Final answer:
To determine the grant size that would make the solar panel project worthwhile to the university, we need to calculate the net present value of the project. This involves calculating the annual cash flows, discounting them at a rate of 10%, and summing up the present values to determine the NPV. The grant size would be equal to the NPV.
Step-by-step explanation:
To determine the size of the grant that would make the solar panel project worthwhile to the university, we need to calculate the net present value of the project. The net present value (NPV) is the sum of the present values of the cash flows over the life of the project, discounted at the given rate of 10%.
Step 1: Calculate the annual cash flows. The annual energy production of the solar panels can be calculated by multiplying the capacity (500 kW) by the hours of full-sun-equivalent (6 hours) by the number of days in a year (365 days). This will give us the total energy production per year in kWh. We can then multiply this by the cost of electricity ($0.15/kWh) to get the annual revenue from the project. Subtracting the annual operating expenses (maintenance, etc.) will give us the annual cash flow.
Step 2: Calculate the NPV. Using the formula for NPV, we can discount each year's cash flow at a rate of 10%. Summing up the present values of all the cash flows will give us the NPV.
Step 3: Determine the grant size. The grant size that would make the project worthwhile to the university would be equal to the NPV calculated in step 2.