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**Engineering Economic Analysis Canadian Edition**

Chapter 9: Other Analysis Techniques

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Chapter 9 … Develops additional alternate methods to solve engineering economic problems: future value benefit-cost ratio payback period sensitivity analysis Links the future value method to the present value and equivalent annual value methods. Uses spreadsheets to perform sensitivity and breakeven analyses.

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**Present and Future Value Methods**

Net Present Value (NPV) What is the present value of future activity? Project cash flows are discounted to an equivalent value, usually at the start of the project (see Chapter 5). Net Future Value (NFV) What is the future value of current activity? Project cash flows are converted to a future value, usually at the end of the project.

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Future Value 1 2 3 4 5 $750 $1500 $1000 $500 FV = ? 5 ≡ Find the value of the cash flows at the end of the 5th year if the rate of interest is 10% compounded annually. (Answer= $ )

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**Economic Criteria Projects are judged against an economic criterion.**

Situation Criterion Fixed input Maximize output Fixed output Minimize input Neither fixed Maximize difference (output input)

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**Economic Criteria Restated for Future Value Techniques**

Situation Criterion Fixed input Amount of capital available is fixed Maximize future value of benefits Fixed output Amount of benefits is fixed Minimize future value of costs Neither fixed Neither capital nor benefits is fixed Maximize net future value (NFV)

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**Type of Projects Independent Mutually exclusive Contingent (dependent)**

The selection of a project is independent of the decision to undertake any other project(s). Mutually exclusive At most one project (including the status quo, or “do nothing” option) can be selected amongst competing alternatives. Contingent (dependent) The selection of a project is dependent on the selection of at least one other project.

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**Problem: Find NFV (i = 10%)**

+ $2000(1.10)6 + $3000(1.10)5 + $2500(1.10)4 + $2000(1.10)3 + $1500(1.10)2 + $1000(1.10) + $500 = $20,060.62 (or find NPV, then (1.10)8) YEAR CASH FLOW $0 1 $1000 2 $2000 3 $3000 4 $2500 5 6 $1500 7 8 $500

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**NFV and Independent Projects**

Select all projects with non-negative net future value (NFV). if NFV > 0, accept project if NFV < 0, reject project if NFV = 0, marginally accept project If all projects have NFV < $0, select the status quo (do nothing) option; invest available funds at the prevailing risk-free interest rate. The selection of independent projects is usually constrained by a capital budget (limited funds).

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**NFV and Independent Projects …**

The NFV is the amount that remains at the end of a project after the annual cash flows are accumulated into the unrecovered capital, plus required returns, throughout the project. Example: find the NFV and the NPV of a project that requires an investment of $500K and has the cash flows shown below if the MARR is fourteen percent. (Answer: NFV = $149,131.52; NPV = $88,297.83). Year 1 2 3 4 Cash Flow $150K $300K $225K $125K

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**Future Value and Present Value Analysis**

PARAMETERS PROJECT A PROJECT B PROJECT C Investment $2500 $3500 $5000 Annual cost $900 $700 $ (G=$100) Salvage value $200 $350 $600 Life (years) 5 Annual revenue $1800 $1900 $2100 (15% growth) MARR 10%

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**Future Value and Present Value Analysis …**

Calculate the NPV and the NFV for Projects A, B, and C. NPVA = $ ; NFVA = $ NPVB = $ ; NFVB = $ NPVC = $ ; NFVC = $

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**Useful Lives Analysis Period**

Project A has a three-year life. Project B has a four-year life. Both projects are valid since each has NFV > $0 (i = 10%). Which project is better? Year Project A Project B $1000 $2000 1 $500 $720 2 3 4 NFV $324.00 $413.32

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**Useful Lives ≠ Analysis Period …**

Because Projects A and B have different lives, the NFV criterion requires that they be evaluated over a common period of analysis (12 years). Hence, Project A will be repeated four times (after the initial invest-ment at t=0) and Project B three times. Year Project A Project B $1000 $2000 1 $500 $720 2 3 $500 4 $1280 5 6 7 8 9 10 11 12 NFV = $ $

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Benefit-Cost Ratio By restating the NPV, NFV, and EACF criteria, we know that an investment is acceptable at a given MARR provided: PV(positive CFs) – PV(negative CFs) ≥ 0 FV(positive CFs) – FV(negative CFs) ≥ 0 EACF(positive CFs) – EACF(negative CFs) ≥ 0 These provisions can be put in terms of the benefit-cost ratio (BCR): BCR = PV(positive CFs)/PV(negative CFs) = EACF(positive CFs)/EACF(negative CFs) If its BCR 1, an investment is acceptable.

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Benefit-Cost Ratio … Example: a firm is considering a project that requires an investment of $600K and has the cash flows shown below. Decide whether the firm should accept this project if its MARR is 15%. Use NPV, EACF, NFV, IRR, and BCR criteria. (Answer: the firm should not accept the project. NPV = $23, < 0; EACF = $ < 0; NFV = $40, < 0; IRR = % < 15%; BCR = < 1). Year 1 2 3 4 Cash Flow $150K $300K $225K $125K

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**Economic Criteria Restated for Benefit-Cost Ratio Method**

Situation Criterion Fixed input Amount of capital avail-able is fixed Maximize BCR Fixed output Amount of benefit is fixed Neither fixed Neither capital nor benefits are fixed 1 candidate: BCR ≥ 1. 2 or more alternatives: use incremental BCR.

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**BCR and Incremental BCR (∆BCR)**

The BCR and other criteria such as the NPV, NFV, EACF, and IRR lead to the same conclusion regarding whether to accept individual projects. Similar to the IRR case, we use incremental BCR (∆BCR) to determine the best alternative among two or more competing alternatives. The BCRs of competing alternatives can not be compared directly even if the lifetimes or analysis periods are equal, as they can for the NPV and NFV cases.

