Answer: To determine the Internal Rate of Return (IRR) of the project, we need to find the discount rate at which the present value of the cash inflows equals the initial investment. Here are the steps to compute the IRR:
Calculate the net cash inflow for each year: The net cash inflow is the cash inflow minus the initial investment.
Year 1: $25,000 - $100,000 = -$75,000
Year 2: $25,000 - $100,000 = -$75,000
Year 3: $25,000 - $100,000 = -$75,000
Year 4: $25,000 - $100,000 = -$75,000
Year 5: $25,000 - $100,000 = -$75,000
Set up the equation: The IRR is the discount rate at which the sum of the present values of the net cash inflows equals the initial investment.
-$75,000 / (1 + r) + -$75,000 / (1 + r)^2 + -$75,000 / (1 + r)^3 + -$75,000 / (1 + r)^4 + -$75,000 / (1 + r)^5 = -$100,000
Solve the equation: We need to solve for r, the discount rate. This can be done using numerical methods such as trial and error or by utilizing software tools or financial calculators. However, let's use an estimation approach here.
We can estimate the IRR by trying different discount rates until we find the one that makes the equation approximately equal. Let's start by trying a discount rate of 10%.
Plug in the discount rate of 10% into the equation:
-$75,000 / (1 + 0.10) + -$75,000 / (1 + 0.10)^2 + -$75,000 / (1 + 0.10)^3 + -$75,000 / (1 + 0.10)^4 + -$75,000 / (1 + 0.10)^5 = -$100,000
The result of the equation with a discount rate of 10% is approximately -$5,329. So, we need to adjust the discount rate.
Try a discount rate of 9%:
-$75,000 / (1 + 0.09) + -$75,000 / (1 + 0.09)^2 + -$75,000 / (1 + 0.09)^3 + -$75,000 / (1 + 0.09)^4 + -$75,000 / (1 + 0.09)^5 = -$100,000
The result of the equation with a discount rate of 9% is approximately $3,282. We are getting closer.
Continue narrowing down the discount rate by trying different values until we find the discount rate that makes the equation approximately equal to zero. Using this estimation approach, the IRR of the project is around 9.97% (approximately).
Note: Keep in mind that the IRR is an estimation using this approach and may not be 100% accurate. For more precise calculations, financial software or calculators that can solve for the IRR directly can be used.