1. CTC 475 Review Is a certain cash flow economically feasible?

2. CTC 475 Methods for Determining if an Alternative is Economically Feasible

3. Objectives Know the various methods for determining if an alternative is economically feasible Be able to use any method for economic feasibility studies

4. Methods for Economic Feasibility Studies Present Worth (PW) Annual Worth (AW) Future Worth (FW) Internal Rate of Return (IRR) External Rate of Return (ERR) Savings/Investment Ratio (SIR) or  Benefit/Cost Ratio (B/C) Payback Period Method (PBP) Capitalized Worth Method (CW)

5. Equivalent Methods PW AW FW IRR ERR SIR or B/C

6. Nonequivalent Methods PBP CW

7. When is an alternative feasible? PW > 0 AW > 0 FW > 0 IRR > MARR ERR > MARR SIR or B/C > 1

8. Net Cash Flows It’s a good idea to use net cash flows (one cash flow at each period). It doesn’t matter with respect to whether a project is feasible or not; however, absolute numbers (ERR and SIR) may differ

9. Example (MARR=10%) EOYCash Flow 0-$40K 1$5K 2$8K 3$11K 4$14K 5 6$11K 7$8K 8$5K

10. Cash flow breakdown Years 1-4: Uniform ($5K) + Gradient ($3K)  n=4  P will occur at t=0  F will occur at t=4 Years 5-8: Uniform ($14K) - Gradient ($3K)  n=4  P will occur at t=4  F will occur at t=8

11. Present Worth PW= -40K+5K(P/A 10,4 )+3K(P/G 10,4 ) +[14K(P/A 10,4 )- 3K(P/G 10,4 )](P/F 10,4 ) PW= -40K+5K(3.1699)+3K(4.3781) +[14K(3.1699)-3K(4.3781)]*0.6830 PW= +$10,324 PW>0 ; therefore, cash flow is economically feasible

12. Annual Worth Find A given P AW=PW(A/P 10,8 ) AW=$10,324(.1874) AW=$1,935 AW>0; therefore, cash flow is economically feasible

13. Future Worth FW=PW(F/P 10,8 ) or PW(1.1) 8 FW=$10,324(2.1436) FW=$22,130 OR FW= AW(F/A 10,8 ) FW=$1,935(11.4359) FW=$22,128 FW>0; therefore, cash flow is economically feasible

14. Future Worth-Alternate Method FW= -40K(F/P 10,8 )+[5K+3K(A/G 10,4 )](F/A 10,4 )(F/P 10,4 ) +[14K-3K(A/G 10,4 )](F/A 10,4 ) FW=-$85,744+($9,144)(6.7949)+($9,856)(4.6410) FW=+$22,129

15. IRR-Find i that gives a PW=0 PW= -40K+5K(P/A i,4 )+3K(P/G i,4 ) +[14K(P/A i,4 )- 3K(P/G i,4 )](P/F i,4 ) i(%)PW 10+$10,324 12+$6,723 15+$1,994 18-$2,064 Interpolate to get an IRR = 16.5% IRR>MARR

16. ERR: Set FW of + using MARR = FW of – using ERR; solve for ERR FW(+) = 5K+3K(A/G 10,4 )](F/A 10,4 )(F/P 10,4 ) +[14K-3K(A/G 10,4 )](F/A 10,4 ) = $107,873 FW(-) = 40K(1+ERR) 8 40K(1+ERR) 8 = $107,873 (1+ERR) 8 = 2.6968 ERR=13.2% ERR>MARR Check: MARR=10%; ERR=13.2%; IRR=16.5%

17. SIR or B/C SIR=PW(+)/PW(-) PW(+)=5K(P/A 10,4 )+3K(P/G 10,4 ) +[14K(P/A 10,4 )- 3K(P/G 10,4 )](P/F 10,4 )=$50,324 SIR=$50,324/$40,000=1.26 SIR>1

18. PBP-Payback Period If MARR=0 how many periods does it take to get your investment back? At 1 year; $5K<$40K At 2 years: $13K<$40K At 3 years: $24K<$40K At 4 years: $38K<$40K At 5 years: $52K>$40K PBP is 5 years

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