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.
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
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
“
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.
