1. CTC 475 Review Bonds Bonds Not straightforward because bonds can be bought and/or sold between the date of issuance and the date of maturity Not straightforward because bonds can be bought and/or sold between the date of issuance and the date of maturity P=Vr(P/A i,n )+F(P/F i,n ) P=Vr(P/A i,n )+F(P/F i,n ) Find P Find P Find F Find F Find I Find I Cash flow frequency, i and n must match Cash flow frequency, i and n must match

2. CTC 475 Comparing Alternatives

3. Objectives Know the steps for comparing alternatives Know the steps for comparing alternatives Know how to determine the possible set of alternatives Know how to determine the possible set of alternatives Know how to develop cash flows using the same planning horizon Know how to develop cash flows using the same planning horizon

4. Steps for Comparing Alternatives 1. Determine the feasible alternatives 2. Define the planning horizon 3. Develop the cash flow profiles 4. Specify the MARR 5. Compare the alternatives 6. Perform supplementary analyses 7. Select the preferred alternative

5. Determine Feasible Alternatives Alternatives can consist of various investment proposals Alternatives can consist of various investment proposals Proposals can be: Proposals can be: Mutually exclusive Mutually exclusive Independent Independent Contingent upon another proposal Contingent upon another proposal

6. Mutual Exclusive At most one project out of the group can be chosen: At most one project out of the group can be chosen: If I have proposals A, B, and C------- only A or B or C can be chosen (not a combination)

7. Independent All, none or any combination may be selected All, none or any combination may be selected Total number of alternatives = 2 m where m is the number of proposals Total number of alternatives = 2 m where m is the number of proposals If there are 4 proposals, the total number of options is 2 4 = 16 alternatives If there are 4 proposals, the total number of options is 2 4 = 16 alternatives

8. Contingent The choice of a project is conditional on the choice of another project The choice of a project is conditional on the choice of another project If A is contingent on B then A can’t be implemented unless B is also implemented

9. Example of Defining Alternatives and Developing Cash Flow Profiles Steps 1 and 3 (planning horizon is the same)

10. Three Proposals-A,B,C EOYABC 0-$20K-$30K-$50K 1-$4K$4K-$5K 2$2K$6K$10K 3$8K$8K$25K 4$14K$10K$40K 5$25K$20K$10K

11. Number of Alternatives 2 3 = 8 alternatives

12. Alternatives ABC Initial Investment 000$0 001$50K 010$30K 011$80K 100$20K 101$70K 110$50K 111$100K

13. Restrictions 1. Budget for initial investment is $50K 2. Proposal B is contingent on proposal A (can’t do B unless A is implemented) 3. Proposals A and C are mutually exclusive (A & C can’t be implemented together)

14. Alternatives ABC Initial Investment 000$0 001$50K 010 $30K (2) 011 $80K (1,2) 100$20K 101 $70K (1,3) 110$50K 111 $100K (1,3)

15. Remaining Alternatives Null or “Do Nothing” Null or “Do Nothing” C only C only A only A only A and B A and B

16. Cash Flow Profiles EOYNullCAA&B 0$0-$50K-$20K-$50K 1$0-$5K-$4K$0 2$0$10K$2K$8K 3$0$25K$8K$16K 4$0$40K$14K$24K 5$0$10K$25K$45K

17. Planning Horizon (PH) Period of time over which service is required Period of time over which service is required Period of time over which receipts continue to occur Period of time over which receipts continue to occur Period of time over which reasonably accurate cash flow estimates can be provided Period of time over which reasonably accurate cash flow estimates can be provided

18. Planning horizon, working life of equipment and depreciable life are not necessarily the same

19. When comparing Alternatives----- The Planning Horizon must be the same

20. Methods: Least common multiple (LCM) Least common multiple (LCM) Shortest life Shortest life Longest life Longest life Some determined life Some determined life

21. Example Alternatives A, B & C have 3, 6, and 5- year lives Alternatives A, B & C have 3, 6, and 5- year lives Least common multiple = 30 years Least common multiple = 30 years Shortest life = 3 years Shortest life = 3 years Longest life = 6 years Longest life = 6 years Standard planning horizon could be 5 years (or 4 years or some other number) Standard planning horizon could be 5 years (or 4 years or some other number)

22. Problems in standardizing the PH LCM-usually assume cash flow patterns repeat LCM-usually assume cash flow patterns repeat Shortest Life-Must estimate the unused portions of the alternatives (salvage value) Shortest Life-Must estimate the unused portions of the alternatives (salvage value) Longest Life-Must estimate cash flow patterns between the shortest and longest life Longest Life-Must estimate cash flow patterns between the shortest and longest life

23. Example of Standardizing the PH and Developing Cash Flow Profiles Steps 2/3 Alternative 1 (use existing equipment) PH=3 years Alternative 1 (use existing equipment) PH=3 years Alternative 2 (buy new $50K) PH=6 years Alternative 2 (buy new $50K) PH=6 years Alternative 3 (buy new $75K) PH=5 years Alternative 3 (buy new $75K) PH=5 years

24. Standardizing PH-Example EOY Alt 1 (3 yrs) Alt 2 (6 yrs) Alt 3 (5 yrs) SalvgSalvgSalvg 000-50K50K-75K75K 14500020K35K20K55K 24500020K25K25K40K 34500020K15K30K25K 420K5K35K10K 520K040K0 620K0

25. Example-LCM EOY Alt 1 Alt 2 Alt 3 00-50K-75K 1450020K20K 2450020K25K 3450020K30K 4450020K35K 5450020K -35K (40K-75K 64500 -30K (20K-50K) 20K 7450020K25K 8450020K30K ……..4500 *-30K@ yrs 12,18,24 *-35K@yrs 10,15,20,25 30450020K40K

26. Example-Shortest Life EOY Alt 1 Alt 2 Alt 3 00-50K-75K 14,50020K20K 24,50020K25K 34,500 35K (20K+15K) 55K (30K+25K

27. Example-Longest Life EOY Alt 1 Alt 2 Alt 3 00-50K-75K 1450020K20K 2450020K25K 3450020K30K 4450020K35K 5450020K40K 6450020K4500

28. Next lecture Methods for Comparing Alternatives: Methods for Comparing Alternatives: Ranking (PW, AW, FW) Ranking (PW, AW, FW) Incremental (all) Incremental (all) Supplementary Analyses Supplementary Analyses Selling the Alternative Selling the Alternative