what is the internal rate of return for an initial outlay of $10,500 resulting in a single cash inflow of $19,932 in 11 years?
To calculate the internal rate of return (IRR) for the given scenario, you can use a financial calculator, spreadsheet software like Excel, or a specialized financial formula. I'll explain the steps using the formula approach:
1. Write down the cash flows: In this case, we have an initial outlay (negative cash flow) of $10,500 and a single cash inflow of $19,932 after 11 years.
2. Apply the IRR formula: The IRR formula solves for the rate of return that will make the net present value (NPV) of the cash flows equal to zero. The formula is as follows:
NPV = CF0 + CF1 / (1+IRR) + CF2 / (1+IRR)^2 + ... + CFn / (1+IRR)^n
Where:
- NPV is the net present value, which should be zero for the IRR calculation
- CF0, CF1, CF2, ..., CFn are the cash flows at time periods 0, 1, 2, ..., n
- IRR is the internal rate of return we want to solve for
3. Set up the equation: Using the given cash flows, we have:
0 = -10,500 + 19,932 / (1+IRR)^11
4. Solve for IRR: Rearrange the equation and solve for IRR. The most efficient way to find the IRR is to use numerical methods or financial calculators. In this case, the IRR is approximately 6.96%.
Therefore, the internal rate of return for an initial outlay of $10,500 resulting in a single cash inflow of $19,932 in 11 years is approximately 6.96%.