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 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 the non-profit (or absorb any losses).

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

There are three sources of revenue for the concert:

1. Tickets will be sold for $14.00 each.
2. A large multinational corporation headquartered in Chicago will donate $2.50 per ticket sold.
3. Each concert attendee is expected to spend an average of $17.00 for parking, food, and merchandise.

On the expense side, there are also three components:

1. A popular national group has agreed to perform at the concert. Normally, the group demands a significant fixed fee to perform, but to reduce the risk for the organizers, the group has agreed to perform for $5.50 per ticket sold.
2. The organizers will pay several companies to operate the parking, food, and merchandise concessions. They will pay $21,000 plus 15% of all parking, food, and merchandise revenue.
3. The organizers will pay the pavilion $95,000 plus $7.00 per ticket sold to cover its operating expenses (production, maintenance, advertising, etc.).

Part A (8 tries; 8 points)
1. What is the estimated contribution margin per ticket sold for the benefit concert (rounded to two decimal places)?   
2. What are the estimated total fixed costs for the benefit concert?   

Part B (8 tries; 8 points)
1. What is the estimated profit from the benefit concert if 10,000 tickets are sold?   
2. How many tickets must be sold in order for concert profit to be $100,000?   
3. Assuming a tax rate of 37% on profits from the concert, what must dollar ticket sales be in order for after-tax concert profits to be $100,000?

Part C (4 tries; 4 points)
1. Assume that the organizers can negotiate the fixed portion of the pavilion's operating expenses. If the organizers expect to sell 10,000 tickets, how much operating fixed costs can they afford to pay and still earn a profit of $100,000 (ignore taxes)?

Answer 1

Solution

Pritzker Music Pavilion

Part A

1. Determination of the estimated contribution margin per ticket sold for the benefit concert:

Contribution margin -
Price of ticket	$14
Donation per ticket	$2.50
Parking, Food and Merchandise	$17
Revenue per ticket	$33.50
Direct costs per ticket:
performance fee	$5.50
Parking, Food and Merchandise	$2.55
Pavilion expenses	$7
total direct expenses	$15.05
Contribution margin -	$18.45

2. Estimated total fixed cost for the benefit concert –

Parking, food and merchandise    $21,000

Pavilion operating expenses         $95,000

Total fixed cost                             $116,000

Part B –

1. Determination of the estimated profit from the benefit concert if 10,000 tickets are sold:

Contribution margin per ticket sold = $18.45

Number of tickets sold = 10,000

Ticket revenue = $18.45 x 10,000 = $184,500

Less: Fixed expenses        $116,000

Estimated Profit                $68,500

2. Determination of the number of tickets to be sold in order for the concert profit to be $100,000:

Desired number of tickets = (fixed cost + target profit)/Contribution margin per ticket

Fixed cost = $116,000

Target profit = $100,000

Contribution margin per ticket = $18.45

Desired number of tickets = (116,000 + 100,000)/18.45 = 11,707

Hence, the benefit concert should sell 11,707 to earn a target profit of $100,000.

3. Assuming tax rate – 37% on profits, determination of the dollar ticket sales to earn after-tax concert profit of $100,000:

After tax profit = $100,000

Tax rate = 37%

After tax rate = 100 -37 = 63%

Profit before tax = $100,000/63% = $158,730

Dollar ticket sales = (fixed cost + after tax profit)/CM ratio

CM ratio = CM/revenue

= $18.45/$33.50 = 55.1%

Dollar ticket sales = ($116,000 + $158,730)/55.10% = $498,603

Part C –

Determination of negotiable operating fixed costs to earn a target profit of $100,000 by selling 10,000 tickets:

Contribution margin from sale of 10,000 tickets = $18.45 x 10,000 = $184,500

Target profit = $100,000

Fixed expenses –

Parking, food and merchandise = $21,000

Pavilion operating expenses - ?

Substituting the values for the formula to computed the desired number of tickets –

10,000 = (pavilion operating expenses + $21,000 + $100,000)/$18.45

$184,500 = pavilion operating expenses + $121,000

Pavilion operating expenses = 184,500 – 121,000 = $63,500

Hence, negotiable fixed portion of the pavilion’s operating expenses = $63,500