# Computing the break-even point

### Problem

The Lake Shore Inn is trying to determine its break-even point. The inn has 50 rooms that are rented at \$60 per night. Operating costs are as follows, in dollars

Salaries      7,200  per month
Utilities     1,500  per month
Depreciation  1,200  per month
Maintenance   300    per month
Maid Service  8      per room
Other Costs   28     per room


Determine the inn's break-even point in (1) number of rented rooms per month and (2) dollars.

### Progress

I know the general formulas:

• Break-even point in Units is obtained by dividing Fixed Costs by Contribution Margin per Unit. The latter is (Unit selling price - Unit Variable Costs)
• Break-even point in Dollars is obtained by dividing Fixed Costs by Contribution Margin Ratio. The latter is (Contribution Margin per Unit / Unit selling price).

However, I cannot figure out the Unit Variable costs. This is is why this problem is so hard for me, even with the formulas.

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I cannot figure out the Unit Variable costs that is why this problem has be so hard for me, even with the formulas. – Daniel Loisi Mar 7 '11 at 4:03
Please state your question in the body, not a comment. Since you are asking a question, it is only polite for you to ask, rather than post in the imperative mode. – Arturo Magidin Mar 7 '11 at 4:09
The unit variable cost would appear to be the extra cost you incur for each rented room. If you rent a room, you take in 60 dollars, but then you must spend, in addition to your fixed costs, 8 in maid service and 28 in "other costs", so you don't really get the entire 60 dollars free and clear, but rather only 60 - (8+28) = 24 dollars free and clear. – Arturo Magidin Mar 7 '11 at 4:28
@Arturo: still one extra zero early in the post. But I liked your answer. – Ross Millikan Mar 7 '11 at 4:30

## 1 Answer

Hint: Unit Variable costs are the costs that increase depending on the number of units that are rented, while the costs per month are fixed. The basic idea is that you spend a certain number of dollars to stay open (taxes, mortgage, desk staff) and there are costs that increase per room rented (cleaning rooms). So what would the Contribution Margin per Unit be? It is defined in the first formula.

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