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.

There are three sources of revenue for the concert:

1. Tickets will be sold for $16.00 each.
2. A large multinational corporation headquartered in Chicago will donate $2.00 per ticket sold.
3. Each concert attendee is expected to spend an average of $19.00 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 $23,000 plus 13% of all parking, food, and merchandise revenue.
3. The organizers will pay the pavilion $90,000 plus $6.00 per ticket sold to cover its operating expenses (production, maintenance, advertising, etc.)

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 $90,000?

Assume that the organizers can negotiate the fixed portion of the pavilion's operating expenses. If the organizers expect to sell 9,000 tickets, how much operating fixed costs can they afford to pay and still earn a profit of $90,000 (ignore taxes)?

Answer 1

Requirement 1: Compute sales revenue to earn after-tax profit of $90,000 as follows

Sales revenue = (Total fixed costs + Before tax target profit) ÷ Contribution margin ratio

                        = ($113,000 + ($90,000 ÷ (1 − 31%))) ÷ 62.24%

                        = ($113,000 + $130,435) ÷ 62.24%

                        = $391,102

Requirement 2: Compute maximum operating fixed costs as follows

Maximum fixed costs = (Number of tickets × Contribution margin per ticket) – Profit

                                    = (9,000 × $23.03) − $90,000

                                    = $117,270

Particulars	Amount	Amount
Revenue for the concert per ticket
Ticket revenue	$16.00
Donations	$2.00
Food, parking and merchandise	$19.00
Total revenue per ticket (a)		$37.00
Less: Variable cost per ticket
Performance fee	$5.50
Food and Parking and Merchandise (19 × 13%)	$2.47
Pavilion rent	$6.00
Total variable costs		$13.97
Contribution margin per ticket sold (b)		$23.03
Contribution margin ratio (b) ÷ (a)		62.24%
Fixed costs
Food, parking and merchandise	$23,000
Pavilion rent	$90,000
Total fixed costs		$113,000