What are the CVP graph and the profit graph?

In cost estimation, we represented linear costs with a straight line having the estimated fixed costs \(FC_p\) as intercept and the estimated unit variable cost \(V_c\) as slope (red line in the graph below). The CVP graph just adds a straight line representing the revenues. Its slope is the unit selling price \(P\) (and, if there were an intercept, there would also be committed fixed revenues like subscriptions; blue line in the graph below):

CVP graph

Figure 1: CVP graph

On this graph, total costs start greater than total revenues (the company makes a loss). The more the company sells, assuming it sells at a price higher than the unit variable cost (i.e. the slope of revenues is steeper than the slope of costs), the more the loss (which is the difference between revenues and costs) diminishes until it becomes null at the break-even point (which I discuss in greater detail later in this chapter). Beyond that point, Operating Income becomes positive and grows with volume.

As we discussed in the previous subsection, since revenues increase by the price \(P\) and costs increase by the unit variable cost \(V_c\) for every additional unit sold, Operating Income increases by the unit contribution margin \(UCM = P - V_c\) every time an additional unit is sold. It is therefore possible to synthesize the previous graph into a single profit graph:

Profit graph

Figure 2: Profit graph

On this graph, the initial loss is equal to the fixed costs, and the break-even point is where the profit (purple line) is 0, i.e. when the contribution margin generated by sales is equal to these fixed costs.

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