Determining Profitability

[joshuasafwattaylor]

Hi you guys I have a Business math-related question that I got wrong for class I got a 01/200 points so I assume I was nowhere near the correct answer. Please help me with the solution. I will post the question and the solution that I had that was incorrect. Thank you so much!!

Question:
Use the information covered this week to complete this assignment.
Leaders of a small Disney World Hotel Resort are trying to assess when their hotel will become profitable. They want to make sure that they have priced their rooms properly. Provided is the cost analysis for the resort:

• Total fixed cost per month for the hotel is (electricity, phone bill, room service) $2,000.
• Total variable cost for each room (guest supplies, breakfast F&B, etc.) is $ 60.
• Room’s sales rate is $185.

Using the cost analysis report numbers from the above scenario, answer the following questions and verify your answer(s) by providing your calculations:

• How many rooms (round-up to the nearest room) need to be occupied to make the hotel start to generate a positive cash flow (i.e., profitable)?
• If the hotel has 10 occupied rooms for the month of July, would it be profitable? If not, what should you recommend to the leaders?

My solution that my professor marked incorrect:
5.2 Determining Profitability.

Fixed costs: $2000/(185-60)
We have our fixed cost of two thousand dollars and we need to divide by our contribution margin of 185-60 =$125.
When we complete the calculation, we find that we need to do a total of $6250.
$6250 in sales is 34 rooms sold. $6250 in sales ate $185 is 34 rooms sold.
This is our breakeven point. So to have a positive cash flow we need to sale at least 35 rooms
If a hotel has 10 rooms sold then it is operating in the red. I would suggest that management try to lower the cost of is fixed costs. Get a cheaper phone and internet plan, Make sure that rooms that are not occupied do not waste electricity. They may also need to focus on some sales tactics such as group sales.

 

[Cubist]

When you round up 34 the answer is 34 not 35. If you were rounding up thirty four point something then the answer would be 35. For example rounding up any of 34.8, 34.5, 34.2 OR 34.00001 all give 35. But note that 34.0 rounded up is still 34, because 34.0=34.

You can quickly check your break-even room occupancy calculation by doing the following. If 34 rooms are occupied:-

the hotel's income is 34*185 = 6290
the hotel's costs are 34*60 + 2000 = 4040
profit = income - costs = 6290 - 4040 = 2250

This is a very large profit, and is obviously quite far beyond the break even point. So, can you see where you went wrong? If not then please post back showing how you calculated the $6250 figure...

When we complete the calculation, we find that we need to do a total of $6250

 

[HallsofIvy]

No, he didn't "round up". 34 rooms is the "break even point" where there would be no loss and no profit. The question asked for the smallest number of rooms that will give a positive profit. That would be 35 rooms.

 

[JeffM]

Cubist is correct your solution is way too high.

The breakeven point is

[MATH]185x = 2000 + 60x \implies x = \dfrac{2000}{185 - 60} = 16.[/MATH]
ALWAYS CHECK YOUR WORK.

[MATH]2000 + 60 * 16 = 2000 + 960 = 2960.[/MATH]
[MATH]185 * 16 = 2960. \ \checkmark[/MATH]
The answer to the question then is 1 + 16 = 17.