Question

You are in charge of a prestigious state university. You currently receive $250 million in state funding at the end of each year. You have current annual costs of $350 million, also paid at the end of each year, which grow at 4% per year. A new law has passed where the state is going to reduce their annual funding by 7% per year indefinitely. (So the funding will be 7% lower starting at the end of this year.) As part of the new law, you are allowed to set a new tuition rate for the end of this year, but once set, you can only increase it at the rate of inflation. Inflation is expected to be 2% per year. If you have 30,000 tuition-paying students, and do not forecast enrollment changing over time, what is the minimum per-student annual tuition to charge at the end of this year to remain solvent? Assume the annual interest rate is 6% and because this is a university, there is no end date for the forecast.

Answer 1

To determine the minimum per-student annual tuition to charge at the end of this year in order to remain solvent, we need to consider the funding, costs, and the expected reduction in state funding.

Let's break down the calculation step-by-step:

1. Calculate the total annual cost at the end of this year:

- Start with the current annual cost of $350 million.

- Apply the annual growth rate of 4% per year.

- Use the formula for compound interest to calculate the future value of the costs after one year:

Future Value = Present Value * (1 + Interest Rate)^Number of Years

Future Value = $350 million * (1 + 4%)^1

Future Value = $350 million * (1 + 0.04)

Future Value = $350 million * 1.04

Future Value = $364 million (rounded to the nearest million)

2. Calculate the reduced state funding at the end of this year:

- Start with the current state funding of $250 million.

- Apply the annual reduction rate of 7% per year.

- Use the formula for compound interest to calculate the future value of the funding after one year:

Future Value = Present Value * (1 - Interest Rate)^Number of Years

Future Value = $250 million * (1 - 7%)^1

Future Value = $250 million * (1 - 0.07)

Future Value = $250 million * 0.93

Future Value = $232.5 million

3. Calculate the tuition revenue needed to cover the shortfall:

- Start with the total annual cost at the end of this year ($364 million).

- Subtract the reduced state funding at the end of this year ($232.5 million).

- This will give us the remaining amount that needs to be covered by tuition:

Shortfall = Total Annual Cost - Reduced State Funding

Shortfall = $364 million - $232.5 million

Shortfall = $131.5 million

4. Calculate the minimum per-student annual tuition:

- Divide the total shortfall by the number of tuition-paying students (30,000) to find the per-student tuition:

Minimum Per-Student Annual Tuition = Shortfall / Number of Students

Minimum Per-Student Annual Tuition = $131.5 million / 30,000

Minimum Per-Student Annual Tuition = $4,383.33 (rounded to the nearest cent)

Therefore, to remain solvent, the university needs to charge a minimum per-student annual tuition of approximately $4,383.33 at the end of this year.