calculation-based questions on Money and finance that are commonly encountered

  calculation-based questions on Money and finance that are commonly encountered 

 

1. If a university receives $1,000,000 in endowment funds and invests them in a portfolio that generates an average annual return of 8%, how much will the endowment be worth after 10 years?

2. A university plans to issue a bond with a face value of $5,000,000 and an annual coupon rate of 6%. If the bond matures in 5 years, what will be the total interest expense paid by the university over the bond's life?

3. A university has an operating budget of $10,000,000 for the academic year. If the university expects to generate income of $2,000,000 from tuition fees and $1,500,000 from research grants, what portion of the budget will need to be funded by other sources, such as donations or endowment income?

4. A university's capital campaign aims to raise $50,000,000 over a 5-year period. If the university receives $10,000,000 in the first year, what is the average amount that needs to be raised annually in the remaining four years to meet the campaign goal?

5. A university's student fees for an academic year amount to $20,000,000. If the university provides financial aid scholarships totaling $4,000,000 to eligible students, what percentage of the student fees revenue is being allocated towards scholarships?

6. A university's endowment is currently valued at $100,000,000. If the endowment distribution policy allows for a 3% annual withdrawal, how much can the university access for operating expenses in the upcoming year?

7. A university receives a government grant of $2,500,000 for a research project. If the university has to allocate 25% of the grant towards indirect costs, how much funding will be available for direct research expenses?

8. A university is planning to purchase a new laboratory equipment worth $500,000. The useful life of the equipment is estimated to be 10 years, with a salvage value of $50,000. What will be the annual depreciation expense associated with this equipment using straight-line depreciation?

9. A university's bookstore generates $1,000,000 in annual revenue from textbook sales. If the average cost of textbooks is 70% of the selling price, what is the average gross profit margin of the bookstore?

10. A university's payroll expenses amount to $5,000,000 annually. If the university expects to receive $3,000,000 in research grant overhead funding, what percentage of the payroll expenses is covered by these grants?

SOLUTIONS

Sure! Here are the solutions to the calculation-based questions:

1. To calculate the future value of the endowment after 10 years, we can use the formula for compound interest:

   Future Value = Principal * (1 + Interest Rate)^Time

   Future Value = $1,000,000 * (1 + 0.08)^10

   Future Value = $1,000,000 * 1.08^10

   Future Value ≈ $2,159,274.16

   Therefore, the endowment will be worth approximately $2,159,274.16 after 10 years.

2. The total interest expense paid by the university over the bond's life can be calculated using the formula:

   Total Interest Expense = Face Value of Bond * Coupon Rate * Time

   Total Interest Expense = $5,000,000 * 0.06 * 5

   Total Interest Expense = $1,500,000

   Therefore, the total interest expense paid by the university over the bond's life will be $1,500,000.

3. The portion of the budget that needs to be funded by other sources can be calculated by subtracting the income from tuition fees and research grants from the operating budget:

   Other Sources = Operating Budget - Tuition Fees - Research Grants

   Other Sources = $10,000,000 - $2,000,000 - $1,500,000

   Other Sources = $6,500,000

   Therefore, $6,500,000 will need to be funded by other sources.

4. To calculate the average amount that needs to be raised annually in the remaining four years to meet the campaign goal, we can divide the remaining amount by the number of years:

   Remaining Amount = Campaign Goal - Amount Received in the First Year

   Remaining Amount = $50,000,000 - $10,000,000

   Remaining Amount = $40,000,000

   Average Annual Amount = Remaining Amount / Number of Years

   Average Annual Amount = $40,000,000 / 4

   Average Annual Amount = $10,000,000

   Therefore, the average amount that needs to be raised annually in the remaining four years is $10,000,000.

5. To calculate the percentage of student fees revenue allocated towards scholarships, we can divide the scholarship amount by the student fees revenue and multiply by 100:

   Percentage = (Scholarship Amount / Student Fees Revenue) * 100

   Percentage = ($4,000,000 / $20,000,000) * 100

   Percentage = 20%

   Therefore, 20% of the student fees revenue is being allocated towards scholarships.

6. The amount that the university can access for operating expenses from the endowment can be calculated by multiplying the endowment value by the distribution rate:

   Accessible Amount = Endowment Value * Distribution Rate

   Accessible Amount = $100,000,000 * 0.03

   Accessible Amount = $3,000,000

   Therefore, the university can access $3,000,000 for operating expenses from the endowment.

7. The funding available for direct research expenses can be calculated by subtracting the allocation for indirect costs from the grant amount:

   Funding for Direct Research Expenses = Grant Amount - (Grant Amount * Indirect Cost Allocation)

   Funding for Direct Research Expenses = $2,500,000 - ($2,500,000 * 0.25)

   Funding for Direct Research Expenses = $1,875,000

   Therefore, $1,875,000 will be available for direct research expenses.

8. The annual depreciation expense associated with the laboratory equipment can be calculated using the straight-line depreciation method:

   Annual Depreciation Expense = (Purchase Cost - Salvage Value) / Useful Life

   Annual Depreciation Expense = ($500,000 - $50,000) / 10

   Annual Depreciation Expense = $45,000

   Therefore, the annual depreciation expense associated with the laboratory equipment is $45,000.

9. The average gross profit margin of the bookstore can be calculated by subtracting the average cost of textbooks from the revenue and dividing it by the revenue, then multiplying by 100 to express it as a percentage:

   Gross Profit Margin = [(Revenue - Cost) / Revenue] * 100

   Gross Profit Margin = [($1,000,000 - $700,000) / $1,000,000] * 100

   Gross Profit Margin = 30%

   Therefore, the average gross profit margin of the bookstore is 30%.

10. The percentage of payroll expenses covered by research grant overhead funding can be calculated by dividing the grant overhead funding by the annual payroll expenses and multiplying it by 100:

   Percentage = (Grant Overhead Funding / Payroll Expenses) * 100

   Percentage = ($3,000,000 / $5,000,000) * 100

   Percentage = 60%

   Therefore, research grant overhead funding covers 60% of the payroll expenses.