A project has the following initial outlay of 11,500 resulting in a single cash flow if 23,876 in 7 years. What is the internal rate of return?
To calculate the internal rate of return (IRR) for a project, you need to use the net present value (NPV) formula. The NPV formula takes into account the initial outlay and the expected future cash flows, discounting them to the present value using the IRR.
Here's how you can calculate the IRR:
1. List all the cash flows associated with the project. In this case:
- Initial outlay = -$11,500 (negative because it's an outgoing cash flow)
- Cash flow in 7 years = $23,876
2. Set up the NPV formula:
NPV = Initial outlay + Cash flow / (1 + IRR)^n = 0
3. We need to solve for IRR, which represents the rate of return at which the NPV equals zero. To do this, we can use trial and error, or utilize built-in functions in software programs like Microsoft Excel or financial calculators.
For example, in Excel:
- Enter the cash flows in separate cells: A1 = -11500 (Initial outlay), A2 = 23876 (Cash flow in 7 years)
- In cell B1, enter the formula: =IRR(A1:A2)
Excel will then calculate and provide you with the IRR. In this case, the IRR is approximately 7.91%.
Therefore, the internal rate of return (IRR) for the project is approximately 7.91%.