1. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. CHAPTER VI Annual Worth Analysis McMc Graw Hill ENGINEERING ECONOMY Fifth Edition Blank and Tarquin

2. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. Learning Objectives: AW over one project life cycle AW calculations Selecting Alternatives by Annual Worth AW analysis for a permanent investment

3. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3 Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. CHAPTER VI 6.1 AW over one project life cycle McMc Graw Hill ENGINEERING ECONOMY Fifth Edition Blank and Tarquin

4. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 4Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.1 Advantages and Uses of Annual Worth Popular Analysis Technique Easily understood – results are reported in $/time period Eliminates the LCM problem associated with the present worth method Only have to evaluate one life cycle of a project

5. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 5Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.1 AW Calculations General in nature such that: AW = PW(A/P,i%,n) AW = FW(A/F,i%,n) Convert all cash flows to their equivalent annual amounts

6. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 6Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.1 Repeatability Assumption Given alternatives with unequal lives The assumptions are: 1.The services so provided are needed forever 2.The first cycle of cash flows is repeated for successive cycles 3.All cash flows will have the same estimated values in every life cycle

7. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6. 1. One or More Cycles Cycle 1Cycle 2Cycle K Annualize any one of the cycles AW assumes repeatability of CF’s Find the annual worth of any given cycle ($/period)

8. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 8Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.1 6-year & 9-year Problem (Ex. 6.1) See Example 6.1 Location A Location B First cost,$ -15,000 -18,000 Annual Lease cost -3,500 -3,100 Deposit return,$ 1,000 2,000 Lease term, years 6 9 Determine which location should be selected, if the MARR is 15% per year.

9. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 9Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.1 6-year & 9-year Problem (Ex. 6.1) Need an 18-year study period for both Means a lot of calculation time! 6-year Project 9-year Project

10. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 10Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.1 Example Consider a project with $3,000 annual operating cost and a $5,000 investment required each 5 years. i = 10% For one cycle EAC = 3,000 + 5,000 (A|P, 10%, 5) = $4,319/yr $5,000 0 1 2 3 4 5 A 1-5 = $3,000

11. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 11Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.1 Multiple cycle..same result! For two cycles EAC = 3000 + 5000 (1+(P|F,.10, 5))(A|P,.10, 10) = 3000 + 1319 = $4319/yr 0 1 2 3 4 5 6 7 8 9 10 $5,000 A 1-10 = $3,000

12. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 12Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.1 AW Requirements Similar to the Present Worth Method, AW analysis requires: A discount rate before the analysis is started Estimates of the future cash flows Estimate of the time period(s) involved

13. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 13 Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. CHAPTER VI 6.2 AW Calculation McMc Graw Hill ENGINEERING ECONOMY Fifth Edition Blank and Tarquin

14. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 14Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.2 Capital Recovery and AW Values Assume the potential purchase of any productive asset One needs to know or estimate: Initial Investment - P Estimated Future Salvage Value - S Estimated life of the asset - N Estimated operating costs and timing Operative interest rate – i%

15. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 15Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.2 Capital Recovery Cost Thus, management is concerned about the equivalent annual cost of owing a productive asset. This cost is termed “Capital Recovery Cost” CR is a function of {P, S, i%, and “n” }

16. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 16Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.2 Capital Recovery Cost (CR) CR = the equivalent annual worth of the asset given: Capital Recovery (CR) is the annualized equivalent of the initial investment P 0 and the annualized amount of the future salvage value F n ………. P0P0 FNFN 0 1 2 3 N-1 N S

17. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 17Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.2 Capital Recovery Cost – CR Given: Convert to: ………. 0 1 2 3 N-1 N P0P0 FNFN $A per year (CRC) P0P0 FNFN 0 1 2 3 N-1 N ……….S

18. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 18Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.2 Capital Recovery Cost COMPUTING CR FOR INVESTMENTS WITH SALVAGE VALUES: Method I - compute EAC of the original cost and subtract the EAC of the salvage value EAC = P(A|P, i, n) - S(A|F, i, n)

19. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 19Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.2 More Traditional CR Approach Method II – Subtract the salvage value from the original cost and compute the annual cost of the difference. Add to the interest that the salvage value would return each year, SV (i). CR(i%)= (P - S) (A|P, i, n) + S(i)

20. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 20 Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. CHAPTER VI 6.3 Selecting Alternatives by Annual Worth McMc Graw Hill ENGINEERING ECONOMY Fifth Edition Blank and Tarquin

21. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 21Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.3 Alternatives by Annual Worth Mutually Exclusive Analysis If pure cost situation – select min. cost alternative If mixed costs and revenues – select the max. AW (i%) alternative Single Alternative Accept if AW positive, else reject

22. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 22Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.3 Example 6.3 Cash Flow Diagram is: 1 2 3 4 5 P=-23,000S = +$1,500 -$650 -$700 -$750 -$800 -$850 A + = $1,200/yr

23. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 23Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.3 Example 6.3 The Capital Recovery component is: 1 2 3 4 5 P=-23,000 S = +$1,500 CR(10%) = -23,000(A/P,10%,5) + 1,500(A/F,10%,5) = -$5,822

24. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 24Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.3 Example 6.3 Revenue – Op Costs are: 1 2 3 4 5 A + = $1,200/yr $650 $700 $750 $800 $850

25. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 25Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.3 Example 6.3 Cost Revenue component is seen to equal (costs treated as positive values): =+550 – 50(A/G,10%,5) = 550 – 90.50 = $459.50 1.8101

26. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 26Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.3 Example 6.3 Total Annual worth (CR + Cost/Rev) CR(10%) = -$5,822 Revenue/Cost Annual amount: $459.50 AW(10%) = -$5,822+$459.50 AW(10%) = $5,362.50 This amount would be required to recover the investment and operating costs at the 10% rate on a per-year basis

27. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 27 Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. CHAPTER VI 6.4 AW of a Perpetual Investment McMc Graw Hill ENGINEERING ECONOMY Fifth Edition Blank and Tarquin

28. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 28Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.4 AW of a Perpetual Investment EAC of a perpetual investment If an investment has no finite cycle, it is called a perpetual investment. If “P” is the present worth of the cost of that investment, then EAC is P times i. EAC=A = P* i Remember: P = A/i From the previous chapter

29. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 29Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. 6.4 AW of a Perpetual Investment Example 6.6 One person received a bonus of $10,000. If she deposits it now at an interest rate of 8% per year, how many years must the money accumulate before she can withdraw $2000 per year forever?

30. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 30Blank & Tarquin: 5th Edition. Ch. 6 Authored by: Dr. Don Smith, Texas A&M University. End of Chapter 6 Lecture Set