# Examples Of Fundamentals Of Economic Decisions

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ISyE 3025
Engineering
Economy

Fundamentals of an Economic Decision

Fundamentals of an
Economic
Decision
Jack R. Lohmann

Tech Research Corporation.

School of Industrial and Systems Engineering
Georgia Institute of Technology

Fundamentals of an Economic Decision

Example

Overview

1

 Illustrate a fundamental choice: Benefits vs. Costs
 Develop formal approach and notation
 Introduce basic decision criterion: Prospective Benefit, Bj(i), and Prospective Cost, Cj(i)

Fundamentals of an Economic Decision

2

Assume a 1-year magazine subscription costs
\$20 and a 2-year subscription costs \$35. As a a special offer, these prices are guaranteed for the next four years if you subscribe today.

Decisions based on differences t 0
1
2
3
4

3

1-Yr 2-Yr Diff. (2Yr-1Yr)
-20 -35
-15
-20
+20
-20 -35
-15
+20
-20

Which would you prefer?

Fundamentals of an Economic Decision

Fundamental choice: Benefits, Costs t 0
1
2
3
4

Benefit
Cost
Diff. (2-1) = Series - Series
-15
0
15
+20
20
0
-15
0
15
+20
20
0
FB
FC
Assume i = 0.03 per year

Fundamentals of an Economic Decision

4

A more formal approach

5

An economic decision criterion includes both:
Measure of Worth
Decision Rule

FB = 20(1.03)2 + 20 = \$41.22
FC = 15(1.03)3 + 15(1.03) = \$31.84
Since FB > FC; choose 2-Yrs

ISyE 3025 Fall 2003 Learning Cycle #2

1

Fundamentals of an Economic Decision

A special interest rate: MARR

Fundamentals of an Economic Decision

6

Interest Rate = 5%
An economical investment?
If MARR < 5%; Yes
If MARR > 5%; No

Fundamentals of an Economic Decision

Fundamentals of an Economic Decision

8

Some notation

Typically, the MARR for:

Ajt = net cash flow, where:

1) individuals represents the min. attractive opportunities to invest in money markets j = index on opportunities
Ajt > 0 is a net receipt,
Ajt < 0 is a net expense, and
Ajt = 0 for t < 0 and t > N

2) corporations represents the min. attractive opportunities to invest in the company Ajt = Bjt - Cjt, where:

Measure of Worth
N

Bj(i) = Σ

Bjt(1+i)T-t,

t=0
N

where i = MARR

Cj(i) = Σ Cjt(1+i)T-t t=0 Typically, T = 0 or N
Decision Rule
Accept (prefer) j if Bj(i) > Cj(i), otherwise reject (not prefer) j

ISyE 3025 Fall 2003 Learning Cycle #2

9

Bjt = Ajt if Ajt > 0, else Bjt = 0,
Cjt = - Ajt if Ajt < 0, else Cjt = 0

Fundamentals of an Economic Decision

Basic Criterion: Benefits and Costs

7

t
Ajt
0 - 100
1 105

i = minimum attractive rate of return (MARR) also known as -marginal growth rate, discount rate, cutoff rate, hurdle rate, yield, among others

Values of the MARR

The role of the MARR

Fundamentals of an Economic Decision

10

An example

11

A manufacturer is considering buying 10 robots to spray paint its product on the assembly line.
Each robot costs \$200,000 and has an expected life of 9 years.
The cost to install all the robots is \$45,000. Each robot is expected to reduce labor costs by
\$50,000 a year but will increase energy costs by \$15,000 a year.
If the MARR = 10% per year, are the robots economical?

2

Fundamentals of an Economic Decision

. . . an example t Problem Data
0
10(-200K)- 45K
1
10(+50K-15K)
2

N=9

Fundamentals of an Economic Decision

12

ARt
- 2,045K
350K
350K

. . . an example

13

t
ARt = BRt - CRt
0 - 2,045K
0 2,045K
1
350K 350K 0
2
350K 350K 0

N=9 350K 350K 0

350K

BR(.1) = 350(F/A,.1,9) = \$4752.8K
CR(.1) = 2045(F/P,.1,9) = \$4822.0K
Reject; note only 1.4% difference!

Fundamentals of an Economic Decision

Summary

14

 A fundamental choice:
Benefits vs. Costs
 Formal approach and notation Î Criterion = MOW + DR
Î MARR
Î Ajt, Bjt, Cjt
 Basic decision criterion:
Î Bj(i), Cj(i)

Three classic economic criteria based on worth:
 Future Worth, FWj(i)
 Present Worth, PWj(i)
 Annual Worth, AWj(i)

Future Worth,
Present Worth,
Annual Worth
Jack R. Lohmann