1. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-1 Developed By: Dr. Don Smith, P.E. Department of Industrial Engineering Texas A&M University College Station, Texas Executive Summary Version Chapter 5 Present Worth Analysis

2. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-2 LEARNING OBJECTIVES 1.Formulating alternatives 2.PW of equal-life alternatives 3.PW of different-life alternatives 4.Future worth analysis 5.Capitalized Cost 6.Payback period 7.Life cycle Cost 8.PW of Bonds 9.Spreadsheets

3. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-3 Sct. 5. 1 Formulating Mutually Exclusive Alternatives  One of the important functions of financial management and engineering is the creation of “alternatives”  If there are no alternatives to consider then there really is no problem to solve!  Given a set of “feasible” alternatives, engineering economy attempts to identify the “best” economic approach to a given problem

4. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-4 Types of Economic Projects  Mutually exclusive alternatives  From a set of feasible alternatives, pick one and only one to execute  Mutually exclusive alternatives compete against each other  Independent projects  From a set of feasible alternatives select as many as can be funded in the current period  The “Do Nothing” (DN) alternative should always be considered

5. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-5 Cash Flow Types for Projects  Revenue – each alternative generates costs and revenues over the estimated life of the project.  Criteria: Select the alternative that maximizes the economic measure of merit  Service – each alternative has only current and future costs over the estimated life of the project.  Criteria: Select the alternative that minimizes the economic measure of merit, which is a cost-based measure

6. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-6 Sct 5.2 Present Worth Analysis of Equal-Life Alternatives  Find PW at a stated interest rate, which is usually equal to or greater than the organization’s established MARR  A process of obtaining the equivalent worth of future cash flows BACK to some point in time. – called the Present Worth Method

7. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-7 Present Worth Approach: Mutually Exclusive Projects  Alternatives must be of equal service, that is, evaluate all alternatives over the same number of years.  For a single project, project is financially viable if PW  0 at the MARR  For 2 or more alternatives, select the one with the (numerically) larger PW value  Examples: PW 1 PW 2 Select $-1500 $-500 Alt 2 +2500 -500 Alt 1 -1200 +25 Alt 2

8. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-8 PW method for independent projects  Select all projects with PW  0 when the MARR is used in calculating the PW values  This assumes no restriction of how much is invested during a given time period.  If investment limit exists, which it usually does, use the techniques of chapter 12

9. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-9 Sct 5.3 Present Worth Analysis of Different-Life Alternatives  For alternatives with un-equal lives the rule is: PW of the alternatives must be compared over the same number of years  Called “ Equal Service ” requirement Approach – 1 of 2 approaches  LCM -- Evaluate the alternatives over the lowest common multiple of lives, e.g., lives of 4 and 6, use n = 12 and assume re-investment at same cash low estimates  Study period -- assume a planning horizon and evaluate the alternatives over this number of years

10. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-10 PW Analysis using LCM Approach  Example 5.2 is a good illustration of LCM method at i = 15% per year  Location A has n A = 6 years and B has n B = 9 o LCM = 18 years; determine both PW values over 18 years o Assume two re-purchases of A at the end of years 6 and 12 o Assume one re-purchase of B at end of year 9 o All cash flow estimates are assumed to continue for 18 years, including the end-of-lease ‘return deposit’  PW A = $-45,036 and PW B = $-41,384  Select location B with the (numerically) larger PW, which has the smaller equivalent PW cost

11. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-11 Sct 5.4 Future Worth Analysis  In some applications, a future worth analysis is preferred  For equal service, determine LCM of lives  Find PW of each alternative  Then compute FW in LCM year at the same interest rate used to find PW of each alternative  For the study period approach, use the appropriate value of “n” to take cash flows forward for each alternative

12. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-12 Sct 5.5 Capitalized Cost Calculations and Analysis  CAPITALIZED COST- Present worth of a project that lasts forever. Analysis method for:  Government or public projects;  Roads, dams, bridges, project that basically possess infinite life;  Infinite analysis period:  “n” in the problem is either very long, indefinite, or infinity.

13. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-13 P/A Factor as “n” approaches infinity  The P/A factor is:  On the right hand side, divide both numerator and denominator by (1+i) n  If “n” approaches  the above reduces to:  Let CC represent “capitalized cost”  Annual amount forever is A = Pi = (CC)i

14. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-14 Examples of capitalized cost analyses  Example 5.4 -- Finds the CC and A values of a county government software system expected to be used for the indefinite future  Example 5.5 -- Compares the CC values for 2 indefinite-life bridge designs – suspension and truss  Example 5.6 -- Uses CC method to compare short life (5 year) and very long life (indefinite) alternatives

15. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-15 Sct 5.6 Payback Period Analysis  Also call payout analysis  Extension of present worth method  Two forms: 1. With no interest -- i = 0% (no-return payback) 2. With an assumed interest rate -- i > 0% (discounted payback analysis)  Technique: estimates the time n p to recover the initial investment in a project, either with or without interest earned

16. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-16 Payback Period Analysis-RULE  Never use payback analysis as the primary means of making an accept/reject decision on an alternative!  Best used as a screening technique or preliminary analysis tool  Historically, this method was a primary analysis tool and often resulted in incorrect selections  To apply, the cash flows must have at least one (+) cash flow in the sequence

17. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-17 Basic Formula for Payback Analysis  Determine the number of years n p that it takes for all negative net cash flows to exactly equal all positive cash flows  If i = 0% and all NCF estimates are the same, the payback calculation simplifies to n p = P/NCF

18. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-18 Payback - Interpretations and Fallacies  Common managerial philosophy is that a shorter payback is preferred to a longer payback period; this is not a good approach from economic vantage  Not a preferred method for final decision making – better as a screening tool  Ignores all cash flows after the payback time period  May not use all of the cash flows in the cash flow sequence.  Refer to Example 5.7 Don’t use no-return (i = 0%) payback for final decisions. It  Neglects any required return on the investment  Neglects all cash flows after time n p including any positive cash flows that contribute to making a positive return on the investment

19. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-19 Sct 5.7 Life Cycle Costs  Another extension of present worth method  Applied to systems over their total estimated system life span  Critical to estimate the system life span in years  Difficulties – estimation of costs far removed from time t = 0  The life cycle may be defined by two main time phases

20. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-20 Life Cycle Concept Two main phases are:  Acquisition Phase  Operations Phase  Many cash flow estimates are needed, thus making the analysis less reliable as the life gets longer  See Example 5.9

21. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-21 Sct 5.8 Present Worth of Bonds  Bond problems – typical present worth application  Common analysis problem in the world of finance  Bond is basically an “ iou ”  Bond – represent “debt” financing  Corporations sell bonds to raise capital  Bonds pay a stated rate of interest (bond dividend) to the bond holder for a specified period of time

22. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-22 Bonds Parameters and Examples 1. Face value, V = $1000 2. Life of the bond, n = 30 years 3. Coupon rate, b = 8% per year, paid quarterly 4. Number of dividend payments per year, c = 4 Bond dividend = I = Vb/c I = 1000(.08)/4 = $20 per quarter

23. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-23 Cash Flow Profile for Bond Purchase Typical cash flow to bond buyer: 0 1 2 n-1 n // Bond Purchase, V at t = 0 Bond interest payments Repayment of the face value

24. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-24 Discounting a Bond  Bonds are seldom purchased for their face value  Most of the time a bond is “ discounted ” in the bond market by a few percentage points  But the face value and the periodic dividend payments remain unchanged  For example, V = $10,000 bond purchased for 98% of V now, but repays full face value, V, in 10 years

25. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-25 Bond Purchase: Example  $5,000 10-year bond that pays 4.5% semi- annually is under consideration  As the potential buyer you require a rate of return of 8% per year, compounded quarterly on your purchase  What should you be willing to pay for this bond now in order to receive at least the required rate of return?

26. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-26 Bond Purchase: Example  Draw the cash flow diagram using “6 month periods” as the unit of time  Bond dividend = $5000(0.045)/2 = $112.50 every 6 months / / / 0 1 2 3 4 18 19 20 A = $112.50 $5,000 PW = ? (willing to pay) “n” is 20 since bond dividend payments are semi-annual

27. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-27 Bond Purchase: Example  Investor requires 8% per year, compounded quarterly  i/qtr = 0.8/4 = 2% per quarter  Effective semiannual rate is (1.02) 2 – 1 = 4.04% per 6 months / / / 0 1 2 3 4 18 19 20 $5,000 A = $112.50 Find the PW at 4.04% of this cash flow series PW = max amount to pay for the bond

28. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-28 Bond Purchase: Example P = 112.50(P/A,4.04%,20) + 5000(P/F,4.04%,20) = $3788  If the bond can be purchased for $3788, or less, the investor will make the required rate of return  If the bond cost more than $3788, the investment is not worth it financially

29. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-29 Sct 5.9 Spreadsheet Applications – PW Analysis and Payback Period  Review the Excel financial functions  NPV and PV functions are useful analysis tools built into Excel  Refer to Example 5.12 and 5.13

30. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-30 Chapter Summary  PW method requires comparison over same number of years – equal service comparison  Alternative comparison using PW – select the alternative with the numerically larger PW value, that is, higher new positive cash flow value, or lower net cost in PW terms  Extension of PW method are: capitalized cost, life- cycle costs, payback period, bonds  Never use payback period as the primary selection method; only as supplemental with other methods such as PW, FW, AW or ROR (as covered in later chapters )

31. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6 th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 5-31 Chapter 5 End of Slide Set