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CTC 475 Review

CTC 475 Review. Matching period and interest interval Continuous Compounding. CTC 475. Methods for Determining if an Alternative is Economically Feasible. Objectives. Know the various methods for determining if an alternative is economically feasible

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CTC 475 Review

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

  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. 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 • AW • FW • IRR • ERR • SIR or B/C

  14. Nonequivalent Methods • PBP • CW

  15. When is an alternative feasible? • PW > 0 • AW > 0 • FW > 0 • IRR > MARR • ERR > MARR • 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 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 • Capital----Debt Capital and Equity Capital • Debt (borrow money or sell bonds) • Equity (sell stock or company earnings)

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

  19. Example (MARR=10%)

  20. Present Worth • PW= -$100+$50(P/F10,1)+$60(P/F10,3)+$100(P/F10,5) • PW= -$100+$50(0.9091)+$60(.7513)+$100(0.6209) • PW= -$100+$45.46+$45.08+$62.09 • PW= +$53 • PW>0

  21. Future Worth • FW= -$100(F/P10,5)+$50(F/P10,4)+$60(F/P10,2)+$100 • FW= -100(1.6105)+50(1.4641)+60(1.2100)+100 • FW= -$161.05+$73.20+$72.60+$100 • FW=+$85 • FW>0

  22. Future Worth-Alternate Method • PW=+$53 • FW=PW(F/P10,5) or PW(1.1)5 • FW=$53(1.6105) • FW=$85 • FW>0

  23. Annual Worth • Find A given P • AW=PW(A/P10,5) • AW=$53(.2638) • AW=$14 • Find A given F • AW=FW(A/P10,5) • AW=$85(.1638) • AW=$14 • AW>0

  24. IRR-Find i that gives a FW=0 • FW = -$100(F/Pi,5)+$50(F/Pi,4)+$60(F/Pi,2)+$100 = 0 Interpolate to get an IRR = 26.4% IRR>MARR

  25. IRR • For some types of cash flows, there can be more than one IRR • You’ll explore this in project 6 • The ERR avoids this problem • The ERR value will be between the MARR and IRR

  26. ERR: Set FW of + using MARR = FW of – using ERR; solve for ERR • FW(+) = $50(F/P10,4)+$60(F/P10,2)+$100 = $245.80 • FW(-) = $100(1+ERR)5 • $100(1+ERR)5 = $245.80 • (1+ERR)5 = $2.458 • ERR=19.7% • ERR>MARR • Check: MARR=10%; ERR=19.7%; IRR=26.4%

  27. SIR or B/C • SIR=PW(+)/PW(-) • PW(+) = $50(P/F10,1)+$60(P/F10,3)+$100(P/F10,5)= $153 • PW(-) = $100 • SIR=$153/$100=1.53 • SIR>1

  28. PBP-Payback Period • If MARR=0 how many periods does it take to get your investment back? • At 1 year; $50<$100 • At 2 years: $50<$100 • At 3 years: $110>$100 • PBP is 3 years

  29. PBP-Advantages • No interest calculations • No decision regarding MARR • Easy to understand • Reflects manager’s viewpoint when capital is limited • Future cash flows are uncertain anyway • Rough measure of liquidity

  30. PBP-Disadvantages • Ignores concept that money has a time value • Ignores + cash flows beyond the PBP • Ignores long-term gains • Best to use as a secondary method

  31. Capitalized Worth • Present value that would pay for the first cost of some project and provide for its perpetual maintenance indefinitely, or • Present worth of some cash flow pattern that repeats indefinitely • For this class CW=AW/MARR=$14/0.1=$140 • $140 at 10% interest would give you $14 every year forever

  32. Capitalized Worth • An indefinite series does not occur in real life; however, this method is sometimes used when considering projects w/ extremely long lives (>=50 years) • Bridges • Highways • Forest harvesting • Endowment funds

  33. Next lecture • Example showing all methods

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