.}80$ per unit.

Given Blue Mouse's cost structure, it will have to sell units to break even on this project $(Q_{BE}).$

Blue Mouse'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 $200,000$ units. However, she also thinks that the demand for Blue Mouse'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 $200,000$ units, what price must it set to break even?

$$ $$87\mathrm{.}36$ per unit

$$72\mathrm{.}80$ per unit

$$69\mathrm{.}16$ per unit

$$80\mathrm{.}08$ per unit