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The margin of safety of a hotel is currently 25 guests per month. Monthly fixed costs are $5000, variable costs per guest $25 and average price per room per night is $45. What will the new margin of safety be if the price per room is increased to $50 per night? (Assume the number of guests remains the same)

Question

The margin of safety of a hotel is currently 25 guests per month. Monthly fixed costs are 5000,variablecostsperguest5000, variable costs per guest 25 and average price per room per night is 45.Whatwillthenewmarginofsafetybeifthepriceperroomisincreasedto45. What will the new margin of safety be if the price per room is increased to 50 per night? (Assume the number of guests remains the same)

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Solution

To calculate the new margin of safety, we first need to determine the new contribution margin ratio. The contribution margin ratio is calculated by subtracting the variable cost per unit from the selling price per unit, and then dividing by the selling price per unit.

Step 1: Calculate the current contribution margin ratio = (Selling price per unit - Variable cost per unit) / Selling price per unit = (4545 - 25) / 45=45 = 20 / $45 = 0.44 (or 44%)

Step 2: Calculate the new contribution margin ratio with the increased price = (New selling price per unit - Variable cost per unit) / New selling price per unit = (5050 - 25) / 50=50 = 25 / $50 = 0.5 (or 50%)

Step 3: Calculate the new margin of safety The margin of safety is calculated by dividing the current margin of safety by the old contribution margin ratio, and then multiplying by the new contribution margin ratio. = (Current margin of safety / Old contribution margin ratio) * New contribution margin ratio = (25 / 0.44) * 0.5 = 28.41 guests

So, if the price per room is increased to $50 per night, the new margin of safety will be approximately 28 guests per month, assuming the number of guests remains the same.

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