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%)

EOY Cash Flow

0 -$100

1 $50

2 $0

3 $60

4 $0

5 $100

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

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

Future Worth-Alternate Method PW=+$53 FW=PW(F/P10,5) or PW(1.1)5

FW=$53(1.6105) FW=$85

FW>0

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

IRR-Find i that gives a FW=0 FW = -$100(F/Pi,5)+$50(F/Pi,4)+$60(F/Pi,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/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%

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

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

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Example showing all methods