1. Engineering Economy Professor: Dr. Miguel Alonso Jr.

2. Outline Value and Interest Cash Flow Diagrams Cash Flow Patterns Equivalence of Cash Flow Patterns Unusual Cash Flows and Interest Periods

3. As an engineer, your job is to produce good results Good results are often accompanied by undesireable effects Costs of manufacturing/construction Selecting the best design requires anticipation and comparison of good and bad outcomes If “good” is defined as positive monetary value, then design decisions may be guided by economic analysis

4. Value and Interest Value is not amount The value of an amount of money depends on when the amount is received or spent This is know as the “Time Value of Money” Example: one dollar a year from now is of less value than a dollar today The difference between an anticipated amount and its current value is called interest and is frequently expressed as a time rate Usually expressed on a yearly basis

5. Example What is the current value of a dollar given to you in a year if the interest rate is 10%? What amount must be paid in two years to settle a current debt of $1,000 if the interest rate is 6%?

6. Cash flow diagrams graphical representation of economic cash flow Horizontal time axis and vertical vectors representing dollar amounts Income is up and expenditures are down Draw the cash flow diagrams for the previous examples

7. Cash flow patterns P-pattern- Single amount (P) occurring at the beginning of n rears F-pattern - Single amount (F) occurring at the end of n rears A-pattern – Equal amount (A) occurring at the ends of each n years G-pattern – End of year amounts increasing by an equal annual gradient (G)‏

8. Equivalence of Cash flow patterns Two cash flow patterns are said to be equal if they have the same value Most of the effort is directed at finding a cash flow pattern that is equivalent to a combination of other patterns F = (F/P) i n P See chart of formulas on pg 521 Examples

9. Unusual Cash Flows and Interest Periods Payments at beginnings of years Annual payments with interest compounded m times per year Continuous compounding Annual compounding with payment every m years Exercise 18.70 to 18.77