1. Lecture 5 Engineering Economics ENGR 3300 Department of Mechanical Engineering Inter American University of Puerto Rico Bayamon Campus Dr. Omar E. Meza Castillo omeza@bayamon.inter.edu http://www.facultad/bayamon.inter.edu/omeza

2. Lecture 5 Present Worth Analysis

3. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Bank Loan vs. Investment Project

4. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Project Cash Flow  Representation of project’s future earnings, along with the capital expenditures and annual expenses (such as wages, raw materials, operating costs, maintenance costs and income taxes) at different time periods is called a Project Cash Flow.

5. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Identifying Project Cash Flows

6. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón 6

7. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón 7

8. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Initial Project Screening Methods  One of the primary concerns of most businesspeople is whether and when the money invested in a project can be recovered. The payback method screens projects on the basis of how long it takes for net receipts to equal investment outlays.  This calculation can take one of two forms: either ignore time-value-of-money considerations or include then. The former case is usually designated the conventional payback method, the latter case the discounted payback method.

9. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Payback Period  Principle: How fast can I recover my initial investment?  Method: Based on cumulative cash flow (or accounting profit)  Screening Guideline: If the payback period is less than or equal to some specified payback period, the project would be considered for further analysis.  Weakness: Does not consider the time value of money

10. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Payback Period: The time it takes to Pay Back  Principle: How fast can I recover my initial investment?  Method: Based on cumulative cash flow (or accounting profit)  Screening Guideline: If the payback period is less than or equal to some specified payback period, the project would be considered for further analysis.  Weakness: Does not consider the time value of money

11. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Convectional Payback Period  Consider the cash flows given in the example of Computer Process Control System. Determine the payback period.

12. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Convectional Payback Period with Salvage Value Example 5.3

13. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón -100,000 -50,000 0 50,000 100,000 150,000 012 3 456 Years (n) 3.2 years Payback period $85,000 $15,000 $25,000 $35,000 $45,000 $35,000 0 123456 Years Annual cash flow Cumulative cash flow ($)

14. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Comments  If the cash flow occur continuously throughout the year, the payback period calculation needs adjustment.  A negative balance of $10,000 remains at t he start of year 4. If $45,000 is expected to be received as a more or less continuous flow during year 4, the total investment will be recovered two tenths ($10,000/$45,000) of the way through the four year. Thus, in this situation, the payback period is 3.2 years.

15. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Benefits and Flaws of Payback Screening Investment Cash Flows for Two Competing Projects

16. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Discounted Payback Period  Is the number of years required to recover the investment from discounted cash flows.

17. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón

18. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón

19. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Present-Worth Analysis

20. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Present-Worth Analysis

21. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Present-Worth Analysis

22. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Present-Worth Analysis  Principle: Compute the equivalent net surplus at n = 0 for a given interest rate of i.  Decision Rule: Accept the project if the net surplus is positive. 2 3 4 5 0 1 Inflow Outflow 0 PW(i) inflow PW(i) outflow Net surplus PW(i) > 0

23. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Net Present Worth: Uniform Flows

24. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Net Present Worth: Uniform Flows

25. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Net Present Worth: Uneven Flows

26. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Net Present Worth: Uneven Flows $75,000 $24,400 $27,340 $55,760 0 12 3 outflow inflow

27. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Present Worth Amounts at Varying Interest Rates

28. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón

29. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Future-Worth Analysis  Net present worth measures the surplus in an investment project at time 0. Net future worth (NFW) measures this surplus at a time other than 0.

30. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Net Future Worth: At the End of the Project

31. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Net Future Worth: At the End of the Project

32. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Net Future Worth: At the End of the Project

33. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Project Balance Concept N0123N0123N0123N0123 Beginning Balance Interest Payment Project Balance -$75,000 -$11,250 +$24,400 -$61,850 -$9,278 +$27,340 -$43,788 -$6,568 +$55,760 +$5,404 Net future worth, FW(15%) PW(15%) = $5,404 (P/F, 15%, 3) = $3,553

34. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Project Balance Diagram 60,000 40,000 20,000 0 -20,000 -40,000 -60,000 -80,000 -100,000 -120,000 01230123 -$75,000 -$61,850 -$43,788 $5,404 Year(n) Terminal project balance (net future worth, or project surplus) Discounted payback period Project balance ($)

35. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Capitalized-Equivalent Worth  Principle: PW for a project with an annual receipt of A over infinite service life  Equation: CE( i ) = A ( P / A, i, ) = A / i P = CE(i)

36. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Capitalized-Equivalent Worth

37. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Capitalized-Equivalent Worth

38. Lecture 5 ENGR 3300 Engineering Economics Inter - Bayamón Homework 3  www.bc.inter.edu/facultad/omezawww.bc.inter.edu/facultad/omeza