1. CTC 475 Review Matching period and interest interval Matching period and interest interval Continuous Compounding Continuous Compounding Continuous Flow Continuous Flow

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

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

5. Present Worth Convert all cash flows to a single sum equivalent at time zero using the MARR

6. Annual Worth Convert all cash flows to equivalent uniform annual costs (EUAC) over the planning horizon using the MARR

7. Future Worth Convert all cash flows to a single sum equivalent at the end of the planning horizon using the MARR

8. Internal Rate of Return Determine the interest rate that yields a future worth (or present worth or annual worth) of 0

9. External Rate of Return Determine the interest rate that yields a future worth explicitly assuming reinvestment of recovered funds at the MARR

10. Savings/Investment Ratio or Benefit/Cost Ratio Determine the ratio of the PW of the savings (+cash flows) to the present worth of the investment (-cash flow)

11. Payback Period Determine how long at a zero interest rate it will take to recover the initial investment

12. Capitalized Worth Method Determine the single sum at time zero that is equivalent at i=MARR to a cash flow pattern that continues indefinitely

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

14. Nonequivalent Methods PBP PBP CW CW

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

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

17. Determining MARR For a company, MARR > Cost of Securing Additional Capital For a company, MARR > Cost of Securing Additional Capital Capital----Debt Capital and Equity Capital Capital----Debt Capital and Equity Capital Debt (borrow money or sell bonds) Debt (borrow money or sell bonds) Equity (sell stock or company earnings) Equity (sell stock or company earnings)

18. Approaches for Establishing MARR Use company’s historic rate of return Use company’s historic rate of return Add a fixed % to firm’s cost of capital Add a fixed % to firm’s cost of capital Different MARR’s for different planning horizons Different MARR’s for different planning horizons Different MARR’s for different magnitudes of initial investments Different MARR’s for different magnitudes of initial investments Different MARR’s for new ventures and cost- improvement projects Different MARR’s for new ventures and cost- improvement projects Use MARR as a management tool Use MARR as a management tool Use avg. stockholder’s return on investment for all companies in the same industry group Use avg. stockholder’s return on investment for all companies in the same industry group

19. Simple Example

20. Next lecture More Complex Example Showing all Methods More Complex Example Showing all Methods