ENGINEERING ECONOMY

Sensitivity Analysis

• Sensitivity analysis

-Engineering economy estimates of parameters such as costsand other cash flow are only an approximation of reality.

-The realized future value of a parameter will be generally different from its estimated value.

-Sensitivity analysis attempts to measure the effect of thisuncertainty (variability) in parameters estimates.

-Sensitivity analysis identifies parameters that have the most impact on an economic decision.

-That is, it identifies the parameters with the highest sensitivity.

- Sensitivity of a parameter is the effect of changing the parameter value on the economic criteria such as PW value.

• Graphical sensitivity analysis

-Sensitivity analysis is often done graphically by plotting the economic criteria as a function of a parameter.

- The plot is over the range where the parameter is most likelyto vary.

-A flat plot indicates insensitivity.

- That is, the parameter has little effect on the economic decision. No need to get very precise estimates for its value.

- A highly variable plot indicates high sensitivity.

- That is, the parameter has a significant impact on economic decision. Estimating its value should be handled with care.

• Example Example 18.1 gives PW vs. MARR for a project.

In this example, PW is highly sensitive to MARR.

• Sensitivity analysis with several parameters

-When several parameters are being analyzed for sensitivity, A spider plot can be used.

-This is a plot of the economic criteria as a function of percent changes from the most likely estimates of parameters.

Example of spider plot (Fig 18.3).

In this example, ROR is

o Insensitive to indirect cost (flat curve), and labor cost;o Moderately sensitive to material cost and capital;o Highly sensitive to sales volume and sales price.

• Sensitivity analysis with three estimates

A common approach is to base sensitivity analysis on three estimates for a parameter: pessimistic, most likely, andoptimistic estimate.

Example 18.3 performs sensitivity analysis of annual cost for three alternatives based on three estimates of parameters.

In this example, parameters are assumed to change together for the pessimistic, most-likely and optimistic scenarios.

This is also known as scenario analysis.

According to the plot below, alternative B is better thanalternatives A and C under all scenarios.

Selecting Alternative B is a good choice.

• Variability and probability

-When a cash flow (parameter) estimate is highly uncertainand the economic decision is highly sensitive to it, aprobabilistic cash flow analysis is useful.-Probability of an event (here the cash flow taken on a value)is typically defined as the long run fraction of time where theevent happens.-If the “event” repeats several times, then one can usehistorical date to estimate the probability. That is, probabilityis estimated as a frequency.

-However, in several situations, especially in one-time engineering projects, not enough historical data is available.

-E.g., for the construction of an exotic tower, the experienced civil engineer estimates that there is a 95% chance (i.e. a 0.95 probability) that the cost will not exceed $1 billion.

-This is a subjective estimate of probability.

• Cash flows as random variables

A random variable is a function that assigns real numbers to events (outcomes of an experiment).

E.g., the salvage value of a machine, S, is $1,500 if themarket goes up (with probability 0.4) and $1,000 if themarket goes down (with probability 0.6).

Then, S is a random variable with the following probabilitydistribution P{S = 1500} = 0.4 and P{S = 1000} = 0.6.

-If the random variable can take on a limited number of values. Then, this is a discrete random variable. E.g., the salvage value of the machine above.

-If the random variable can take on an uncountable number of values. Then, this is a continuous random variable.

-E.g., you may estimate that the monthly fuel consumption of your car is equal likely to be between $200 and $250. Then, this consumption is a continuous random variable.

EXAMPLESUSING SPIDER PLOT GRAPH

USING OPTIMISTIC-MOST LIKELY-PESSIMISTIC (O-ML-P) TECHINIQUE

SENSITIVITY GRAPH(SPIDERPLOT)

An analysis tool applicable when the breakeven analysis does not fit the project situationMakes explicit the impact of uncertainty in the estimates of each factor of concern on the economic measure of merit

EXAMPLE 4-10

Investigate PW over a range of + 40% changes in estimates for a. Capital investmentb. Annual net cash flowc. Market valued. Useful Life

PW(10%) = -$11,500 + $3,000 (P / A, 10%, 6) + $1,000 (P / F,10%, 6) = $2,130

SENSITIVITY GRAPH (SPIDERPLOT) OF FOUR FACTORS

-% DeviationChanges inFactorEstimate

+%Deviation Changes in Factor Estimate

PW (10%)

- 40 -30 -20 -10 +10 +20 +30 +400

-1000

-2000

-3000

-4000

1000

3000

4000

5000

6000

7000

$2130

Annua

l Net

Cas

h Flow

, A

Useful L

ife, N

Market Value, MV

Capital Investment

2000

REVELATIONS OF SPIDERPLOTShows 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

REVELATIONS OF SPIDERPLOTIn this example

Present worth is insensitive to MVPresent worth is sensitive to I, A,

and N

MEASURING SENSITIVITY BY A COMBINATION OF FACTORS

1. Develop a sensitivity graph for the projecta. For most sensitive factors, improve estimates and reduce range of uncertainty

2. Use sensitivity graph to select most sensitive project factors. Analyze combined effects of these factors on project’s economic measure of merit by:a. Additional graphical technique for two most

sensitive factorsb. Determine the impact of selected

combinations of three or more factors -- scenarios

Optimistic-Most Likely-Pessimistic

Establish optimistic (the most favorable), most likely, and pessimistic (the least favorable) estimates for each factor.

The optimistic condition, which should occur about 1 time out of twenty, is when all factors are at their optimistic levels. Similarly for pessimistic condition.

The most likely condition should occur roughly 18 times out of 20.

Perform EW calculations under each condition for insight into the sensitivity of the solution.

The results can be seen on a spider plot for further insight.

Consider investment in a new crane. Assume a MARR of 8%.

Estimation Condition

Optimistic (O) Most Likely (M) Pessimistic (P)

Investment, I $240,000 $270,000 $340,000

Useful life, N 10 yr 8 yr 5 yr

Market value, MV $20,000 $15,000 $8,000

Annual revenues, R $100,000 $80,000 $50,000

Annual expenses, E $10,000 $15,000 $20,000

Considering O-ML-P for I and R (fix E, MV, and life at their ML levels). Value in each cell is the PW for the project.

Investment, I

Revenues, R Optimistic (O) Most Likely (M) Pessimistic (P)

Optimistic, (O) $256,568 $226,568 $156,568

Most Likely, (M) $141,636 $111,636 $41,636

Pessimistic, (P) -$30,764 -$60,764 -$130,764

This suggests that perhaps some additional effort should be place on getting refined estimates of revenues. Of course, the complete study needs to consider the other factors.

THE END!!!!! :D

BY:THE J-TEAM