# 3.0: Prelude to Cost-Volume-Profit Analysis

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As president of the Accounting Club, you are working on a fundraiser selling T-shirts on campus. You have gotten quotes from several suppliers ranging from $$\8$$ to $$\10$$ per shirt and now have to select a vendor. The prices vary based on whether the T-shirts have pockets, have long sleeves or short sleeves, and are printed on one side or both. You are confident that you can sell them for $$\15$$ each. However, the college charges clubs a $$\100$$ “student sale” fee, and your T-shirt sales must cover this cost and still net the club enough money to pay for your spring trip Figure $$\PageIndex{1}$$: Balancing Cost, Volume, and Profit. Managers employ cost-volume-profit (CVP) analysis to determine the sales level at which they break even or balance their revenue with their expenses. (credit: modification of “Balance Swing Equality” by “Mediamodifier”/Pixabay, CC0)

In addition, several of the vendors will give volume discounts—the more shirts you purchase, the less each shirt costs. In short, you need to know exactly which style of T-shirt, vendor, and quantity will allow you to reach your desired net income and cover your fixed expense of $$\100$$. You decide on a short-sleeve shirt with a pocket that costs $$\10$$ each and that you can sell for $$\15$$.

This $$\5$$ per shirt “gross profit” will first go toward covering the $$\100$$ student sale fee. That means you will have to sell $$20$$ shirts to pay the fee $$\left (\frac {\ 100}{ \ 5}=20 \text{ shirts} \right )$$. After selling the first $$20$$ shirts, the $$\5$$ profit will be available to start paying for the cost of the trip. Your faculty advisor has calculated that the trip will cost $$\125$$ per student, and you have $$6$$ people signed up for the trip. This means the sale will need to generate an additional $$\750$$ from the sale ($$6$$ students $$\times \ 125$$). At $$\5$$ per shirt you will need to sell $$150$$ shirts to cover the student costs $$\left (\frac {\750}{\5} \right )$$. So, you will need to sell a total of $$170$$ shirts: $$20$$ to cover your fixed cost of $$\100$$ and an additional $$150$$ to cover the student’s cost of the trip ($$\750$$). What you have just completed is a cost-volume-profit analysis. In this chapter, we will explore how managers can use this type of analysis to make a wide range of decisions about their business operations.