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BCR and ∆BCR … Example: a company needs a new network and it is considering two systems. System M costs $120K to acquire/install; they estimate its annual net benefit will be $45K for four years. System N’s estimated net benefit will be $40K per year for three years at a cost of $85K to acquire/install. Determine which system the company should acquire if they use a 10½ percent rate of return. Use the BCR. (Answer: acquire System M. BCRM = ; BCRN = ; BCRMN = )

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**BCR and Competing Alternatives**

Example: Moose County has three alterna-tives for a new road. Benefits and costs are shown below. Expected road life is 50 years and MARR = 10%. Apply BCR and ∆BCR. Road First Cost Annual Benefits Annual Operating Costs A $25,000 $3200 $200 B $35,000 $3800 $250 C $50,000 $6050 $350

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Payback Period Defined as the time taken for the cumulative cash flows of an investment to reach zero. Accept an investment if its payback period ≤ the maximum allowable payback period. Notes about payback period: Payback is an approximate method that ignores the time value of money. After the maximum allowable payback period, all cash flows are ignored. The payback method will not necessarily produce a recommended alternative that is consistent with valuation and rate of return methods.

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Payback Period … Focuses exclusively on liquidity (no concern for profitability). Liquidity: how quickly the investment can be recovered from the project’s cash flows. All other methods of project evaluation focus on profitability (not liquidity). Ignores the time-value of money, i.e. implicitly assumes that MARR = 0%. The opportunity cost of the project balance, or the unrecovered portion of the capital investment, is ignored. Project Balance = –P + ∑(ORi – OCi), i = 0,1, … N.

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**Payback Period … Project balance at any point during its life is:**

Simple payback: a project’s unrecovered investment without discounting. Discounted payback: a project’s unrecovered investment taking into account the opportunity cost (i.e., interest charges or required return) of the unrecovered investment. Generally, annual net cash flows (revenues less costs) will cause a project’s balance to become more positive over time. The project balance is negative until the initial investment has been fully recovered.

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**Payback Period … t* Project Balance = $0 + t3 t1 t2 –**

– t1 t2 t3 t* First Cost Year 1: Benefits – Costs

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**Payback Period … Year Cash Flow: Project A Cash Flow: Project B**

–$15,000 1 $1000 $3000 2 $2000 3 4 $4000 5 $5000 6 $6000 7 $7000 8 $8000

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Payback Period … Projects A and B both have payback period = 5 years (project balance = 0 after five years). They have very different profitability profiles: Project A is more profitable than Project B by the end of its lifetime. Since we focus only on liquidity (how fast the initial investment is recovered), the payback method makes us indifferent between projects A and B.

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**Payback Period … Payback period = 3 + 300/1000 = 3.3 years.**

Compare 3.3 years to an industry threshold to determine if the project is acceptable. If similar investments require, on average, three years to recover, this project would be rejected. Year Cash Flow Project Balance –$1000 1 –$500 –$1500 2 +$500 3 +$700 –$300 4 +$1000

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**Payback Period … Discounted Payback Period Year Cash Flow**

Opportunity Cost (10%) Project Balance –$15000 1 $3500 –$1500 –$13000 2 –$1300 –$10800 3 –$1080 –$8380 4 –$838 –$5718 5 –$571.8 –$2789.8 6 –$278.98 $431.22

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Payback Period … Discounted payback period = 5 + $2789.8(1.1)/$3500 = years. If the industry average discounted payback period for this type of project is > years, this project is acceptable. Otherwise, it is not. We can see that the NFV is $ (> 0), therefore the project should be considered acceptable.

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Payback Period … We can also use a present value approach for the discounted payback period. Find the point at which the cumulative PVs of the cash flows becomes 0. For the same example. Discounted payback period = years (same as above). Note, the NPV = $ If the discounted payback period ≤ the life-time, a project should be considered accep-table since this means that NPV ≥ 0. Regret-tably, such a criterion is not always specified.

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**Sensitivity & Break-even Analysis**

Economic data represent projections of expenditures and returns. These projections ultimately affect our decisions. To consider our choice of a decision more fully, we should play a “what if” game to determine the amount of change in a project parameter that might alter the decision. This allows us to make an assessment of the inherent risk in a project, i.e. the probability of different outcomes due to uncertainty in the project variables.

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**Sensitivity & break-even analysis …**

Projected and actual cash flows may differ due to: Technological change: changes to production costs Changes in the size and number of competing firms Introduction of new products: substitutes or complements Changes to key macroeconomic variables, e.g. inflation, unemployment, economic growth, exchange rate International events

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**Sensitivity & break-even analysis …**

Sensitivity example: System cost = $200,000; annual profit = $36,000; salvage value = $23,500; lifetime = 10 years; MARR = 12%. Use sensitivity analysis to determine which project components affect the NPV most.

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**Sensitivity & break-even analysis …**

Break-even example: using the information from the sensitivity example, find the break-even values for the initial investment and for the annual profit (the parameters to which the NPV is most sensitive).

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**Sensitivity & break-even analysis …**

Scenario example: using the information from the sensitivity example, perform a scenario analysis. Worst case: $210,000 investment, $33,000 annual profit, $17,500 salvage value, lifetime eight years, MARR 13%. Best case: $195,000 investment, $37,500 annual profit, $26,500 salvage value, lifetime eleven years, MARR 11½%.

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Suggested Problems 9-22, 23, 29, 32, 41, 43, 45, 56, 59 (use kW/hp).

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Chapter 9 Net Present Value and Other Investment Criteria

Chapter 9 Net Present Value and Other Investment Criteria

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