Energy Project Financing : Resources and Strategies for Success

228 Energy Project Financing: Resources and Strategies for Success

The value of IRR is typically determined through a trial and error

process. An expression for the present worth of an investment is written

without specifying a value for i in the time value of money factors. Then

various values of i are substituted until a value is found that sets the

present worth (PW) equal to zero. The value of i found in this way is the

IRR.

As appealing as the flexibility of this approach is, there are two ma-

jor drawbacks. First, the iterations required to solve using the trial and

error approach to solution can be time consuming. This factor is mitigated

by the fact that most spreadsheets and financial calculators are pre-pro-

grammed to solve for an IRR value, given a cash flow series. The second

(and more serious) drawback to the IRR approach is that some cash flow

series have more than one value of IRR—i.e., more than one value of i sets

the PW expression to zero. A detailed discussion of this multiple solution

issue is beyond the scope of this appendix but can be found in White, et

al. [1998], as well as most other economic analysis references. However,

it can be shown that, if a cash flow series consists of an initial investment

(negative cash flow at t = 0) followed by a series of future returns (positive

or zero cash flows for all t>0) then a unique IRR exists. If these conditions

are not satisfied, a unique IRR is not guaranteed and caution should be

exercised in making decisions based on IRR.

The concept of internal rate of return as a measure of investment

worth can be generalized as follows:

Measure of Worth: Internal Rate of Return

Description: An interest rate, IRR, is determined which yields a pres-

ent worth of zero. IRR implicitly assumes the reinvestment of recovered

funds at IRR.

Calculation Approach:

Find IRR such that PW = (^) ΣAtP|F,IRR,t = 0.
t = 1
n
Important Note: Depending upon the cash flow series, multiple IRRs may
exist! If the cash flow series consists of an initial investment (net negative
cash flow) followed by a series of future returns (net non-negative cash
flows), then a unique IRR exists.