Page 602 - Marine Structural Design

578 Part V Risk Assessment

Assume that the cash expenses (including the initial investment C, associated with the
project) at the end of each period are C,, . The present value expression of cash expenses, C, is:

C=C- Cn
n=O (1 + i)”
Then the NPV of the project [denoted by NPV(i)] is defined by the difference between I and Cy
i.e.

A positive NPV for a project represents a positive surplus, and we should accept the project if
sufficient funds are available for it. A project with a negative NPV should be rejected, because
we could do better by investing in other projects at the market interest rate i or outside the
market.
Internal Rate of Return (IRR)
The IRR is another time-discounted measure of investments similar to the NPV criterion. The
IRR of a project is defined as the rate of interest that equates the NPV of the entire series of
cash flows to zero. The project’s IRR, is mathematically defined by:

NPV(irr) = z- Fn = 0
,,=o (1 + irr)”
Note that Eqn. (A.4) is a polynomial bction of irr . A direct solution for such a function is
not generally possible except for projects with a life of four periods or fewer. Therefore, two
approximation techniques are generally used, one using iterative procedures (a trial-and-mor
approach) and the other using Newton’s approximation to the solution of a polynomial.