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 $800,000 (initial capital investment). The city engineer has collected the following financial information for the complex project: Annual upkeep costs: $120,000 Annual utility costs: $13,000 Renovation costs: $50,000 for every five years Annual team user fees (revenues): $32,000 Useful life: Infinite Interest rate: 8% If the city can expect 40,000 visitors to the complex each year, what should be the minimum ticket price per person so that the city can break even

Answer 1

To determine the minimum ticket price per person for the city to break even, calculate the annual costs and revenues. Using the formula Break-even Price = (Annual Costs - Annual Revenues) / Number of Visitors, the minimum ticket price per person should be $2.78.

Step-by-step explanation:

To determine the minimum ticket price per person for the city to break even, we need to calculate the annual costs and revenues. The annual costs include upkeep costs, utility costs, and renovation costs. The annual revenues are the team user fees. We can calculate the break-even point by dividing the total annual costs by the number of visitors. The formula is: Break-even Price = (Annual Costs - Annual Revenues) / Number of Visitors. Let's calculate it:

Annual Costs = Annual Upkeep Costs + Annual Utility Costs + (Renovation Costs / 5)

Annual Revenues = Annual Team User Fees

Break-even Price = (Annual Costs - Annual Revenues) / Number of Visitors

Plugging in the values: Annual Upkeep Costs = $120,000, Annual Utility Costs = $13,000, Renovation Costs = $50,000, Annual Team User Fees = $32,000, Number of Visitors = 40,000

Annual Costs = $120,000 + $13,000 + ($50,000 / 5) = $120,000 + $13,000 + $10,000 = $143,000

Annual Revenues = $32,000

Break-even Price = ($143,000 - $32,000) / 40,000 = $111,000 / 40,000 = $2.78

Therefore, the minimum ticket price per person should be $2.78 for the city to break even.

Answer 2

To break even, the minimum ticket price per person for the softball complex should be $4.60.

Step-by-step explanation:

To calculate the minimum ticket price per person that would allow the city to break even, we need to consider the annual costs and revenues associated with the softball complex. The annual costs include upkeep costs, utility costs, and renovation costs. The revenue comes from the annual team user fees.

Considering the infinite useful life of the complex, the present value of the annual costs can be calculated using the formula:

PV = C/(1 + r)^n

where PV is the present value, C is the annual cost, r is the interest rate, and n is the number of years. Therefore, the present value of the annual costs is:

PV = ($120,000 + $13,000 + $50,000/5)/(1 + 0.08/1)^1 + ($120,000 + $13,000 + $50,000/5)/(1 + 0.08/1)^2 + ... = $183,900

To break even, the minimum ticket price per person should be:

Ticket Price = Annual Costs / Number of Visitors = $183,900 / 40,000 = $4.60 per person.