$1)$ This homework should be completed manually $($use calculators but not computers$)$

$($you can use Excel or any other software of your choice for Problem $1$ part b$)$

$2)$ Please be specific in your computations by using the appropriate formulae

$3)$ Make sure to show your calculations

$4)$ State your decision clearly at the end of your solution

$1.(6$ pts$)$ Evergreen Fertilizer Company produces fertilizer. The company$$s fixed monthly cost is $$35,000,$ and its variable cost per pound of fertilizer is $$0\mathrm{.}5.$ Evergreen sells the fertilizer for $$0\mathrm{.}65$ per pound.

a$.$ Determine the monthly break$-$even volume for the company.

b$.$ Graphically illustrate the break$-$even volume for the Evergreen Fertilizer Company.

$2.1.(6$ pts$)$ The College of Business at Tech is planning to begin an on$\text{'}$ ne MBA program. The initial startup cost for computing equipment, facilities, course development, and staff recruitment and development is $$350,000.$ The college plans to charge tuition of $$16,000$ per student per year. However, the university administration will charge the college $$12,000$ per student for the first $95$ students enrolled each year for administrative costs and its share of the tuition payments.

a$.$ How many students does the college need to enroll in the first year to break even?

$$b$.$ If the college can enroll $87$ students the first year, how much profit will it make?

$$c$.$ The college believes it can increase tuition to $$25,000,$ but doing so would reduce enrollment to $34.$ Should the college consider doing this?

$$

$3.$ Case: Constructing a Downtown Parking Lot?

The town of Draper, with a population of $25,000,$ 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$$s public works director, has developed plans for a facility that would cost $$3$ million to construct. To pay for the project, the town would sell municipal bonds with a duration of $30$ years at $5\%$ interest. Kelly also estimates that five employees would be required to operate the lot on a daily basis, at a total annual cost of $$140,000.$ It is estimated that each car that enters the lot would park for an average of$5\mathrm{.}5$hours and pay an average fee of $$3\mathrm{.}30.$ Further, it is estimated that each car that parks in the lot would $($on average$)$ cost the town $$0\mathrm{.}50$ in annual maintenance for cleaning and repairs to the facility. Most of the downtown businesses $($which include a number of restaurants$)$ are open $6$ days per week.

$$

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?

$$Important hint: First of all for solving $($a$),$ you need

identify all components of prices$($benefits$,$ revenues$),$ variable and fixed costs on annual basis.

then, you will need to calculate the annual capital recovery payment$$ A for a capital expenditure of$$ X$$ million over T$$ years at d $\%$ interest using formula $($known to you from accounting or finances$$ or benefit $$cost analysis courses$)$: