By subtracting total costs from revenue, we obtain Yin-Yang’s profit graph. This gives us the standard profit equation — Yin-Yang Yogurt Shoppe serves best chocolate-vanilla

The Yin-Yang Yogurt Shoppe serves the best chocolate-vanilla frozen yogurt in the city. Each cup of yogurt sells for $4, with variable costs amounting to $2 per cup. Yin-Yang’s fixed costs equal $3,000 per month.

Required:

a. Graph Yin-Yang Yogurt Shoppe’s total costs as a function of the number of cups of yogurt sold (going from 0 to 2,500 cups of yogurt in increments of 500 cups). What does the y-intercept (i.e., the point where the total cost line crosses the y-axis) represent? What does the slope of the total cost line represent?

b. Add a plot of the Yin-Yang Yogurt Shoppe’s total revenue (as a function of the number of cups of yogurt sold) to your graph from part (a). Identify the breakeven point in your graph. Identify the profit and loss areas.

c. Construct a profit graph for the Yin-Yang Yogurt Shoppe. Form a single line that depicts Yin-Yang’s profit as a function of the number of cups of yogurt sold. What does the intercept of the profit line represent? What does the slope of the profit line represent? How do you interpret the point at which the profit line crosses the horizontal (i.e., x) axis? Identify the profit and loss areas.

d. Suppose Yin-Yang pays taxes at the rate of 40% of profit. How does this affect the profit line?

e. (Advanced) Assume you do not have unit-level data; in other words, assume you only know that Yin Yang’s monthly fixed costs equal $3,000 and that its contribution margin ratio is 50% (you gather this information from Yin Yang’s financial statements). Construct a profit graph that allows you to identify Yin Yang’s breakeven point and profit and loss areas.

SOLUTION

The “vanilla” cost graph would have units (in this case, cups of yogurt) on the x-axis and dollars (total costs) on the y-axis. With regard to the total cost line, the intercept, $3,000, represents Yin-Yang’s monthly fixed costs and the slope, $2, represents Yin-Yang’s variable cost per cup of yogurt. The following graph depicts Yin-Yang’s total costs as a function of the number of cups of yogurt sold:

We can readily add Yin-Yang’s revenue line to our previously-constructed cost graph. The revenue line will start at the origin (after all, if we sell 0 cups we have $0 in revenue) with a slope of $4, representing the price per cup of yogurt. The point where the revenue line crosses the total cost line is the breakeven point. We can drop a line down to the x-axis to read off the required unit sales. We can drop a line to the y-axis to determine the required revenue.

If the revenue line is above the total cost line, Yin-Yang will earn a profit. Conversely, if the revenue line is below the total cost line, Yin-Yang will incur a loss. All of these relationships are depicted on the following graph:

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By subtracting total costs from revenue, we obtain Yin-Yang’s profit graph. This gives us the standard profit equation:

Profit before taxes = (Price – unit variable cost) Quantity – Fixed costs.

For Yin-Yang, we have:

Profit before taxes = $2 Number of cups of yogurt sold – $3,000.

This line is depicted on the following graph.

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The point where the profit line crosses the y-axis represents the net profit when zero cups of yogurt are sold. That is, revenues, variable costs, and contribution margin are all zero. Thus, profit at zero cups of yogurt = –fixed costs = –$3,000.

The slope of the profit line = the unit contribution margin; in Yin-Yang’s case, this is $4 - $2 = $2. The point where the profit line crosses the x-axis represents the breakeven point, or the point at which profit = $0. The profit and loss areas can be identified by the profit line’s position relative to the x-axis. If the profit line is above the x-axis, Yin-Yang earns a positive profit. Conversely, if the profit line is below the x-axis, Yin-Yang will incur a loss.

Yin-Yang’s revised profit graph is presented below. Notice the kink in the profit line because of the tax. The dotted line represents the original, untaxed profit, and the solid line represents the after tax profit. The two lines are the same below the breakeven point because no tax is due if the firm makes a loss. The after-tax profit line is below the pre-tax profit line when the firm makes a profit. The slope of the after tax line is smaller by the tax paid.

It is possible to construct a “revised” CVP graph without using data on units, as indicated below. In this case, we represent Yin-Yang’s profit as:

Profit before taxes = (.50 Revenue) – $3,000.

Notice that we are plotting a net contribution line in place of the revenue and total cost lines. The slope (or the steepness) of the contribution line is determined by the contribution margin ratio, which in this case is .50. Moreover, the higher the contribution margin ratio, the steeper the contribution line.