The owner of a greenhouse and nursery is considering whether to spend $6,000 to acquire the licensing rights to grow a new variety of rosebush, which she could then sell for $6 each. The per-unit variable cost would be $3. How many rosebushes would she have to produce and sell in order to make a profit of $6,000?

The Cost, volume, and profit (CVP) analysis helps manager to evaluate capital projects. It is conducted by companies to determine how much of sales must be made to achieve break-even and target profits. This analysis works on several assumptions, these are:

- Selling price per unit is constant.

- Variable cost per unit is also constant.

- Fixed cost remains constant.

- The stocks produced will must be sold.

To conduct CVP analysis, a contribution income statement is prepared. This is a one of the internal reports prepared by management and the equation to it is as follows:

(SP * Quantity) - (VC * Quantity) = CM - Fixed Cost = Operating Income

where

SP = Selling price

VC = Variable cost

CM = Contribution margin

The above given equation can be used for break-even analysis. To do so, simply solve it for "Quantity". Likewise, it can also be used to determine how much units must be sold to achieve a desired/target profit. The focus here is to determine the quantity that must be sold to achieve a target profit of $6,000. Simply put the given information in the equation and find the quantity;

⇒ (6 * Quantity) - (3 * Quantity) - 6,000 = 6,000

OR Quantity (6 - 3) = 6,000 + 6,000

OR Quantity = 12,000 / 3

⇒ Quantity = 4,000.

So, 4,000 units must be sold to achieve a target profit of $6,000.