Engineering

Economy

Fundamentals of an Economic Decision

Fundamentals of an

Economic

Decision

Jack R. Lohmann

Copyright 1999. Georgia

Tech Research Corporation.

All rights reserved.

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

Copyright 1999. Georgia

Tech Research Corporation.

All rights reserved.

Future Worth, Present Worth, Annual Worth

Overview

ISyE 3025

Engineering