The Pritzker Music Pavilion in downtown Chicago is a technologically sophisticat

Question

The Pritzker Music Pavilion in downtown Chicago is a technologically sophisticated and uniquely designed performing arts venue that hosts live concerts attended by over half a million patrons a year.  A group of local organizers, led by a prominent local businesswoman, would like to use the pavilion for a concert to benefit Ceres, a non-profit, national network of investors and environmental organizations working with companies and investors to address sustainability challenges such as global climate change.  If the pavilion management agrees to host the concert, the organizers will donate all profits to Ceres (or absorb any losses).

Based on the following revenue and cost information, the organizers would like answers to several questions.

On the expense side, there are also three components:

Questions:

1. What is the estimated contribution margin per ticket sold for the benefit concert?  

2. What are the estimated total fixed costs for the benefit concert?

3. What is the estimated profit from the benefit concert if 10,500 tickets are sold?   

4. How many tickets must be sold in order for concert profit to be $100,000?   

5. Assuming a tax rate of 31% on profits from the concert, what must dollar ticket sales be in order for after-tax concert profits to be $100,000?

6. Assume that the organizers can negotiate the fixed payment for the pavilion's operating expenses.  If the organizers expect to sell 10,500 tickets, how much can they afford to pay and still earn a profit of $100,000 (ignore taxes)?

Explanation / Answer

1. Sales per ticket = 15.5+2+17 = 34.5

Variable expenses per ticket = 6+15%*17+7 = 15.55

So contribution margin per ticket = 34.5 - 15.55 = 18.95

2. Total fixed costs = 21000+85000 = 106,000

3. Profit = 10,500*contribution margin - fixed costs = 10,500*18.95-106,000 = 92,975

4. Profit before fixed costs = 100,000+106,000 = 206,000

So no of tickets sold = 206,000/contribution margin = 206,000/18.95 = 10,870.71, or rounding off to 10,871

5. Pre-tax profit = 100,000/(1-31%) = 144,927.5

Profit before fixed costs = 144,927.5+106,000 = 250,927.5

So no of tickets sold = 250,927.5/contribution margin = 250,927.5/18.95 = 13,241.56, or rounding off to 13,242

6. Contribution margin in dollars = 10,500*contribution margin = 10,500*18.95 = 198,975

To get profit of 100,000, total fixed cost should be 198,975-100,000 = 98,975

Out of this, the fixed cost for parking, food, merchandise = 21,000

So remaining fixed cost for pavilion = 98,975-21,000 = 77,975

Hope this helped ! Let me know in case of any queries.

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