To determine the project's internal rate of return (IRR), one must calculate the net present value (NPV) of its cash flows at different rates until finding the rate that sets NPV to zero, which is a process typically performed using financial calculators or spreadsheet software when exact cash flow numbers are available.
The question is asking for the internal rate of return (IRR) of a project considering the investment, cash flows, and terminal cash flows over the project's 4-year life. The given data includes the operating cash flow, cost of new equipment and its depreciation, market value of the equipment at the end of the project, net working capital and its recovery, and the tax rate. To calculate the IRR, you need to find the net present value (NPV) of the project at different discount rates until the NPV equals zero. This iterative process involves projecting the after-tax cash flows across the project's life and discounting them back to their present value to account for the time value of money.
Typically, the IRR is found using financial calculators or spreadsheet software that have built-in functions to compute IRR given a series of cash flows. There isn't enough information provided to directly calculate the IRR in this context. However, to approach this manually, you would set up the equation for NPV at zero and solve for the discount rate which would be the IRR. Remember that the IRR is the discount rate that makes the NPV of all cash flows (both incoming and outgoing) from a project equal to zero.