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 Be able to use any method for economic feasibility studies

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)

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

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

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

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

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

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)

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

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

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

Nonequivalent Methods PBP CW

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

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

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)

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

Example (MARR=10%) EOYCash Flow 0-$100 1$50 2$0 3$60 4$0 5$100

Present Worth PW= -$100+$50(P/F 10,1 )+$60(P/F 10,3 )+$100(P/F 10,5 ) PW= -$100+$50(0.9091)+$60(.7513)+$100(0.6209) PW= -$100+$45.46+$45.08+$62.09 PW= +$53 PW>0

Future Worth FW= -$100(F/P 10,5 )+$50(F/P 10,4 )+$60(F/P 10,2 )+$100 FW= -100(1.6105)+50(1.4641)+60(1.2100)+100 FW= -$ $73.20+$72.60+$100 FW=+$85 FW>0

Future Worth-Alternate Method PW=+$53 FW=PW(F/P 10,5 ) or PW(1.1) 5 FW=$53(1.6105) FW=$85 FW>0

Annual Worth Find A given P AW=PW(A/P 10,5 ) AW=$53(.2638) AW=$14 Find A given F AW=FW(A/P 10,5 ) AW=$85(.1638) AW=$14 AW>0

IRR-Find i that gives a FW=0 FW = -$100(F/P i,5 )+$50(F/P i,4 )+$60(F/P i,2 )+$100 = 0 i (%)FW 10+$85 9+$88 11+$81 15+$66 20+$41 25+$10 30-$27 Interpolate to get an IRR = 26.4% IRR>MARR

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

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

SIR or B/C SIR=PW(+)/PW(-) PW(+) = $50(P/F 10,1 )+$60(P/F 10,3 )+$100(P/F 10,5 )= $153 PW(-) = $100 SIR=$153/$100=1.53 SIR>1

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

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

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

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

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

Next lecture Example showing all methods