The minimum ticket price per person for the city to break even should be approximately $3.96.
How did we get the value?
To determine the minimum ticket price per person for the city to break even, we need to consider both the costs and the revenues associated with the softball complex.
The annual costs include:
1. Annual upkeep costs: $121,000
2. Annual utility costs: $12,000
3. Renovation costs: $47,000 every five years (we can calculate the annual cost by dividing this by 5, since renovations happen every 5 years)
The annual revenues include:
1. Annual team user fees (revenues): $34,000
Now, let's calculate the annual renovation cost:
Annual renovation cost = Renovation costs / Renovation cycle
= $47,000 / 5
= $9,400
Now, calculate the total annual cost:
Total Annual Cost = Annual upkeep costs + Annual utility costs + Annual renovation cost
= $121,000 + $12,000 + $9,400
= $142,400
Now, calculate the annual revenue:
Annual Revenue = Annual team user fees (revenues) * Number of visitors
= $34,000 * 36,000
= $1,224,000
Now, calculate the annual profit or loss:
Annual Profit or Loss = Annual Revenue - Total Annual Cost
= $1,224,000 - $142,400
= $1,081,600
Now, to break even, the annual profit or loss should be zero. Therefore, the total annual revenue should equal the total annual cost.
Let "P" be the ticket price per person. The total annual revenue is then given by:
Total Annual Revenue = Number of visitors * Ticket Price per person
= 36,000 * P
Setting this equal to the total annual cost:
36,000 * P = $142,400
Now, solve for P (ticket price per person):
P = $142,400 / 36,000
P = $3.9556
So, the minimum ticket price per person for the city to break even should be approximately $3.96.
Complete question:
A city has decided to build a softball complex, and the city council has already voted to fund the project at the level of $840,000 (initial capital investment). The city engineer has collected the following financial information for the complex project: - Annual upkeep costs: $121,000 - Annual utility costs: $12,000 - Renovation costs: $47,000 for every five years - Annual team user fees (revenues): $34,000 - Useful life: Infinite - Interest rate: 8% If the city can expect 36,000 visitors to the complex each year, what should be the minimum ticket price per person so that the city can break even?