# 1\$ of extra fixed costs = 1\$ of extra sales?

A silly thought, “Does one dollar of extra fixed costs needs one extra dollar of sales to recover it?”

A logical answer is “one dollar“.  What if I would tell you that by far this is not true? What????  I am dump?

### A Very Interesting Use of Contribution Margin (CM)

#### What is Contribution Margin (CM)?

Contribution Margin (CM) is a very valuable financial tool in variable costing.  It’s highly used in menu engineering but it can also give answers to several other interesting financial areas.  One of them relates to the question raised above regarding the impact of fixed cost increases on sales and profits.

Let’s see how we can get a clear and accurate answer to the above question and how it can be used by hoteliers and restaurateurs.

#### How does contribution margin work?

Contribution Margin is the selling price of a product minus its variable costs.  Let’s say that a burger’s selling price is \$5 and all its variable costs (food, wages and other) are \$3.  Then its CM is \$2.

Therefore, we can sum up figures regarding ‘Burger’s CM’with 100 burgers sold in the following table 1:

 Per burger 100 burgers sold % of sales Selling price \$5.00 \$500.00 100.00% Less: Total variable costs -\$3.00 -\$300.00 -60.00% Contribution Margin (CM) \$2.00 \$200.00 40.00% Fixed costs -\$1.00 -\$100.00 -20.00% Operating Profit (Before Tax) \$1.00 \$100.00 20.00%

We can see on table 1 above that the contribution margin of the burger is \$2 which is 40% of burger sales.  This figure shows that at a selling price of \$5 and a quantity 100 burgers sold, there are left \$200 to cover fixed expenses of \$100 and also for an operating profit (before income tax) of \$100.

### Why 1\$ of extra fixed costs ≠ 1\$ of extra sales?

One of the answers CM can provide is how much extra sales a business needs to make in order to cover each \$ increase in its fixed costs.  A logical answer would be “an equivalent amount of dollars”.  This answer by far it is not true.  This happens because as sales increase by \$1, automatically its variable costs increase since they behave in the same manner as sales .  This entails that the business needs first, to cover the increase in its relevant variable expenses and secondly, any increase in its fixed costs.

#### What is the correct answer?

One of the uses of contribution margin can help us answer this question.  Looking at table 1 we can see that CM % is 40% (0.40).

The assumptions we make here are that selling price and required profit remain the same.

##### Approach 1

In order to find the amount of extra sales we need to make in order to offset exactly the \$1 increase in FC we need to do the following simple calculation.  We divide the \$1 increase by the contribution margin % and we get the right answer.  Thus, we have \$1/0.40=\$2.5.  Therefore, we need \$2.50 of extra sales in order to cover a \$1 increase in fixed costs.

##### Approach 2

Another method to calculate the same value is based on the formula used in Cost-Volume-Profit analysis (C-V-P).

Required new \$ sales = (Old fixed costs + new fixed costs + required profit)

(CM%)

Let’s say that fixed costs from table 1 increase by \$10.

(\$100+ \$10 + \$100)=    \$210 = \$525 required sales.

(CM%)                   (0.40)

So we can see that in order to cover the \$10 increase in fixed costs we need to generate more sales of \$25 which is 2.5 times higher than the increase in fixed costs.

Thus, the restaurant needs to sell 5 more burgers in order to recover the extra fixed costs. Table 2 below shows clearly the new expected operating outcomes.

Another interesting element is that the proportion of fixed costs and operating profit in relation to sales have now changed to 20.95% and 19.05% respectively.

Table 2

 Per burger % of sales 105 Burgers sold Selling price \$5.00 100.00% \$525.00 Less: Total variable costs -\$3.00 -60.00% -\$315.00 Contribution Margin (CM) \$2.00 40.00% \$210.00 Fixed costs -\$1.10 -20.95% -\$110.00 Operating Profit (Before Tax) \$0.90 19.05% \$100.00

#### Hotel example

Imagine a hotel with the following operating performance in table 3:

 Average Daily Room Rate (ADR) = \$120, Variable Costs at 40% of sales % of sales Room sales \$120,000.00 100.00% Less: Total variable costs -\$48,000.00 -40.00% Contribution Margin (CM) \$72,000.00 60.00% Fixed costs -\$24,000.00 -20.00% Operating Profit (Before Tax) \$48,000.00 40.00%

In case that you decide to hire more people or give raises to staff and this decision will increase salaries by \$5000 annually, sales must increase by (\$5000/0.60) = \$8333 (1.67 times more) in order for the hotel owner to maintain the same profit level.

These \$8333 extra sales means that the hotel needs to sell approximately 69 more rooms (\$8333/120) in order to maintain the same profit level.

## Conclusion

Contribution margin is a very interesting financial figure with multiple uses for restaurateurs and hoteliers.  Hospitality business owners and managers can easily determine the importance of controlling their fixed expenses since they may affect significantly profitability.  In addition, they can be much more cautious in situations they need to make decisions that will increase their fixed costs.  Employees could be more responsible as well, If they knew the impact of wasting food and other material on the business.

Do you find the use of contribution margin interesting?

What does happen if the selling price and/or profit change?

How do I calculate the required \$sales for Operating Profit After Taxes?