Natural Fragrance, Inc., began operations on January 1, 2012. The company produc

Question

Natural Fragrance, Inc., began operations on January 1, 2012. The company produces a hand and body lotion in an eight-ounce bottle called Eternal Beauty. The lotion is sold wholesale in 12-bottle cases for $80 per case. There is a selling commission of $16 per case. The January direct materials, direct labor, and factory overhead costs are as follows:

Part A - Break-Even Analysis

Instructions:

1. Determine the fixed and variable portion of the utility cost using the high-low method. Round the per unit cost to the nearest cent.

2. Determine the contribution margin per case. Enter your answer to the nearest cent. For example, 89.458 would be entered as 89.46

Contribution margin per case: $

3. Determine the fixed costs per month, including the utility fixed cost from part (1). Enter your answers to the nearest whole number. For example, 89.45 would be entered as 89 and 89.56 would be entered as 90.

4. Determine the break-even number of cases per month. Round your answer to the nearest whole number.
cases

Explanation / Answer

Here's how hi-low method works. It's easier to understand if you know an answer and can look at it worked backwards. You're always picking out the highest production and the lowest production to make a comparison. You can ignore the rest. So let's just make up two production levels and some costs, using simple numbers.

The two production levels will be 10 units and 15 units. Fixed costs are $25. Variable costs are $1 per unit.

10 units = $25 + variable costs
15 units = $25 + variable costs

10 units = $25 + (10 units x $1)
15 units = $25 + (15 units x $1)

10 units = $25 + $10 = $35 total
15 units = $25 + $15 = $40 total

You can see that the $25 doesn't change cause it's fixed. The difference in total costs was caused entirely by the variable costs. It went up $5. But also notice the entire variable costs is not $5. That's only the difference in costs.

Now, let's go backwards. You cannot see the portion in blue because you don't know that information. That's what you're trying to find out. So everything that follows is actually how you do the high-low. The preceeding was just to help show why it works and what's behind it.

We know the change in units is 5. And we know the change in cost is $5. So you take cost and divide by units: $5/5 units = $1 per unit.

Since only variable costs can cause that change, that has to be variable. So we now know our variable is $1 per unit. But this still would not tell us what portion of $35 and $40 is the variable.

So now we can take the variable cost that we know and multiply by units:
10 units x $1 variable = $10

Now we know $10 of the $35 (for 10 units) is variable. So $35 - 10 = $25 fixed. Whatever's left over must be fixed.

You only need to do that last step with one category, but you can prove it to yourself by doing the other one too:
15 units x $1 variable = $15
$40 total costs - $15 variable = $25 fixed

$25 fixed: same number and it "checks."

High-low can be a little difficult to understand at first, but with some practice is not that difficult.

Once you have that, you need to add in the fixed and variable for the utilities to your other costs. You need to make sure you don't add the entire $230 under the fixed overhead costs.

Break-even is fixed divided by contribution margin. The contribution margin sales price less variable costs, so it's what is "left over" for each unit after variable costs. You need that in order to cover the fixed costs. By dividing, you're figuring out how many units at that amount it will take in order to just cover the total fixed costs.

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