# Module07 - Principles of Engineering Economy Economic...

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Principles of Engineering Economy Economic Equivalence and Interest Factors Part I

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Key Concepts Last Module: Interest Factors (Compound Amount and Present Worth) This Module: Interest Factors Interest factors: Continue with equal payment series factors and dealing with continuous compounding and continuous cash flows
Equal Payment Factors Goal : to transform any cash flow diagram into an an economically equivalent equal payment series of length N and size A Relies on discounting and compounding to accomplish this task.

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Single Payment Analysis Sinking Fund Factor convert to 0 1 2 3 . . . . . . . . . . . . . . N F 0 1 2 3 . . . . . . . . . . . . . . N A A A A . . . . . . . . . . . . . .
Equivalent by the Sinking Fund Factor 0 1 2 3 . . . . . . . . . . . . . . N F 0 1 2 3 . . . . . . . . . . . . . . N A A A A . . . . . . . . . . . . . . Question: If I pull ( F ) from an account after N periods, how much ( A ) did I put into the account for each of the previous N periods? Single Payment Analysis Sinking Fund Factor

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What is A , given F ? F 0 1 2 3 . . . . . . . . . . . . . . N A A A A . . . . . . . . . . . . . . Sinking Fund Factor Equal Payment Series
What is A given F ? From the compound amount factor: Sinking Fund Factor F = A (1 + i ) N - 1 i A = F i (1 + i ) N - 1 = F ( A / F , i , N )

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Example Fugro, an oil service firm from Amsterdam, won a three year contract from the State of California to provide Highway Pavement Structure Data Collection and Inventory services valued at EUR6.5 million. Assume this is a Source: Amsterdam Bureau, “Fugro Gets Order For Infrastructure Projects,” Dow Jones International News, December 2, 2009.
Solution Draw the cash flow diagram: A A EUR6.5M 0 1 2 3 A A = F i (1 + i ) N - 1 = EUR6.5M 0.06 (1 + 0.06) 3 - 1 = EUR2.04M

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Alternatives to the Formula Look up the factor value using the tables for discrete compounding and discrete cash flows Use a spreadsheet (PMT Function in GoogleDocs and Excel):
convert to 0 1 2 3 . . . . . . . . . . . . . N P 0 1 2 3 . . . . . . . . . . . . . N A A A A . . . . . . . . . . . . . Single Payment Analysis Capital Recovery Factor

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Question: If I put P into an account, how much ( A ) can I pull from the account for each of the next N periods? Equivalent by the Capital Recovery Factor 0 1 2 3 . . . . . . . . . . . . . N P 0 1 2 3 . . . . . . . . . . . . . N A A A A . . . . . . . . . . . . . Single Payment Analysis Capital Recovery Factor
What is A , given P ? 0 1 2 3 . . . . . . . . . . . . . N A A A A . . . . . . . . . . . . . P Capital Recovery Factor Equal Payment Series

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What is A given P ? Converting from our knowledge of
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## This note was uploaded on 01/11/2012 for the course EIN 4354 taught by Professor Tufecki during the Fall '08 term at University of Florida.

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Module07 - Principles of Engineering Economy Economic...

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