Engeco Chap 11 Breakeven And Sensitivity Analysis

CHA PT ER 11 BREAKEVEN AND SENSITIVITY ANALYSIS

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INTRODUCTION In the previous chapter, the estimates of revenues, costs, other quantities for the eng eco analysis were assumed with high degree of confidence. It is called assumed certainty. The decisions based on this sometimes called decisions under certainty. However, it is very rare care whereby the estimates of quantities can be assumed as certain. The element of doubt exists as to the economic results that will be obtained from an engineering project.

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RISK 

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Risk and uncertainty are similar in that they both present the problem of not knowing what future conditions will be Risk offers estimates of probabilities for possible outcomes Uncertainty does not provide estimates of probabilities for possible outcomes This book treats them as interchangeable

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PRINCIPLE 6: Make Uncertainty Explicit (recognize and make known) We need to determine to what degree, changes in an estimates would effect a capital investment decision. In other words: To determine how sensitive a given investment is to changes in particular factors (ex: annual revenues, project life, MV, annual costs) that are not known with certainty. If a small changes in the relative magnitude of a factor will reverse an investment decision, the decision is said to be highly sensitive to that factor.

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FOUR MAJOR SOURCES OF UNCERTAINTY •

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Possible inaccuracy of cash-flow estimates used in the study Type of business relative to the future health of the economy Type of physical plant and equipment involved Length of study period

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POSSIBLE INACCURACY OF CASH-FLOW ESTIMATES How much source information is available  How dependable is the source information  Uncertainty in capital investment requirements is often reflected as a contingency above actual cost of plant and equipment (commonly used) 

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TYPE OF BUSINESS INVOLVED RELATIVE TO HEALTH OF ECONOMY Some businesses will typically be more at risk of declining when there is a general decline in the economy --- when the economy has gone into recession

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TYPE OF PHYSICAL PLANT AND EQUIPMENT INVOLVED 

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Some types of structures and equipment have definite economic lives and market values – they may be used in a multitude of settings. Other dwellings and equipment, being made for very specific and singular functions, may have little or no resale value SEMESTER JANUARY 2009

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LENGTH OF STUDY PERIOD The longer the study period, the greater the level of uncertainty of a capital investment

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SENSITIVITY ANALYSIS 

4. 5. 6.

Sensitivity – The degree to which a measure of merit (i.e., PW, IRR, etc…) will change as a result of changes in one or more of the study factor values. Sensitivity Analysis Techniques Breakeven Analysis √ Sensitivity Graph (spider plot) √ Combination of factors

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BREAKEVEN ANALYSIS Technique commonly used when an uncertain single factor (EG: capacity utilization) determines the selection of an alternative or acceptability of an engineering project For given alternative, if best estimate of actual outcome of common factor is higher or lower than the breakeven point, and assumed certain, the best alternative becomes apparent

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Indifference between alternatives (EWA = f1(y); EWB = f2(y) EWA = EWB; f1(y) = f2(y) : Solve for y (a common factor of interest) Economic acceptability of engineering project EWp = f(z) = 0 The value of ‘z’ is the value at which we would be indifferent between accepting or rejecting the project SEMESTER JANUARY 2009

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BREAKEVEN PROBLEM INVOLVING TWO ALTERNATIVES

Most easily approached mathematically by equating an equivalent worth of the two alternatives expressed as a function of the factor of interest

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BREAKEVEN ANALYSIS FOR ECONOMIC ACCEPTABILITY OF AN ENGINEERING PROJECT Most easily approached by equating an equivalent worth of the project to zero as a function of the factor of concern Because of the potential difference in project lives, care should be taken to determine whether the coterminated or the repeatability assumption best fits the situation SEMESTER JANUARY 2009

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EXAMPLE APPLICATIONS OF BREAKEVEN ANALYSIS 

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Annual revenue and expenses Solve for annual revenue required to equal annual expenses. Rate of return Solve for the rate of return on the increment of invested capital at which two given alternatives are equally desirable. Market (or salvage) value Solve for the future resale value that would result in indifference as to preference for an alternative.

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EXAMPLE APPLICATIONS OF BREAKEVEN ANALYSIS 

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Equipment Life Solve for the useful life required for an engineering project to be economically justified. Capacity utilization Solve for the hour utilisation per year at which an alternative is justified or at which two alternatives are equally desirable.

