Energy Project Financing : Resources and Strategies for Success

222 Energy Project Financing: Resources and Strategies for Success

The concept of equivalence can be used to break a large, complex

problem into a series of smaller, more manageable ones. This is done by

taking advantage of the fact that, in calculating the economic worth of a

cash flow profile, any part of the profile can be replaced by an equivalent

representation at an arbitrary point in time without altering the worth of

the profile.

Question: You are given a choice between (1) receiving P dollars today

or (2) receiving the cash flow series illustrated in Figure A-5. What must

the value of P be for you to be indifferent between the two choices if i =

12%/yr?

Figure A-5. A cash flow series

Analysis Approach: To be indifferent between the choices, P must have a

value such that the two alternatives are equivalent at 12%/yr. If we

select t = 0 as the common point in time upon which to base the analysis

(present worth approach), then the analysis proceeds as follows:

PW(Alt 1) = P

Because P is already at t = 0 (today), no time value of money factors are

involved.

PW(Alt 2)

Step 1— Replace the uniform series (t = 3 to 7) with an equivalent single

sum, V 2 , at t = 2 (one period before the first element of the series). V 2

= 2,000 * (P|A,12%,5) = 2,000 * 3.6048 = 7,209.60

Step 2— Replace the single sum V 2 ,with an equivalent value V 0 at t = 0.

PW(Alt 2) = V 0 = V 2 * (P|F,12,2) = 7,209.60 * 0.7972 = 5,747.49

Answer: To be indifferent between the two alternatives, they must be equiva-

lent at t = 0. To be equivalent, P must have a value of $5,747.49.