Question

The town of Draper, with a population of 20,000, sits adjacent to State University, which has an enrollment of 27,000 students. Downtown Draper merchants have long complained about the lack of parking available to their customers. This is one primary reason for the steady migration of downtown businesses to a mall several miles outside town. The local chamber of commerce has finally convinced the town council to consider the construction of a new multilevel indoor parking facility downtown. Kelly Mattingly, the town’s public works director, has developed plans for a facility that would cost $4.5 million to construct. To pay for the project, the town would sell municipal bonds with a duration of 30 years at 8% interest. Kelly also estimates that five employees would be required to operate the lot on a daily basis, at a total annual cost of $140,000. It is estimated that each car that enters the lot would park for an average of 2.5 hours and pay an average fee of $3.20. Further, it is estimated that each car that parks in the lot would (on average) cost the town $0.60 in annual maintenance for cleaning and repairs to the facility. Most of the downtown businesses (which include a number of restaurants) are open 7 days per week.
Required:
a. Using break-even analysis, determine the number of cars that would have to park in the lot on an annual basis to pay off the project in the 30-year time frame.
b. From the results in (A), determine the approximate number of cars that would have to park in the lot on a daily basis. Does this seem to be a reasonable number to achieve, given the size of the town and college population?

Answer 1

Answer: See explanation

Explanation:

a. Let the break even sales be represented by x.

Firstly, we will calculate the total fixed cost which will be:

Investment = $4.5million/30 = $150,000

Add: Annual labor cost = $140,000

Add: Interest = 8% × $4.5million = $360,000

Total Fixed cost = $650000

The total variable cost will be: = 0.60 × x = 0.60x

Therefore, total cost:

= fixed cost + variable cost

= 650000 + 0.60x

Total revenue = Selling price × sales

= 3.20 × x = 3.20x

Break even point will now be:

Total revenue = Total cost

3.20x = 650000 + 0.60x

3.20x - 0.60x = 650000

2.60x = 650000

x = 650000/2.60

x = 250000

Therefore, number of cars that would have to park in the lot on an annual basis to pay off the project is 250000.

b. The approximate number of cars that would have to park in the lot on a daily basis will be:

= 250000/365 days

= 684.91

=685 cars