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Unformatted text preview: Principles of Engineering Economy Economic Equivalence Part I Key Concepts • Last Module: Interest Factors • This Module: Economic Equivalence • Here, we use the interest factors to establish the equivalence of two cash flows diagrams. Compound Amount Factors Quick Review! Present Worth Factors Quick Review! Annual Equivalent Factors Quick Review! Establishing Economic Equivalence • Magnitude and timing of cash flows • Interest rate – Equivalence can be established for a given set of interest rates over time period N , but if any of these rates change, equivalence must be reestablished • Common unit of time – Generally defined by the compounding period of the interest rate • Common unit of measure – Single monetary unit must be chosen Economic Equivalence Properties 1. Economically Equivalent cash flows have the same monetary value at the same point in time 2. Can be established at any point in time 3. Can be established over any number of periods 4. Difference between two economically equivalent cash flows is zero 5. Does not require a constant interest rate over the study period 6. Can be established using current dollars and a market interest rate or real dollars and an interest free inflation rate Principle 1 • Economically Equivalent cash flows have the same monetary value at the same point in time – If two sets of cash flows are redrawn as their single period cash flow equivalents at the same period in time, and these cash flow equivalents are the same, then the original sets of cash flows are equivalent Example • An Argentine development bank and the binational commission running the Yacyreta dam on the Paraguayan border agreed to create a $563.4 million fund to complete the project by 2008. The government provided the following payments: $196.4 million in 2005, $169.5 million in 2006, $112.7 million in 2007 and $84.8 million in 2008. Source: “Argentina Govt Bank in Pact to Fund Yacyreta Dam Project,” Dow Jones Newswires, January 20, 2005. Example • Assuming end of year cash flows and an annual interest rate of 6%, show that this payment schedule is economically equivalent to a single cash flow of $593 million at the end of 2007. Source: “Argentina Govt Bank in Pact to Fund Yacyreta Dam Project,” Dow Jones Newswires, January 20, 2005. Solution • Draw the cash flow diagram: A07=? 05 06 07 08 84.8 196.4 169.5 112.7 Solution • Draw the cash flow diagram: • Solve for A07 : A07=? 05 06 07 08 84.8 196.4 169.5 112.7 A 07 = $196.4M(1 +0.06) 2 +$169.5M(1+0.06) +$112.7M + $84.8M (1+0.06) = $593.05M Principle 2 • Economic Equivalence can be established at any point in time: – There is no restriction as to what period we establish economic equivalence; it is easy to restate it at any time period as it only requires the application of a compound amount factor or present worth factor for a single payment Example • Consider the previous example where we established equivalence at the end of 2007. Now determine the equivalence of the single cash flow (at the end of 2007) at Solution • Draw the cash flow diagram: P=?...
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 Fall '08
 tufecki
 Inflation, 1920, 1916, 1918, 1911, 1925

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