The method of calculating the financial internal rate of return

Internal rate of return: It is a basic indicator that reflects the economic effect of the project. It refers to the discount rate when the present value of net cash flow in each year is equal to zero during the construction and production service period of the investment project.

This method of analysis takes into account the time value of money and can measure the profitability of each scheme, so it is one of the important methods of investment analysis.

Calculation formula: n

ci－co）•ai ＝0

i=1 where:

CI is the cash inflow in the ith year.

CO is the cash outflow for the ith year.

ai is the discount factor for year i.

n is the sum of the years of service in construction and production.

n is the sum of years since the start of construction.

i=1i is the internal rate of return.

In the manual calculation, several discount rates are used to try the calculation until the discount rate when the net value is equal to or close to 0 is found. If the NPV is positive, the higher discount rate will be used to calculate it, and if it is negative, the lower discount rate will be used to re-try.

As long as the net present value is calculated, the IRR function in Excel can be used to directly derive the financial internal rate of return.

1. The formula for calculating the internal rate of return is as follows:

where: FIRR – Financial Internal Rate of Return.

CI – Cash inflows.

CO – cash outflow.

ci-co)t – net cash flow for period t.

n - the calculation period of the project.

2. Steps to calculate the internal rate of return:

1) In calculating the net present value.

If the NPV is positive, the NPV is used to calculate the higher discount rate of IRR.

until the net sum of the present value of the measured net is close to zero.

2) Continue to increase the discount rate until a net present value is calculated to be negative. If the negative value is too large, the discount rate is lowered and then measured to a negative value close to zero.

3) Linear interpolation is used according to the discount rate of two adjacent plus and minus net present values close to zero.

Find the internal rate of return.

Calculation formula:

1) Calculate the present value coefficient of annuity (p a, firr, n) = k r;

2) Check the table of present value coefficients of annuity, find the two coefficients (p a, i1, n) and (p a, i2, n) adjacent to the present value coefficient of the annuity and the corresponding i1 and i2, and meet the requirements of (p a, il, n) >k r> (p a, i2, n);

3) Calculate the FIRR using the interpolation method:

firr-i2)/(i1—i2)=[k/r-(p/a，i2，n)]/[(p/a，i1，n)—(p/a， i2，n)]。

The internal rate of return is the discount rate when the total present value of the capital inflow is equal to the total present value of the capital flow and the net present value is equal to zero. Without the use of an electronic computer, the internal rate of return is trialled using a number of discount rates until the discount rate at which the net present value is equal to or close to zero is found. The internal rate of return is the rate of return that an investment aspires to achieve, and it is the discount rate when the net present value of the investment is equal to zero.

It is the rate of return that an investment aspires to achieve, and the bigger the metric, the better. In general, the project is feasible when the internal rate of return is greater than or equal to the benchmark rate of return. The sum of the discounted value of the annual cash flows of the investment project is the net present value of the project, and the discount rate when the net present value is zero is the internal rate of return of the project.

In the economic evaluation of the project, the internal rate of return is divided into financial internal rate of return (FIRR) and economic internal rate of return (EIRR) according to different levels of analysis.

Extended Materials. Internal rate of return is a macro concept indicator, the most popular understanding is the ability of the project's investment income to withstand currency depreciation and inflation. For example, the internal rate of return of 10% means that the project can withstand a maximum of 10% currency depreciation or 10% inflation every year during the operation of the project.

At the same time, the internal rate of return also indicates the ability to resist risks during the operation of the project, for example, the internal rate of return of 10% indicates that the maximum risk that can be tolerated during the operation of the project is 10% per year. In addition, if a loan is required in the operation of the project, the internal rate of return can indicate the maximum tolerable interest rate, and if the loan interest has been included in the economic calculation of the project, it indicates the maximum floating value of the loan interest in the course of future project operation.

For example, if the IRR is benchmarked at 8% and inflation is assumed to be around 8%. If it is equal to 8%, it means that when the project operation is completed, there is no money except for the "salary" received by "yourself", but it is still feasible. If it is less than 8%, it means that there is a high probability that the project operation will be at a loss when the project operation is completed.

Because of inflation, the money you make in the future is likely to not cover the costs you are investing now. Projects with a longer payback period are particularly important for IRR metrics. For example, the general investment period of hotel construction is about 10-15 years, and the investment and operation period of large-scale tourism development is more than 50 years.

This is the most popular and practical meaning of the internal rate of return.