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Example 10-1: Breakeven Analysis AC MOTOR, 100Hp Alpha Beta $ $ Investment 12,000 16,000 Operating expenses/year 5.04X 4.05X Maintenance expenses/year 500 250 Taxes and insurance/year 187 240 MARR = 15%, useful life 10 yrs X = number of hours of operation per year AW(15%)Alpha = 12,000(A/P, 15%, 10) + 5.04X + 500 + 187 AW(15%)Beta = 16,000(A/P, 15%, 10) + 4.05X + 250 + 240

At breakeven point, AWα = AWβ. SEMESTER JANUARY 2009

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Equating AWα = AWβ 2,490 + 5.04X + 500 + 187 = 3,190 + 4.05X + 250 + 240 5.04X + 3,177 = 4.05X + 3,680 X = 508 hrs/year

AW (15%) 9,000

α

7,000

β

5,000

3,000

Select α

1,000

Select β Hours of operation per year, X

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1,000 1,200 1,300 17

SENSITIVITY GRAPH (SPIDERPLOT) An analysis tool applicable when the breakeven analysis does not fit the project situation. Makes explicit the impact of uncertainty in the estimates of each factor of concern on the economic measure of merit (PW, AW, FW).

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EXAMPLE 10-4: Sensitivity Graph The cash-flow estimates of a piece of new equipment with useful life of 6 years are as follows: Capital investment, I $11,500 Revenues/year $ 5,000 Expenses/year $ 2,000 Salvage value, SV $ 1,000 Investigate PW over a range of + 40% changes in estimates for a. Capital investment b. Annual net cash flow c. Salvage value d. Useful Life SEMESTER JANUARY 2009

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The basic equation using PW:

This equation is termed “the best estimate”: PW(10%) = -$11,500 + $3,000 (P / A, 10%, 6) + $1,000 (P / F,10) = $2,130 This value occurs at the intersection point of the spider plot.

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Revenues/year = $5,000 SV = $1,000 Expenses/year = $2,000 I = $5,000

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When the capital investment, I varies by ± p% the PW is

PW(10%) = -(1 ± p% / 100)($11,500) + $5,000(P/A, 10%, 6) - $2,000(P/A, 10%, 6) + $1,000(P/F, 10%, 6)

(P/A, 10%, 6) = 4.3553 (P/F, 10%, 6) = 0.5645 SEMESTER JANUARY 2009

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SENSITIVITY GRAPH (SPIDERPLOT) OF FOUR FACTORS PW (10%) Ca pi

7000

ta

lI

nv es

tm en

6000

t

5000

$2130

4000

n n A

3000

t e lN

ua

,A

o Fl

w

l efu

L

h s Ca

N , e if

Us

e, SV

alu Salvage V

2000

-% Deviation Changes in Factor Estimate

1000

- 40

-30 -20 -10

-1000

0

+10

+20

-2000 -3000

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18.5%

+30 +40 +%Deviation Changes in Factor Estimate 22

REVELATIONS OF SPIDERPLOT 

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Shows the sensitivity of the present worth to percent deviation changes in each factor’s best estimate Other factors are assumed to remain at their best estimate values The relative degree of sensitivity of the present worth to each factor is indicated by the slope of the curves (the “steeper” the slope of a curve the more sensitive the present worth is to the factor) The intersection of each curve with the abscissa shows the percent change in each factor’s best estimate at which the present worth is zero

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REVELATIONS OF SPIDERPLOT  

In this example Present worth is insensitive to SV Present worth is sensitive to I, A, and N From the spiderplot it is obvious that the investment, I , can be increased by 18.5% without causing the project’s PW (10%) to become negative.

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PITFALLS OF RISK-ADJUSTED MARR 

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A widely used industrial practice for including some consideration of uncertainty is to increase the MARR Even though intent of risk-adjusted MARR is to make more uncertain projects appear less economically attractive, opposite may appear to be true Cost-only projects are made to appear more desirable as the interest rate is adjusted upward to account for uncertainty SEMESTER JANUARY 2009

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REDUCTION OF USEFUL LIFE 

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By excluding those revenues (savings) and expenses that may occur after a reduced study period, heavy emphasis is placed on rapid recovery of capital in early years of a project’s life This method is closely related to the discounted payback technique and suffers from most of the same deficiencies (ignore the cash flows after the payback period)

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