# How do you compute the volume or revenue at target profit?

The target profit analysis allows managers to determine the number of units or the total sales revenues needed to earn a desired Operating Income, ideally one which is sufficient to pay taxes and still remunerate investors properly. Here, we can go relatively quickly: the target profit is a break-even where the desired profit is treated as a fixed cost to be covered by the contribution margin; alternatively, the break-even is a target profit where the desired profit is null (break-even analysis is therefore a special case of target profit analysis where target profit is equal to zero). This means that we just need a slight alteration of previous formulas:

\begin{aligned} OI_{tp} & = Q_{tp} \times UCM - FC_p \\ FC_p + OI_{tp} & = Q_{tp} \times UCM \\ \frac{FC_p + OI_{tp}}{UCM} & = Q_{tp} \\ & \leftrightarrow \\ Q_{tp} & = \frac{FC_p + OI_{tp}}{UCM} \end{aligned}

where $$Q_{tp}$$ is the volume at target profit and $$OI_{tp}$$ is the desired level of profit. Moreover:

\begin{aligned} OI_{tp} & = R_{tp} \times CMR - FC_p \\ FC_p + OI_{tp} & = R_{tp} \times CMR \\ \frac{FC_p + OI_{tp}}{CMR} & = R_{tp} \\ & \leftrightarrow \\ R_{tp} & = \frac{FC_p + OI_{tp}}{CMR} \end{aligned}

where $$R_{tp}$$ is the total revenues at target profit. That’s it! In the following video, I just compare the different approaches for computing breakeven and target profit points.

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