## Target Profit Analysis

### Learning Outcomes

• Define target profit analysis and use it to make sales volume calculations

Minnesota Kayak has a few investors who are interested in getting a return on their investment.  They have talked with your supervisor, and between them all, would like to get $30,000 a month in profit to divide between them. You have been tasked with figuring out how many kayaks need to be sold in order to get the investors their return! Target profit analysis helps us to know how much in dollar sales a company will need to reach a certain profit point. This is one of the key uses of the CVP analysis. Once the basic data is calculated, it can offer a great deal of insight and help in planning. Minnesota Kayak Company needs to sell 28 kayaks in our example to break even. The equation method or the formula method can be used with the same result. Remember the formula method is simply a shortened version of the equation method, so both ways should come to the same conclusion. With the previous information you can then figure out, the dollar sales needed to break even: $28\text{ kayaks}\times\500\text{ per kayak}=\14,000\text{ in sales}$ What if they now want to show a$30,000 a month profit?

So with that information we now have the following:

 Price per kayak $500 variable costs per kayak$225 Contribution margin per kayak $275 Fixed costs/month$7,700

With this information, how many kayaks do we need to sell to show a $30,000 profit at the end of the month? It is the same exact formula we used to calculate the break-even point! Remember, we put -0- for the profit in when we were looking to break-even. We simply replace the -0- with$30,000 and now we can calculate how many kayaks we need to sell to meet our profit goal. Pretty neat huh?

Using the equation method:

$\begin{array}{rcl}\text{Profit}&=&\text{Unit CM}\times\text{Q}-\text{Fixed Expense}\\\30,000&=&\275\times\text{Q}-\7,700\\\30,000+\7,700&=&\275\times\text{Q}\\\dfrac{\37,700}{275}&=&\text{Q}\end{array}$

So we now need to sell 138 kayaks to profit $30,000! How much in sales do we need? 138 ×$500 each= $69,000 in sales. Note: Whenever you are doing break-even or target profit analysis, you should round units up. If you used your calculator to divide$37,700 by 275, you would have gotten 137.090909. Why did we round up to 138 kayaks? Well, you can’t sell only 0.09 of a kayak, so you will either sell 137 or 138. If you round down to 137 units and then plug it into the formula to calculate profit, then your profit only ends up being $29,975 – just short of our$30,000 target profit we stated. So we have to round up to 138 kayaks to meet our target profit (and in this case, slightly exceed, as selling 138 kayaks leads to a profit of $30,250). How would we get there using the formula method? $\text{Unit Sales to attain the target profit}=\dfrac{\text{Target Profit}+\text{Fixed expenses}}{\text{Unit CM}}$ So in our kayak case $\begin{array}{rcl}\text{Unit sales needed}&=&\dfrac{\30,000+\7,700}{\275}\\&=&\dfrac{\37,700}{\275}\end{array}$ So again, we need 138 kayaks sold to make a$30,000 profit!

138 kayaks × $500 selling price per kayak =$69,000 in sales.

We can now plug in any amount of desired profit and calculate how many units we need to sell! This is amazing information for business owners and managers to have available. But see the importance of good numbers for your fixed and variable costs? Keep in mind how much a small difference in costs can affect our profit!