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Economic Equivalence
IE 226
IE 226
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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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Example
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 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.
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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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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)
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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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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
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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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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)
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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 20052006: 6% compounded semiannually
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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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 .
 Fall '09
 TONKAY

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