Question

Plainview Arts Center is planning a fundraising dinner.
The event will be held in a city park. The city will charge $1,000 for use of the space, and private
security will be hired for $400. $1,500 will be spent on advertising. A local band will be hired. The
band will be paid $600 plus 12% of ticket sales.
Dinner will be catered buffet style, and will cost $25/person (gratuities optional for guests).
Ticket price will be $90.
Required:
a) How many tickets must be sold to break even?
b) What will be the profit if 120 tickets are sold?
c) An alternative plan has been proposed, to hold a banquet style dinner at a good hotel.
Ticket price would be $150. The hotel would provide the banquet at a costs of $60/guest, plus
mandatory 20% gratuity. There would be no rent or security costs, and advertsing cost
would remain the same. There would be no band; instead, a local television celebrity would
be hired for $2,200 to serve as master of ceremonies. If this plan were adopted, how many tickets
would have to be sold to earn the same profit as computed in (b) above?

Answer 1

Answer (a):

Ticket price = $90

Variable cost = Buffet cost per person + Variable component cost paid to band

= 25 + 12% * 90

= $35.80

Contribution margin per ticket sold = 90 - 35.80 = $54.20

Fixed cost = cost for use of space + Private security charges + Advertising cost + Fixed cost component of band cost

= 1000 + 400 + 1500 + 600

= $3,500

Number of tickets required to be sold to break-even = Fixed cost / Contribution margin per ticket sold = 3500 / 54.20 = 64.58 or 65 (rounded off)

Number of tickets required to be sold to break-even = 65

Answer (b):

Profit if 120 tickets are sold = Contribution margin per ticket * Number of tickets - Fixed cost

= 54.20 * 120 - 3500

=$3,004

Profit if 120 tickets are sold = $3,004

Answer (c):

Ticket price = $150

Variable cost = Buffet cost per person with gratuity = 60 + 60 *20% = $72

Contribution margin per ticket sold = 150 - 72 = $78

Fixed cost = Advertising cost + hiring charges of television celebrity = 1500 + 2200 = $3,700

Tickets required to be sold to earn $3004 profit = (3700 + 3004) / 78 = 85.95 or 86 units

Tickets would have to be sold to earn the same profit as computed in (b) = 86