Ch_4_Economic_Equivalence

Ch_4_Economic_Equivalence - Economic Equivalence IE 226 1...

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1 Economic Equivalence IE 226 IE 226 2 Principle 1 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
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3 Example Example An Argentine development bank and the bi-national 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 has and will provide the following payments: $196.4 million in 2005, $169.5 million in 2006, $112.7 million in 2007 and $84.8 million in 2008. 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. 4 Solution Solution Draw the cash flow diagram: Solve for A 07 : A 07 =? 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
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5 Principle 2 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 Consider the previous example: We established equivalence at the end of 2007. Now determine the equivalence of the single cash flow at time zero (2004) 6 Solution Solution Draw the cash flow diagram: Solve for P : P=? 04 05 06 07 08 84.8 196.4 169.5 112.7 P = $196.4M (1 + 0.06) + $169.5M 2 + $112.7M 3 + $84.8M 4 = $497.93M P = $593.05M 3 = $497.93M
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7 Principle 3 Principle 3 Equivalence can be established over any number of periods May be established as a series of cash flows over time Using the previous examples, establish equivalence over the years 2005, 2006, 2007 and 2008 8 Solution Solution Draw the cash flow diagram: Solved for P : P = $593.05M (1 + 0.06) 3 = $497.93M A = P ( A / P ,6%,4 ) = $497.93M(0.2886) = $143.70M A …………. . A=? 04 05 06 07 08 84.8 196.4 169.5 112.7
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9 Principle 4 Principle 4 Difference between two economically equivalent cash flows is zero This is because they take on the same value at the same point in time Useful notion because we care about the differences between two cash flow diagrams (and the similarities cancel each other out) 10 Principle 5 Principle 5 Does not require a constant interest rate over the study period Example: Revisit the original payment plan, but assume the following interest rates: Years 2005-2006: 6% compounded semi-annually Year 2007: 12% annually Year 2008: 1.5% per month Now that we have these new interest rates we wish to assume an equivalent cash flow of $607M million at the end of 2007
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11 Solution Solution Draw the cash flow diagram: Solve for A 07 : A 07 =? 05 06 07 08 84.8 196.4 169.5 112.7 6.09% 12% 19.56% 07 $84.8 $196.4 1 0 0609 $169.5 1 0 12 $112.7 1 0 1956 $606.83 M M( + . )(1+0.12)+ M( + . )+ M (+ .
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This note was uploaded on 01/24/2011 for the course IE 226 taught by Professor Tonkay during the Fall '09 term at Lehigh University .

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Ch_4_Economic_Equivalence - Economic Equivalence IE 226 1...

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