1. MIE 754 - Class #3 Manufacturing & Engineering Economics Concerns and QuestionsConcerns and Questions Quick Recap of Previous ClassQuick Recap of Previous Class Today’s Focus:Today’s Focus: –Chap 2 - Computations Involving Interest (continued) Hmwk #2 Due next class:Hmwk #2 Due next class: –Chap 1 - Probs: 1, 6, 11, 12, 13

2. Concerns and Questions?

3. Quick Recap of Previous Class b Terminology b Equivalence b Time Value of Money b Simple and Compound Interest b Present and Future Values

4. Cash Flow Diagrams F occurs n periods after P What if you know F and want to find P? F=P(1+i) n P=?

5. Example of moving money through time: Suppose I=6%, F=1191.00, and n=3 How much is this equivalent to now? Additional examples

6. Cashflow Series: Uniform b P occurs one time period before the 1st uniform cashflow (A) b F occurs at the same time as the last uniform cashflow (A) b (P/A i,n), (A/P i,n), (F/A i,n), (A/F i,n) b Be consistent in time units for i and n b n is ALWAYS = # of A’s of uniform cashflow series

7. Cashflow Series: Uniform P F A A A A

8. Lotto Example b If you win $5,000,000 in the Virginia lottery, how much will you be paid each year? How much money must the lottery commission have on hand at the time of the award? Assume interest = 3% per year and that there are 20 payments.

9. Several Additional In-Class Examples

10. Cashflow Series: Gradient b Cash flows change by a constant amount each time period b Easiest if align with a uniform series b Then follow guidelines for uniform series b We’ll only be concerned with two factors (P/G i,n) and (A/G i,n)

11. Cashflow Series: Gradient b 4 Types of Gradient positive and increasingpositive and increasing positive and decreasingpositive and decreasing negative and increasingnegative and increasing negative and decreasingnegative and decreasing b Several Examples

12. Cashflow Series: Special Considerations b Deferred Cashflows In-class examplesIn-class examples b Changing Interest Over Study Period In-class examplesIn-class examples

13. Nominal and Effective Interest Rates b r% compounded ‘x’-ly b i = r/m interest per compounding period, where r= nominal rate and m= # of compounding periods b 12% compounded quarterly is 3% every quarter (every 3 months) b 12% compounded semi-annually means?

14. Example b You deposit $500 into a savings account earning 6% compounded semiannually. How much money is in the account after 4 years?

15. Effective Interest Rate b i eff = (1 + r/M) m - 1 where b M = number of interest periods per year b r = nominal interest rate b m = number of interest periods of concern

16. Examples

17. More Examples b What is the effective 1/2 year (semi- annual) interest rate for 12% compounded quarterly?

18. More Examples b A variety of cashflow diagram types and effective interest b In-class examples for: UniformUniform GradientGradient SingleSingle

19. Where does the i eff formula come from?

20. Economic Effectiveness  Present Worth - equivalent worth of entire cash flow at t= 0  Annual Worth - equivalent uniform annual series  Future Worth - equivalent worth at t=n  Rate of Return (Chap 4)  Benefit-Cost Ratio (Chap 7)