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 Ceres (or absorb any losses).
Based on the following revenue and cost information, the organizers would like answers to several questions.

1. There are three sources of revenue for the concert:
2. Tickets will be sold for $15.50 each.
3. A large multinational corporation headquartered in Chicago will donate $2.00 per ticket sold.
4. Each concert attendee is expected to spend an average of $17.00 for parking, food, and merchandise.
5. On the expense side, there are also three components:

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 $6.00 per ticket sold. 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. The organizers will pay the pavilion $85,000 plus $7.00 per person attending to cover its operating expenses (production, maintenance, advertising, etc.)

Required:
a. What is the estimated contribution margin per ticket sold for the benefit concert?
b. What are the estimated total fixed costs for the benefit concert?
c. What is the estimated profit from the benefit concert if 10,500 tickets are sold?
d. How many tickets must be sold in order for concert profit to be $100,000?
e. 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?
f. 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)?

Answer 1

Answer:

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

contribution margin per ticket = ($15.50 + $2 + $17) - ($6 + $2.55 + $7) = $34.50 - $15.55 = $18.95

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

total fixed costs = $21,000 + $85,000 = $106,000

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

estimated profit = (10,500 x $18.95) - $106,000 = $92,975

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

number of tickets sold = ($106,000 + $100,000) / $18.95 = 10,870.71 ≈ 10,871 tickets sold

e. 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?

$100,000 / (1 - 31%) = $144,927.54

number of tickets sold = ($106,000 + $144,927.54) / $18.95 = 13,241.56 ≈ 13,241.56 tickets sold

f. 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)?

contribution margin increases to $18.95 + $7 = $25.95

10,500 = ($21,000 + $100,000 + ?) / $25.95

$272,475 = $121,000 + ?

? = $151,475

you can pay up to $151,475 in fixed expenses to the pavilion