Nominal and real interest rates

Both compounding and discounting use the discount rate, which is the expected future alternative value of money, sometimes the present or real interest rate or a separate value, depending on the given term limited value of money (this will be discussed below).

When evaluating projects, you must choose one of the methods for bringing all cash flows to the base year. If the discount method is used, then all cash flows are in line with the first (or zero) year. When using the compounding method, all cash flows lead to the last nth year.

When estimating the amount of cash flows, taking into account the time factor, the most common problems are:

1) the difficulty of choosing the appropriate interest rate;

2) inconsistency in the use of interest rates.

The value of the interest rate reflects the cost of capital for the investor, for example, the level of yield on government bonds. Since the value of money in real terms can decrease over time due to inflation, the project analysis uses the following two rates:

the real interest rate (r) is the rate of return on capital excluding inflation. In the case of using the real interest rate, it is necessary to calculate cash flows at constant prices, that is, to neutralize the impact of inflation;

nominal (present) interest rate (i) is the rate of return from the investor's position in the private market, which includes inflation (t) and is therefore determined by summing up the real rate of interest and the value of the inflation rate:

i = r + t ,

where r is the real interest rate (return on investment); t is the rate of inflation.


 If inflation is at a significant rate, then the nominal interest rate is calculated according to the formula of compound interest:

i = r + t + r•t ,

where r•t is an inflation premium.

An inflation premium is a premium for inflation expectations, which investors add to the real, risk-free level of income (rate of return).

The value of the real rate is determined by the equation:

r = (1 + i) : (1 + t) - 1If

only real (constant) prices are used in the project analysis, then annual production operating costs and benefits should not be increased by inflation to determine the cost of capital.

Consider the impact of inflation on nominal and real levels of income of the company. We will determine how the change in the rate of inflation will affect the value of nominal income and the level of profitability before and after tax (Table 6 and 7). Calculate nominal rates of return according to different rates of inflation - 20, 100 and 150% per year.



The nominal rate of return in the first scenario is 140%, in the second - 300, in the third - 400%.

The calculations given in Table 6 show that with an increase in the rate of inflation, nominal income from investments increases at a higher rate, and vice versa, with a slow decrease in inflation, nominal yields decrease more rapidly.



As you can see, with a sharp decrease in inflation, tax payments are initially made at the expense of purely inflationary income (component i). Then the real income, adjusted for inflation (component ri), begins to decrease, and in the future the repayment of tax liabilities should be carried out at the expense of its own real income from the investment project. Therefore, analysts in analyzing the financial attractiveness of the project, which is implemented at a certain level of inflation, should take into account some mutually influencing indicators: the nominal profitability of the project, its real profitability, tax rate and inflation rate. It should be remembered that highly effective projects are more sensitive to inflationary processes, their nominal yield increases sharply in the context of rising inflationary processes, but with a decrease in inflation, the rate of decline in yields occurs ahead of the pace.



Inconsistency in the use of interest rates is the most common mistake in project analysis. The confusion of real rates with the present causes a certain distortion of some flows of benefits and costs at the expense of others. In most cases, when analyzing projects conducted by international organizations, real indicators of benefits and costs are used, even in the absence of direct data on real capital rates.

Separate inflation scenarios provide for three possible options for the ratio of the nominal rate of interest with the rate of inflation:

1) r = t — the increase in the real value of funds does not occur due to the fact that the increase in their future value absorbs inflation;

2) r > t — the real future value of funds increases, despite inflation;

3) r < t — the real future value of funds decreases, that is, the investment process is unprofitable.