Chapter 5. The method of replacementing loans

For a project with a specified flow of payments and the associated IRR , the concept of a substitute loan is introduced, where the interest rate is the IRR ,which by analogy with a loan is used for calculate interest and payments of principal debt. The relationship between NPV and the amount of discounted interest of the replacementing loan as a function of the discount rate has been established. We study the properties of these functions, the relationship between their roots and, ultimately, the possibility of changing signs, which depends on multiplicity (even or odd) of the IRR values. It is shown that the areas of the operating profitableness of the investor and the recipient with positive and negative signs of the function of the amount of discounted interest respectively represent quite arbitrary alternating intervals of the discount rate. The principle of identification of these areas , which using the multiplicity (even or odd) of the IRR value is established.