Python (four Formulas)

IT 518 Systems Engineering & Integration

Chapter 8: Economic Considerations and Models

Part 3

1 © Copyright 2020 Bill Pierce

Time Value of Money

• Limited resource – best use

• Project vs. project evaluations difficult

• Need “common denominator” • Money earns interest

• Today’s dollar worth more than future dollar

• Question is “how much more?”

2

Life Cycle Costs & Income Analysis

• Provides basis for project/alternative cost comparisons

• Interest Formulas • i = annual rate of interest (%) • n = number of interest yielding time periods (usually annual) • P = Principle amount (current dollar value) • A = Single amount in a series of n equal amounts at end of each interest

period

• F = Sum of compound amounts of A at interest rate i

3

Compounding – Single-Payment Compound-Amount

4

(1 + 𝑖)𝑛 Single-Payment Compound-Amount Factor

𝐹 = 𝑃(1 + 𝑖)𝑛 Eqivalence Formula

Summary of Interest Formulas

5

Geometric-Gradient-Series Formula

• Annual money flows increase or decrease over time by a constant percentage • g designates percentage change in magnitude of money flow from one period

to the next

• Magnitude of the tth flow is related to flow F1 defined as follows

6

𝐹𝑡 = 𝐹1(1 + 𝑔) 𝑡−1 𝑡 = 1,2, …,𝑛

Geometric-gradient series with g > 0

Economic Equivalence

• Economic Equivalence: two (or more) cost comparisons must have same • Sums of money

• Time frames

• Interest rates

• Wide range of formulas, tools, and techniques for evaluating economic equivalence • Ex: At an interest rate of 10% for 8 years, a principle amount of $1 is equivalent

to $2.144

• Appendix E: Interest Factor Tables

• Also calculated as (1 + 𝑟)𝑛= (1 + .1)8= 2.14358881 rounded to 2.144 • r = interest rate period

• n = number of time periods

7

Equivalence Function Diagrams (1)

• What value of i will make a principle amount of $1,500 equivalent to a final sum of $5K in 10 years (n=10)?

8

From the diagram, i is between 12% and 14%, from the slope of the curve, about 13%, the point of intersection.

Calculation: 𝑖 = ( 𝐹

𝑃 ) 1

𝑛 − 1

Equivalence Function Diagrams (2)

• What value of n will make a principal amount of $4,000 equivalent to a final sum of $8,000 if interest is 8%?

9

From the diagram, n is between 9 and 10 years.

Calculation: 𝑛 = ln(

𝐹

𝑃 )

ln(1+𝑖)