Question

Rocky Mountain Waterpark sells half of its tickets for the regular price of $75. The other half go to senior citizens and children for the discounted price of $35. Variable cost per guest is $15 for both groups , and fixed costs total $60,000 per month. What is Rocky Mountain's breakeven point in total guests? Regular guests? Discount guests?

Answer 1

The Rocky Mountain Waterpark's break-even point in total guests is 1500, with 750 regular guests and 750 discount guests needed to cover fixed and variable costs.

Step-by-step explanation:

The Rocky Mountain Waterpark break-even point analysis requires understanding the costs involved and how many tickets need to be sold to cover those costs. The waterpark must determine the number of regular and discount tickets that need to be sold to reach their break-even point. Since the fixed costs are $60,000 and the variable costs are $15 per guest for both regular and discount tickets, we can calculate the break-even point using the contribution margin approach.

First, calculate the contribution margin per ticket for both regular and discount tickets:
Contribution margin per regular ticket = Regular ticket price - Variable cost per regular ticket
Contribution margin per discount ticket = Discount ticket price - Variable cost per discount ticket

For regular tickets: Contribution margin per regular ticket = $75 - $15 = $60
For discount tickets: Contribution margin per discount ticket = $35 - $15 = $20

Now we can find the break-even point in total guests by using the following formula:
Break-even point in guests = Fixed costs / Average contribution margin per ticket

Since half of the tickets are sold at regular price and half at a discount price, the average contribution margin needs to be calculated. Let's assume we will sell X number of total tickets, then X/2 tickets would be sold at regular price and X/2 at a discounted price. The total contribution from these sales would be (X/2 * $60) + (X/2 * $20).

Therefore, the average contribution margin per ticket is [(X/2 * $60) + (X/2 * $20)] / X. Simplifying this gives us an average contribution margin of ($60 + $20) / 2 = $40.

With this information, the break-even point in total guests would be $60,000 / $40 = 1500 guests.

Since we know that half of the guests are regular and half are discount guests, the break-even point for regular guests is 1500 / 2 = 750 regular guests, and the same for discount guests.

Answer 2

Break even in total guests is 1500 guests.

Break even in Regular guests is 750 guests.

Break even in Discount guests is 750 guests.

Step-by-step explanation:

Break even in units is the total number of units where the total revenue equals total cost. The formula for break even in units is,

Break even in units = Fixed costs / Contribution margin per unit

a.

To calculate the composite break even point or a common break even point when there are more than one product, we use weighted average contribution per unit.

Weighted average contribution per unit = Contribution per unit of Product A * Weight of product A in sales mix + Contribution per unit of product B * Weight of Product B is sales mix

Weighted average contribution margin per unit = (75 - 15) * 0.5 + (35 - 15) * 0.5 = 40 per unit

Break even in total guests = 60000 / 40 = 1500 units/guests

Break even per product = Total break even in units * weight of product in sales mix

Break even in Regular guests = 1500 * 0.5 = 750 units

Break even in Discounted guests = 1500 * 0.5 = 750 units