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

CTC 475 Comparing Alternatives

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

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

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

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)

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

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

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

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

Number of Alternatives 2 3 = 8 alternatives

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

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)

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)

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

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

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

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

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

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

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)

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

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

Standardizing PH-Example EOY Alt 1 (3 yrs) Alt 2 (6 yrs) Alt 3 (5 yrs) SalvgSalvgSalvg K50K-75K75K K35K20K55K K25K25K40K K15K30K25K 420K5K35K10K 520K040K0 620K0

Example-LCM EOY Alt 1 Alt 2 Alt K-75K K20K K25K K30K K35K K -35K (40K-75K K (20K-50K) 20K K25K K30K …… yrs 12,18,24 10,15,20, K40K

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

Example-Longest Life EOY Alt 1 Alt 2 Alt K-75K K20K K25K K30K K35K K40K K4500

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