Hingham Academy, a private school, serves $500$ students: $200$ in the middle school $($grades $6$ to $8)$ and $300$ in the high school $($grades $9$ to $12).$ Each school group has its own assistant principal, and there is one principal, Brian Silk, for the academy. For any single student, almost all of Hingham's costs are indirect. Hingham currently has five indirect cost categories, which are listed in the following table. Silk wants to develop an activity$-$based costing system for the school. He identifies four activitieslong dashacademic instruction, administration, sports training, and community relationshipslong dashrelated to the educational enterprise.

Silk and his team identify the number of students as the cost driver of academic instruction and administration costs and the number of team sports offered by the school as the cost driver of sports training costs. The cost of maintaining community relationshipslong dashdealing with the town council and participating in local activitieslong dashis a facility$-$sustaining cost that the school has to incur each year. This table shows the percentage of costs in each line item used by each activity.

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Part $1$

Requirement $1.$ What is the overall cost of educating each student? Of this cost, what percentage is the cost of academic instruction? Of administration?

Begin by calculating the total cost of each activity for each cost category.

Actual Resource Cost Used by Each Activity

Academic

Sports

Community

$2021$

Indirect Cost Categories

Instruction

Administration

Training

Relationships

Expenditures

Teachers' salaries and benefits

Principals' salaries and benefits

Facilities

Office staff salaries and benefits

Sports program staff salaries and benefits

Total

Part $2$

Determine the formula to calculate the overall cost of educating one student. Next, enter the amounts to calculate the per$-$student cost.

Part $3$

$/$

$=$

Overall cost of educating one student

$/$

$=$

per student

Part $4$

The cost of academic instruction is

enter your response here$\%$ of the total overall cost. $($Round your answer to the nearest percent.$)$

Part $5$

The cost of administration is

enter your response here$\%$ of the total overall cost. $($Round your answer to the nearest percent.$)$

Part $6$

Requirement $2.$ Silk is dismayed at the high cost of sports training. Further examination reveals that $ $250$ comma $000$ of those costs are for ice hockey, a sport pursued by a total of $45$ students. What would be the overall cost of educating each student if the ice hockey program is eliminated and its cost saved?

Determine the formula to calculate the cost if the hockey program is eliminated. Then, enter the amounts in the formula.

Part $7$

$($

$)/$

$=$

Overall cost of educating one student

$($

$)/$

$=$

per student

Part $8$

Requirement $3.$ For the $2022$ school year, Hingham charges an annual fee of $ $1$ comma $200$ for any student who wants to play ice hockey. As a result, $10$ of the less$-$motivated students drop the sport. Assuming the costs of the school in $2022$ are the same as in $2021,$ what is the overall cost of educating each student in $2022?$

Determine the formula to calculate the overall cost of educating one student when a fee is charged for the hockey program. Next, enter the amounts in the formula. $($Round your answer to the nearest whole dollar.$)$

Part $9$

$($

$)/$

$=$

Overall cost of educating one student

$($

$)/$

$=$

per student

Part $10$

Requirement $4.$ Consider the costs of the academic instruction activity and assume they are fixed in the short run. At these costs, Hingham could serve $550$ students. What is the cost of the academic instruction resources used by Hingham's current $500$ students? What is the cost of unused academic instruction capacity?

The cost of the academic instruction resources used by Hingham's current $500$ students is $

enter your response here.

Part $11$

What is the cost of unused academic instruction capacity? First, determine the formula to calculate the unused academic instruction capacity. Then, enter the amounts in the formula and calculate the cost of excess capacity. $($Round all your calculations to the nearest whole number.$)$

Part $12$

$=$

Cost of excess capacity

$=$

Part $13$

What actions can Silk take to reduce the cost of academic instruction per student in the short run?

Silk must try to

recruit fewer

recruit more

students to the school. If the student population is going to

be expanding to

be stable

around $500$ students, and Silk's plan is to

cut "excess academic instruction capacity,"

cut "excess administration,"

it could cause long$-$term damage to the school. Silk would have to

increase the number of sections in each grade and hire inexperienced teachers.

reduce the number of sections in each grade and let go of experienced teachers.

Part $14$

In the long run?

Silk should consider

doing away with

keeping

expensive activities like the ice hockey program, which

lowers

raises

the cost per student substantially even after a

large

small

fee is charged to students who choose to play the sport.

The cost of academic instruction is$($Round your answer to the nearest percent.$)$The cost of administration is$($Round your answer to the nearest percent.$)$The cost of the academic instruction resources used by Hingham's current $500$ students is $$.$Silk must try tostudents to the school.If the student population is going to$500$Silkaround $500$ students, and Silk's plan is toSilkSilk would have toSilk should considerexpensive activities like the ice hockey program, whichexpensive activities like the ice hockey program, whichthe cost per student substantially even after athe cost per student substantially even after afee is charged to students who choose to play the sport.

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Data table

Percentage of Costs Used by Each Activity

Academic

Sports

Community

$2021$

Indirect Cost

Instruction

Administration

Training

Relationships

Expenditures

Teachers' salaries and benefits

$55\%$

$10\%$

$10\%$

$25\%$

$$4,000,000$

Principals' salaries and benefits

$10\%$

$55\%$

$7\%$

$28\%$

$400,000$

Facilities

$35\%$

$10\%$

$50\%$

$5\%$

$3,100,000$

Office staff salaries and benefits

$10\%$

$55\%$

$10\%$

$25\%$

$280,000$

Sports program staff salaries and benefits

$30\%$

$15\%$

$45\%$

$10\%$

$490,000$

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