IRR and NPV

Evaluation of the effectiveness of an investment undertaking is a mandatory procedure before making a final decision on investing in it. There are a number of methods of project analysis, among which the most common are NPV, IRR, PI, DPP, DP, ARR. Each of these abbreviations is a tool for analyzing the project according to different criteria, which together give the investor important information for making an objective investment decision.

The main criteria for evaluating investment projects

The most important thing for people who want to invest their money and make a profit is the calculation of NPV and IRR.


Let's dwell on what these criteria are.


NPV (from the English Net Present Value) is the net present (current) value. This indicator characterizes the change in cash flows. It is calculated as the difference between all incoming investments and the costs of implementing the project (current expenses, loan repayment, etc.), taking into account the accepted discount rate. In other words, with a positive value of this indicator, investors can hope that the cash flows generated by the main activity of the project will cover all costs and bring the expected profit at a level not lower than the discount rate.


NPV refers to those indicators that can be calculated quickly, immediately after the receipt of an investment proposal. It gives as a result an absolute value, based on which, you can choose the most attractive from several sentences. To calculate the current value, the following formula is used:


NPV

where is:

• CFt – flow of money for a period of time t;
• r – the value of the barrier rate;
• CF0 – initial cash flow, basically it is equal to the amount of investment capital.
• Net cash flow, as a rule, is determined for each area of activity (investment, operating, financial) separately. The most problematic point is the correct establishment of the discount rate. To calculate it, there are a number of methods (CAPM, WACC, ROE - ROA, Gordon model, risk premium method) on various basic bases.

Using the result is very simple. If the value of the net discounted income is greater than zero, then the offer is of interest and can be approved. If the indicator is less than zero, this indicates that the project has no prospects to recoup the investment and bring profit. With values close to zero, a positive decision is usually made only when profit is not the only important criterion, and other factors play an important role (entering a promising market, social component).


Internal Rate of Return)If you use this tool to compare several initiatives, then the one with a higher NPV is preferable.


IRR (from the English Internal Rate of Return) is an internal rate of return (return). It represents the maximum allowable value of investments, that is, such a discount rate at which the NPV indicator is zero (the cost of the initiative and the income from it are equal).


As such, there is no separate formula for calculating the IRR, it is found by changing the net present value formula:

IRR

where is:

• CF – the flow of money generated by the investment project;
• IRR – internal rate of return;
• CF0 – initial cash flow.

The formula can have another form, for example, as follows:



where is:

• n is the number of time intervals;
• It is the amount of investment made during period t.
• However, the most commonly used estimate is using a graph on which the calculated two NPV values are located, one of which is slightly below zero, and the other is slightly higher. The values are connected by a straight line, at the point of its intersection with the abscissa axis and the value of the indicator closest to the real one is located.

If, as a result of the calculation, the rate of internal profitability is less than the price of attracting financing (rates of return), then such a project is unprofitable for implementation. Otherwise, it can be taken into development.

Features of key criteria for the effectiveness of the project

Since both methods are extremely popular among economists and financiers, it is worth studying in more detail which of them is able to give more objective information. The comparative characteristics of the NPV and IRR criteria show that each of these financial instruments has its own strengths and weaknesses.

Distinctive features of NPV are:

The direct dependence of the indicator on the scale of the business: the larger the investment and the greater the volume of cash flow, the higher the value of the current value indicator will be.
Influence on the value of the criterion of the financing structure by time intervals. If the project goes through all the stages of costs (project, initial investment, liquidation costs), then its value is likely to be minimal.


The influence of the length of the time lag between the investment and the timing of the start of operation of the facility, the longer the break, the smaller the NPV value. In addition, the dynamics of the barrier rate can greatly affect the discounted amount of investment.


The numerical value of the indicator is mainly influenced by such factors:

• The rate of discount.
• The pace of the production process: less costs – more profit – more revenue.
• The scale of the company, the dependence on the number of products produced, sales volumes, the amount of investment.
• With all the convenience of this method of calculation, it is not suitable for comparing investment projects that differ greatly from each other in at least one of the above factors. Consequently, such comparisons require a different, more flexible, criterion.

The advantages of the internal rate of profitability include:

• The ability to make a comparison between projects that have different duration, production rates and investment scales.
• The ability to evaluate not only investment projects, but also other alternative financial instruments (for example, a deposit on a bank deposit). If the IRR of the investment undertaking turns out to be higher than the interest rate on the deposit, then it is more profitable to invest in the project.
• Показатель IRRQuick determination of the feasibility of further analysis of the proposed project after its rapid assessment for the rate of internal profitability. In this case, the IRR is estimated relative to WACC (weighted average cost of capital). If the IRR is greater than the WACC, then the venture promises profit, but if the values are less or equal, then we should expect a negative flow of money in the future.

The IRR can be used as a discount rate. The greater the difference between the internal rate of return and the regulatory profitability, the more interesting the investment proposal.However, the criterion of the internal rate of profitability has its drawbacks, among them:

• The inability to show an increase in the cost of the project in absolute terms.
• Difficulty of calculation and the possibility of obtaining an incorrect result with an unsystematic structure of cash flows (with alternating negative and positive values).
• Financiers in the NPV - IRR pair prefer to use the second method more, since there is no need to calculate the discount rate for it, as for the net present value. In addition, the result in determining the rate of profitability of the internal is calculated as a percentage, so it is more convenient to use it when comparing relative values (percentages), and the net discounted value is calculated in banknotes, respectively, less adapted for comparison. Although most textbooks claim that NPV indicates the amount of value added created by the initiative, it should therefore be preferable.

Often, the above key indicators produce results that contradict each other. The reason for this may be the discount rate included in the calculation or the non-standard structure of financial flows. At the same time, NPV characterizes the size of future income, and IRR - the rate of its receipt. Which option is better to stop at? Specialists in financial analysis recommend in this case to choose the criterion of the current value, since it takes into account the variable rate of discount, and the main purpose of the investment is the amount of profit, and not the speed of its receipt.



As can be seen from the above, IRR and NPV are key indicators of the effectiveness of the investment offer. Taking them as a basis, the investor or business owner can calculate other auxiliary indicators, such as the profitability index (PI), discounted payback period (DPP), weighted average rate of investment return (ARR).