Introduction
Internal Rate of Return (IRR) is a key financial metric used in investment analysis. It represents the rate at which the net present value of cash flows from an investment equals zero. In other words, it is the rate at which the investment breaks even. Calculating IRR is a complex process that involves finding the root of an equation, which is why most people use Excel or financial calculators to do it. However, it is also possible to calculate IRR using an annuity table, which is a table that shows the present value of an annuity for a range of interest rates and periods.
Annuity Table Basics
An annuity is a series of payments made at fixed intervals, such as monthly or annually. An annuity table is a tool that shows the present value of an annuity for a range of interest rates and periods. The table is divided into rows and columns, with each row representing a different interest rate and each column representing a different time period. The values in the table represent the present value of an annuity of $1 per period, discounted at the corresponding interest rate.
For example, suppose you have an annuity of $1,000 per year for 5 years, and the interest rate is 10% per year. The present value of this annuity can be found in an annuity table by looking up the intersection of the row for 10% and the column for 5 years. In this case, the present value of the annuity is $3,790.79.
IRR Calculation Using Annuity Table
To calculate IRR using an annuity table, you need to follow these steps:

Determine the cash flows for the investment: The first step is to determine the cash flows associated with the investment. These can be positive or negative, depending on whether the investment generates income or requires expenses. For example, suppose you are considering an investment that requires an initial outlay of $10,000, generates cash inflows of $2,000 per year for 5 years, and has a salvage value of $3,000 at the end of the 5th year.

Find the present value of the cash flows: The second step is to find the present value of each cash flow using the annuity table. To do this, you need to discount each cash flow at the appropriate interest rate and time period. For example, the initial outlay of $10,000 has a present value of $10,000 (i.e., it is a cash outflow), while the cash inflows of $2,000 per year have a present value of $7,721.69 (calculated using the annuity table for 5 years at 10%). The salvage value of $3,000 has a present value of $1,620.93 (calculated using the annuity table for 5 years at 10%).

Calculate the net present value of the cash flows: The third step is to calculate the net present value (NPV) of the cash flows by summing the present values of all the cash inflows and outflows. In this case, the NPV is $657.38.

Determine the IRR: The fourth step is to determine the IRR by finding the interest rate that makes the NPV equal to zero. To do this, you need to use the annuity table to find the interest rate that corresponds to an NPV of zero. In this case, the IRR is 13.5%.
Conclusion
Calculating IRR using an annuity table can be a useful technique for analyzing investment opportunities. By following the steps outlined in this article, you can calculate IRR using an annuity table with confidence. Remember, IRR is just one financial metric to consider when evaluating investments, and it should be used in conjunction with other metrics, such as payback period and net present value.