Economic Equivalence

Lecture No.3Chapter 2Fundamentals of Engineering EconomicsCopyright © 2008

At Issue – How Do You Compare Two Different Money Transactions? Consider the following two cash receipts.

Which option would you prefer?

0 1 2 3 0 1 2 3

Option 1 Option 2

$1,000

$1,200

Which Option Would You Prefer?

What do we mean by “economic equivalence?”

Why do we need to establish an economic equivalence?

How do we establish an economic equivalence?

Economic Equivalence

Definition - Economic Equivalence Economic equivalence exists between cash

flows that have the same economic effect and could therefore be traded for one another.

Even though the amounts and timing of the cash flows may differ, an appropriate interest rate (discount rate) makes them equal.

Using Compound Interest to Establish Economic Equivalence

0

1 2 33 4 5

$2,042

5

F

0

At 8% interest, what is the equivalent worth of $2,042 now 5 years from now?

If you deposit $2,042 today in a savingsaccount that pays 8% interest annually,how much would you have at the end of5 years?

=

Practice Problem

Solution

5$2,042(1 0.08)$3,000

F

Example 2.2 Equivalence

$2,007$1,500

50

At what interest rate would these two payments be equivalent?

i = ?

Steps to Establish an Economic Equivalence

Example 2.3 Equivalence Calculation

0 1 2 3 4 5

$100$80

$120$150

$200

$100

0 1 2 3 4 5

V=

Compute the equivalent lump-sum amount at n = 3 at 10% annual interest.

Equivalent Worth Calculation at n = 3.

At What Interest Rate Are These Two Transactions Equivalent?

0 1 2 3 0 1 2 3

Option 1 Option 2

$1,000

$1,200

Select the base period at n = 3.

0 1 2 3 0 1 2 3

Option 1 Option 2

$1,000

$1,200

$1, 000(1+i)22

2

0.0912

1,000(1 ) 1,200

(1 ) 1.22ln(1 ) ln1.2ln(1 ) 0.0912

19.54%

i

iii

i ei

Base period

Lottery Problem – What interest rate are the two payoff options equivalent?

0 1 2 3 4 5 24 25

$10.57M

$167M

0

Solution – about 4.5%Period Amount Interest Rate Present Worth

0 10.57 0.045 10.5701 10.57 0.045 10.1152 10.57 0.045 9.6793 10.57 0.045 9.2624 10.57 0.045 8.8645 10.57 0.045 8.4826 10.57 0.045 8.1177 10.57 0.045 7.7678 10.57 0.045 7.4339 10.57 0.045 7.113

10 10.57 0.045 6.80611 10.57 0.045 6.51312 10.57 0.045 6.23313 10.57 0.045 5.96414 10.57 0.045 5.70815 10.57 0.045 5.46216 10.57 0.045 5.22717 10.57 0.045 5.00118 10.57 0.045 4.78619 10.57 0.045 4.58020 10.57 0.045 4.38321 10.57 0.045 4.19422 10.57 0.045 4.01323 10.57 0.045 3.84124 10.57 0.045 3.67525 10.57 0.045 3.517

Sum 167.304